View of Sir Isaac Newton's Philosophy (1728)

A

V

E

I o

Sir

i

ISAAC NEWTON*

PHILOSOPHY.

LONDON: Printed by S.

PA LM

E

A*

Ottfl

R,

1728.

Qf\ 8 03

/v

To

SIR

the

Noble and Right Honourable

ROBERT WALPOLE.

SIR, Take

the liberty to fend you this view of Sir I s A A c E w-

N

TON'S

philofophy, which ,

if

were performedfuitable to the dignity of the fubjeft, might it

not be a prefent unworthy the

For his phiacceptance of the greateit perfon. affords us the true of the account lofophy only

A

2

DEDICATION. operations of nature, which for fo many ages had imployed the curiofity of mankind though no one before him was furnifhed with the ftrength of mind neceflary to go any depth in ;

this difficult fearch.

However,

I

am encouraged

to hope, that this attempt, imperfect as

it

is,

to

give our countrymen in general fome concep tion of the labours of a perfon, who fliall al ways be the boaft of this nation, may be re ceived with indulgence by

one,

under whofe

fo much hapat admiration the pinefs. my furprizinginventions of this great man, carries me to con

influence thefe

kingdoms enjoy

Indeed

who not only muft of the raife the glory country, which gave him but that he has even done honour to hu birth ceive of

him

as a perfon,

;

man

by having extended the greateft and moft noble of our faculties, reafon, to fubje6ls, which, till he attempted them, appeared nature,

to be

ted

wholly beyond the reach of our limi And what can oqivc us a capacities.

more

DEDICATION. of our own condition, pleafing profpetf than to fee fo exalted a proof of the ftrength

more

of that faculty, whereon the conduit of our lives, and our happinefs depends ourpaflions ;

our motives to a&ion being in fuch and manner guided by our opinions, that where all

our whole behaviour will be

thefe are juft,

praife-worthy tain you,

But why do

?

SIR,

I prefume to de with fuch reflections as thefe,

who muft have the fulleft experience within your own mind, of the effects of right reafon ? For

to

what other fource can be afcribed that

amiable franknefs and unreferved condefcenfion among your friends, or that mafculine

perfpicuity

and ftrength of argument, whereby you draw the admiration, of the publick, while you are engaged in the moft important of all caufes the liberties of

mankind?

/

I

humbly crave

leave to

make

the only ac

knowledgement within my power, for the benefits, which

DEDICATION. which I

receive in

common

with the

countrymen from thefe high fcribing

reft

talents,

of my

by fub-

my felf

S 1

R,

Your moft faithful, and

Mofl humble Servant,

HENRY PEMBERTON.

PREFACE. iip the following papers many years ago at the defire of fome friends , wbo> upon my taking care of the late edition of c Sir I s A A c N E w T o N "s Principia. perfwaded me to make them

ITlrew

>

I

publick.

laid hold of that opportunity,,

when my thoughts

were afrejh employed on this fubjeffy to revife what I had formerly And I vow fend it abroad not without fome hopes of anwritten. fwering thefe two ends. Myfrft intention was to convey to fuch^asare not tifed to

mathematical reafoningjome idea of the philofophy of a perfon y univerfal reputation, and rendered our nation

who has acquired an

famous for thefe fpeculations in the learned world. To which purterms of art as much as pofflble^ and ta pofe I have avoided ufing as I was obliged to ufe. 'Though this caution at prefent^ fmce many of them are become fa our language^ from the great number of books wrots

ken care

to define fuch

was

lefs neceffary

the

miliar words

to

in it uponphilofophicalfubjectS) and the courfes of experiments^ that have of late years been given by feveral ingenious men. The other

view Ihad^ was to encourage fuch young gentlemen as have a turn for the mathematical fciences> to purfue thofejludies the more chcarfully^ in order to underftand in our author himfelfthe demonftrations of the And to facilitate their progrefs herein^ 1 in things I here declare.

NEW

proceed ft ill farther in the explanation of Sir ISAAC For as I have received very much pleafure from philofophy. perufmg his writings^ I hope it is no illaudable ambition to endeavour the rendering them more eafily underjloody that greater numbers may tend

to

TON V

enjoy the fame

fat isfaft ion*

It will perhaps be expetted^ that

lar of a perfon ^ obliged. it

was

What

I JJoouU fay fomething

whom

particu

Imttft always acknowledge my felf to be I have to declare on this head will be but foort

to

in the very loft years of Sir I

s

A A cV

life>

that

mucb >

for'

I had the ho-

PREFACE. veur of bis acquaintance.

Mr.

a

PoJenus,

periment of his,

Tbis happened on the following occajiw. from a new ex thought the common opinion about the force of moving

Trofeffor in the Univerfity of Padua,

was overturned, and the truth of Mr. LibnitzV notiqn in t: matter fully proved. The contrary of what Polenus had averted I demonstrated in a paper, which <Dr. MEAD., who takes all opportu bodies

was pleafed to foew Sir ISAAC NEW This was fo well approved of by him, that he did me tie ho nour to become a fellow-writer with me, by annexing to what I had written, a demonftration of his own drawn from another confedera tion. When I printed my difcourfe in the philofophical tr anfaff ions,, I nities of obliging his friends,

TON.

put what Sir ISAAC had written in a fcholium by it felf, that I might not feem to ufnrp what did not belong to me. But I concealed his name,, mt being then fufficiently acquainted with him to ask whe^

was willing I might make life of it or not. In a little time after he engaged me to take care of the new edition he was about making vf his Trincipia. This obliged me to be very frequency with

ther he

him, and as he lived at fome difance from me, a great mw.be} between us on this account. When I had the hoi, r of his converfation, I endeavoured to learn his thoughts upon VL\ -:a-

letters faffed

ticalfuljeffs,

>;.

and jomething

hiflorical concerning his inventions, that

had not been before acquainted with. I found, modern mathematicians, than

he

I

had readfewer of the

have expected ; but his own him with what he might have an occafwn for in the pnrfnit of anyfubjeffi he undertook. I have often heard him cenfure the handling geometric alfubje'cls by algebraic calculations; and his book of Algebra he called by the name of ~Univerfal Arithmetic in oppofnion to the injudicious title of Geometry, which Des Cartes had one could

prodigious invention readily fnpplied

given

to

the treatife, wherein he foews,

hew

the geometer

may

ajjlft

bis

invention by fitch kind of computations. Ue frequently praifed SJufius, Barrow and Huygens/^r not being influenced by the falfe tajle, which

He ufedto commend the laudable attempt of Hugo the ancient analyfis^andvery much efteemedApolfe&ione rationis for giving us a clearer notion of that

then began to prevail.

deOmerique

to reftore

loniusV book

De

cinalyfis

than we

had before.

T)r. Barrow

may

be

ejlemed as hav ing

PREFACE. ing Jkewn

(i

compafs of invention equal\

Jems, our author

excepted

only

if not

fuperiw

ISAAC

but Sir

-,

to

any of the

NEWTON

hii\-

fcveral times particularly recommended to me Huygens'j file and manner. He thought him the mojl elegant of any mathematical wri ter of modem times^ and tie waft jnjl imitator of the antients. Of

and form

their tafie,

Sir Is A

AC

always profeffed even cenfure biwfelf for not fclki. :~e than he did and freak with re bem y clofely gret of b/s wi (hike at the beginning of his mathematicalfindies^ in applying himfelf to the works of DCS Cartes and other algebraic wri himfelf a

of demcnfiration

idmirer

g\

I haze heard him

:

\

ters, before tion.,

had confidered the

he

which fo

excellent

a writer

with that atten

elements t/Euclidc

4s

deferves.

to

the hiflory of his

what relates to his difcowries of the methods of ftries and and <.f his theory of light and colours, the world has been fnfinformed of already. The frfl thoughts which gave rife

inventions^

fluxions^ ficiently

,

he had^when he retired from Cambridge in 1 666 on As he fat alone in a gar den > he fell into a account of the plague. [peculation on the power of gravity : that as this power is not found to his 'Principia^

fenfibly diminiflied at the remoteft diflance

from the center of the earth; neither at the tops of the loft /eft buildings y nor even on the fjimmits of the highefl mountains ; it appeared to him to

which we can

reafonabk

rife,

conclude^ that this power mitft extend much farther than thought ; why not as high as the moon^ faid he to himif/a, her motion muft be influenced by it $ perhaps foe is reher orbit thereby. However., though the power of gravity to

s ufnally

faff

?

and <

weakened in the little change of diftance^ at which we can place our felves from the center of the earth yet it is very pojfibley the*: fa high as the moon this pew er may differ much in ftrength from

is ror fenfibly

;

what

it is

here.

T'o

make an efimatc,

this diminution^ he confidered

taintd in htr

(

with

-

rbit by the force (f gravity,

vd s are carried round

the

i

; be the degree (f that if the moon be rtno doubt the f

hiirfeif,

/.

.

Andlyco-

'

periods of the feveralplanets wit thiii if

any />/ ixer like gravity

dtcreafe in the duplicate

t

,

the fur., he j in their courfcs, its

i.

i

cf

[a]

il:

f

/

difiance.

1'his

PREFACE. be concluded by fuppofing them to move in perfect circles concentric al to tie fun, from which the orbits of the great eft pan of them do

much

Suppq/tng therefore the power of gravity, when moon, to decreafe in the fame manner, he computed whether that force would be fufficient to keep the moon in her orbit.

not

extended

differ.

to the

In ibis computation, being abfenf from books, he took the common eft/ matt life among geographers and our feamen, before Norwood had mea~

77

that 60 Englijb miles were contained in one degree But as this is a very faulty each degree containing about 69 of our miles, his com

Cured the earth,

of latitude on the furface of the earth. fuppcfition,

'>

putation did not anfwer expectation whence he concluded, that fome other caufe muft at leaft join with the aftion of the power of gravity On this account he laid afide for that time any farther on the moon. ;

'But fome years after, a letter which he thoughts upon this matter. received from Dr. Hook, put him on inquiring what was the real

fgure, in which a body let fall from any high place defcends, taking the motion of the earth round iis axis into confederation. Such a body, having the fame motion, which by the revolution of the earth the place has whence it falls, is to be confidered as projected forward and at the fame time drawn down to the center of the earth. This

gave moon

j

occafion to his refuming his former and Picart /';/ France having lately

thoughts concerning the

meafured the earth, by

to be kept in her orbit purely ufing his meafures the moon appeared and confeqtiently, that this power decreafes by the power of gravity ; (is 'yon recede from the center of the earth in the manner our author

had f'ci

formerly conjectured.

ibed- by

a falling body

to

Upon an

be

this principle he found the line dtellipfis> the center of the earth be-

And the primary planets moving in fuch orbits round ing one focus. the fun, he had the fatisfa'ction to fee, that this inquiry, which he undertaken

out of curiofay, could be applied to the Hereupon he compufcd near a dozen proportions to the motion of the primary planets about the fun. Several reliiting after this, fome difcourfe he had with 2)r. Hal Icy, who at I

merely

ateft purpofes*

Ca>

V,o c

made him a

?.*iiin

vift, engaged Sir

ISAAC

the confideration of this fubjeft

;

NEWTON

to

and gave cccafwn to

PREFACE. to his writing tie treatifc which he publiJJjed under the title of ma thematical principles of natural philofophy. This treatife, full of

f^lch a variety of profound inventions^ was compofed by him from fcarce any other materials than the few proportions before mentioned^

in the fpace of one

year and an

half.

though his memory was much decayed^ 1 found he perfectly undtrftood his own writings^ contrary to what I had frequently heard in difconrfe from many perfons. This opinion of theirs might arife perhaps from his not being always ready at fpeaking on thefefub'/eZts^

when

it

might be expected he fljould.

But as

to this^ it

may be

obferved, that great genius's are frequently liable to be abfent, not only in relation to common life^but with regard tofome of the parts offcience

they are the beft informed

Inventors feem to treafure

of.

np

in their

what they have found out^ after another manner than thofe do The former-, the fame things^ who have not this inventive faculty. when they have occafon to produce their knowledge are in fome meafure obliged immediately to invcfigate part of what they want. For minds^

',

this they are not equally Jit at all times fo it has often happened, that fuch as retain things chiefly by means of a very ftrong. memory^ have appeared offhand more expert than the difccverers themfehes. :

As to the moral endowments of his mind, they were as much to be admired as his other talents. But this is a eld Heave others to exfpatiate in. I only touch upon what I experienced my felf during the

f

c

few years I was happy in his friendfiip. "But this I immediately difcovered in him, which at once both furprized and charmed me : fher his extreme great age^ nor his univerfal reputation had d him jliff in opinion., or in any degree elated. Of this

have alnwft daily experience. The Remarks I by letters on his 'Principia were received with the Mmofl goodnefs. Tbtju were fo far from beiug any ways difpleatfi him^ that on the contrary it occafwucd him to /peak many kind

I had

occafion to

continually feat

of

me

':od 'rt

to

him

my friend'r, and to honour me with a

He

publick teftimoi>y

approved of the following treat ife> a As many alterations were of which ws read together. opinion.

aljo

[a

2 ]

PREFACE. would have been

Je in the L'te edition of bis Trincipia, fo there

this many more if there bad been a fufKcieut time. "But whatever of comin to endeavour I my kind may le thought wanting^ fupply frail rt on that look. I bad reafon to believe be expefted fucb a thing

from me, and I intended

had printed

have publifoed

it in

his

time, after I treatife Sir

life

and a mathematical

the following difcourfe,

NEWTON

ISAAC

to

written a long while ago* containing the him to let that piece principles of fluxions, for I bad prevailed on go abroad. I had examined all the calculations^ and prepared part been but as the latter of the of the treatife had never

had

.'/

part

figures-,

was about letting we have other papers, in order to "But his death put a flop to that defupply what was wanting. js to my comment on the cPrincipia y I intend there to defif>u. moufti'ttte whatever Sir ISAAC NEWTON has fet down without Ttfs proo^ and to explain all fitch expreffwns in his book, as Ifrail he

fnijhed*

judge

neceffary. '

an

to

had fame

1'b/s

comment 1 foalI forthwith put

englifr tranjlation

time by me.

A

of

his

to the

prefs,

which I have

'Principia^

more particular account of my whole denew memoirs cf literature for

jign has already been publijked in the the month of march 1727.

Ibave

prefentcd

NEWTON, If

which

my readers with a

I have

jufl

copy of verfcs on Sir

J am prcud to reckon among the I bad any apprebenjion that this piece

ai.

,

1 fjoiild

of poetry ftood in need might know-, that r .

f-f

be deftrous the reader

(ixteen years old,

(ii:

ISAAC

a young Gentleman^ number of my de-fir eft friends*

received from

and was obliged But 1 Jhall

to finijb

his compofi-

'

tic

to

r,

{hortfpace of time. that tic loldnefs of the

digrejfions

only

take the liberty

will be

left

judged of

who are acquainted with PINDAR.

A

POEM

POEM O N

ISAAC NEWTON.

Sir

\ O NEWTON'S

genius, and immortal fame Th' advent'rous mule with trembling pinion ibars. Thou, heav'nly truth, from thy leraphick throne Look favourable down, do thou affift My lab'ring thought, do thou infpire my long. NE w T o N, who firft th' almighty's works difplay'd, And fmooth'd that mirror, in whofe polifh'd face l

f

fcT"

The

now confpicuous ftiines great creator open'd nature's adamantine gates,

;

Who And

to our

NEWTON

minds her fecret powers expos'd

demands the mule;

;

hand facred hand

his facred

Shall guide her infant fteps ; his Shall raife her to the Heliconian height,

its lefty top inthron'd, her head Hail nature, hail, Shall mingle with the Stars. Goddeis,Siandmaid of th' ethereal power,

Where, on

O Now lift thy

head, and to

Shew thy long hidden

Of

ancient fame, immortal

The

th'

admiring world

Thee the PLATO'S lelf,

beauty.

wile

Stagy rite, and Syracufian fagc,

From

A POEM From black

obfcurity's abyfs to raife,

(Drooping and mourning

With

thy wondrous works) Like meteors thele

o'er

vain inquiry ibught.

In their dark age bright Ions of wifdom fhone

But

at

thy

NEWTON.

on Sir ISAAC

NEWTON

all their

:

laurels fade,

They fhrink from all the honours of their names. So glimm'ring ftars contract their feeble rays, When the fwift luftre of AURORA'S face Flows o'er the skies, and wraps the heav'ns in light.

THE

Deity's omnipotence, the caufe,

Th' original of things long lay unknown. Alone the beauties prominent to fight (Of the celeftial power the outward form) Drew praife and wonder from the gazing world.

As

\Vhen the deluge overfpread the earth, Whilft yet the mountains only rear'd their heads Above the furface of the wild expanle,

Whelm'd deep below

the great foundations lay,

Ibme kind angel at heav'n's high command Roul'd back the riling tides, and haughty floods, Till

And

to the ocean thunder'd out his voice

The Back

:

the fwelling and imperious waves, foaming billows and oblcuring lurge,

Quick

all

to their channels

Recoil affrighted

:

and

their ancient feats

from the darklbme main

.Earth raifes Imiling, as new-born, her head, with frefh charms her lovely face arrays.

And So

his extenfive

thought accomplifh'd

The mighty task to Of ignorance away,

firft

drive th' obftrufting mifts

beneath whole gloom Th' infhrouded majcfty of Nature lay. He drew the veil and fwell'd the fpreading

How

had the moon around

th' ethereal

fccnc.

void

Rang'd,

A POEM

on

Sir

ISAAC NEWTON,

Rang'd, and eluded lab'ring mortals care, Till his invention trac'd her iecret fteps,

While

fhe inconftant with unfteady rein

Through

endlefs

mazes and meanders guides

unequal courfe her changing carr Whether behind the fun's fuperior light

In

its

She hides the beauties of her radiant

:

face,

when

confpicuous, Imiles upon mankind, Unveiling all her night-rejoicing charms. When thus the filver-trefled moon dilpels

Or,

The And

frowning horrors from the brow of night, with her Iplendors chears the fullen gloom,

While lable-mantled darknels with

The And

r

me upon fbmc

Let

his veil

vifage of the fair horizon fhades, over nature Ipreads his raven w ings

While

fleep

fits

;

unfrequented green

heavy on the drowfy world,

Seek out Ibme

Where

Bow

folitary peaceful cell, darklbme woods around their

low, and ev'ry

hill's

gloomy brows

protended fhade

Obfcures the dusky vale, there

filent dwell, contemplation holds its Hill abode, There trace the wide and pathlels void of hcav'n, And count the ftars that fparkle on its robe.

Where

Or

elle in fancy's wild'ring

mazes

loft

the verdure fee the fairy elves Dance o'er their magick circles, or behold,

Upon

In thought enraptur'd with the ancient bards,

Medea's baleful incantations draw

Down But

from her orb the paly queen of night.

chiefly

NEWTON

let

me

Ibar with thee,

And

while furveying all yon ftarry vault With admiration I attentive gaze,

Thou

fhalt

defcend from thy

celeftial feat,

And

A POEM And

waft aloft

my

ISAAC

on Sir

NEWI

high-afpiring mind,

k {hew me there how natuse has ordain'd

Her fundamental Through

And

all

teach

laws, fhalt lead my thought the wand'rings of th' uncertain moon,

me

all

her operating powers.

She and the fun with influence conjoint Wield the huge axle of the whirling earth, And from their juft direction turn the poles,

Slow urging on the progrefs of the

The And

o'er the skies

You, Iplendid

The

Now

years.

conftellations leem to leave their leats,

with Iblemn pace to move.

rulers

leas obey, at

of the day and night,

your

refiftlefs

fway

they contrad their waters, and expofe dreary defart of old ocean's rei;

The The craggy

rocks their horrid fides difcloie

Trembling the

And

failor

;

views the dreadful fcene,

cautioufly the threat 'ning ruin fhuns. fhallovv waters hide the lands,

But where the

There ravenous deftrudion lurks conceal'd, There the ill-guided veflel falls a prey, And all her numbers gorge his greedy jaws. But quick returning lee th' impetuous tides

Back

to th' abandon'd ihores impell the main.

Again the foaming feas extend their waves, Again the rouling floods embrace the fhoars, And veil the horrours of the empty deep. Thus the obfequious feas your power confels, While from the furface healthful vapours rile Plenteous throughout fhe atmofphere diffus'd, Or to fupply the mountain's heads with Iprings,

Or

fill

That

May

the hanging clouds with needful rains,

friendly ftreams, and kind rcfrefhing fhow'rs fun-burnt thirfty plains, gently lave the

Or

A

PoEiM on

ISAAC NEWTON.

Sir

Or to replenifh all the empty air With whollbme moifture to increale

Of

and

earth,

blefs the labours

the fruits

of mankind.

O NEWTON, whether flies thy mighty foul, How fhall the feeble mule purfue through all The

To

unbounded thought, unfeen recefles dark

vaft extent of thy

That even leeks

th'

penetrate of providence immenle. thou the great dilpenfer of the world

And

who with infpiration taught'ft greateft bard to fend thy praifes forth

Propitious,

Our

Thou, who

When

Who And

to

gav'ft

NEWTON

thought

;

;

who

fmil'dft ferene.

bounds he

ftretch'd his fwelling Ibul ftill benignant ever bleft his toil, deign'd to his enlight'ned mind t' appear its

Confefs'd around th' interminated world

To me O

Thy

:

thy divine infufion grant

(O thou in all Ib I may ling

That

^

infinitely

good)

thy everlafting works, inexhaufted ftore of providence,

In thought effulgent and rclbunding verle. could I Ipread the wond'rous theme around,

O

Where

To To To

the

wind

cools the oriental world,

the calm breezes of the Zephir's breath, where the frozen hyperborean blafts,

where the

From

boift'rous tempeft-leading Ibuth

deep hollow caves lend forth Thou ftill indulgent parent of mankind, Left humid emanations Ihould no more Flow from the ocean, but diffolve away their

Through the long feries of revolving time And left the vital principle decay,

their ftorms.

/ ;

By which the air fupplics the fprings of life Thou haft the fiery vifag'd comets fonn'd [b]

;

\Yith

A POEM

on Sir ISAAC

With vivifying fpirits all replete, Which they abundant breathe about

NEWTON,

the void,

the prolifick foul of things. longer now on thee amaz'd we call,

Renewing

No No

longer tremble at imagined ills, comets blaze tremendous from on high.

When

Or when

W

extending wide their flaming trains hideous grafp the skies engirdle round,

7

ith

And For

Of

fpread the terrors of their burning locks.

thele through orbits in the lengthening fpace many tedious rouling years compleat

Around

And And

To

move

regularly on

;

myftick periods their obeylancc pay ruler of the skies

him majeftick his

Upon

He

the fun

with the planets in harmonious orbs,

throne of circled glory

fixt.

fome god confpicuous to the view, Or elle the fubftitute of nature leerns, or

Guiding the courfes of revolving worlds.

He

taught great

NEWTON

the all-potent laws

Of gravitation, by whole fimple power The univerle exifts. Nor here the fage Big with invention ftill renewing ftaid. But O bright angel of the lamp of day, How fliall the mufe difplay his greateft toil ? Let her plunge deep

Or

in

Aganippe's waves,

in Caftalia's ever-flowing ftream,

That

re-infpired

How NEW TON The yellow

me may

fing to thee, dar'd advent'rous to unbraid

treffes

of thy fhining

hair.

Or

didft thou gracious leave thy radiant fphere, And to his hand thy lucid fplendours give,

T' unweave

the light-diffufing wreath, and part

The

A POEM

on

Sir

ISAAC NEWTON.

glories of thy golden plumes with laborious, and unerring care,

The blended

He

How

diff'rent

?

and imbodied colours form

Thy piercing light, with juft diftinftion found. He with quick fight purfu'd thy darting rays, When penetrating to th' oblcure receft Of Iblid matter, there perfpicuous law,

How

of each body lay

in the texture

The power Hence

Thy

that feparates the diff'rent beams. over nature's unadorned face

bright diverfifying rays dilate

Their various hues fwift

Defending

Thy In

its

:

and hence when vernal

rains

have burft the low'ring clouds,

fplendors through the diflipating mifts fair vefture of unnumber'd hues

Array the fhow'ry bow. At thy approach The morning rilcn from her pearly couch With rofy blulhcs decks her virgin cheek The ev'ning on the frontifpiece of heav'n His mantle Ipreads with many colours gay ; The mid-day skies in radiant azure clad, The fhining clouds, and filvcr vapours rob'd In white tranfparent intermixt with gold, With bright variety of fplendor cloath All the illuminated face above.

W hen hoary-headed winter back T

To

the chill'd pole, there foliury

retires fits

Encompals'd round with winds and tempefts bleak In caverns of impenetrable ice,

And

from behind the diffipated gloom Like a new Venus from the parting lurge The gay-apparell'd fpring advances on ;

When

thou

And from

in thy meridian brightnels fitt'ft, thy throne pure emanations flow

[b

]

or

A POEM Of

on Sir ISAAC

NEWTON.

glory burfting o'er the radiant skies let the mufe Olympus' top afcend,

:

Then

And And

extend her view,

o'er Theflalia's plain

O

thy beauties o'er. Mountains, whole fummits gralp the pendant clouds, count,

Tempe,

all

Between

their wood-invelop'd flopes embrace green-attired vallies. Every flow'r Here in the pride of bounteous nature clad

The

Smiles on the bolbm of th' enamell'd meads.

Over

Of

the fmiling lawn the filver floods Peneus gently roul along,

fair

While the

reflected colours

from the

flow'rs,

And verdant borders pierce the lympid wavo. And paint with all their variegated hue The yellow fands beneath. Smooth gliding on The waters haften to the neighbouring fea. Still

the pleas'd eye the floating plain purfues;

At length,

in Neptune's wide dominion loft, Surveys the Ihining billows, that arile Apparell'd each in Phoebus' bright attire :

Or from a far ibme tall majeftick fhip, Or the long hoftile lines of threatening fleets. Which o'er the bright uneven mirror fweep, In dazling gold and waving purple deckt

;

of old, when haughty Athens power Their hideous front, and terrible array

Such

as

Againft Pallene's coaft extended wide, And with tremendous war and battel Hern

The

trembling walls of Potidaea fhook. with pendants curling with the breeze upright mafts high brittle in the air,

Creftecl

The

Aloft exalting proud their gilded heads. filver waves againft the painted prows

The

Raife their rcfplcndent bofoms, and impearl

The

A POEM

on

Sir

ISAAC NEWTON.

The fair vermillion with their glift'ring drops And from on board the iron-cloathed hoft Around the main a gleaming horrour cafts ; Each flaming buckler like the mid-day fun, Each plumed helmet like the filver moon, Each moving gauntlet like the light'ning's

And But

:

blaze,

like a ftar each brazen pointed Ipear. lo the facred high-erefted fanes,

Fair citadels, and marble-crowned towers,

And

(lately towns their heads

lumptuous palaces of

Magnificent

arife,

upon

Bearing on high a wreath of

But

filver light.

mule the high Pierian hill, Behold its maggy locks and airy top, Up to the skies th' imperious mountain heaves The Ihining verdure of the nodding woods. fee

my

See where the

Behold each

filver

Hippocrene flows, and rill

glitt'ring rivulet,

Through mazes wander down

And

the green delcent^

fparkle through the interwoven trees.

Here

reft

a while and humble homage pay ?

Here, where the lacred genius, that infpir'd Sublime M^ONIDES and PINDAR^ breaft. His habitation once was fam'd to hold.

Here thou,

O HOMER,

Thee, the kind mule

And

led thee to the

offer'dft

up thy vows $

CALLIOP^A

empyrean

:

heard,

feats,

There manifefted to thy hallow'd eyes The deeds of gods- thee wile MINERVA taught The wondrous art of knowing human kind ; Harmonious PH OE B u s tun'd thy heav'nly mind,

And Even

fwell'd to rapture each exalted lenfe

MAR

MARS

;

the dreadful battle-ruling god, taught thee war, and with his bloody hand s

[nftrudcd

A POEM

on

Sir

ISAAC NEWTON.

Inftru&ed thine, when in thy founding \\ e hear the rattling of Bellona's carr,

The yell of dilcord, and the PINDAR, -when mounted on

lines

din of arms. his fiery fteed,

Soars to the fun, oppofing eagle like to the fierceft rays.

His eyes undazled

He

firmly featcd, not like

Strides his Iwift-winged

And The

born

aloft ftrikes

GLAUCUS'

fon,

and fire-breathing horfe,

with his ringing hoofs

brazen vault of heav'n, fuperior there

Looks down upon

the ftars,

whole radiant

light

Illuminates innumerable worlds, That through eternal orbits roul beneath.

But thou

all hail

immortalized Ion

Of harmony, all hail thou Thracian bard, To whom APOLLO gave his tuneful lyre. O might'ft thou, ORPHEUS, now again revive, And NEWTON fhould inform thy lift'ning ear

How the Of

foft notes,

and loul-inchanting

ftrains

own

lyre were on the wind convey 'd. taught the mule, how found progreffive floats Upon the waving particles of air,

thy

He

When harmony

in ever-pleafing ftrains,

Melodious melting

With

Through

And

at

each lulling

fall,

foft alluring penetration fteals

the enraptur'd ear to inmoft thought, its filken bands.

folds the ienfes in

So the fweet mufiek, which from ORPHEUS' touch fam'd A M p H i o N'S, on the founding firing

And

Arole harmonious, gliding on the air, Pierc'd the tough-bark'd and knotty-ribbed woods, Into their faps foft infpiration breath'd

And

taught attention to the ftubborn oak. great HENRY, and brave MARLB'ROUCH led

Thus when

Th'

A POEM

on

Sir

ISAAC NEWTON;

Th' imbattlcd numbers of BRITANNIA'S Ions, The trump, that Iwells th' expanded cheek of fame, That adds new vigour to the gen'rous youth, And rouzes fluggilh covvardize it lelf, The trumpet with its Mars-inciting voice, The winds broad breaft impetuous fweeping o'er Fill'd the big note

of war.

Th'

inlpired hoft

With new-born ardor prefs the trembling GAUL Nor greater throngs had reach'd eternal night, Not if the fields of Agencourt had yawn'd Expofing horrible the gulf of

Or

roaring

Danube fpread

And overwhelm'd But

Nor

let

their

the wand'ring

fate

;

arms abroad, legions with his floods. his

mule

at length return

yet, angelick genius of the iiin,

In worthy lays her high-attempting long

Has blazon'd forth thy venerated name. Then let her fweep the loud-relbunding lyre Again, again

each melodious firing to tremble with thy praile.

o'er

Teach harmony

And ftill thine ear O favourable grant, And me mail tell thee, that whatever charms, Whatever

beauties

bloom on

nature's face,

Proceed from thy all-influencing light. That when arifing with tempeiluous rage,

The North impetuous

rides

upon the clouds

Difperfmg round the heav'ns obftruftive gloom, And with his dreaded prohibition ftays

The kind

effufion

of thy genial beams

Pale are the rubies on

AURORA'S

;

lips,

No more the roles blufh upon her cheeks, Black are Peneus' Dreams and golden lauds In Tempe's vale dull melancholy fits, every flower reclines its languid head.

And

;

A POEM By what high name

on Sir ISAAC

fhall I

invoke thee, fay,

Thou

life-infufmg deity, on thee

I call,

and look propitious from on high,

While now to thee 1 offer up my prayer. O had great NEWTON, as he found the

By which Ibund <

.

>

had he,

NEWTON.

caufc,

rouls thro' th' undulating air,

baffling times refiftlefs

Dilcover'd what that liibtle

power,

fpirit is,

Or whatfoc'er diffufivc elfe is fpread Over the wide-extended univcrle,

Which

reflect: the light, their ftraight direction to divert

caufes bodies to

And from The rapid

beams, that through their furface pierce. th' icy arms of age,

But fmce embrac'd by

And

his

Ev'n

quick thought by times cold hand congeal'd, left unknown this hidden power ^

NEWTON

Thou

from the race of human kind

Some With

other worthy of an angel's care,

feleft

infpiration animate his brcaft,

And him

inftrudYin thefe thy iecret' laws. to whofe fpacious view,

O let

not

Now

unobftru&ed,

NEWTON,

all th'

extenfive fcenes

Of the ethereal ruler's works arife When he beholds this earth he late

;

adorn'd,

Let him not lee philofbphy in tears, Like a fond mother iblitary fit,

Lamenting him her dear, and only child. But as the wife PYTHAGORAS, and he, Whofe birth with pride the fam'd Abdera With expectation having long furvey'd This fpot

their antient feat, with

boafts,

joy beheld

Divine philolbphy at length appear In all her charms majeftically fair,

Conducted by immortal

N E w T o N'S

hand

:

A POEM So may he

That

ftiall

on

Sir

NEWTON.

ISAAC

fee another lagc a rife, then no more maintain her empire :

Imperious ignorance \\ith haughty fway Shall ftalk rapacious o'er the ravag'd globe fhalt protect thete .

Then thou, ONE WTO N, The humble tribute of the

grateful mule-

line-?.

j

Ne'er Ihall the lacrilcgious hand dcfpoil

Her

laurel'd temples,

whom

his

name

prelerves

:

And were me

equal to the mighty theme. Futurity fhould wonder at her long ; Time fhould receive her with extended arms, Seat her confpicuous in his rouling carr, And bear her down to his extreameft bound.

FABLES With

Of Of

with wonder

how

tell

Terra's 16ns

iron force unloos'd the fhibborn nerves

hills,

and on the cloud-inmrouded top But if the vaft

Pclion Ofla pil'd.

Gigantick deeds of favage ftrength demand Aftonifhment from men, what then fhalt thou,

what

exprefTive rapture of the foul,

When The

thou before us, NEWTON, doft difplay labours of thy great excelling mind ;

When The

thou unveileft

all

the

wondrous

icene,

vaft idea of th' eternal king,

in his angry arm thunder hanging o'er our trembling heads Hut with th' effulgency of love replete,

Not dreadful bearing

The

And () T

1

clad with power, which form'd th' extenfive heavens.

he, whole enterprising hand nbars the golden and relucid gates

happy

Of

th'

empyrean dome, where thou enthron'd

Philofbphy l.iy

art leated.

Thou

lullain'd

the firm hand of evcrlafting truth ]

Ddpjfeft

A POEM Dclpileft

all

the

on

injuries

ISAAC

Sir

of time

NEWTON.

:

Thou

never know'ft decay when all around, Behold Antiquity obfcures her head.

Th' Egyptian towers, the Babylonian walls, And Thebes with all her hundred gates of brafs, Behold them fcatter'd like the duft abroad. \\

now

hatever

Whatever

fhall,

is

flourifhing

muft

and proud,

know devouring

age.

Euphrates' ftream, and feven-mouthcd Nile, And Danube, thoti that from German ia's Ibil

To

the black Euxine's far remoted

ftiore,

O'er the wide bounds of mighty nations iweep'ft In thunder loud thy rapid floods along.

Ev'n you

To you

fhall feel inexorable

the fatal

day

fhall

time

come

;

no more

Your

torrents then fhali (hake the trembling ground. longer then to inundations fwol'n Th' imperious waves the fertile paftures drench, But fhrunk within a narrow channel glide ;

No

Or through

the year's reiterated courle

When

time himlelf grows old, your wond'rous ftreams Loft ev'n to memory fhall lie unknown

Beneath obfcurity, and Chaos whelm'd. But ftill thou fun illuminateft all

The azure regions round, thou guideft ftill The orbits of the planetary fpheres ; The moon ftill wanders o'er her changing courle, And ftill, O NEWTON, lhall thy name iuryive As long

When

as nature's

hand

:

directs the world,

ev'ry dark obftru&ion fhall retire,

And ev'ry fecret yield its hidden ftore, Which thee dim-fighted age forbad to lee Age

And

that alone could ftay thy rifing foul. could mankind among the fixed ftars,

E'en

A POEM E'en to

To

th'

thofe

Whole

on Sir ISAAC

NEWTON.

extremeft bounds of knowledge reach,

unknown innumerable

funs,

glimmers from thofe diftant worlds, Ev'n to thole utmoft boundaries, thole bars light but

That fhut the entrance of

th' illumin'd

fpacc

Where angels only tread the vaft unknown, Thou ever fhould'ft be feen immortal there In each new iphere, each new-appearing liin, :

In fartheft regions at the very verge Of the wide univerfe fhould'ft thou be ieen.

And

lo, th' all-potent

goddefs

With her own hand thy

NATURE

great, thy juft

takes

reward

Of

immortality ; aloft in air See fhe dilplays, and with eternal gralp Uprears the trophies of great NEWTON'S fame.

R.

[c i]

GLOVER*

CO

N-

THE

ONTENTS.

C

DUCT!

N

method of INTRO reasoning

ISAAC

philofophy

BOOK CHAP,

Sir

concerning in

The

'j i

pag.

I.

i Of the laws of motion The frft law of motion proved The fecond taw of motion proved The third law motion proved of

CHAP.

NEWTON

.

Further proofs

i.

effetts

of percujjion

p p

, ,

^

,

p

^

p.

4P

of the laws of motion

^

The perpendicular defcent of bodies p. The c oblique defcent of bodies in a Jlraight line 7 p. The curvilinear defcent of bodies p .g The perpendicular afcent of bodies faj The oblique afcent of bodies p The fower of gravity proportional to the quantity of\ matter in each ?p. <fo body The centre of gravity of bodies n '

1

i

1

1

Ihe mechanical powers The lever

P.

o

2.

~^

The wheel and axis The pulley -ri

/

p.

80

/'

rcrew

P-

8

I

he iveare

The T/

5

.

,

lblC*.

J 1 The inclined plain '

/'

p.

84 The

CONTENTS. The pendulum

Vibrating Filtrating

The

line

8<;

in

a

in a

p. ibid.

circle

cycloid

of fwifteft defcent

p.

91

p.

93

The centre of oscillation p. 94 bodies made by pendulums p 9 8 Experiments upon thepercujjion of The centre of percujjion 100 p. .

motion of projectiles defer ipt

ion of the conic feftions

difference

3

Of Of

.

4.

Bodies are

refiftance in the

of

duplicate proportion

elaftic fluids

^ and

their refftance

r

p.

117

p.

145

P'

p.

he rendered elaftic The degree of refinance in regard to the proportion the and of the fluid body denfity of

In rare

o

of their?

velocities

Of

o

i

P

centripetal forces the fluids

refifted

How fluids

i

p.

between abjolute and relative mot ion, 7

as alfo between abfolute and relative time

CHAP. CHAP.

p.

may

p.

149 j

j

between the

^ ^

and

uncompreffed fluids p. i In compreffed fluids T p. The degree oj rejlftance as it depends upon the figure of bodies In rare and uncompreffed fluids i ^ j p. In j r g compreffed fluids p.

BOOK CHAP,

i

Jenfible

.

II.

That the planets move in a fpace empty of^

l61

matter

the world The fyjlem defcribed of The planets Juffer no fenfible

refiftance

p. in their motion

are not kept in motion a fluid by That all fpace is not full of matter without vacancies 'ihey

p.

p.

1

p.

162. i

66

167 1 69

CHAP.

CONTENTS. i

HAP.

in motion the that keeps Concerning r & the caaCe J > p.

2. -iiry

f lands

<nv influenced l\ a centripetal

power directed tol

r

1

the

170

3

I

P'

\

The

the this dufH-f power is reciprocally in flrengtk of the cate $ dijlance proportion of in the motions The caufe of the planets p of t he irregularities correction p. of their motions That the p. of the world is not eternal

...

175 178

.

A

180

frame

CHAP.

l

7

fun

Of

3.

the motion

moon and the other fecondary of the

planets

That

they

are influenced a centripetal directed") hy force as the their are primary primary, influ-j> p.

toward

enced by the fun

That the power called the moon gravity extends to ufually That the fun a&s on the fecondary planets The 'variation of the moon That the circuit of the moons orlit the

fun

in the

conjunction

and

182,

j

quarters,

and

i

p.

po

ibid.

p.

105

p.

i

is

increafed by~) dim'mijhed in //;<?>

<?

8

j

oppofition

The diftance of the moon from the earth in the quarters'^

and

in the

by the

conjunction

and

oppofition

is alter

edf

p.

Thefe irregularities

in the

moons motion varied

ly

the?

the earth and fun $ change of diftance between The period of the moon round the earth and herdiflance\ varied hy the fame means j

*

The motion of the nodes arid the inclination of the\ moons orlit j P* The

motion

cf

eccentricity

200

j

fun

the

apogeon

and

change

of the\ j P*

.,

.

2oi 2

x

"

The

CONTENTS. The inequalities of the other fee ondary planets deducible^i

from

CH

A

P. 4.

%are

tbefe

Of

of the moon

J

comets

not meteors, nor placed totally without the\ r n

j

(

J

P-

M

P-

MI

p.

233

p.

154

planetary Jyjtem The fun a els on them in the fame manner as on the?

c

j

planets Their orbits are near to parabola s cowff that appeared at the end of the year

probably performs its period in another comet in 7 5

3

i

6 So.,0

575 j^rr,

^W>

comets move in planes more different from} one another than the planets J The tails of comets p. The ufe of them p. 245,

The

poffible ufe

CHAP.

5

.

Of

of the comet

the bodies

of

it

the

jelf fun and planets

That each of the heavenly bodies attrattive

power} and that

is

the

p.

3

8

145, 2,46

endued <with an-\

force of the

fame( off

on others is proportional to the quantity body matter in the body attraffed

In the rejl of the planets That the attractive power is of the fame nature

and

*

'

J

This proved in the earth In the fun

the fun, and in all the planet s> the fame with

2.

144

p.

248

p.

150

p,

15

i

iri

therefore zV

gravity

T,.at the attractive

proportional

in each

of thefe bodies is in the matter quantity of body},

power

to the

ibid.

attracting

//

CONTENTS. m

That each particle of which the fun and planets compofed is endued with an attracting power, the Jlrcngth of which cate

is

reciprocally

in

the

{

dupli-(

proportion of the dijlance

The

power of gravity univerfally belongs to all matter p. ~\ The different the fame body upon the furface weight of cf the fun, the earth, Jupiter and Sat urn ^ the re ( fpcctive devftties of thefe bodies, tion between their diameters

CHAP.

6.

the fluid parts in which fluids

Of

The manner

and

2 j 9

the propor-f

J

of the planets prefs

p.

The motion of waves on the furnace of water Tloe motion of found through the air The of found

269

p.

2.70

p.

velocity

the tides Concerning The figure of the earth The effect of this figure upon the power of gravity it has The upon pendulums

2.64

p.

2.82,

p.

183

p.

2.96

p.

301

p.

302,

Bodies defcend perpendicularly to the furface of the earth p. The axis of the earth changes its direction twice a^i

304

effect

and twice a month year, The figure of the fecondary planets

BOOK CHAP, The fun

i

.

s

j ibid.

III.

the caufe of colours inherent in the compofed of rays of different colours p.

Concerning light

is

The re fraction of light p. $ i <;, Bodies appear of different colour by day -light, be caufe'') fome reflect one kind of light more copioufly than** p. the rejl,

The

effect

and

other bodies other kinds

of

of mixing rays of different colours

lio-ht

li<rht *

i

S

310 315?

N p.

334

CHAP.

CONTENTS. CHAT,

i

Light

is

Of the properties of bodies whereon their colours depend not reflected the folith by impinging againjl j * farts of bodies The particles which are tran parent Mies compofe p. 541 .

f

Caufe of opacity

p.

bodies in the

Why

open day -light have different colours p.

The great bodies confidered porofity of

CHAP.

3

.

Of the

p.

refraction, reflation,

and

inflection

of

colours are re framed oj different differently the incidence in each kind

Rays

ihe fine

of bears a

angle oj

given proportion

to the

fine of refraffion j"

between light and bodies

is

mutual

*

p

.

p.

bodies refleft part of the light incident upon them\

and tranfmit another part Sir

ISAAC

357

of raysj

has alternate and reflection p. fits of eafy tranfrmffion Li^Jt times Thefe fits found to return p. alternately many thottfand

Why

44

355

light.

p.

The proportion between the refractive powers in diffe-\ rent bodies j Unttuous bodies refraft moft in proportion to their denfity 7 he action

541 3

3

68

3

6?

371 375 .,

.

,

)

NEWTON

's conjecture concerning the') caufe of this alternate reflection and tranfmijjion^ p.

37^

^

of light The inflettion of light

p.

377

CHAP. How

4. Of optic glaffes. the rays are refracted light

of

by

a fpberical fur-*)

f P

faceofglafs

How they are refraffed by two fuch furfaces How the image of objects is formed by a convex glafs Why

convex gkjfes help the fight in old age^ and cave glajfes tfffift fiyort-fighted people

The wanner in which vifion

is

[d]

'

377

p.

380

p.

381

p.

384 Of

con-*)

performed by the eye

3

CONTENTS. Of telefcopes

with fwo convex glares four convex glafles

Of telefcofes with Of telefcofes 'with Of microfcopes Of the imperfection f

Of the

reflecting telefcope '

5

.

Of

the inner

Of

the of tele (copes arifinr ** from

r ? i I1 the light rejrangwility oj

rent

CHAP.

one convex and one concave glafs

the ramkonu

3-9Jj <wd 398, 3<>5> *w ^ 4 p. 3^6, 35>?j in the inner rainbow 40 i

rainbow

p.

Of the outter bow Of a particular appearance

3

5>4>

p.

Conclujion

405

p.

ERRATA. r. F. 24. for I read K. p-f}- I- penult, f. 45. p. 91. 1. 3. f. 48. r. fo. ibid. 1. if. J p. 96. 1. 23. dele the comma after </. p. 140. 1. n. p. 144. 1. if. f. threefold, r. twofold, p. 162. 1. if. f". y. r. ->-. p. 19^. i. r. alvayi. 1. and J. f, F. 200. r. C. 101. 1. ). 8. h r. p. 199. p. 3. f. p. permit, ufcends. Tww/2 nfcmd. ibid. 1. 10. f. JtjcenJs. r. JrfceaJ p. 208. 1. 14. f. WTO. r. NTO. In fig. 110. draw a Jme where place W. p. 216. 1. penult, f. *Rtm. r. from / through r, tiJl it meets the circle motion, p. 211. l.ij. f. AF. r.AH. p.2Ji. J. 23. after imtntion put a full point, p. zf?. 1.

81. PAGE tor p.

49.

r.

if. 1.

line 4. read /n

ult. f.

fi.

p. dele

40. 91.

r.

ff/

42.

1.

Pnctpts. p. 40.

p. 83.

18.

f.

1.

ult. f.

AGFE.

r.

43.

I.

.

r.

HGFC.

.

ADCB,

p. r. J,

f. 1.

penult,

f. DE. r. B T. p. 178. 1. 17. f. | T r. 369. 1. i, 3. r. ffeutto- topaz., p. 378. 1. 12. f. thut. ifotf. p. 379. 1. if. f. convergt. r. diverge, p. 384. 1. 7. f. optic glfi. r. cptic-ntrvt. p. 391. 18. r. 4J fo r 78. p. 391. 1. 18. after telefcoft add 6e abtut loo/m /pw^ and the. in ;fr. 161. / put t. p. 399. 1. 8. r. AH, A*. Sec. p. 400. 1. 19. r. AT, Af. A<r, AT, A$ p. 401. 14. j.fe 163. The pages 374, 37f, 376 are erroneoufly numbered jjf, 37^, 377 > and tie 382, .383 are numbered 381, 381.

dele

the

199.

comma

1.

after rtmnrkablt.

19. r./*. p. 361.

1.

12.

p.

f.

iff.

/.

r.

J.

t,

ulr.

p.

.

.

A LIST

of fuch of

the

SUBSCRIBERS NAMES As

are

come

to the

HAND

of the

AUTHOR Mr Zacb. Allen Rev. Mr Allerton

,

Fellow

of

d'Aguefleau, Chaacelier

France

tie

Reverend Mr Abbot, MOnfeigneur

Emanuel

Coll.

Thomas Abney,

of

Camb.

Capt. George Abell iht Hon. Sir JohnAnftruther,

Ztar.

Efq;

Mr. Nathan Abraham Arthur Achefon, Eart. William Adair Rev. Mr John Adams, Fellow of

Sir

Mr

Sidney Coll. Cambridge

Mr William Adams Mr George Adams Mr William Adamfon,

Scholar

o/Caius Coll. Camb. Mr Samuel Adee, fell, of Corp.

Chr. Cell. Oxon

Mr Andrew Adlam Mr John Adlam Mr Stephen Ainfworth Aifcor.

Mr

EookRobert Akenhead at Newcaftle upon Tyne Albinus, M. D. Anatom. ,

tf</Cbirerg

in

Acad. L.B.Prof.

George Aldridge, M. D. Mr George Algood

Mr

Aliffe

Robert

Allen,

Jonathan Ayleworth, Jun. /^i

B

Thomas

Anfon, Efej; Rev. Dr. Chriftopher Anftey Mr IGac Antrabus

His Grace the Duke of Bedford Right Honourable the Marquis ef

Mr

Right Hon. the Earl of Burlington Right Honourable Lor a" Vtfcount

Jofhua Appleby John Arbuthnot, M. D. William Archer, E(q;

Mr

Thomas

Archer, Efa\

Coll.

John Armftrong, SurveyorGeneral o/His Majefty's Ord nance

Mr Armytage Mr Street Arnold, Surgeon Mr Richard Arnold Mr Afcough Mr Charles Afgill

William

Afliurft, Efo of Htnningham, EfTcx

Bowmont

Batcman

John Archer, Merchant of

Amfterdam

Rt.Rev. LJ. Bp. of Bath and Wells Rt. Rev. Lord Bijlwp o/'Briftol Right Hon. Lord Bathurft

Richard Backwcll, Eftj; William Backmell, Merck.

Mr

Edmund Backwell, Sir Edmund Bacon

Cent.

Richard Bjgfliaw, c/Ojkes, Efq; Tho. Bagfliaw, cf Bakcwell, Eft; Rev. Mr. Bagfhaw Sir Robert liaylis

Jefus Coll. Cambridge

fflltr

S. B

Ayerft

Mr St. Amand Mr John Anns

Richard Adi, Efq; of Antigua Mr Am, Fellow-Commoner of

Mrs

Mr Mr

Rowland Aynfworth,

Sidney Coll. Cambridge

Caftle

Mr Thomas Afhurft Mr Samuel Afhurft Mr John Askew, Merchant Mr Edward Athawes, Merchant Mr Abraham Atkins Mr Edward K.eofey Atkins * A

Honourable George Baillie, Efo Giles Bailly, M.D. ^/Briftol Mr Serjeant Baines

Rev.

Mr. Samuel

den. of St.

Baker,

Reft-

Paul's.

Mr (3eorge Baker Mr Francis Baker Mr Robert Baker Mr John Bakcwell Anthony Bxam, Efy M. D.

Charles Bale,

Mr

SUBSCRIBERS NAMES. Mr

of Exeter

Fellow

Atwell,

Oxon

Coll.

Mr Savage Atwood Mr John Atwood Mr James Audley

Mr Battcly, M. A. Student of Chrift Church, Oxon Mr Edmund Baugh Rev. Mr. Thomas Bayes

Mr Mr

Edward Bay ley, M. D. of Ha-

Rev.

Rev.

John A jfr.cn Benjamin A very, L.L. D.

Sir

Mr

Ball, Prebendary

of

Mr

Pappillon

Mr

Levy

Rev.

Coll.

Mr

Merchant

Ball,

Ball

Cambridge

Thomas Mr

Rev.

nuel Coll.

Mr Henry

Wisbech,

of

Mr John Barber, Apethettry in Coventry Henry Steuart Barclay, of CoBarclay

,

Canon

of

Bcok-

Barker,

Benjanvn

m London

Francis BarklUad

Mr Thomas

Mr

Barrett, Efq; Barrett

Mr Humphrey

fVlr

Bartholomew,

y College, Renjarrin Bartlett Htnt) hjitletr

Oxon

]amr:- Uartlett

Mr Newton

Bjrcon, of Trinity

Co!'

mbndgc

Mr.

m

Da.-

F.I low of

Mr Mr

Mr

Mr

B.'tle*',

James Blew Y/i!Jiam Biizard

Henry Blunt Elias Bocket

Thomas Bockin^ Charles

Samuel

Bois

Efe);

Cambridge

j-lr

F%

Mr

Dr

Pcrjnj/lcne,

M. A,

Judith Booth

Thomas Thomas

Boot'et

Efej;

Borrct,

Bciij/irnin Belli

:

L

H,-iiry Bofville,

1

fwortb

Eft;

Bjthcll, of Rile in

Dr George York-

Mm.

r>iiii,n.n

[>,,.iii-n

y

In

r/

Du

Joieph Bolton, of London

Mr John Bond John Bonithon, A/. A. Mr James Bon wick, Kookfeller in London ?

Mf-

burton

Bttlidi,

Boehm,

William Bogdani John Du Bois, A

Swindon w

i

M.D. me I-

Mr Hum pi uy

of CliefterfielJ

C

F.ft,

Mr Mr

Efa; /'/;;

[iscl.jiLir in

Cl,r.;f -'plicr

W.l'uui

Mr Mr Mr Mr Mr Mr Mr Mr

Rev.

Clnries biTfijid

Hugh

Ejqi

Biandtord

Thorrm Boone, Efo

Trinity Col).

(hire,

Tliorm;- B-tt.

Arch-

Efq;

Thomas Bcre, L L.e MM. John Berkley, Mr Main ice Bcikiey, icn.

Hagh

!^trs

Peter Bathuifr,

Martin Benfon,

William Benfon, i*.>. Rev. Richard Btnt.'y, D D.

Mr

Thomas

derry,

of Cork,

deaf on of B^rks

John Bernard,

ton

iJirnlley, Eft;

Mark B.v,

Mr Mr

,

Bennet,

Samuel Eenion,

of

o/Emanuel Cambridge

Dr Biomer

Finney Beifield, oftkelnncrTerople Mr Benjamin Bell

itr

Blackwal/,

Arthur B.ancy, Efqj

Michael Beecher

Rev.

Mr

James Blackwood,

ham

Mr ?/lr Tiv.ir.ias

Mr Mr Mr

Rev

William Beecher, of Howbcrry,

Mr George

0/Umvei!;

Mr

A.

A/.

Bcaii,

Leonard Belt, Gent. William Bcnbow, Efy, Mr Mai tin Bendall

Barnard

Richird Barrett, A/. D. Mr Barrow, dpothecxry William Birrowby, M. D. Edward B^rry, M. D. o/Corke

Mr

Mr

E/tj;

jonath.n Blackwel, Efq^

Mr Humphrey Bell Mr Phineas Bell

Barker, Ejq;

.

Mr Rev.

D. cf VVor-

A/.

I

Efo

Windfor Mr David Barclay feller

Beachcrofc

Magdalen CoJltgc, Cambridge George Beaumont John Beaumont, Ef<j\ of Clap-

Jairny, Efej;

Mr

WiJJJam Blacker, Eff,

Rowland Blackman,

Rev. Mr Charles BJackmore, of Worcerter

Bearcroft

Sir

Surgeon

Mr

Rev.

College,

JolVph

Rev.

Cambridge

Banyer,

Mr

of

certer

Mr

St.

Henry Blaake, Efq; Henry Blaake Mr George Black Steward Blacker, Efy;

ProfrJJbr

UiUVtrjtry

Beacon, /^; Philip Bcarcroft

Richard Beard,

Bailer

John Bamber, M. D. Rev. Mr Banyer, Fellow of Ema-

Rev.

the

in

Mr Thomas Mr William

Oxon

Bifhop, Fellow of John's College, Oxon Bird, of Reading

Edinburgh Mr Benjamin Beach

Mr Jacob Bill, of Andovcr Mr Edward Ballad, o/Trin.

Rtv.

Lam

of

^Exeter

Eirchinflia,

Richard Bifcoe

Dr

Mr. Alexander Baynes,

Mr Tho.

Chicbefter

Mr

Mr Hawley

Chi-

of

chefter

BaJgay

Rev.

M. D.

John Baylcy,

Mr

College,

vant

Robert Auften, Bart.

Sir

John BiJlingflej George Binckes

Rev.

!5att,

Batr,

London

Siivanus Bevan, Afotli<,

Calverly B;wick, jun. Henry bigg, S. Warden

D

New

'nn.

J/>

College, Oxo'i

William Billers,

Billers

;

ni

cf

Mr Mr Mr

Bowks,

John Bowles

Thomas Bowles Dtvcreux Bowly Biadecl, Lfy,

Rev.

SUBSCRIBERS NAMES. Mr

Rev.

James Bradley, Profejfir

Oxford

in of Aftronomy,

Mr

Job Bradley,

in

Rookftller

Mr John Bradley Mr Bradfiiaw, Fellow

Rev

Mr Mr Mr

of

Cambridge

Jefas College,

Blackfliaw

Thomas Brand

Mr

Edmund

Bret

John Bnckdale,

Mr

Rev.

Abraham

A.

A/.

Bridges, Efq;

George Briggs, Efq; John Bridges, Efq, Brook Bridges, Efq; Orlando Bndgman, Efq; Charles

Bridgman

William Bridgman, o/Trini-

ty College,

Cambridge Briggs, Bjrt.

Humphrey

Robert Bnftol,

Efq;

Jacob Brook Hrooke, ofOr\e\ Coll.Oxofl

Thomas Brookes James Brooks William Brooks, Efq; Rev. Mr William crooks Stamp Brooksbank, Efq;

Murdock

Hroorrur

William brown, Efq;

Mr Mr Mr

'

William Bryan, Efq\

Mr

Rtv.

Brydam

Chnftopher Buckle, Efq; Samuel Buckley, Efq;

Mr Sir

|-

udgen John I'ull

Hal/, E/TrX,

Rev.

Mr

Burron, Richard Burton, Ffq;

Dr Simon Burton Mr Thomas Burton, M.AFdlorc of Caius College, Cam-

Rev.

Mr

Efq;

Richard Tullock

Mr

Nathaniel Carpenter

Henry

Carr,

Efq;

John Cair, Efq; John Carrurhcrs, Efq; Rev. Dr. George Carter,

Prt-

icfl of Oriel College

Mr

Mr

Samuel Carter

Edward

Carreret, Efa\ in

Virginia,

Wiiliam C^rtlich

Jimes Maccirtney,

Byam, Governonr

Mr Mr

Edward Byam, Merchant

Mr John Byrom

Merch.

Efq;

Carcwrighr, of A mho William Cjrtwnght,

Trinity College,

Mr

Re-^irer.d

of Antigua

Mr

era>

Efq;

Button, of Newcaftle

upon Tyne Hon. Edward

l

Stackpolc-

Robert Cartes, jun.

jun. Efq;

Samuel buiy Mr William Bufh Fev. Mr Samuel Butler

Mr Jofeph

of

John Carleton Richard Carkon, P/Chefter-

Honourable

britige B-jry,

j

County of

field

Mr

Mr

the

Court

Mr

Samuel burton, of Dublin, Efq; William Burton, Efq;

Rtv.

in

Campbell,

Mrj. Elizabeth Caper DelJiilers Caibonel

Francis Burton, Efq; John Burron, Efq;

of

Cambridge

William

Gary, of

Bnftol

Mr Mr Mr

Lyndford Carjl

John Cafe John Cnftle

Reverend Hon.

Mr

Cattle

William Cayley,

Cotiftd at

C?dJX, Efq; His Grace (he Archbishop of

terbury Right Hon.

Hn

the

(Jr.ue the

Can

Lord Chancellor

Duke o/Chandois

V.'illiam

Mr Mr

Mr Mr Mr

iv. Lord B'jlop of Chirhtftcr Loril bill), of Cloufert

Mr

l-'t.

I-

Rev.

in Iiclanrl /'/.

/'t'v.

Lord Bifhop of Cloyne * A 2

Chamber?,

Efq\

Nehcmiah Champion R-ichard Champion

Matthew

The Right Hon. the Earl of Carlifle 'Right Hon. Earl Cowper if. l<ev. Ltrd Btjl'opof Carlifle Rt.

Jofnh Bullock, of Faulkbourn-

Court,

broke, Efq;

Mr

Sarah Brown John Prowne

John Erowning, of Briftol John rowning Noel Broxholme, M.D.

Cambridge Reverend Mr John Cambden John Campbell, of SnckpoJe-

Burrow, Efq; James Burrow, Efq; Wil.iam Burrow, A. M.

John

r./<),

William Calvert of Emanutl

Mrs

Mr Richard brown, of Norwich Mr Duncumb Briflow, M. William Bradgate Mr William Brown, o/Hull Mrs

Herttordfliirc,

Mr

Benjamin Burroughs Jeremiah burroughs, Efq; Rev. Mr Jofeph burroughs

Jofeph Broad

Peter Brooke, of Meer, Efq;

Mr

Cambr.

Mr

Chriftoplier

Efq;

John Bridgen

Fellow of Caius Coll.

Felix Calvert, c/.sllbury, Efq; Peter Calvert, cf Huuidown in

College,

John Eurridge, Efq; James Burrough, Efq; Beadle and

William Brcnc

Chctwynd

Cornelius Cjiiaghau, Efq; Mr Charles Cal(jj.;!i in

Gilbert burner,

College, Cambridge Peter burrel Efq;

Brai.cker

Braxton

Mr

Gilbert Hurner, Efq; Thomas Burner, Efq;

Mr

Hon. Lord

Hon. Lorit Jules' Cavcndilh The Hon. Lord Cardrofs Kt. Hon. Lord Cadlemain Right Hon. Lord St. Clare

Mr

Bramfield, Efq;

Caft. David Braymer Charles Brent, 0/Briftol Rev

Mr Mr Mr Mr

Pt Hon. Lord Clinton A'/.

l\t.

['urges

hif Excellency Will. Burnet, ffq; Governour of New- York Traftord Burnfton, o/Trin.

Mr Thomas

Sir

D.

Thomas

Jofeph Brand, Efq;

Mr Mr

Mr

Rev.

Robert Bragge

Mr Mr

Richard Bundy

Alexander Bunyan

Jofcph Bradfhaw

Champion

Mr Mr

Mr Riv.

Ebcnczer burgefs, Efq; Robert Burlefton, A; B.

Chefterfield

Rev.

Mr

Rev.

Chnndler, Efq;

George Channel Channing Jof-ph Chappe'I, Attorney

at Briftiil

Rice Charlton,

4$

thtc.vj

at BnftoJ

St,

SUBSCRIBERS NAMES. St.

Mr Mr

John Charelton, Efq; Richard Charelton

Thomas

Chafe, of

Henry Coape,

;

sbon,

Nathaniel Coatfworth Rev. Dr. Cobdcn, Chaplain

Merchant

Patricius

M. D.

Hon. Col.

John Codrington, of

Marmadukc

Right Hon.

Cogliill,

Efq;

PoleCbaworth of the Inner

Tem

to

William Chefelden, Surgeon her Mjefly

Hall, in

Cambridge, Efq;

Cholmely, Gentleman Com moner of New-College, Oxon

Thomas Church,

Efq;

Reverend Mr St. Clair Reverend Matthew Ciarke William Clark

Mr

Mr

Bartholomew Clarke,

George Clarke, Efq; Samuel Clarke, of the Inner-TernPie, Efq;

Reverend

Mr

Alured Clarke, Pre-

bendaiy o/Wmchefter Rev. John Clarke, D. D.

Dean

ef Sarum Clark, A. B. o/Trinity College, Cambridge Matthew Clarke, M: D. Rev. Renb. Clarke, Refor

Mr John

Mr

of Norton, Leicefterfhire Robert Clarke, of Briftol

R-ev.

Mr

FJV. Samuel Clarke, D. D. Thomas Clarke, Merchant

Mr Mr

Rev.

Houfe, Cambridge Richard Clay William Clayton, o/Marden, Efqj Samuel Clayton, Efq; Mr William Clayton

Richard Clements, of

Ox

ford, Bfokfeller

George

Clifford,

jua.

Am.fterciam

George Clitherow, George Clive, Efq;

Mr

Edward Collet

Mrs

Mr

Efq;

of Greenwich,

Peter Collinfon

Co! more,

Fellow

of

Magdalen College, Oxon Rev. Mr John Colfon Mrs Margaret Colftock, o/Chichefter

Rene de

John Conduit, Efq; John Coningham, A/. D.

Edward

Conftable, o/Read-

Mr Conybeare, M. Mr James Cook

Mr Mr

A.

Efq;,

Dr. Clopton, of Bury Stephen Clutttibuck, Efq;

Mr Mr

Rev.

William John's

ollege,

Mr

Efq;

New

Coll.

Oxoa

Mr John Craig Mr John Cranfton,

Arch.

Mr John Creech James Cread, Efq;

Mr William

Crery

Crew

of

Hall,

",

Chefliire, Efq;

Thomas

Mr

Crifp, Efq;

Richard Crifpe

Mr Samuel

Cufwick

ef Trinity

Col

lege, Cambridge T-Ir John Crook

Ttllow

of

Oxon

of North-Hall

John Copeland John Copland, M. B. Godfrey Copley, Efy

Pleas

Thomas Cox Thomas Cradock, M. A.

Tobias Croft,

Cooke, c

Mr Cooper,

Common

Edward Cowpsr

deacon of Gogh or John Craiter, Efq;

Oxon

Charles Cope, Efq; Rev. Barclay Cope

Mr

Rev.

Re^'.

Thomas Cooke

St.

of

of

Mr

Rev. Mr John Cowper Sir Charles Cox

John Crew,

John Cooke Benjamin Cook William Look, B L. of St. John's College,

The Hon. Spencer Cowper, Efq; One of the Jujlicei of the Court

Rev.

hit Excellency William Conolly, one of the Lords Jufticet cf

ing Rev. Rev.

John Coufsmaker, jun. Henry Coward, Merchant. Anthony Afiiley Cowper, Efq;

Mr Mr Mr

Combe, Efq; John Condor

la

Mr

Rev.

in

Mr Mr Mr

>amuel Cox, Cox, of

John Colvil

Capt.

Mr

Suflex, Efq; Peter Courthope

Nathaniel Collief

Edward

Peter Cottingham, Efq;

John Cottington John Hinde Cotton James Coulter George Courthop, of Whiligh

John Collet Mrs "Mary Collett Mr Samuel Collet

Thomas Collins, M. D.

Dr. Henry Coftard Dr. Cotes, of Pomfret Caleb Cotefworth, M. D.

Mr

Mr

Mr

Briftol,

Solomon du Cofta

Sir

Henrietta Collst

James Cooke, Efq; John Cooke, Efq;

John Clayton

Thomas Clegg

Theophilus Clements, Eft;

Mr

Chriftian Colebrandt

James Colebrooke, Efq; Mr William Coleman, Merchant

Mr

Clarkfon, of Peter-

Mr

Mr Mr Mr

Benjamin

Cambridge

William Cofsley, of

Mr

Ireland

Thomas Ciarke

Mr

lege,

Boohfeller

Cole, Gent.

Anthony Collins

Efq;

Charles Clarke, o/~Lincolns-Inn,

Elizabeth Cornwall Library of Corpus Chrifti Col

Charles Colborn

Mr tf Clare-

Mrs

Mr

Thomas Coke

Mr

Dr Edward Cole

James Chetham, Efq; Mr James Chetham Charles Child, A. B.

Mr

Francis Coghlan, Eft; Sir

ple, Efq;

Mr

Henry Cornclifcn, Efq; Mr John Cormfti

Rev.

Wraxall, Somerfetfliire

Chaworth, of Anfley,

Mr Francis Corbetc Mr Paul Corbett Mr Thomas Corbet

Rev. to the

London

Btfyop of

Robert Chauncey, Mr Peter Chauvcl

Richard Corbet,

Sir

Efq;

Mr L

Dr Crofle, therine Hall

Rev.'

IJafltr of K.3-

Chriflopher Crowe, Efq;

George Growl, Hon.

Nathaniel

Efq;

Crump,

Efq;

ef

Antigua

Mrs Mary Cudworth Alexaodcr Cunningham,

Efq;

hcorj

Su SCRIBERS Henry Cunningham, Mr Cunningham

Dr

Mr

Mr Mr

Eft;

William Curtis

Henry Curwcn,

Hn

Right Rev.Ld.Bifiop of Durham Right Rev. Ld. Bificp cf St. Da vid

Right Hon. Lord Delaware

Mr

Donne

Mr

Delhammon

Rev.

Mr

Mr

Right Hon. Dalhn, Baron of Ireland

Lord

Chief

Surgeon Daniel, Dean

Dr Richard of Armagh

Mr

Mr

Knight of

,

Mr

Right Rev.

Dr. George Dickens, of Liver

Mr

Da vies Davenport,

Eft];

Pierce Dodd, A/. D. Right Hon. Geo. Doddinton, Eft, Rev. Sir JohnDolben, ofFindoa,

Nehemiah

Donellan, Efq; Paul Doranda, Eft;

M

of tht Inner-

Eft;

of

of

ChnA-

Davies, Attorney at Law Dawkms, Merch.

William

Rowland Dawkin, c/Glamorganfhire, Efq;

Mr

Mac

Peter

Dowel],

Efy,

John EccleirOn James Eckerfall, E Edgecumbe, Rev. Mr Edgley Rev. Dr Edmundfon, of St. John's Coll.

PrefiJent

Cambridge

Arthur Edwards, Efq; Thomas Edwards, Eft; Vigerus Edwards, Eft; Gift. Arthur Edwards

Mr Mr

Edwards William Elderton

-

Elizabeth Elgar Gilbert Eliot, o/Minto.B.**, one of the Lords of Seflion

John Elliot, Merchant George Ellis, of Barbadoes,

Mr

Sir

Eft;

John Ellifon, of Sheffield Richard Ellys, Bart.

Library

Chrift-Church, Oxon Feltew Dris, A. M-

Thomas Emmerfon, Eft; Mr Henry Emmet Mr John Emmet Thomas Empfon, of the Midd':

Mr Mr

Edmund

^Trinity Coll. Cambridge George Drummond, Eft; Lord Provoft of

Colin

Edcnburgh

Drummond,

ef thilofofhy in

tht

Dr

Pafchal Ducaflc,

if Ferns

of Emanuel Cambridge

Eft,

Mr Thomas lingeir Mr Robert England Mr Nathaniel Englifh Rev. Mr En fly, Mmifter Scotch Church

Dean

College;

Francis Emerton. Gent.

Temple, Prkfi/for

Vnn'trj.ty

of Kdinburgh

Rev.

Day

William Eaft Peter Eaton

Mr

Cotes, Efq; Rich. Drewett, of Fareham of Chriftopher Dnffield,

Henry Dry, Eft; Richard Ducanc Efq;

Nathaniel

Thomas Eames Mr. Jabez. Earlc

Mr

William Dawfonne, Eft; Thomas Day, Efq;

Deacon

fir

Sir

Downer

Mr

John Day

and Right Han. Lord

Mrs

James Downes Francis Henry Drake, Kit.

John Dawfon Edward Dawfon, Efq; Mr Richard Dawfon

Mr Mr Mr

Oxon

WillianxDrake, ^"Barnoldfwick-

Queen's College, Cambridge

John Daviej, Church, Oxon

William

Mr Mr Sir

Alexander Davie, Efq; Rev. Dr. Davies, Mufler

Mr

College,

John Dowdal, Efo

Jermyn Davers, Bart. Capt. Thomas Davers

Mr

Mr

Dillingham Dinely Difney, ef Bennet

Wadham

Sir

Col?.

Theophilus, Lord Bifiop o/E!phia Rev.

Eftj;

D. James Dougla.s Mr Richard Duvcy, A. B. of

Efq;

Eftj;

Ertkine

John Diaper Rivers Dickenfon

Hon. Edward Digby,

Peter Davall, Eft;

Henry Davenant,

Dunflar,

Surgeon-

.

Mr

B*rt.

Darcy

Mr Serjeant Darnel Mr Jofeph Dafh

Mr Mr

Deverell,

James

Rev.

Danvers Coniers

the Bath

Temple,

ftnwn, Efy;

Jacob Desboverie, Efq;

Robert Dixon,

James Danzey,

James Duncan

John Duncombe, Eft; William Duncombe

Mr

James Dupont, of Trinity Cambridge

College, Cambridge

Timothy Dallowe

Mr

Dufrelhay

Capt. Jonathan Dennis Daniel Dering, Efq;

Capt. John Dagge

Rev.

Daniel

Thomas Dugdale Mr Humphry Duncalfe, Merchant

WiHiam

Denne William Denne

Mr Thomas Mr Samuel

Thomas Dade

Eft;

Mr Mr

John Dundafs,^. of Duddin-

pool

Dromore

Rt. Rev. Lord Bifiop of

Sir

Staunton Degge. A. B. of

in Briftol

Right Hon.LordDigby Right Rev. Le-rd Bifiop cf Derry Rev. Lord Right Btfiop of

Mr Mr

Burt.

Edward Deering, Eft; Simon Deggc, E(q\ Trinity Col. Cambridge Rev. Dr Patrick Delaney

Grace the Duke of Devonfhire Grace the Duke of Dorfet

Mr

Matthew Deckers,

Sir

Eftj;

John Cafwall, of London,

Merchant Dr Jacob dc Caflro Sarmcnto

Ji'n

George Ducket,

James Dearden, of Trinity College, Cambridge

Curtis of Sevenoak

Mr

NAME

William Deane

John

Efl'ington,

in

Efq;

-c

/

Rotterdam

SUBSCRIBERS NAMES. Mr Charles

Rtv.

Efte, e/Chrift-

Hon. and Rev. Mr. Finch, Dean

Church, Oxon Ether fey. Apothecary Henry Evans, of Su:r), Efq; llaic

Mr Rev i/r

.

Ewer,

Hon.

Mr Mr

Charles Ewer Mr Richard Exton

Pleas.

Edward Eyre, Efq; Henry Samuel tyre,

Mr

Cambridge

Right Hot. Earl of Godolphin Right Hon. Ludy Betty Germain

Mr

Right Hon. ZWGarlet Right Kcv. Bt/Jjop of G'iouceftcr Right Hon. Lord St. George

Francis Forefler

Mr Mr Mr

E>rc

Forefter, Efq;

BtJJiOf

of

femes and Loghlin

EJward

Potter

Mr Thomas College,

Mr

Farnaby, of Mcrton

Oxon

D. D. Canon of

Mr

Abel

Founereau,

College,

Merchant

Chnftopher Fowltr

Mr John Fowler, r/Nurthamp. Mr Jofeph Fowler Hon.

Sir

William Fownes, Ear.

George Fox,

Efq;

Efq;

Efq;

Dr.

Mr Abraham

of

Thomas Frederick, Efq; Gentle man Commoner of New College,

Francis Fauquicre, Efq; De la Fay, Efq;

Oxon Thomas Freeke, Efq; Mr Jofeph Freame

Thomas De

lay Fay, Efq;

De la Fay Nicholas Fazakerly, Efq; Governour Feake

Capt. Lewis

Mr John

Fell, of Attercliffc

Martyn Fcllowes,

Efq,

.Gorton Fellows, Efq;

Mr Thomas Fellows Mr Francis Fennell Mr Michael Fenwick John Ferdinand, Tern pie,

of

Ralph Freke, Efq; Patrick French, Efq;

Edward French, Dr. Frew ia

M. D. D.

A/.

Mr Thomas Fro ft Thomas Fry, o/Hanham, Glouthe Inner-

EJq,

Mr Jimes Feme, Surgeon Mr John Ferrand, of Trinity C'vlege, Cambridge Daniel Muflaphia Fi.Jalgo

Mr Mr

Richard Freeman, Efq; Francis Freeman, of Briflol

Mr

John Fieind,

Filler

MK; Cdia Fiennes

Certerfliire, Efq;

Mr RowhnJ

Fry, Merchant Francis Fu'jim, Efq;

Rev.

Mr

n-jcl

Fuller,

Fellow of

Ema-

College, Cambridge Fuller

Mr John Thomas

Mr

Fuller,

William

A/.

MonfitHT Galvao,

Mr Jofeph Gimbol, of Baibadoes Mr Jofeph Gimonfon

Mr

Henry Garbrand

Rtv.~M.r Gardiner Nathaniel Garland Nathaniel Garland, jttn. Joas Garlcnd James Garland Mrs Anne Garland Edward Garlick Alexander Garrett Mr John Gafcoygne, Merchant Rev. Dr Gasketh

Mr Mr Mr Mr

D.

Full wood, */

Mr Mr

Henry Gatham John Gay

Thomas

Franks

Mr Faukener Mr Edward Faulkner Charles

Gale, //;;

Excellency

Envoy of Portugal James Gambler, Efq;

Mr Mr

Efq;

Frankland, Dean Gloucester Fredtrick Frankland, Efq; Mr Jofeph Franklin

Farrel, Ffq; Farrer, Efq;

John Farrington,

Magdalen Cambridge

Rev.

Thomas

Dennis Farrer,

of

Edward Foy,

William Farrel

James

His

Chrift-CHurcb, Oxon Rtv. Dr. Robert Foulkes Rev. Mr Robert Foulks, M. A. Fellow

Jonathan Gale, of Jamaica

Roger

Peter Fofter

/vir

Efq;

Mr John Falconer, Merchant Daniel Falkiner, Efej, Charles Farewell, Efq;

Kr. Hon. Lord Chief B. iron Gilbert

Mr

Jofeph Foikett

Peter Foulkcs,

Den Heer Page] Mr Thomas Fairchild Thomas Fairfax, of the Middle

Grace thi Duki of Grafcon

Martin Folkes, Efq; Dr Foot

Mrs Alice Forth Mr John Forthe

Kingfmill Eyre, Efq;

Right Rev. Jofnh, Lord

Ha

Fiercher

John Efq;

Fyme Francis Fayram, Bogkftlltrm

London

Michael Finn, of Trinity

College,

Jofeph Eyles Right Hon. Sir Robert Eyre, Lord Chief Juftice of the Cvnimon

Temple,

Mr

F.fq;

Hon. John Fitz-Morris, Efq;

Sir

Rev. James Fynney, D. D. Pre bendary of Durham Capt.

Efq;

John Finch

Philip Finchtr

Efq;

John Eylcs, B*r.

Mr

York Edward Finch,

of

Mr Hugh

Hun

Coll.

Gearing, Efq;

Gee

Mr Edward Gee, of C llfge, Cambridge Mr Jofhua Gee, fen. Mr Jofhua Gee, jun.

Queen's

Richard Fitz-Gtrald, o/Gray'sInn, Efq Mr Thomas Gerrard Edward Gibbon, Efq; John Gibbon, Ffq; Mr Harry Gibbs Rev. Mr Philip Gibbs

Thomas

Gibfon, Ffq;

Mr John (jibfon Mr Samuel Gideon Rev.

Dr

Clandifh Gilbert,

ef

Trinity College, Dublin

Mr

John Gilbert John Girardcx, Efq; Mr John Girl, Surgeon Rfv. Dr. Gilbert, Dean of Exe ter, 4 Books

tingdon

Mr

SUBSCRIBERS NAMES. Mr Mr

Mr

Gisby, Apothecary Richard Glauville

Mr Thomas

m

Rot-

Mr

Mr

Mr Rene Mr

Thomas Goldney

Gooday, Efq Pillow John Goodrick, Efq; Commoner of Trinity Coll.

William Gordon, Bar. Eight Han, Sir Ralph Gore, B*rt. Arthur Gore, /'/./.

Gore

John Charles Goris Mr William Coding, M.A. Wiiliam Goflin, Ffq; Mr William GolTip, A. B. cf Rev.

Triiv Coll.

Cambridge

John Gould, jun.

Efq;

Nathaniel Gould, Efq}

Mr

Thomas Gould Mr Gowan, of Leyden

Rev.

Stephen Griggman Grillct

J.

U.

8c

Mr Jofeph Grcvt, Merchant Mr John Henry Gri^man, Mer

Gwillir, Efqi

Marmai'uke Gwynne,

Efqi

cf

Gravefinde,

perim. Philofophy

Profef-

and

Aftronomy in

Kx-

Charles Gray cf Colchefter John Greaves Francis Green

Dr Green, in

Profejfir

of Phyfick

J.

Cambridge

Mr George Green, B. Mr Perer Green Mr Matthew Green Mr

Mr Mr Mr Mr

D.

Stephen Greenhill, of

i

l<i\lht

Hon. Lord

Hervey

unfdon Right Hon. Lord John iladdon, M. B. of Chrift !

Church, Oxon Mr Hames

Jeilis

Arthur Greenhi.l

Grtenway,

of

Mr

Hare,

Efq;

Beckingham

of

Mr Mark Harford Mr Trueman Harford Edward

Hon.

Harley,

n;r

jor.arhan

Mr

of BarbadoeJ,

Jciemiah Harmin

Barrows

Manli-.w

lev.

M.

T^lr

Re:.

B.

Mr Mrs

H.ill

Mr

Hal]

Efy

J-.fy

HJTJJS. Ffq;

James Harris, Efq; William H.irris, of Sarum, Ffq-T

Hal)

F;arcis Hail, Place

Ff-i;

Harlowe Henry Harmage

Mr

r>fi\n

Harris

Thonia^ Harris

Mr

Hani.',

hlnilirn Hi/lory

Htnry

in

Kent

Il;nry Hartingron,

Efq;

Dr. Hall A:r

Attcr-

Jonathan Hardey

Henry Haie,

Mr Mr

Hallied

Hili,

Mr

Cuft.

Mrs Mary I'aines Edward Haiftwel!,

Abraham

EM.

Hardwick, M. D. cf Bri-

Thomas Hardwick,

n<y

Right Hon. Earl of Hertford Rt. HOD. LJ. Herbert, of Chcrbury Right Hon. Lord lerbcrt

Mr Char!^

Jofrph Greer.up

Randolph Thavies Inn

William Hardrefs,

Mr

Robert Hale, r/"j; ^ r Phiiip Hale

Cambridge

Hankey

ftol

Efo

Nathaniel Green, Apothecary

College,

Man.

Harbord Hirbord, of Gunton in Norfolk, Efq; Richard Harcourt, Efq;

Peter

Efqi

Griffon

Oihniel Hagt-err,

Samuel Green, Gent.

Cambridge

Mr Thomas Hardey John Harding, Efq;

r

Leyden

Dr Gray

Mr Mr Mr

Mr

Rev.

Walter Grainger

Hand, Fellow of Ema-

Sir

H.

John Grant

for

Mr

Samuel Handly Gabriel Hanger, Efq; James Ilannott, of Spittle-Field;,

Grange Samuel Grey,

Mr

Book-

York

in

Roderick Gwynne, Efq; David GaufeJ), Efy; of Leyton

Thomas Grainger

S'

feller

Mrs Martha Hammond Mr John Hand nucl College,

Ralph Gullton Matthew Gundry, Efa; Nathaniel Gundry, Efyj Mrs Sarah Gunfton Charles Gunter Niccol, Efq;

U/tivtr/ity

of Edinburgh

Mr

Mr

George Graham

Moifunr

for cf Divinity in the

Mr John Hamilton Mr Thomas Hammond,

Rev.

Mathurin Guiznard, Efq; John Guifc Rev. Mr John Guife

Richard Graham, jun. Efqi

Mr Mr Mr Mr

Hu]]fey,E/^;

Mr

Richard Grimes

M.D. an</Poliater Leidcniis Rev. Mr Grofvcnor Mr Richard Grofvcnor

Thomas

Savilian.

John Ilamerfe

r

Sir

Sir

Francis

\

Modern

ProfelT of

Ox.

in

John ILmilton, Efq; Andrew Hjrmlton, Efq; Rev. Andrew Hamilton, D. D. jfrcb- Deacon of Rap hoe William Hamilton, Proftf-

chant Bart.

Thomas Goodwin

Mr Mr

in

M.D.

Griffiths,

&

Reg. Hilh

Edmund

Merchant

Johannes Groeneveld,

Jonathan Goldi'myth, M. D. Rev. Mr William Goldwin

Rev. Mr Hales William Hallet, of Exeter, M. D. Edmund Ihlley, L. L. D. Aftro.

Oxon

in

Richard Gray,

Thomas

Jofeph Godfrey

Cambridge Henry Goodrick,

Mo

Rotterdam

Joleph Godman, Ef[\ Capt. Harry Goff

Mr

Mid

{Catherine Gregory muel Gray, Efqi

S

Capt. John Godlec

Sir

cf

Mrs

Peter Godfrey, Efq;

Mr

cf the

ProfelT.

Gregory,

dern Hi/1,

Glover, Merchant

John Goddard, Merchant, teidam

Mr

Thomas Gregg, Temple

dle

Mr

John Glover. Eft, Mr John Glover, Merch.vit

of St.

James's

Rev.

Mr

i>i

Proffff-r

of

Cambridge

Richard Harris I'

T!IH

j

ll.irnlon

William Huriforj Mr Hr.nry H^rt Mofc ILrt Sir

SUBSCRIBERS 'NAMES. T

u/V

Mr

ohn Hartop, fart. Peter Harvey

Henry Harwood, Efrj; John Harwood, L. D. Kobert Profe

Hiflel,

John Hildrop, M. A. the

Majler of

Free- School

in

Marlborough

Mr E/y

George Hatley, Efq; Mr William Havens C.i/>f.

Mr

Rev.

John Hawkins

Francis

Hildyard, Bookfeller

York

in

Rev.

Sir

Francis Head, Bart.

Hill, Eft;

Temple. Efa\ Robert Hinde, Efc\

Mr

Peter Hinde,

Rev.

Mr

Edmund Thomas

Capt. Joleph Hifcox, Merchant

Mr

Mr

Benjamin Heath

Cornelius Heathcote, f/Cutthoy,

M. D.

Mr James

Hamilton, Merchant

Sir Gilbert

Hafleden Heathcote

Mr Thomas

Mr

Abraham Heaton

-Anthony Heck, Efq; John Hedges, Eft; Paul Heegcr, jun. Dr Richard Heifliam

Mr

Mr Mr

Mmh.

Jacob Henriquts John Herbert, Apothecary of Lynn-

Regis Mr Samuel Herring Mr John Hetherin^ton Mr Richard Hett, Boolfilltr

John Heywood Samuel Hibbcrdine

Nathaniel Hickman,

Mr

M. A.

Samuel Hickman

Rev.

Mr

Hiffe,

Schtdm*fltr at

Kenfington Banger Higgens Samuel Highland

Mr Mr M-

Jofeph H'ghmo.e

John Hughes

Mr T

B.

Hodges, M. A. of Jefus

Mr Mr

Oxon

Hodgfon, Majler of the Matbematicki m Cbrift's

Humphreys,

Fellow of Trin. Coll.

Efq; of Hart- Hall,

Oxon

John Hunt James Hunter, Efcj; Mr William Hunter

Mr

Jofrph Jory Hodges

David

Cambridge Maurice Hunt,

Mr Hunt,

Mr

M.D. Humes

Hulfe,

Guftavus

Mr

John Huflcy, cf

Sheffield

Ignatius Hufley, Efq;

Mr

Rev. A/.

A.

Cbriftopher HufTey,

Reftor cf

Weft- Wick-

Mr Hodfon Edward Hody, M. D.

ham in Kent Thomas Hutchinfon,

Samuel Holden,

Commoner of SidneyCollege, Cambridge Rev. Hutchinfon, cf Hart-

Mr Thomas Hook

Mr Adam

Holden, of Greenwich

Rogers Holland, Efo Mr James Holland, Merclmnt

Mr Mr Mr Mr of

Mrs

Elizabeth

College, Oxon Thomas Hyam, Merchant

John Hooker, Eft}-, Mr John Hoole Mr Samuel Hoole

cf

I

Right Hon. the Earl tf

Hooke

Mr Thomas Hope 1 hamas Hopgood,

Tri

John Hyde Hyett, Gent. Commoner Pembroke College, Oxon

Mr

John Hook Le Hook

Huxley,

of

Cambridge M. A. cf Brazen

Nofe

Holiis

John Hollifter

Mr Mr

Oxon

nity College,

John Hollings M. D.

Mr Mr Mr

Mr

Hall,

Mr Sandys Hutchinfon,

Richard Holland M- D.

Mr Thomas

Fel~

Efqi

lots

Efq;

Mr jVlr

Mr

Sir

Eoianucl College, Cambridge Vcv. Samuel Holt T^Iatthew Holworthy, Eft}-,

Efy\

Edgley Hewer, Efq; Robert Hey (ham, Efq; Mr Richard Hey wood

Oxon Capt. Robert Hudlbn, jun.

Mr Wiiliam Hoare Mr William Hobman

Hewer

Heugh,

Ed ward Howard, Efo

5'.

Nathaniel Hodges

How

Richard

William Howard, Efq; Rev. Dean Robert Howard Thomas Hucks, Efq; Mr Hudsford, cf Trinity Col!.

Rev.

Edward Holloway Th;mas Holmes Rev. Mr Holmes, Pillow

Fit

Mr

Hot)-

Sir

llolpital

in

Coventry George Hepburn, M. D.

;.

Dean Hinton Robert Hirt

College,

John Heathcoie, Efc William Heathfotc, Efq;

Thomas Houghton Thomas Houlding

James How, Ejq; John How, of Hans Cope, Efa Mr John Howe

Edward

lames Head, Efq; 1 ticmas Heames, Efq; Heath, Efqi Heath, /</;

Stephen Horfeman

Mr Mr

Mr Mark Hawkin?, Surgeon Mr John Hill Mr Walter Hawkfworth, Merck. Mr Rowland Hill, of St. John's Mr Francis Hawling College, Cambridge Mr ]o!ia lljxley, of Sheffield Samuel Hill, Efq; Mr Rkhard Hayden, Mtrcbant Mr Humphrey Hill Rev. Mr Richard Hill Cherry Ihyes. M. A. Mr Thompfon Haync Mr Peter St. Hill, Surgeon Mr Samuel Haynes Mr William Hinchiift, BofkMr Thomas Haynes feller Mr John Hay ward, Surgeon Mr Peter Hind Mr lofeph Ha^ ward, p/"Madera, Benjamin Hinde, of the Innerbier chant

Mr Henry Home Mr John Horfeley Samuel Horfeman, M. D.

Rev.

Mr

Mr Hilgrove Mr James Hilhoufe John

Richard Hopkins Richard Hopwood, A/. D.

Sir

Edward Jackfon,

Mr Mr

Hay

Efq;

Stephen Jackfon, Merchant Cuthbcrt Jackfon Rev. Mr. Peter Jackfon Jofliua Jackfon John Jacob, f'/q;

Mr

Cent.

Mr

SUBSCRIBERS NAMES, Mr

Jacobens Jofeph Jackfon, of London, GoUfmith Rev. Sir George Jacobs, of Houghton in Norfolk

Mr Mr

Henry ]acomb John Jacques, Apothecary Coventry Samuel Jacques, Surgeon at

in

Mr

Uxbridge V/iiiiam J imes, Efq;

Mr

Rev. <jf

Mr Mr

David James,

Reflor

Mr

M. A.

Jones,

lege,

Mr

of Jefus Col

Oxon

Jacob Jones

Mr James Jones, Rtflar e^Cound, Salop Mr Somerfet Jones, A. B. of Rev.

(

Mr Mr

Oxon

hnft Church,

Wroughton, Bucks

New

of

Chelfea

Hofpital

fits

Rev. Dr Richard Ibbetfon Idle, of the Middle Temple,

John

Samuel Jeake Samuel Jebb David Jefferics Rev. Mr Jofeph Jefferies

cellor

Mr Mr

L.

the

Killale

Ft. Rev. Lord Bifljof of Killdare

Reverend

Lord

Btfl>op

John Ingilby, Efq; Martin Inn vs, of Brifto', Gtnt. and John Innys MeJJieurs William

more

John's College, Kendall

Oxon

Mr Robert Mr Clayton

Kendrick

John \\: John Kcivp,

of tf.e

Tcm-

pie, Efr,

Mr Chidiock Kent Samuel Kent, Efq, Rev Mr Samuel Kerrick,Ft//o Church CoJJege, of Chrift

Mr

Hon. James Johnfon, Efq, Jurin, M. D.

James Rev. Mr Rob. Johnfon, S.T.D. College,

Cambridge

Mr

Mr in

Ifaac

Johnfon Michael Johnfon. Merchant R.ot r erdam

Mrs

Cam

King King

Hon. Colonel Pearcy Kirke

Mr

Thomas Knap

Rev. Samuel Knight, D. D. Prebendnry of Ely

Mr

Robert Knight, jun, Francis Knowllyes, Efqi Mr Ralph KLnox

Edward

Jones, Efq; Chancellor St. David's of (he Dtocefeof

Efq,

Matthias J.ine

Thomas Lambert, of Ledburgh,

Daniel

Mr

John Lampe

Lambert

Dr. Lane, of Hitchin

Hert-

in

fordfhire

Mr

Timothy Lane

Rev. Dr. Lsney, Mufltr of

Pem

broke Hall, Camtr. z Books Peter de Langley Rev. Mr Nathaniel Lardner Mr Larnoul

Mr

Henry

Lafcclles, of Barba-

Mr John

<j/Bimop's

Laurence, Refltr

Waremouth

Mr Roger Laurence, M. A. Mr Lavington Mr William Law, Profejfir

of

Moral Philofophy in the Uniof Edinburgh Mr John L*wtoa,(fthExci{kverjlty

Godfrey Laycock, cf Hal-

lifax

Benjamin King, of Antigua,

Efq;

Mr

Mr

Mr

Oliver St. John, Efq;

Trinity

John Langrord William Larkman William Lambe, of Exeter^

Office

Cambridge.

Library of King's College, bridge

of

Lyn

Efq;

L-Jngharne

does, Merchant

Robert Jocelyn, Efq; Rev. Mr Samuel Jocham

Fellow

Hugh

M. A. Vicar York (hire

Rev.

hfq;

Middle

Rev.

Mr

Mr Kidbey Mr Robert Kidd

Bookfelleri

Jobber, Efq;

George Johnfon,

of

Mr William Kay, PecJor of Wigginton, Yorkshire Benjamin Keene, Efq; Hon. Major General Kellum Mr Thomas Kemp, M. A- of St.

Books D. Chan

Jenkins Samuel Jennings, of Hull Library of Jefus Coll. Cambridge

o/London,

of

Rev.

e/Derry

Thomas

Lord Bifoop

Reverend

Kill

Jeffries, Efq;

2

Kmgfale

I'ifcount

Right

Mr Mr Mr

Lord

Honourable Gerrard,

Hight the MidJle-

Duke of Kingfton

Grace the

Right

Laay Jekyll Ralph Jenifon, Efq; David Jenkins. L.

Right Honourable Lord

Mr Mr Mr Mr

Robert Lacy James Lamb, Efq;

at

Temple Efq;

Edward

Lymington

Mr

Mr

Bartholomew Jeffrey, of Middle Temple, Efq;

I'ifcount

Rev. Lord Bijljof of London Right Rev. Lord Bifliop of LandafF

College, Oxon Richard Lingley, Efq;

Oxon

Edward Jafper Edward Jauncy, of

Hon. Ld.

John Lade,

Benjamin James Robert James, of St. John's,

Sw-Theodore Janfien, Bart. Mr John Jarvis, Surgeon Dartrord in Kent

lit.

Rt.

John [ones, Surgeon John jope. Fellow of

Collegr, Oxon Charles Joy, Efq; Daniel I vie, Efq;

Hon. Lord Vifceunt Lonfdale

Rt.

Mr

Charles Leadbetter, Teacher

of the Mathematicks James Leakc, Backfiller Bath

Mr

i

Stephen Martin Leak, Efq; Rev. Mr Lechmere William Lee,

Mr Lee, of Chnll Church, Oxoa Rev. Mr John Lee Mr William Leek Rev. Mr Leefon Feter Legh, of

Lymc

in

Cbc-

fhirc, Efq;

*

B

Robert

SUBSCRIBERS NAMES. Robert Leguarrc.o/Gray's-Inn,

Mr Mr

/*5

Lyonel Lyde, Efq; Dr. George Lynch

Mr

Lchunt

John Lchunt, o/Cantcrbury Francis Leigh, Efq, John Leigh

Lewis Thomas Lewis

Mr New Sir

M.

Rn:

His Grace the

College Library

Henry

Bar.

Liddell,

Henry

Peter's College,

of St.

Cambridge

Rev.

Mr

Mr Mace Mr Jofeph Macham,

Livingftone, One of

the Clerki of Seflion

Salisbury Lloyd, Efq;

Mr John

Lloyd, A.

B. of

Mr

Nathaniel Lloyd, Merchant

Samuel Lobb, Bookfeller at Chelmsrord William Lock, Efq, Mr James Lock, 2 Books Mr Jofhua Locke Charles Lockier, Efq;

Mr Mofes Loman, jun. "Mr Longley Mr Benjamin Longuet

Mr Mr

Grey Longueville Robert Lord Mrs Mary Lord

Mr

in

Mackmen,

Mac

Colin

of the

Laurin,

Mathematicks

Uaiverf/ty of

in

Chichefter

Malihurr, Efq; Efq;

Mr

James Mandy

Charles Lowndes, Efq, Mr Cornelius Lloyd

Rev.

Mr

Robert Lucas, Efy\ Coll. Richard Lucas

Ifaac

Lucy

Edward Luckin,

Mr

J-ohn

RecJor of

Mahera

Manley, Efq; Thomas Manley, of

Efq;

Ludbey

Lambert LuJlow, Efq; William Ludlow, Efq, Peter Ludlow, Efq; John Lupton, Efq; Nicholas Lukr, Ffc

Mr Mr Mr

John Manley William Manley

Benjamin Manning Rawleigh Manfel, Efa; Henry March, Efq;

Mr

Rev.

Mr

Henry

Marfliall

Rtv. Nathaniel Marfhall, D. D. Canon c/Windfor

Matthew Martin, Efe Thomas Martin, Efq;

Mr Mr Mr

John Martin James Martin Jofiah Martin Call. Samuel Martin, ^/"Antigua John Mafon, Efq; Mr John Mafon, o/Grccnwicb Mr Charles Mafon, A. Fell.

M

o/Trin.

Col).

Cornelius

Cambridge

Mafcn

Mr

Mafterman Robert Mather, of

Mr

the

Middle-

Rev.

Mr

Mathews Mathew

William

Mr

John Matthews

Mrs Hefter Lumbrofo deMattos Rev. Dr. Peter Maturin, Dean of Killala

William Maubry, Efq; Gamaliel Maud Rev. Mr Peter Maurice, Trea~ furer of the Cb. of Bangor Henry Maxwell, Efq;

Mr

of Pollock,

John Marke Sir George Markham Mr John Markham,

Rev.

Dr. Robert Maxwell, of Fellow's Hall, Ireland

Mr May Mr Thomas

Mayleigh

Thomas Maylin, ;'. the Inner-

Tctnple, Efq;

Luderj, Merchant

the-

John Marfh, Efq; Mr Samuel Marfh Robert Marmall, Efq; Recorder of Clonmell

Efq;

Bellingham Manleveror,

M. A.

Mr George Marley Benjamin Marriot, of

Exchequer

John Maxwell, jun.

John Mande

Dr. Bernard Mandcville

William Lowndes, Efq;

Mr

.

Mr Thomas Malya John Mann Mr William Man

Mr

Efq; one

on gentMajejlfi Solicit

Temple, Efq;

Henry Mainwaring, of OverPeover in Chefhire, Efq; Mr Robert Mainwaring, of London, Merchant Caf-t. John Maitland Mr Cecil Malcher

Dr. Manaton

Laurence-Lane

Thomas Marley, his

Dr. Richard Middleton Maflcy

Efq;

Mr Madox, Apothecary Mr Ifaac Madox, Prebenda ry of

Mr

Mr

Edinburgh

Macmahon,

Galatius

ProfeJJor in the

Mr

Jofhua Lover, c/Chichefter

Sir Bartlet

of Antigua,

EJV

Mr

Richard Malone,

Hants, Efq;

Love,

John Machin, ProfeJJbr of Aftronomy m Grcfham College

Sydenham

Benjamin Lorkin

William Loup Richard Love, of Bafing

Mrs

Mr

Rev.

Richard Lockwood, Efq; Mr Bartholom. Lottus, 9 Books William Logan, M. D.

Mr Mr

Merchant

Mr Mackay Mr Mackelcan William

Jcfus College

Mr

,

The Rt. Hon. Lord Manfel The Rt. Hon. Ld. Micklcthwait TheRt. Rev. Ld. Bifiop of Menb

Lifter

Mr George Rev.

ller

worth

William Limbery Robert Lindfay, Efq; Count eft cfLippe Rev. Dr. James Liflc

Duke of

Manchc-

The Rt. Hon. Lord Viftount Molef-

Liddell, Efq;

Mr

James Markwick

ral of Ireland

Hii Grace the Duke of Monfaguc Hn Grace the Duke o/MontroiTe

Percival

William Markcs

of

Mr Mr

Mr

Mr Hon.

Jofhua Lyons

Efq;

Hon. Charles Maynard, Efq;

Thomas Maynard,

Ffq;

Dr. Richard NJayo

Mr Samuel Mayo Samuel Mead, Efq; Richard Mead, M. Rev.

Mr

D

Meadowcourt

flru.Mr Richard Meadowcourt, fellya of MertOiv Coll. Oxoo Mr Mearlbo

Mr

SUBSCRIBERS NAMES. Mr Mr

Charles Medlycotr, Eft}

Morgan Morgan,

Weem,

Efq;

William Morland, Fell. of Trin. Coll. Cambr. i Books

Thomas Morgan,

Bart.

Mr

Mr

Rev.

i

Robert Menzies, of

Sir

General Nicholfon

Francis Morgan, Efq;

George Medcalfc David Medley, ; Books

Thomas Mercer, Merchant

Af.

D.

Mr

John Morgan, of Briftol Benjamin Morgan, HighMfter of St. Paul's-School Hon. Co/J.Val. Morris, of Ant gua Mr Gael Morris Mr John Morfe, of Briftol Hon. Ducey Morton, Efq;

Mr

John Merrill. Efq; Mr Francis Merrit Dr. Menins Mr John Henry Mertins Library of Merron College

Mr William Mefle, Apothecary Mr Motte Mr Metcalf Mr Thomas Metcalf, of Trinity Mr William Mount Coll.

head

Coll.

Cambridge

Mr Abraham m

Mr

Meure, of Leather-

John Mac Farlane Dr. John Michel Dr. Robert Michel, of Blandford Mr Robert Michell Nathaniel Micklethwait, Efq; Mr Jonathan Micklethwair, Merchant

Mr

John Midford, Merchant Midgley Rev. Mr Miller, 2 Books Rev. Mr Milling, of tht Hague

Mr

Moyfer

Jofcph

N His Grace the Rt. Rev. Ld.

Duke

Mr

of Newcaftle

BiJJtop

of

Norwich

Stephen Napleton, M. D. Mr Robert Nafli.M. A. Fellow of

Wadham

College,

Oxon

Rev.

bridge, 6 Books

Monk,

J. Sir -William

Newcome Mr Henry Newcome

Mr

Colonel

Rev.

Mr

Efq;

John Montagu John Montague, Dean of

Francis Jarvis

Moor

Moore

Richard Moore,

of Hull,

5

in

Mr

Mr

New

Charles Morgan,

of

of

Thomas Newnham

College, Ffq;

Catherine

Sir Ifiac

Warwickshire Mordant, Gentleman Com

moner of

John Newington, M. B. Greenwich in Kent Mr Samuel Newman

Mrs

William Moore Charles Mordaunt, ef Walton,

Sir

Newey, Dean

Mrs Anne Ncwnham Mr Nathaniel Newnham, fen. Mr Nathaniel Ncwnham, jun.

Books

Mr

Newland

Mr Benjamin Newington, M.A.

Monfon, Bart.

Durham, D. D.

Mr Mr Mr

Richard

Rev. John Chichefter

Apothecary

Edward Montagu,

Mr

Oxon

Sir

Mr

BoohfelUr

O

Rtv. Dr. Newcome, Senior-Fdlov of St. John's College, Cam

John

Thomas Norman, Lewes

Right Hon. Lord Orrery Rev. John Oakes

Oxon

Monro, M. D.

at

Mr Mr

Robert Myddleton, Efq; Robert Myhil, Efq;

David Mitchell, Efq; Mr John Mitton

Mr

Mr

Richard Nutley, Efq; John Nutt, Merchant

William Mingay D. John Mifaubin, A/. Mrs Frances Mitchel

Abraham de Moivre John Monchton, Efq;

Stephen Noquiez, Efq;

Mr

Murden

Mr Benjamin Mills Mr Theophilus Firmin Nalh Mr Henry Mills, RecJor of Dr. David Natto Meaftham, Hetnl-Mafter of Mr Anthony Neal Mr Henry Neal, of Briftol Croyden-School Thomas Milner, Efq; Hampfon Nedham, Efq; Gentle man Commoner of Chrift Church Charles Milner, M. D.

Mr

James Nimrao, Merchant tf Edinburgh David Nixon, Efq; Mr George Noble

Mr Muftapha

Rev. Rev.

Mr

Mr

Anthony Ncrris Henry Norris Rev. Mr Edward Norton

Dr. Edward Mullins

Mr

Surrey

Mr Samuel Nicholfon John Nicholfon, M. A- Refltr of Dor.aghmore Mr Joins Nicholfon, 3 Books

Mr Mr Mr

William Ockenden Elias

Ockcnden

Oddie

Crew

Offley,

Efq;

Jofeph Offley, Efq; William Ogbourne, Efq; Sir William Ogbourne

James Oglethorp, Efq; Mr William Okey John O!d field, M. D. Nathaniel Oldham, Efq; William Oliver, M. D. of Bath John Olmins, Efq; Arthur Onflow, Efq;

Paul Orchard, Efq,

Robert Ord, Efq; John Orlebar, Efq; Rev. Mr George Osborne Rev. Mr John Henry Ott Mr James Ottey

Mr

Jan.

Oudam, Merchant

tu

Rotterdam

Mr

Overall

John Overbury, Efq; Charles Overing

Mr Mr

Thomas Owen

.;

Charles Owfley, Efq;

Mr Mr

John

Owen

Thomas Oyles

Newnham

Newton, iz Books

P.

Michael Newton

Newton

Right Htn. Conntefi of Pembroke,'

William Nicholas, Efq, John Nicholas, Efq;

John Niccol,

Efq;

B a

10 Books Right Hon. Lord Paifley Right Hon. LaJy Paifley

III

SUBSCRIBERS NAMES. Tit Right Hon. Lord Parker Chriftopher Pack, Af. D. Mr Samuel Parker, Merchant at Briftol

Mr

Thomas

Surgeon at

Page,

Briftol Sir

Gregory Page, Bar. William Palgrave, M. D. Fellow of Caius Coll. Cambridge

William

Palhfter, Efq;

Harry Pelham, Efq; James Pelham, Efq; InnerJeremy Pemberton,0//6< Temple, Efq; Camb. of Pembroke-Hall, Library

Mr

Thomas

Capt.

Palmer, Efq; Samuel Pa mer, Efq; Henry Palmer, Merchant :

Mr Thomas

Efq;

Rev.

William Parker, Efq;

Rev.

Edmund

Mr

Mr John

Percevall

Mr Edward

Percevall

Percevall

Jofeph

Mr Henry Parker, Af. A. E.CV. Dr. Perkins, Prebend, Mr John Parker Mr Farewell Perry Mr Samuel Parkes, of Fort St. Mr James Petit Rev.

in

George

of Ely

Mr Daniel Parminter Mr Paroler, Attorney

Mr John

Rev. Thomas Parn, Fellow of Trin. Coll. Cambr. 2 Books

Honourable Coll. Pettit,<?/ Eltham

Mr

Rev

Therms

of Trin.

Coll.

Mr Henry

Rev.

Cambridge Parratt, in

M. A.

Hunting-

ton (hire

Thomas

Stannier Parrot, Gent.

Parry, B. D.

cj

Jefus Coil.

Eft]-,

Oxon

Paul, of Gray 's- Inn, E/j; Jofiah Paul, Surgeon

Robert Paunceforte,

Ejq;

of Hinton St.

George, Efq; Henry Pawfon, of York,

Mr

Merchant

Payne Samuel Peach

Marmaduke Peacock, Mer

chant

in

Rotterdam

Flavell Peake.

Capt.

Efq;

Edward Pearce

Rev. Zachary Pearce, D. D.

James

Pearfe, Efq;

Thomas

Pearfon, Efq; John Peers, Efq; Samuel Pegg, of St. John's

Mr

College, Cambridge Peirce, Surgeon at Bath

Mr

"Mr Adam Peirce

Swanzey,

Buckley Phillips

Phipps, of Trinity

College of

Thomas

-

Potter,

John's College,

John Powel

Mr

Daniel

Powis,

Mr

Mr Mr Mr

St.

Efq;

Powlc Efq;

fames Pratt Jofeph Pratt Samuel Pratt Prefton,

City-Remembrancer

John Price Samuel Price Nathaniel Primat

Capt. Rev.

Mr

of

Oxon

Mr

Prior, Efq;

Henry Proftor, Apothecary John Pryfe, of Newton Hall in Montgomeryshire

Mr Mr Mr

Thomas Purcas Robert Purfe

John Putland George Pye, M. D. Samuel Pye, M. D. Mr Samuel Pye, Surgeon

at

Briftol

Cambridge

The Phyfiological Library

Port

Mr

Sir

John Phillipfon, Efq; William Phipps, L. L. D.

Mr Mr Mr

Thomas

John Porter Jofeph Porter

Mr of

Pool, Apothecary

Dr. John Pringle

Efq;

College,

Mr Mr Mr Mr Mr

Thomas

Phillips, Efq;

Mr Thomas

Paulin

Edward Pawlet,

Mr Mr Mr

Peyton, of St. John's

William Phillips,

Mr

Robert

Mr Mr

Mr Henry

College, Cambridge Daniel Phillips, M. D.

Thomas Phillips, Efq; Mr Gravet Phillips

M. D.

Right Hon. Benjamin Parry,

Mr

Kent

in

John

Parratt,

Thames-

of

Street

Parne, Fdlow

Reclor of Holywell

Petitt,

Ifaac Polock Benjamin Pomfret

Thomas

John Prat,

Mr John Petit, of Aldgate Mr John Petit, of Nicholas- Lane

Raft-India

M. D.

Alexander Pope, Efq; Arthur Pond

Penny

Penton

MrFrancisPenwarne.a/ Liskead in Cornwall Mr Thomas Penwarne

Mr John Palmer, of Coventry Mr Samuel Palmer, Surgeon Parker, Gent.

Mr Mr Mr

Philip Pennington

Mr Henry

Thomas

Efq;

Fitz-Williams Plumptre,

Henry Plumptre, M. D. John Pollen, Efq; Mr Jofhua Pocock Francis Pole, of Park-Hall, Efq;

Penii

Philip Pendock, Efq;

Edward Pennant,

John Plumptre,

in the

Edinburgh

Mr Edmund

Mr

Pyle, of Lynn John Pine, Engravtr

Pichard

William Pickard

John Pickering Robert Pigott.c/Chcfterton, Efq; Mr Richard Pike

Hit Grace the

Henry Pinfield,o/Hampftead,Ey^; Charles Pinfold, L. L. D. Rev. Mr. Pit, of Exeter College,

Rev. Mr. Queftion, M. A. Exeter College, Oxon Jeremiah Quare, Merchant

Oxon Mr Andrew Pitt Mr Francis Place Thomas Pi.ivtr, Efq; Rev. Mr Plimly Mr V/illinm Piomer William Piummer, Efq; Mr Richard Plumpton

Duke

of

Queen-

borough tf

R Hit Grace the

Duke of Richmond

Rt. R'v. Ld Kifoop of Rashr.e The Rf. He-. LcrJ John R.

The

Rev.

Mr Water

Briftol

Rainfbrp,

of

SUBSCRIBERS NAMES. Mr

Thomas Robirfon,

John Ranby, Surgeon

Rev.

Mr

lUwthew Robinfon.

Rand

Mr

Richard Randall

Rev.

Mr Herbert RandoIph.A/.^.

Mofcs Rapcr, Efq; Matthew Riper, Efq;

Mr Mr

William Raftrick, o/Lynne

M.

Ratcliffe,

A

of-

Pem

broke College, Oxon Mr John Rarcliffe

N'rs Elizabeth

Ravell, Ffq;

Mr Mr

Richard Rawlms Robert Rawlinfon A.

Mr

B.

Cambr.

of Trinity College,

Mr

Walter

Ray Hugh Raymond

Coll

Robert Raymond,

Rt. Hon. Sir

LordChiefJuflice of the K. ing's

Bench

Mr

Alexander

Samuel Read, Efq; Rev. Mr James Read

Philip

Efq;

Reve

William Reeves, Merch. of Briftol Richard Reynell, Apothecary

Mr

Richard Ricards

John Rich,

Mr

Efcourt

Richards,

Prebend, of Wells

Rev.

Mr

Richards,

Llanvyllin,

in

Reftcr

cf

Montgomery

-

fliire

William Richardfon,

c/ Small/

in

Derby fb)re, Efq; Richard Richardfon

Mr Mr Thomas

Comm.

College, Oxon Samuel llo^efton,

Ronayne,

Mr

de

la

F.//.

Efq;

James RounJ William Roundeil, o/Chrift

of

his

Eft;

Efq; Comptrol

Majefly'i

Thomas

Dr.

Samuda John Samwaies

Mr

Rev. Mr Daniel Sanxey John Sargent, Efq;

Mr Mr

Saunderfon Charles Savage, jun.

r

John Savage

Mr

Rev.

Samuel Savage

Mr

William Savage Jacob Sawbridge, Efqi John Sawbridge, Efq; Mr William Sawrey

Humphrey

Rev.

of

Sayer, Efq; L. L. D. Cancel-

Durham

Mr

George Sayer, >a\er

Herm. OfterdykSchacht, A/. D. 6c M. Theor. & rrafl. in AcaJ.

Lug Bat. Prof. Meyer Schamberg, A/. D. Mrs Schcper,, of Rotterdam Dr. Scheurchcr

Mr Mr

John Ruftatr, Gent.

Ruth

Wilham Rutty, M. D.

Thomas

Schole:

Cd-<-iid Score,

Workt

Roberts, Bart.

Richard Roberts, Efq; Caft. John Roberts

of Exeter,

Secre

the Rtyal Society tary of

Thoma<; Scot, r/Efl

:

Daiiiel Scoit, L. I

Malti's Ryj.l, Efq;

JTV

Mr

Richard Scrafton,

Rev

Mr

Mr

PC

His Grace the Dn>;e efSt. Albans id Earl

Rf. Re^.

Ld Bf

in

;hr

Rt. Rev. LjrJ

-nr

ocol,

Rt. Hon. Lord ^\ Iney Rt. Hon. Lor.

Scurry, Surgeon Seeker

ScJgwick .-in

o/Sal;sb.

:

Rt Hon. Tin'

Win-

of

Mr Thomas

Rt. Hon.

E

Prebtn-

Durham

Jary of

Durham Mr John Ruft

Rt. Hon.

M. D.

Samuel Sanders, Efq; Wil hm Sanders, Efq;

Mr Thomas

Richier, Efq}

Dudley Rider, Ejq; Richard Rigby, M. D.

ler

Salisbury

Richardfon, Apo

Edward R'ggs, Thomas Ripley, Sir

Jofeph Sager, Canon (f Church of

Robert Saltcr Lady Vanakcr Sambrooke Jcr. Sambrooke, Efq; John Sampfon, Efq;

lei

thecary

Edward

Mr

Wiliiam balkcld

Exton Sayer,

John Rowe, Efq; Mr John Rowe Dr. Rowel, of Amfterdam

2,achias

of the Pell-Office,

Mrs Mary Savage

Roque

Church, Oxon Mr Roufe, Merchant Cuthbert Routh, Efq;

Mr

Books

Sadler, 2

Mr Mr

r>

Benjamin Role well. jun. Jofeph Rothcry, M. A. ArchDeacon of Derry Guy Rouffignac, M. D.

Mr Mr

Edwaid

Alexander Sanderbnd,

John Rudge, Efqi Mr James Ruck Rev. Dr. Rundle, Prebendary cf

of Briftol, Efq; Francis Richards, M. B.

Rev.

Mxjejly's

General of Ireland Edmund Rolfe, Efq; Henry Roll, Efq; Gent.

Mr

Leonard Reresby, Efq; Thomas Reve, Efq;

Mr

o/Hriflol

John Rogerfon, E/q;hn

Rev.

JohnRenton, o/Chrift-Church,

John Reynolds

Bttrt.

the

Sabine

Efc the

Mr Francis Rogers Rw.MrSam. Rogers,

Mr

Mr

from

Denmark

Thomas Sadler,

,'

juhn Rodcs,

Sir

extraordinary

of

Mupnra

Rev.

Robinfon

Efy;

Andrew Reid

Mr

King

cf Merton College, Oxon Lancelot Roilefton, ef Wattnal,

Felix Renolds, Efq;

Gabriel

ry

;>.

Rockc

Rev.

Mrs Mary Reade Mr Thomas Reddall

Mr

/).

r/'New

Raymond

Mr John Read, Merchant Mr William Read, Merchant Mr Samuel Read Mr

The Rt. Hon. Lord Shclburn Excellency Btron Sollentho',

Hn

fa;

Chriftophtr Robinfon, cf Shef field, A. M. Mr Henry Robfnfon Mr William Robinfon

John Rochforr, Mr Rolrigues

Rev.

Anthony

I-

1'ancred Rob,nfnn, A/. Nicholas Robinfon, A/.

Se'.varJ

' -

ury

'crd

Mi

SUBSCRIBERS NAMES. Mr Mr Mr Mr Mr

Adam

Jofcph Sewel

Thomas

Edmund

Confal at

Shallet,

jun. Surgeon

Mr

>Rev. Thomas Sharp, ArchDeeuon of Northumberland

John Shaw, jun. Jofeph Shaw

Shell

Richard Shephard Shepherd of Trinity Coll.

Oxon

Mrs Mary

Shepherd William Shcppard Rtv. Mr William Sherlock, A/. A. William Sherrard, L. L D. John S her win, E/Jjj Air Thomas Sherwood Mr Thomas Shewell

Mr

Mr

ccfe

Temple, Efij; James Smith, Efq;

Morgan Smith,

Mr Mr

Jacob Sandwich Robert Simpfon,

Mr

Hookftlltr

Efq\ Beadle

and

Caius Coll. Cambr.

Robert Simpfon Mathematicks

the

verfity

in

Profejjor of in the Urn-

o/"Glafcow

Henry Singleton, Efa\ PrimiSerjennt of Ireland Rev. Mr John Singleton Rev. Rowland Singleton

Mr

Mr Mr

Singleton, Surgeon

Jonathan SifFm Francis Sitwe!),0/R.enimaw, Ffy Ralph Skcrrcr, D. D.

Thomas

Mr Mr Mr

Skinner, Efqi

John Skmncr Samuel Skinner, John Skrimpftiaw

-Frederic SUre,

M. D.

in the

Mr John

Smith, Surgeon

in

Chi-

Elima Smith, tf Tid IJle of Ely

Mr George Sne!!, of

Mr Mr

Samuel

Smyth

Benjamin Steel John Stcbbing, of

Snell

Mr Mr

Stephens, of Glouceftcr

Jofcph Stephens James Steuarto/Gutters, 27.tr. Mr Robert Steuart, frofeffor of Philofophy,

University of

Oxon

Bennet Stevenfon Rev. Hon. Richard Stewart, Efq; Major James Stewart Ctift.

Bartholomew Stibbs

Mr Denham Stiles Mr Thomas Stiles, /fa. Mr Thomas Stiles, jun. Rev. Mr Stillmgrlcet

Mr

Mr George

/^,

Somers, Efy

Mr Thomas

Coll.

Ox.

Mr Joleph Spence Abraham Spooner Conrad Joachim Springcl William Stammers Charles Stanhope

of Trinity

Story Stratfield

Dr. Stratford, Canon Chrift Church, Oxford

Rev.

Mr Mr

Efo

Story,

Cambridge

Mr Thomas

Rev-.

Mr

Mr

Richard Stonehewcr Stoner,

William Strahan, L. L. D.

Soresby

Thomas Southby, Efyi Sontley South, Efq,

Sir

Thomas

College,

Edwin Sommcrs, Merchant

Sparrow MrSpeke,o/ Wadham

Lanca-

Mr Sto&on, Wntch-Mritr Mr Robert Stogdon Rev.

Mr Adam

the

Fellow of Corp.

Chr. Coll. Cambridge John Stevens, of Trinity

Cockin r

in

Edinburgh

Mr Stevens,

Stephen Soime, Efy, Fellow Com moner of Sidney Coll. Cambr.

^

John's

Martis Stehelin, Mitch.

fliire

Snow Thomas Snow

Ralph

Sole,

St.

Cambridge

College,

Mr John

Mr Edward Snllmgflect Mr John Srillingfleet Mr William Stith Mr Stock, of Rochdall in

Norwich

William Snell William Snelling, Ffy, William Sneyd, Eft;

Mr Mr

Reflir

Eflex o/ Had flock,

Mr Mr

Mr

Gyles's, in the

bnabiin

Mr Thomas Starges,

Rev.

College,

Ward Smith Skirner Smith

Mr

Stanfal, Efq,

Samuel Stanton

Mr

Jofcph Smith

Dr.

Mr

Rev.

Allyn Smith Toihua Smith

Mr

Thomas

Natural

Co

in

chefter

S:.

St.

Sir

John Smith

Rev.

Sibley, jun.

Stone

John Smith, Surgeon ventry, 2 Books

Mr Mr

Abraham Shrc'ghly John Shore, Efo Rev. Mr Shove Bartholomew Shower, Efij;

of

of

Dr. Steigcrthal

Eft;

Smith,

County of Bucks John Smith, Efq;

Rev.

Mr

Mr

Rev.

in

Kcnr, Efti

Unntrfi-

of Cambridge, iz Hooks Robert Smith, o/Bnfto!, Efqi William Smith, of the Middle-

Comm.cf Trinity Coll. Camb.

rellore of

tn the

Efq;

Dr. Stanley, Dean

Afaph Mr John Stanly Eaton Stannard, Eft;

Temple Stauyan, Efa; Mrs Mary Stanyrorrh Profe/or

ty

Mr Mr Mr

Silver,

Com

0/Bnftol

Smart John Smibart Robert Smirh, L.L.D.

John Shipton, Surgeon John Shipton, fen. Mr John Shipton, jun. Francis Shipwith, Efq; Fellow rlr

Mr

Thomas Stanhope John Stanley

Rev.

Mr Mr

c/Aftronomy

Edw. Sheldon, e/Winftonly

-Mr Thomas

Mr

George Stanley,

William Sloane, Efa; William Slop-r, E/q; Wi.liam Slopcr, EJ<j; FcLev

Shear?

Shim, of Greenwich

Bar.

mon r of Trin. Cdi. Cambr. Dr. Sloper, Chancellor of the Dio-

Archdeacon Sharp

John

Chcrterfield,

Sir

Arthur Shallet

James Sharp,

Mr Mr Mr Mr Mr Mr Mr

of

Hans Sloane,

Sir

Barcelona

Mr

Slater,

Scwtl!

Lancelot Shadwell

Capt. William Stratton Rev. MrStreat

Samuel Strode, Efq; Mr George Strode Rev. Mr John Strong

tf

SUBSCRIBERS NAMES-/ Mr

Hen. Commodore Stuart Alexander Stuart, M. D. Charles Stuart, Af.

Rev. Richard

D.

Rev.

Mr

Lewis S'ucly p

Mi JohnSturges, o/ loomsbury Mr Sturgeon, Surgeon in Bury Htn. Lady Suaflb Mr Gerrard Suffield Mi William Sumncr, c/Windfor Sir Robert Sutton, Kf. of the Bath Rev. Mr John Sutton

Mr

William Swinburn, Efq; Rev. Mr. John Swinton, M. A.

Symmonds, Edward Syngc

Surgeon

Jofhua

Mr

Rev.

Thomas

Thomlinfon

Thomplon Coley, Efq; William Thompibn

William Thompfon, A. B.

of Trinity Coll.

Cambridge

Mr Thoncas Mr Thornbury, I'tcar of Thamc Sir

James ThornhilJ,

3

Books

Mr

Thornhill William Thornton, Efq; Mr Catlyn Thorowgood

William Thorfeby, Efq; William Thurlbourn, Bookfeller in

Hi i Grace

Chancery William Tiffin, o/Lynn Tigh, Efq, Right Hon. Richard Tighc, Efq;

Tuam

Right Hon. E*rl of Tankervillc Rt. Hon. Ld. Vifceunt Townfhend, One of His MAJiJiy't Principal Secretaries of State

Right

Honourable Lady Vifcounteft

Townfhend Right Hon Ld I'ifctunt Tyrconnel The Honoutabl: Lord Trevor Charles

laibor,

General

Efq;

Solicitor-

.

Francis Talbot, Efq; John Ivory Talbor, Eft; George Taibut, M. A.

Mr Mr

Mr Abraham Tilghman Mr George Tilibn Rev.

Mr Rev.

Talbot

Mr John

Rev.

Mr Rev.

John Tatnall Arthur Ta.ldeur

Mr

John Tayleur Arthur Taylor, Efq; Jofeph Taylor, Efq; Simon Taylor. Efq; Rev. Mr Abraham Taylor Brook Taylor, L. L. D. William Tempeft, Efq, William Tenifon, EJq; Dr. Tenifbn Rev. Dr. Terry, Canon pfChrift Church, Oxon Theed, Attorney Lewis Theobald lames Theobalds Eft; Robert Thiftlethwayte, D. D. Wtrdtn of Wadham Coll. Oxon

Mr Mr

Mr

Mr Mr

William Tyfon

Samuel Tyflcn

Edward Tyzack

Cuft.

Rt. Htn. Lord Vifcount Vane Rev. Mr Thomas Valentine Mr Vallack , of Ply mouth 1

Mr John Vanderbank Mr Daniel Vandewall Mr John Vandewall, Merchant Mr Edward Vaus

Mr

George Virgoe

Mr

Frederick Voguel, Merchant

Mr Thomas

Touch

Ic

Rt. Hon. the Earl of Winchelfear

Mr NehemiahToWgood Edward

Town

Thomas Townfliend, Townfon

John Tracey,

Efq;

of Stanway

in

Capt. Richard Tracey Samuel Travcrfe, Merchant

Charles Trelawny,

Student

Church

Fredric Trench, Efq;.

Mr Edmund

Rt. Rev. Ior</B//7;0/>0/\Vinche{ler Rev. \Vade Sir Charles Wager

Mr

Glouceftcr, E/q;

of Chrift

Vickers

W

Mr Charles Tough

John Towers

Inn, Efq;-

Mr Mr

Trench

Rev. Mr WagftarTe Rev. Dr. Edward Wake

Mr

Mr

Jafper Wakefield

Samuel Walbank

Mr W'albndge Mr Waldron Edmund Waldrond, A/. A. Mr Walford, of Wadharn CoH. Oxon Mr Edward Walker

Rev.

Mr Samuel College,

Walker, ^"Trinity

Cambridge

Mr Samuel Trench

Mr Thomas Walker

Richard Trevor, Efq; Thomas Trevor,

Henry

Hon.

Hon.

Mr

Mr

(bt City

Robert Vmer, Efq;

Torriano

James

Jofeph Townfcnd, Ef<\\ To wnfhend,o/ Lincoln's

Mr

near

Vigor, of Weftbury College near Briftol

Charles

Hon.

-of

Mr Mr

William

Richard Topham, Efq-t Dr. Torey George Torriano, of Weft-Ham,

Mr

Mr. Robert Turner, Colcheder John Turton William Turton

Rev.

Han. John Verney, Efq^ William Vefey, Efqt Rev. Mr John Veley

Tifler

Mr Tomkins Mr William Tomlinfnn

of Norwich Thomas Tanner Taterum .of Clapham Henry Tatham

Mr Mr Mr Mr Mr

John

C*pt. Jofeph Tollbn

Thomas Tanner, D. D. Chan cellor

Mr Tilfon William Tims

Mr

Dr. D-iniel Turner

in

Edmund

the Archbifliop of

Efq;

Thomas Truman

Cambridge

Thurfton, Efq; Alafler

Rv.Mr T.

Mr

John Twiftleton, of York, Efq;

Mr

Mark

Trotter, L. L. D.

John Trubfliaw,

Col. Tyrrell

Mr John Thorpe

Gerrard Swartz

Mr Thomas Swayne

Mr

Mr

John Trevor

Trimble, Metch. in Rmterd. Rev. Dr. Trimncll, Dean of Winchcilcr

Waller, Efq;

William Waller, Efq;

Mrs Waller Mr John Waller, c/Lincofn's-Inn

Mr

George Wallis

Mr William

Wallis

Mr

SUBSCRIBERS NAMES. MrEdwar.lV/almney, Edward Wi'pole, Efq,

Mr Peter

Books

i

Walton, Efq; Piter Wari.u uu of Turd

Cheflme, /:j; Richard \Virburton,

r,

in

jttn.

Mr

Efq,

Mi: Howard W ard, Knox Ward, Mr John Ward, P.-ofeJfirofR.'hctoric in Grefham College William Ward, L. L. D. Mr Richard Warring cob Warn Richard Warner

J.i

Mr

Mr Edward Waltficld Mr Watkins Mr Thomas Watkis,

Rev.

Mr

cf

Mr

Ifaac

William

Jufcph

Mr Mr

William

Books

Weamen

cf

A

Humphrey Webb, 11. Edward Weofter, of

Efq;

Edwin-

ftowe, Efq;

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Lite

Weil

Weftern,

Prebendary of

//;

Amfterdam Dover- Street

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of : he Jf.nntl of

j;

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Mr

Efq;

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Williams,

College, Oxon Francis Wiiliams

Mr

Coll. Adam William/on R( bcit Willimott |ohn Willis, Efq; Edward Wilmor, A/. D. Mr Robert Willmott

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John Windfor

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T

r/W

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orcefter

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John \Voi fter, Merchant Rev. Dr. William Wotton

John

Wowen of the Middlein

Henry* Wright, cf Molberly,

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Wright William Wright, of Baldock,

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John's College, Rt. Hon.

St.

Cambridge

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LJ.

Ccmmon

Chief Jujiice of the Pleas, of Ireland

Mr

Wyeth Thomas Wyndham,

Rev.

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Herbert Weftfaling, Efq; Wefftein and Smith, AlcJJieiirs 'in

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n

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in

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W

Efq; Efq;

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John Woodhoufc,

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Rev.

Trinity College, Cambridge

Mr

Efq;

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Rt. Hon.

Anne;

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Daniel Wcflcomb,

Rcfior cf

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Mrs

D. D.

,

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St.

A. B.

Howton Witrcn, Cambridge

Rev.

V

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2

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irtingham Retfor of John Witton,

\\ liliam Vv'oodtord, A/.

hitehead

W

Mr

&

D.

V

Thomas Woodcock, Thomas Woodford,

White

W

John

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.

Dicklcburgh Rei; Mr hitfi-.-Id Mr Nathaniel Whitlock

John

William

Scholar of

Cambm

!'"

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Y\ bite,

:iite

.

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Phil.

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Rev. Mr \Vhitehcad, Ftl'cw cf ]''m.nud College, Cambridge

Efq;

Richard Watts, A/.D.

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ward

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Rnbat

Joe!

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I',

Caius College,

Mr

Rev.

John Witter

Jacobus Wittichius, in Acad. Lugd. Bat. Prof.

Mr John

Mr

Watfon Mr John Watfon Mr Thomas Watfon

Rev.

Mi

Jo! n

Rev. Mr Waflungton, Fellow cf Peterhoulc, Cambridge

W

i..ftcn

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6

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Knutsford T Robert atley,

Efq;

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of the

Wit home,

Inner-Temple

/

1

,

Ir

W iihtrs.o/Gray's-Irm, Efq;

Mr Con way

iiam Whitiker Taylor White,

<

Abraham Vvinterbottom

Will.

-rephen V. hatley

.11

Mr

Mr

Mr EJward Wharton

Walter

Mr John

Mr

John

Yard!ey,5r^.

Thomas Yates Mrs Yeo, of Exeter, Sir William Yonge Luly York Nicholas

Efq;

Wynne

Young, Temple, Efq;

/

Coven.

Eoolftlhr

cf the Inner-

Hitch Young, I Rev. Edward Ycung,

L. L.

D.

INTRODUCTION. HE manner,

in

which

Sir ISA AC

NEWT ON

has publifhed his philofophical difcoveoccafions them to lie ries, very much concealed from all, who have not made the mathematics particularly their ftudy.

He

liver, in

of

his inventions,

which

once, indeed, intended to de a

more

familiar

relates to the

way, that part

fyftem of the world

;

but upon farther confederation he altered his defign. For as the nature of thofe difcoveries made it impoffible to prove

diem upon any other than geometrical

principles ; he appre hended, that thofe, who fhould not fully perceive the force of his arguments, would hardly be prevailed on to exchange their former fentiments for new opinions, fo very different

B

from

what

INTRODUCTION.

i

what were commonly received

He

a .

therefore chofe rather

to explain himfelf only to mathematical readers; and declined to inftruft fuch in any of his principles, who, the

attempting

his method of reafoning, could not, at his difcoveries, have been perfuaded of of appearance E w T o N'S dodrine But now, fince Sir I s A A c their truth. has been fully eftabliflied by the unanimous approbation of all, who are qualified to underftand the fame ; it is without doubt

by not comprehending the

firft

N

to be wifhedj that the

whole of

his

phy might be univerfally known.

improvements in philofoFor this purpofe therefore

the following papers, to give a general notion of our to great philofopher's inventions to fuch, as are not prepared read his own works, and yet might defire to be informed of I

drew up

the progrefs, he has made in natural knowledge ; not doubting but there were many, befldes thofe, whofe turn of mind had led

diem

into a courfe of mathematical ftudies, that would take

great pleafure in tafting of this delightful fountain of fcience. I

a.

man

T

is

a juft remark, which has been

mind,

that nothing

templation of truth

;

is

more

and that

all

made upon

fuitable to

men

defire after

are

it,

the

moved with

a ftrong

honourable to excel

knowledge ; efteeming and holding it, on the contrary, difgraceful

therein

;

ftake,

err,

it

or be in any

way

deceived.

hu

than the con

And

this

to

mi-

fentiment

by nothing more fully illuftrated, than by the inclination of men to gain an acquaintance with the operations of na

is

ture

;

which

difpofition to enquire after the caufes *

Philofoph. N.u.princ. math. L.

iii.

of

thino-s

is

introduft.

fo

INTRODUCTION. fo general, that all

men

of

r

letters,

3

find themfelves

I believ e,

influenced by it. Nor is it difficult to allign a reafon for this, if we confider only, that our defire after knowledge is an ef fect

of that

which

tafte for the

and die

life,

fublime and the beautiful in things O ',

chiefly conftitutes the difference life

of brutes.

Thefe

between the

human

inferior animals partake

with us of the pleafures, that immediately flow fr^m the bo dily fenfes and appetites ; but our minds are furnifhed with a

by which we are capable of receiving various degrees of delight, where the creatures below us perceive no

fuperior fenfe,

Hence

difference.

arifes

and elegance in belonging to us,

that purfuit of grace and in all things

our thoughts and actions,

which

principally creates

imployment

for the active

mind of

thoughts of the human mind are too extenfive to be confined only to the providing and enjoying of what is for the neceffary fupport of our being. It is this tafte, which

man.

The

has given rife to poetry, oratory, and every branch of litera From hence we feel great pleafure in con ture and fcience. ceiving ftrongly, and in apprehending clearly, even where the paflions are not concerned. Perfpicuous reafoning ap pears not

only beautiful

ftrength and

particularly

when

fet forth

in

its

full

ft;

O

defire of

knowledge: O '

and the fame

fublime and the beautiful directs us to chule

the productions of nature for the fubject of our our creator having fo adapted our minds to

contemplation lij

but,

partakes of the fublime, and not dignity, but warms and elevates the foul. This is the

only pleafes, fource of our tafte for the

;

it

condition,

:

wherein he has placed

B i

us,

that

all

his vifible

works,

INTRODUCTION. before we inquire into their make, the moft lively ideas of beauty and magnificence.

ftrike us

works,

3

BUT

.

minds

if

there be fo ftrong a pailion in contemplative a all fuch ; certainly receive

for natural

philofophy

particular pleafure in being difcoveries,

who

advancements ledge

mud

informed of

Sir

alone has been able to

in the true courfe leading

whereas

:

with

this

ISAAC NEWTON'S

make any great to natural know

important fubject had before been uas cannot be re negligence,

fually attempted with that flected on without furprize.

Excepting a very few, who, by purfuing a more rational method, had gained a little true knowledge in fome particular parts of nature ; the writers in

had generally treated of it after fuch a manner, as they thought, that no degree of certainty was ever to be ho ped for. The cuftom was to frame conjectures ; and if upon this fcience

if

comparing them with things, there appeared fome kind of agreement, though very imperfect, it was held iufficient. Yet at the fame time nothing lels was undertaken than intire fyflems,

and fathoming

as if the fecret caufes

by

infinite

wifdom,

flighted Whereas the only understandings. that can afford us any profpect of fuccefs in this

endeavours of our

method,

once the greateft depths of nature ; effects, contrived and framed could be fearched out by the at

of natural

weak

work, is to make our enquiries with the utmoft and by very flow degrees. And after our moft dili gent labour, the greateft part of nature will, no doubt, fore ver remain beyond our reach.

difficult

caution,

4.

THIS

INTRODUCTION. THIS

neglect of the proper means to enlarge our knowledge, joined with the prdumption to attempt, what was quite out of the power of cur limited faculties, the Lord

BACON judicioufly

obftruion

obferves to be the great

to the

a

Indeed that excellent perfon was the firft., who exprefly writ againft this way of philosophizing ; and he has laid open at large the abfurdity of it in his admirable treatife, of fcience progrefs

.

NOVUM ORGANON SCIENTIARUM;

intitled

likewife defcribed the true method,

and has there

which ought to be followed.

y. THERE are, faith he, but two methods, that can be taken in the purfuit of natural knowledge. One is to make a hafty tranfition from our firft and flight obfervations on

and then to proceed upon thofe things to general axioms, axioms, as certain and unconteftable principles, without far ther examination.

The

other

method

;

(

which he obferves

to be the only true one, but to his rime unattempted ; ) is to cautiously, to advance ftep by ftep, referving the

proceed

mod

for the laft refult

general principles Concerning the firft of thefe

of our inquiries

b .

two methods j where

objections, to appear againfl any fuch axioms taken up in hafte, are evaded by fome frivolous diftinction, when the ax

which happen

iom

it

felf

ought rather to be corrected

c

he affirms, that

;

ages cannot make it fuccefsful ; becaufe this original error in the firft digeftion of the mind d himfelf ) cannot afterwards be remedied ; as he (

the united endeavours of

all

exprefles

whereby he would a

b *

Signify to us,

Nov. Org. Sclent. L.i, Aphorifm. Nov. Org. L. i. Aph. 19. Jbid. Aph. 25.

d 9.

that if Aph. 30.

gelKone mentis

we

fet

out in a

Errorc a'o

exa-llcntu

fun&ionum

a

di-

>-V

re-

mcdiorum fequcntium non cur

wro:

INTRODUCTION.

6

wrong way

no

;

diligence

or

we

art,

can ufe, while we our de-

follow fo erroneous a courfe, will ever bring us to

And

figned end.

doubtlefs

it

cannot prove otherwife ; for

in this fpacious field of nature, if once

we

fhall

immediately path, ever wander with uncertainty.

THE

6.

many

his

a

we

forfake the true

felves,

and muft

for

of fucceeding in fo faulty a method Lordfhip endeavours to prove from the

notions and prejudices, to

falfe

which the mind of man

And

fince this judicious writer apprehends, that are fo exceeding liable to fall into thefe wrong tracts of

expofed

men

our

impoffibility

of philofophizing is

lofe

.

thinking, as to incur great danger of being milled by them, even while they enter on the true courfe in purfuit of na b ture ; I truft, I fhall be excufed, if, by mfifting a little par ticularly

upon

this

argument,

I

endeavour to remove what

ever prejudice of this kind, might pofTibly entangle die

of any of 7.

His

Lordfhip has reduced thefe prejudices and c diftinct heads

modes of conception under four 8.

mind

my readers.

THE firft head

contains fuch, as

falfe

.

we

are

fubjecl:

to

from

the very condition of humanity, through the weaknefs both of our fenfes, and of the faculties of the mind J ; as feeing,

author well obferves, the fubtilty of nature the greatcft fubtilty of our fenfes or acuteft this

far

reafonings

exceeds c .

One

of

INTRODUCTION. of the der

modes of conception,

falfc

this

head,

7

which he mentions un

the forming to our felves a fanciful fimin natural This he illuftrates tilings.

is

and regularity

plicity

by the following inftances

move

in

perfect ther three elements,

ceed the other in

And

the conceiving the ; planets to the adding an orb of fire to the oand the fuppofing each of thefe to ex

circles

;

of the fame nature

without any proof, that kinds of matter only b .

philofopher

that light,

;

juft in

rarity,

a decuple proportion

the ailertion of

is

As in

alfo

this

.

DES CARTES,

made up of

things are

all

a

three

opinion of another

palling through different

me

diums, was refracted, fo as to proceed by that way, through which it would move more fpeedily, than through any other

c

The

.

fecond erroneous turn of mind, taken notice of

this head, is, that all men are in fome degree prone to a fondnefs for any notions, which they have once imbibed ; whereby they often wreft things to reconcile

by

his

Lordfhip under

them to thofe notions, and neglect the confideration of what ever will not be brought to an agreement with them ; juft as thofe do, who are addicted to judicial aftrology, to the obfervation of dreams, and to fuch-like fuperftitions ; who care fully preferve

the

memory of

confirm their prejudices, and ftances, that

make

againft

eyery incident, which ferves to out of their minds all in flip

let

them d There .

is

alfo a farther impe

this

knowledge, mentioned under the fame head by noble writer, which is ; that whereas, through the weak-

nels

and imperfection of our fenfes, many things are concealed.

diment

to true

Aph. Princ. Phil. Part. 3,

.

52.

c

Fcrm.it, in

d

Nov.

O

Opcr.

;

from

INTRODUCTION.

8

natural

effecl: in producing greateft affected by are minds our ordinarily moft appearances ; our organs on the makes which impreflion ftrongeft that, to judge of the real impor we are of fenfe

from

us,

which have the

apt ; whereby a So, becaufe tance of things in nature by a wrong meafure fenfes more our ftrike the figuration and the motion of bodies .

other properties, DBS CARTES immediately than moft of their of natu not allow will and his followers any other explication

than from the figure and motion of the parts which example we fee how juftly his LordBy b this caufe of error to be the greateft of any obferves ; fhip ral appearances,

of matter. fince

it

fal

rife to a fundamental principle in a fyftem that not long ago obtained almoft an univer-

has given

of philofophy, reputation.

9.

THE

s

E are the chief branches

which

this

of thofe obftructions to

author has reduced under

his firft knowledge, The fecond head contains the head of falfe conceptions. errors, to which particular perfons are more efpecially obno c xious One of thefe is the confequence of a preceding ob.

fervation

nions,

:

that as

we

are expofed to be captivated

which have once taken

pofleiTion of our

by any opi minds fo in ;

knowledge has been much corrupted by the ftrong attachment of men to fome one part of fcience, of which they reputed themfelvcs the inventers or about particular, natural

,

which they have

fpent

been apt to conceive a >

it

much

of their time

;

and hence have

to be of greater ufe in the ftudy of na-

Aph. 50.

I

c

Aph.

53.

Ji

tural

INTRODUCTION.

9

A

R i s T o T L E, who redu like tural philofophy than it was ced his phyfics to logical difputations ; and the chymifts, who that nature could be laid open only by the force :

thought,

a

Some again are wholly carried away by an excelTive veneration for antiquity ; others, by too great fondnefs for the moderns ; few having their minds fb well balanced, of their

fires

.

of the ancients, nor yet to b To this is real improvements of later times the defpife added by his Lordfliip a difference in the genius of men, that fome are moft fitted to obferve the fimilitude, there is in as neither to depreciate the merit

.

things,

while others are more qualified to difcern the par

ticulars,

wherein they difagree

both which difpofitions of

;

but to the prejudice of philofophy men are run into excefs in each ; while one fort of genius dwells to apt too much upon the grofs and fum of things, and the other

mind

are ufeful

upon

trifling

I o.

:

minuteneffes and fliadowy diftinctions

UNDER the third head of prejudices and

this writer confiders fuch,

nite ufe

as follow

c .

falfe

from the lax and

notions indefi

of words in ordinary difcourfe ; which occafions great

ambiguities and uncertainties in philofophical debates (as ano 3 ther eminent philofopher has fince fliewn more at large ;) in-

fomuch

that this our author thinks a ftricl: defining of terms to be fcarce an infallible remedy againft this inconvenience e And for the common perhaps he has no fmall reafon on his fide .

:

inaccurate fenfe of words,

given them by a

definitions,

Aph. 54.

Aph. 56. .

notwithftanding the limitations will offer I

d

it

Locke,

felf fo

conftantly to

On human undcrftanding, B. iii.

Nov. Org

Aph. 59.

55

C

the

io

INTRODUCTION.

the mind,

as

Of

eminent inftance

in die great disputes, the word attraction in

we have

a very

that have been raited

fhall

Words are

this

of which life of philofophy be obliged hereafter to make particular mention \ Some thus to be guarded againft are of two kinds.

about the

we

and circumfpedion

to require great caution

be deceived thereby.

for us not to

names of

things, that are only

b

imaginary

fuch words

;

are wholly to be rejected. But there are other terms, that al c lude to what is real, though their fignification is confufed And thefe latter muft of neceflity be continued in ufe ; but their fenfe cleared up, and freed, as much as poifible, from .

obfcurity.

THE

laft general head of thefe errors comprehends follow from the various feels of falfe philofophies ; which this author divides into three forts, the fophiftical, em

II.

as

fuch,

pirical,

and

d

fuperftitious

.

By

the

firft

of thefe he means

a philofophy built upon fpeculations only without experi ments e ; by the (econd, where experiments are blindly ad

hered

f

to,

the third,

without proper reafbning upon them ; and by of in nature fixed mens minds ei wrong opinions

ther through falfe religions, declarations of the true g

or

from mifunderftanding the

.

II. THESE are the four principal canals, by which this ju dicious author thinks, that philofophical errors have flowed in

upon

us.

And a k c

he rightly obferves, that the faulty method of

In the conclufion. Nov. Org. L. i. Aph. 59. Ihid.

Ibid.

Aph. 60. Aph. 6:

Aph. 63. Aph. 64. 5 Aph. 65. I

proceeding

INTRODUCTION.

n a

proceeding in philofophy, againft which he writes , is fo far from a/lifting us towards overcoming thefe prejudices ; that he apprehends it rather fuited to rivet them more firmly to the

mind b

How great reafon

.

then has his Lordfhip to call this error, and the bane of

way of philofophizing the parent of

c knowledge ? For, indeed, what elfe but miftakcs can ib bold and prefumptuous a treatment of nature produce ? have

all

the wifdom neceflary to frame a world, that we fliould think fo eafily, and with fo flight a fearch to enter into the moft fecret fprings of nature, and difcover the original caufes of

we

things ? what chimeras, what monfters has not this prepofterous method brought forth ? what fchemes, or what hypothe-

of the

fubtileft wits has not a ftricter enquiry into nature not to be ridiculous and abfurd ? manifefted but overthrown, only fis's

Every new improvement, which we make in this fcience, lets more and more the weaknefs of our guefles. Dr.HARVEY, by that one difcovery of the circulation of the blood, has of many ages up diflipated all the {peculations and reafonings

us fee

on the animal oeconomy. A s E L L u s, by detecting the la fhewed how little ground all phyficians and phiin conjecturing, that the nutritive had lolbphers part of the i

cteal veins,

aliment was abforbed by the mouths of the veins fpread upon and then P E c QJJ E T, by finding out the thora

the bowels

:

cic duct, as evidently

was

perfifted

proved the vanity of the opinion, which were known, that the

in after the lacteal verTek

alimental juice was conveyed immediately to the liver, there converted into blood, *

b

See above,

Nov.Org.

4,

L.

and

5. i.

Aph. 69.

13.

As

INTRODUCTION.

ii

As

13.

thefe tilings fet forth the great abfurdity of pro

us how far ceeding philofophy on conjectures, by informing the operations of nature are above our low conceptions ; fo on the other hand, fuch inftanccs of fuccefs from a more in

that our bountiful maker ha, judicious method (hew us, not left us wholly without means of delighting our felves in That by a juft way of of his wifdom. the

contemplation

inquiry into nature,

we

could not

fail

of arriving the

very remote from our apprehensions ; argues from the experience of mankind.

felf

force of guns fhould

at difcoveries

Lord B If,

A co

N him-

fays he, the

be defcribed to any one ignorant of

them, by their effects only ; he might reafonably fuppofe, that thofe engines of deftruclion were only a more artificial compofition,

powers

:

than he knew, of wheels and other mechanical it could never enter his thoughts, that their

but

immenfe force fhould be owing to a peculiar fubftance, which would enkindle into fo violent an exploiion, as we fince he would no where fee experience in gunpowder :

the leaft example of any fuch operation

earthquakes and thunder,

;

except perhaps in

which he would doubtlefs look

upon as exalted powers of nature, greatly furpailing any art of to imitate. In the fame manner, if a ftranger to the ori

man

were fhewn a garment made of it, he would be from imagining fo ftrong a fubftance to be fpun out of the bowels of a fmall worm ; but muft certainly believe ginal of filk

very far

it

either a vegetable fubftance, like flax or cotton

;

or the na

Or had covering of fome animal, as wool is of flieep. been told, before the invention of the magnetic needle

tural

we

among

us,

that another people

was

in

polTeiTion of a certain

contrivance

INTRODUCTION.

13

contrivance, by which they were inabled to difcover the pofition of the heavens, with vaftly more eafe, than we could do ; what could have been imagined more, than that they

were provided with fome this

aftronomical inftrument for

fitter

we ? That any ftone fhould have fo amaz as we find in the magnet, muft have been

purpofe than

ing a property, the remoteft from our thoughts

14.

BUT

a .

what furprizing advancements

in the

knowledge

may be made by purfuing the true courfe in philowhen thofe fearches are conducted by a inquiries

of nature fophical

;

genius equal to fo divine a work, Sir

ISAAC

will be

N E w T o N'S

bed underflood by That my

difcoveries.

considering reader may apprehend as juft a notion of thefe, as can be con veyed to him, by the brief account, which I intend to lay be fore

him

the

rulleft

ISAAC

;

I

have

fet

manner

NEWTON

I

apart this introduction for explaining, in am able, the principles, whereon Sir

proceeds.

For without a

clear

concep

impoflible to form any true idea of the of the inventions of this great excellence fingular philofopher. tion of thefe,

it is

I y. THE principles then of this philofophy are ; upon no confideration to indulge conjectures concerning the powers and

laws of nature, but to

make it our endeavour with all diligence

and true laws, by which the conftitution The philofopher's firfl care muft be regulated.

to fearch out the real

of things is to diftinguiflh,

what he

fees to

a

4

Ibid.

be within

his

power, from what

Aph. 109. is

INTRODUCTION.

14

his reach ; to aflume no greater degree of know than what he finds himfelf poffeiTed of; but o advance ledge, flow and cautious fteps ; to fearch gradually into natural caufby

is

es

beyond

;

to fecure to himfelf the

knowledge of the moft immediate

caufe of each he extends his views farther appearance, before to caufes more remote. This is the method, in which philofo-

phy ought

to be cultivated

more

things, as the

dantly more

:

we

;

which does not pretend

but will perform abun to the unskilful to feem not perhaps

airy fpeculations

(hall

to fo great

;

much, but our real knowledge will be greater. And that fome ocertainly it is no objection againft this method, thers promife, what is nearer to the extent of our wifhes fince

know

fo

:

this,

if it

of, will

will not teach us all

we

however give us ibme true

Nor has when he

other can do. his labour loft,

could defire to be informed light into nature

;

which no

the philofopher any reafon to think finds himfelf ftopt at the caufe firft

difcovered by him, or at any other more remote caufe, fhoit of the original for if he has but fufficiently proved any one fo far into the real conftitution of he has entered caufe, :

things,

has laid a fafe foundation for others to

work upon,

has facilitated their endeavours in the fearch after yet diftant caufes ; and befides, in the mean time he

may

and more apply

the knowledge of thefe intermediate caufes to many ufeful Indeed the being able to make purpofes. practical dedu ctions

from natural

caufes,

conftitutes the

great diftinction

between the true philofophy and the falfe. Caufes affumed upon conjecture, muft be fo loofe and undefined, that nothing particular can be collected caufes,

which

from them.

But thofe

are brought to light by a ftrict examination

of

INTRODUCTION.

15-

Hence it appears to have of things, will be more diflinft. been no unufeful difcovery, that the afcent of water in pumps to the preflure of the air by its weight or faring ; the caufes, which make tlie air gravitate, and render though for notwithstanding we are igno be unknown it elaftic,

is

owing

:

whence

rant of the original,

we may

thefe powers of the air are de

much advantage from the bare yet of thefe powers. If we are but certain of the de knowledge of wherewith force, gree they act, we fhall know the extent of what is to be expected from them we fhall know the greatefl rived

;

receive

;

which

by pumps to raife water ; and fhall thereby be prevented from making any ufelels efforts towards improving thefe inftruments beyond the limits preheight, to

fcribed to

ledge this

is

it

poflible

them by nature

whereas without fo much know we might probably have wafted in attempts of much time and labour. How long did philofo;

as this,

kind

to no purpofe in phers bufy themfelves endeavouring to perfect the glaffes into fome new til] telefcopes, by forming ;

figure

ISAAC

NEWTON

demonftrated, that the effects of tele fcopes were limited from another caufe, than was fuppofed ; which no alteration in the figure of the glaffes could remedy ?

Sir

What method

Sir

ISAAC

NEWTON

the

improvement of telefcopes

But

at

prefent

ces, this

we

have

I

fhall

fhall

himfelf has found for

be explained hereafter

proceed to illufbate, by

a .

fome farther inftan-

diiKnguifhing character of the true philofophy, which

now under

confideration.

It

was no

trifling difcove

that the contraction of the mufcles

of animals puts their limbs in motion, though the original caufe of that contraction

ry,

Book

III. Chip, iv

remain-

INTRODUCTION.

16 remains a

and perhaps may always do

fecret,

much

knowledge of thus

only has given

rife

to

fo

for the

;

many

fpecuthe mufcles, of the force and artificial difpofition upon and has opened no narrow profpect into the animal fabrick. The finding out, that the nerves are great agents in this alations

ftion, leads us yet nearer to the original caufe, and yields us a wider view of the fubject. each of thefe fteps affords us

And

afliftance towards reftoring this animal motion, when impair ed in our felves, out the feats of the injuries, to

which

it is

by pointing obnoxious. To neglect

hitherto advance

no

confefled by

that

all,

which we

downwards with

when any body to describe in b

its

plainly

becaufe

we

ridiculous.

(hall relate hereafter, that the

call

can It

is

greatly improved philofo-

gravity,

occafions

them

a velocity equably accelerated

a ;

to

power

mo\e

and

that

thrown forwards, the fame power obliges it motion that line, which is called by geometers

we

whence

we can

eftimate

which makes

are ignorant of the caufe,

But although

the fpring, lefs

all this,

is

a parabola yet bodies gravitate. :

is

GALILEO

we

phy, by {hewing, as in bodies,

farther,

this its

power

effects.

we

are unacquainted with

in nature

When

is

derived, neverthe-

a

body falls perpendicu known, how long time it takes in defcending from any height whatever and if it be thrown forwards, we know the real path, which it defcribes ; we can determine in what larly,

it is

:

and with what degree of

fwiftneHs muft be pro finking againfl any object defired ; and can alfo afcertain the very force, wherewith it will itrike.

direction,

jected, in order to

we

Book

it

its

I.

Chap.

2.

b

14.

]bid.

85,

<s

Sir

INTRODUCTION. Sir

IsAAcNEWTON

has farther taught,

17

that this

power of

extends up to the moon, and caufes that planet to gravitation as much towards the earth, as any of the bodies, which

gravitate are familiar to us,

if

would,

a

placed at the lame diftance the planets gravitate towards :

he has proved likewife, the fun, and towards one another that

motions follow from

all

and

;

that their refpective

All

this gravitation.

this

he

lias

demon-

upon indifputable geometrical principles, which cannot be rendered precarious for want of knowing what it is, which caufes thefe bodies thus mutually to gravitate any more than ftrated

:

we

can doubt of the propeniity in all the bodies about us, to defcend towards the earth ; or can call in qucftion the fore-

mentioned proportions of

And

that principle.

as

GAL

i

which are

L E o,

GALILEO

has

f

built

hewn more

upon fully,

than was known before, what effects were produced in the motion of bodies by their gravitation towards the earth ; fo Sir I s A A c N E w T o N, by this his invention, has much advan ced our knowledge in the celefrial motions. By difcovering

moon

that the

the earth;

gravitates towards the fun , as well as towards laid thofe intricacies in the moon's

he has

open

motion, which no aftronomer, from obfervations only, could b and one kind of heavenly bodies, the comets, ever find out :

have their motion before

no

I 6.

fuccefs

true

now

knowledge

DOUBTLESS

it

mould have 3

k

clearly afcertained

See Book II. Ch. See Book II. Ch.

at all

filenced, at once, 3,4. of

3.

of

this treatife.

this treatife.

whereof we had

,

might be expected,

3.

;

c

I

that fuch

every cavil. c

furprizing

But we

Sec Clup. 4.

|

D

have

INTRODUCTION.

i8

have feen the contrary. For becaufe

this

philofophy profefles

of our faculties, and is modeftly to keep within the extent rather than to make any confefs its to imperfections, ready to cover the de fruitlefs attempts to conceal them, by feeking with the vain oftentation of rafh and fects in our

knowledge

taken an occafion to groundlefs conjectures ; hence has been insinuate that we are led to miraculous caufes, and the occult qualities

17.

of the fchools.

BUT

the

of thefe accufations

firft

is

very extraordina

If by calling thefe caufes miraculous nothing more is ry. meant than only, that they often appear to us wonderful and

not eafy to fee what difficulty can be raifed works of nature difcover every where ; fuch proofs of the unbounded power, and the confummate wifdom of their author, that die more they are known, the furprizing,

it is

from thence

more they

for the

will excite

our admiration

to be infifted on, that the

culous can have no place here, the ordinary courfe of things.

and

:

common when The

it is

too manifeft

word mira what is above implies

fenfe of the it

other imputation, that the of our not perceiving account upon what produces them, contains in it great ambiguity. That fomething relating to them lies hid, the followers of this thefe caufes are occult

philofophy are ready to acknowledge, nay deiire it fhould as pointing out proper fubjects for fu is very different from the proceeding

be carefully remarked, ture inquiry. But this

of the fchoolmen in the caufes called by them occult. were underftood to operate in a

as their occult qualities

ner occult, and not apprehended by us

S

;

fo they

For

man

were obtruded

INTRODUCTION.

19

truded upon us for fiich original and eflential properties in bo a great dies, as made it vain to feek any farther caufe ; and was attributed to them, than any natural appearances er

power

authorized.

For inftance, die

rife

of water

pumps was

in

afcri-

bed to a certain abhorrence of a vacuum, which they thought fo to affign to nature. And this was fo far a true obfervation,

move, contraiy to its ufual courfe, into the fpace, which otherwife would be left void of any fenfible matter ; and, that the procuring fuch a vacuity was the appa

that the water does

But while we were not in power, called an abhorrence of a

rent caufe of the water's afcent.

the leaft informed

how this

vacuum, produced the vifible effects ; inftead of making any advancement in the knowledge of nature, we only gave and when the an artificial name to one of her operations what fo was any appearances re beyond puflied {peculation :

quired, as to have it concluded, that this abhorrence of a va cuum was a power inherent in all matter, and fo unlimited as to render

it

impofTible for a

vacuum

to exift at

all

;

it

then

became a much

greater abfurdity, in being made the foun dation of a moft ridiculous manner of reafoning ; as at length evidently appeared, when it came to be difcovered, that this rife

of the water followed only from the preiTure of the air, it felf no farther, than the power of that caufe.

and extended

The as

fcholaftic ftile in difcourfing

if

of thefe occult

qualities,

they were effential differences in the very fubftances,

of which bodies confifted, was certainly very abfurd; by it tended to But no difcourage all farther inquiry.

reafon

fuch

any

ill

confequences can follow from the confidering of which confefTedly are not traced up to

natural caufes,

D

1.

their

INTRODUCTION.

ao

How

their firft original.

we

fhall

come

ever

to the

know

caufes of things, otherwife than ledge of the feveral original ? all intermediate caufes which we can difcover by ftoring up Are all the original and effential properties of matter fo very

obvious, that

not probable.

none of them can efcape our It

is

much more

likely,

by our

effential properties are difcovered ftricter

examination fliould

18.

BUT

in order to clear

effential properties tle

diftin&ly.

bring more

of matter,

We

firft

that, firft

view ? This

if

obfervations,

a

to light.

this point concerning us confider the fubjecl: a

up

let

is

fome of the

are to conceive, that the matter,

the lit

out of

which the univerfe of things is formed, is furnifhed with cer tain qualities and powers, whereby it is rendered fit to anfwer But every property, the purpofes, for which it w as created. of which any particle of this matter is in it felf poffeffed, and r

the union of this parti is not barely the confequence of with other portions of matter, we may call an effential pro whereas all other qualities or attributes belonging to perty

which cle

:

which depend on their particular frame and compofiare not effential to the matter, whereof fuch bodies are

bodies, tion,

made ot

;

becaufe the matter of theie bodies will be deprived only by the diffolution of the body, with

thofe qualities,

out working any change in the original constitution of one Extenfion we appre fingle particle of this mafs of matter.

hend lity

to

be one of thefe

another. Thefe

effential

two belong

properties,

and impenetrabi and

univerfally to all matter

are the principal ingredients in the idea,

matter ufually excites in the mind

,

Yet

which

this

as the idea,

;

word

marked by

INTRODUCTION. by

this

name,

derftandings,

is

but

u

not purely the creature of our own un^is taken for the reprefentation of a certain

fubftance without us

;

if

we

fhould difcover, that every part

of the fubftance, in which we find thefe two properties, fhould likewife be endowed univerfally with any other cffenall thefe, from the time they come to our no tial qualities ; tice,

many not;

muft be united under our general idea of matter.

How

fuch properties there are actually in all matter we know thofe, of which we are at prefent apprized, have been

found out only by our obfervations on

more a nor are

tilings

;

how many

may bring to light, no one can fay ; that we are provided with fufficient me

farther fearch

we

certain,

thods of perception to difcern them all. Therefore, fince we have no other way of making difcoveries in nature, but by gradual inquiries into the properties of bodies ; our firft ftep

muft be

to

admit without diftinclion

all

the properties,

which

and afterwards we muft endeavour, as far as we are able, to diftinguiih between the qualities, wherewith the very fubftances themfelves are indued, and thofe appearances,

we

obferve

;

refult from the ftructure only of compound bodies of the obferve in things, are the which we Some properties, attributes of particular bodies only ; others univerfally belong Whether fome of the to all, that fall under our notice.

which

qualities

and powers of particular bodies, be derived from dif

of matter entring their composition, cannot, in die piefent imperfect ftate of our knowledge, abiolutely be decided ; though we nave not yet any reafon to conclude, ferent kinds

but that

all

the bu^

with which

we

out of the very fame kind of matter,

converfe,

and

are fram J .

that their diftin6l

INTRODUCTION;

it

the va by their ftrufture ; through

qualities are occafioned only riety

whereof the general powers of matter are caufed to pro

duce

different effects.

On

the other hand,

that whatever ftily conclude,

is

we

fhould not ha-

found to appertain to

all

mat

under our examination, mufr. for that reafon ter, and not be derived from be an efTential only property thereof, fome unfeen difpofition in the frame of nature. Sir I s A A c

which

falls

N E w T o N has found reafon to conclude, that gravity

perty univerfally belonging to

all

the perceptible

is

a pro

bodies in the

and to every particle of matter, whereof they are But yet he no where aflerts this property to be compofed. And he was fo far from having any deelTential to matter. of it as fuch, that, on the eftablifhing contrary, he has fign a given fome hints worthy ot himfelf at a caufe for it ; and exuniverfe,

prefly fays, that he propofed thofe hints to {hew, that he no fuch intention b

had

.

19. IT appears from hence, that it is noteafy to deter mine, what properties of bodies are erTentially inherent in the matter, out of which they are made, and what depend upon their frame

and compofition.

But certainly whatever pro

found to belong either to any particular fyftems of matter, or univerfally to all, muft be considered in philofophy ;

perties are

becaufe philofophy will be otherwife imperfect. Whether thofe properties can be deduced from fome other appertain ing to matter, either among thofe, which are already known, or among fuch as can be difcovered by us, is afterwards to be

fought for the farther improvement of our knowledge. But this * At the end ofhis Optics. in

Qu. jj.

I

b See the

fame

tre.uifo,

Advertifemenr

ia

;.

inquiry

INTRODUCTION: cannot properly have place in the deliberation about ad mitting any property of matter or bodies into philofophy ; for

inquiry

that purpofe it is only to be confidered, whether the exiftence Therefore of fuch a property has been juftly proved or not.

what

caufes of things are rightly received into na tural philofophy, requires only a diftincl and clear conception to decide

of what kind of reafoning is to be allowed of when we argue upon the works of nature*

THE

10.

as

convincing,

be fo abfoproofs in natural philofophy cannot For the fubjetts of

lutely conclufive, as in the mathematics.

that fcience are They purely the ideas of our own minds,. be reprelented to our fenfes by material objects, but they

may

are themfelves the arbitrary productions of our own thoughts ; fo that as the mind can have a Rill and adequate knowledge

of

its

own

ideas,

But

perfect.

the reafoning in geometry can be rendered knowledge the fubject of our con

in natural

templation is without us, and not fo compleatly to be known : therefore our method of arguing muft fall a little fhort of abfolute perfection. It is only here required to fteer a juft courfc

between the conjectural method of proceeding, againft which I have fo largely fpoke ; and demanding fo rigorous a proof, as will reduce all philofophy to

mere

fcepticifm,

and exclude

all

of making any progrefs in the knowledge of nature* profpecl: 11. ence,

THE conceffions, are

few fimple

by

Sir

ISAAC

precepts.

which

are to be allowed in this

NEWTON

fci

included under a very

INTRODUCTION. ai.

THE

firft

is,

that

more

caufes arc not to be received

to explain the appearances philoibphy, than are fufficient of nature. That this rule is approved of unanimously, is e-

into

vidcnt from thofe expreflions fo frequent that nature does nothing in vain ;

all philofothat a varie

among and

phcrs,

And is needlefs. ty of means, where fewer would fuffice, for complying with this reafon there is the higheft certainly For fhould we indulge the liberty of multiplying, the caufes of things, it would reduce

rule.

without neceflity,

all fince the only proof, philofophy to mere uncertainty which we can have, of the exiftence of a caufe, is the ne Therefore where ceflity of it for producing known effects. ;

one caufe

is

fufficient,

if there

really fhould in nature be

two, which is in the laft degree improbable, we can have no poffible means of knowing it, and confequently ought not to take the liberty of imagining, that there are

a3 firft,

For

.

THE

fecond precept

is

more than one.

the direct confequence of the

that to like effects are to be afcribed the

inftance, that refpiration in

men and

fame

in brutes

is

caufes.

brought

about by the fame means ; that bodies defcend to the earth here in E u R o p E, and in A M E R i c A from the fame principle ; that the light of a culinary fire, and of the fun have the fame manner of production ; that the reflection of light is effected in

the earth, and in the planets by the fame

a 4. fon for

power

;

and the

like.

THE third it.

It

is

of thefe precepts has equally evident rea only, that thofe qualities, which in the fame

body can neither be leflened nor

increafed,

and which belong to

INTRODUCTION. to

all

bodies that are in our

power

to

make

trial

to be accounted the univerfal properties of

all

upon, ought bodies

what

ever.

precept is founded that method of arguing by which no progrefs could be made in na without induction, For as the qualities of bodies become tural philofophy.

IN

known

this

to us

by experiments only

we

;

have no other way of

finding the properties of fuch bodies, as are out o/ our reach to experiment upon, but by drawing conclufions from thofe

which

fall

The

under our examination.

only caution here

and experiments, we argue required upon, be numerous enough, and that due regard be paid to that occur, as the Lord BACON very judiall objections, that the obfervations

is,

ciouily directs plied with, trability

And

a .

when by

admonition

this

virtue of this rule

and extenfion

to all bodies,

is

fufficiently

we

com

afcribe

impene though we have no fen-

experiment, that afiords a direct proof of any of the cenor that the fixed ftars leftial bodies being impenetrable ; fible

are fo

much

as

For the more perfect our

extended.

inrtru-

whereby we attempt to find their vifible magni infomuch that all the fenfible tude, the lefs they appear magnitude, which we obferve in them, feems only to be an

ments

are,

;

optical deception

by the

fcattering

of their

light.

However*

fuppofe no one will imagine they are without any magni tude, though their immenfe diftance makes it undifcernable I

by

us.

After the fame manner, if <jv.

Org. Lib.

i.

it

can be proved, that

all

Ax. 105.

E

bodies

INTRODUCTION.

16'

bodies here gravitate towards the earth, in proportion to the quantity of folid matter in each ; and that the moon gravitates to the earth likewife, in

it

;

and that the

in

proportion to the quantity of matter towards the moon, and all

fea gravitates

the planets towards each other; and that the very comets have the fame gravitating faculty ; we mail have as great reafon to

conclude by other.

this rule,

For indeed

that

all

bodies gravitate towards each

this rule will

more

ftrongly hold in this

than in that of the impenetrability of bodies ; becaufe there will more inftances be had of bodies gravitating, than cafe,

of their being impenetrable.

15-.

lofophy

Te is

i

s is

that

founded

;

*

method of induction, whereon all phiwhich our author farther inforces by

this additional

precept, that whatever is collected from this induction, ought to be received, notwithftanding any conje ctural

hypothecs to the contrary, till fuch times as it mall be contradicted or limited by farther obfervations on nature.

BOOK

'i

ft

BOOK

I.

CONCERNING THE

MOTION

BODIES

of

IN GENERAL.

CHAP. Of

the

LAWS

of

AVING I

I

MOTION.

thus explained Sir

NEWTON'S method

mall now proceed to intended account of his difcove-

philofophy, ,

my ries. tifes.

ISAAC

of reafoning in

I

Thefe are contained in two treaIn one of them, the MATHEMA

TICAL PRINCIPLES OF NATURAL PHILOSO PHY,

his chief

defign

is

to

/hew by what laws the heavenly

E i

motions

28

ISA AC

Sir

BOOK!

NEWTON'S

motions are regulated ; in the other, his OPTICS, he difcourfes of the nature of light and colours, and of the action between and bodies. This fecond treatife is wholly confined to light

the fubject of light

:

end concerning other

at the except fome conjectures propofed hitherto lie more which of nature, parts

In the other

concealed.

treatife

our author was obliged to

by explaining ma for even fome of the moil nature: of a more ny things general fimple properties of matter were fcarce well eftablifhed at that fmooth the way to

time.

his principal intention,

We may therefore

reduce

Sir I

AAc

s

N E w T o N'S do

under three general heads ; and I fhall accordingly di In the firft I fhall fpeak vide my account into three books. ctrine

of what he has delivered concerning the motion of bodies, without regard to any particular fyftem of matter ; in the fe cond I fhall treat of the heavenly motions ; and the third fhall be employed upon light. a.

IN

the

firft

part of

my defign, w e r

muft begin with an

account of the general laws of motion.

THESE laws are fbme univerfal affections and proper of matter drawn from experience, which are made ufe of as axioms and evident principles in all our arguings upon the .

ties

motion of

bodies.

afTume in

their demonftrations

For

exhibiting the proof of

as it is

them

the cuftom of geometers to

fome

propofitions,

fo in

all

without

our rea-

; philofophy, foning muft be built upon fome properties of matter, firft ad mitted as principles whereon to argue. In geometry thefe ax

ioms are thus aflumed,

on account of

their beino; fo evident o as

CHAP.

make any proof

as to

no

PHILOSOPHY.

i.

in

form

properties fince

evident;

it

But in philofophy

needlefs.

of bodies can be in

this

29

manner received

has been obierved above,

that

we

for felf-

can con

clude nothing concerning matter by any rcafonings upon its nature and efTence, but that we owe all the knowledge, we

have thereof, to experience. Yet when our obfervations on matter have informed us of fome of its properties, we may fecurely reafon upon them in our farther inquiries into nature. And thefe laws of motion, of: which I am here to {peak, are

found tion Sir

fo univerfally to

known, which

ISAAC 4.

is

NEWTON

T H E firft law

is,

belong to bodies, that there is no mo not regulated by them. Thefe are by

reduced to three that

all

a ,

bodies have fuch an indifference

to reft, or motion, that if once at reft they remain

fturbed by fome power acting

upon them

:

but

fo,

if

till

di-

once put

they perfift in it ; continuing to move right for after the power, which gave the motion,

in motion,

wards perpetually, is

removed

;

and

alfo

preferving the fame degree of velocity communicated, not flopping or re

or quickness, as was

firft

mitting their courfe,

till

interrupted or otherwife difturbed by

fome new power imprefTed. y. ftate

THE fecond law of motion of any body, whether from

tion to reft,

is,

that the alteration of the

reft to

motion, or from

or from one degree of motion to another,

ways proportional

to the force impreiTed. Princip. philof.

pag-13,

mo is al

A body at reft, when

14.

atted

Sir I

30 acted

s

AAc

N E w T o N'S

BOOK

I.

to that power, moving in yields which the power applied is directed ; and or greater degree of velocity, according to

upon by any power,

the fame line,

moves with a

in lefs

the degree of the power ; fo that twice the power fhall com municate a double velocity, and three times the power a If the

threefold velocity.

body be moving, and the power

upon the body in the direction of its motion, die body fhall receive an addition to its motion, as great as the motion, into which that power would have put it from a impreffed act

(late

of

reft

;

but

if

the

power impreffed upon a moving bo its former motion, that power fhall

directly oppofite to

dy act

then take away from the body's motion, as much as in the oit would have added to it. Laftly, if the power be

ther cafe

impreffed obliquely, there will arife an oblique motion dif fering more or lefs from the former direction, according as

new impreflion is greater or lefs. For example, if the boA (in fig. I.) be moving in the direction A B, and when it is

the >*

.

74- dy

at the point A,

A C,

the

body

a

power be impre fifed upon it in the direction from henceforth neither move in its firft

fhall

direction

A B, nor

but

take a courfe as

fhall

in the direction of the adventitious

A D between them

:

and

power, if

the

impreffed be juft equal to that, which firft gave to the body its motion ; the line A D fhall pafs in the middle between A B and A C, dividing the angle under into laft

power

BAG

tw o equal parts ; but if the power laft impreffed be greater than the firft, the line AD mall incline moft to AC ; whereas r

if

the

laft

incline

impreffion be

moft to A B.

lefs

To

than the

firft,

the line

AD

fhall

be more particular, the fituation of the

CHAP.

PHILOSOPHY.

i.

31

A D is always to be determined after this manner. be die fpace, which the body would have moved certain portion of time ; through in the line A B during any that body, when at A, had received no fecond improvided likewife, that A F is the part of the line A C,

the line

AE

Let

Suppofe pulfe. through which die body would have moved during an equal had been at reft in A, when it received portion of time, if it then if from E be drawn the impulfe in the direction A C a line parallel to, or equidiftant from A C, and from F an other line parallel to AB, thofe two lines will meet in the :

line

A D.

6.

THE

third

and

laft

of thefe laws of motion

when any body ads upon upon

the other

other body

is

another,

that

is,

the action of that

body

equalled by the contrary reaction of that

upon the

firft.

THESE laws

of motion are abundantly con firmed by made from them, in relation to the motion of bodies, how complicated foever, are found to 7.

this,

that

all

the deductions

agree perfectly with obfervation. at large in the next chapter.

This

fhall

But before

be (hewn more

we

proceed to fb

chufe here to point out thofe appearan proof ; ces of bodies, whereby the laws of motion are firft fuggefted

diffufive a

I

to us.

8.

DAILY

body, which

obfervation

we once

makes

fee at reft,

it appear to never puts it

us,

that

any

felf into frefh

motion

:

Sir Is A

32

AC

NEWTON'S

motion ; but continues always by fome power applied to it.

AGA

9.

and

it,

i

whenever a body

N,

motion fome time

in that

in the

it is left

to

is

fame

once

after the

place,

BOOK!. till

in motion,

moving power

it

removed

continues

has quitted

Now if the body continue to move

it felf.

but a fingle moment, after the moving power has left it, there why it fhould ever flop without

can no reafon be afligned,

fome

For

external force.

it is

plain,

that this continuance of

caufed only by the body's having already mov ed, the fole operation of the power upon the body being the the motion

is

putting it in motion ; therefore that motion continued will equally be the caufe of its farther motion, and fo on without end.

The only doubt that can remain,

communicated continues it,

ceafes to act

decreafe.

;

And

intire,

whether

this

motion

power, that caufed

does not gradually knguifh and fufpicion cannot be removed by a tranfi-

or whether this

is,

after the

it

ent and flight obfervation on bodies, but will be fully cleared thofe more accurate proofs of the laws of motion, are to be confidered in the next chapter,

up by which 10.

L A s T L y,

bodies in motion appear to affect a ftraight

courfe without any deviation, unlefs when difturbed by fome adventitious power acting upon them. If a body be thrown perpendicularly upwards or downwards, it appears to continue in the fame ftraight line during the whole time of its motion. If a

body be thrown from the line,

viate

in

any other direction, it is found to de which it began to move, more and

in

more

CHAP.

PHILOSOPHY.

i.

33

continually towards {he earth, whither it is directed but fince, when the weight of a body does weight by not alter the direction of its motion, it always moves in

more

its

:

a ftraight

line,

declining from

without doubt in its

firft

courfe

is

this

other cafe the body's is cau-

no more, than what

As this appears at firft fight to be mail have a very diftincl: proof thereof in the next chapter, where the oblique motion of bodies will be particularly confidered.

fed by

weight alone.

its

we

unqueftionable, fo

THUS we

II.

fee

how

the

firft

of the laws of motion

But agrees with what appears to us in moving bodies. here occurs this farther confideration, that the real and abfolute

motion of any body

are our

felves

earth whereon dies to

move

our own.

alib

we

in

is

not

vifible

conftant motion

dwell

fo far only,

;

to us

along

:

for

with

we the

infomuch that we perceive bo motion is different from

as their

When

a body appears to us to lie at reft, in the motion, it has received, without continues only reality forth If we any power to change that motion. putting throw a body in the courfe or direction, wherein we are it

carried our felves

;

fo

given to the body, fo motion, it had, while if

it appeared to us to be at reft. But body the contrary way, although die body us to have received by fuch an impulfe as much

we impel

appears to

much motion as we feem to have much we have truly added to the

a

motion, as when impelled the other way ; yet in this cafe we have taken from the body fo much real motion, as we feem to have given it. Thus the motion, which we fee in bodies,

F

is

Sir I

34is

s

AAc

not their real motion, but onty relative with refpeft to us

;

and the forementioned obfervations only fhew us, that this in this relative or apparent firft law of motion has place motion. However, though we cannot make any obfervation on the abfolute motion of bodies, yet by immediately

in vifible motion, reafoning upon what we obferve difcover the properties and effects of real motion.

Ii.

WITH

now under

regard to this

confideration,

firft

we can

law of motion, which is the foregoing ob

we may from

moft truly collect, that bodies are difpofed to con tinue in the abfolute motion, which they have once received,

fervations

without increafing or diminishing their velocity.

body

appears to us to

change the motion, which

it

When

a

really preferves without has in common with our felves

lie at reft,

it

:

and when we put it into vifible motion, and we fee it conti nue that motion ; this proves, that the body retains that de gree of its abfolute motion, into which it is put by our acting if

we

upon

it

to

real motion,

its

:

give

it it

fuch an apparent motion, which adds that addition ; and if our acl:preferves

ing on the body takes off from its real motion, it continues afterwards to move with no more real motion, than we have left it.

13.

AGA

i

N,

we do not

obferve in bodies any difpofition or

power within themfelves to change the direction of their mo tion ; and if they had any fuch power, it would be difeafily

For fuppofe a body by the ftrudlure or difpofition parts, or by any other circumftancein its make, was in

covered

of its

dued

CHAP.

PHILOSOPHY.

i.

35

power of moving it felf ; this felf-moving prin fhould be thus inherent in the body, and not which ciple, on any thing external, mufl change the direction depend wherein it would ad, as often as the pofition of the body fo that for inftance, if a body was lying be was changed

duecl with a

:

fore

me

in fuch a polition,

principle difpofes the

me of

;

body

that the direction, to

wherein

this

move, was pointed directly from

then gradually turned the body about, the direction felf-moving principle would no longer be pointed di

if I

this

rectly

from me, but would turn about along with the body. which appears to us at reft, were furnim-

Now if any body,

ed with any fuch felf-moving principle ; from the body s ap muft conclude, that this felf-mov pearing without motion we ing principle lies directed the fame way as the earth is car rying the body

and fuch a body might immediately be put by turning it about in any degree,

;

into vifible motion only

that this felf-moving principle

might receive a different

di

rection.

14.

FROM

that if a

thefe confiderations

body were once abfolutely

it

very plainly follows, not being fur;

at reft

nimed with any principle, whereby it could put it felf into motion, it muft for ever continue in the fame place, till acted and alfo that when a body is put no power within it felf to make any and confequently change in the direction of that motion that the body muft move on ftraight forward without declin

upon by fomething into motion,

it

external

:

has

;

But it has before been fliewn, that ing any way whatever. bodies do not appear to have in themfelves any power to

F i

change

Sir I

36

s

AAc

N E w T o N'S

BOOK I.

this firft law change the velocity of their motion therefore of motion has been illuftrated and confirmed, as much as can be from the tranfient obfervations, which have here been dif:

upon y and eftablifhed by more courfed

iy.

-

BUT

in the next chapter all this will be farther

correct obfervations.

I /hall

now

fecond pafs to the

law of motion

;

when it is afTerted, that the velocity, with which any body is moved by the aclion of a power upon it, is pro wherein,

portional to that power ; the degree of power is fuppofed to be meafured by the greatnefs of the body, which it can move with a given celerity. So that the fenfe of this law is, that if

any body were put into motion with that degree of fwiftas to in one hour the length of a thoufand yards ; pafs

nefs,

the power, which would give the fame degree of velocity to a body twice as great, would give this lefler body twice the velocity,

caufing

it

to defcribe in the

fame fpace of an hour

two thoufand yards. But by a body twice as great as another, I do not here mean {imply of twice the bulk, but one that contains a double quantity of folid matter, 1 6.

WHY the power, which can move a body twice as great

wkh the fame degree of velocity, fliould be called twice as great as the power, which can give the lefler body the fame velocity, is evident. For if we fhould fuppofe the

as another

greater body to be divided into two equal parts, each equal to the lefler body, each of thefe halves will require the fame

degree of power to body,

as the lefler

move them with

body

it

the velocity of die lefler

felf requires

;

and therefore both thofe

CHAP.

PHILOSOPHY.

i.

or the

thofe halves,

whole greater body,

37

will require the

moving power to be doubled.

THAT

the moving power being in this fenfe doubled, 17. fhould juft double likewife the velocity of the fame body, feems near as evident, if we confider, that the effect of the

power applied muft needs be the fame, whether

that

power

be applied to the body at once, or in parts. Suppofe then the double power not applied to the body at once, but half of it firft, and afterwards the other half ; it is not conceivable for what reafon the half laft applied fhould come to have a dif ferent effect upon the body, from that which is applied firft ;

as it muft have, if the velocity of the body was not juft dou So far as experience can deter bled by the application of it, can mine, we fee nothing to favour mch a fuppofition.

We

not indeed

make

(

by reafon of the conftant motion of the earth

)

upon any body perfectly at reft, whereby to fee whether a power applied in that cafe would have a different effect, from what it has, when the body is already moving ; but we find no alteration in the effect of the fame power on trial

account of any difference there

may

be in the motion of the

The earth does not al power applied. the fame bodies with degree of velocity ; yet we ways carry find the vifible effects of any power applied to the fame bo

body,

when

the

is

dy to be at all times the very fame and a bale of goods, or other moveable body lying in a fliip is as eafily removed from place to place, while the fhip is under fail, if its morion :

be fteady,

as

when

it is

fixed at anchor.

Sir

:}8

1 8.

the

Now

whole of

this this

BOOK!

ISAAC NEWTON'S experience

is

alone fufficient to fliew to us

law of motion.

the fame power will always pro 19. S i N c E we find, that duce the fame change in the motion of any body, whether that body were before moving with a fwifrer or flower mo tion ; the change wrought in the motion of a body depends to the only on the power applied to it, without any regard and therefore the degree of motion, body's former motion which the body already pofTefTes, having no influence on the :

power applied fame power tion ot the

to difturb

its

operation,

will not only be the

body

;

but

we

fame

the effects of the

in all degrees

of

mo

have likewife no reafon to doubt,

but that a body perfectly at reft would receive from any pow er as much motion, as would be equivalent to the effect of the

fame power applied to that body already in motion. a body being at reft, any number of fhould be equal powers fucceffively applied to it ; pufhing it forward from time to time in the fame courfe or direction.

ao.

AGAIN, fuppole

Upon the application of the firft power the body would begin to move when the fecond power was applied, it appears from ;

what has been

come double;

faid,

that the

the third

motion of the body would be treble the motion of the

power would

body ; and fo on, till after the operation of the laft power the motion of the body would be as many times the motion, which the

And

firft

power gave it, as there are powers in number. number of powers will be the

the effect of this

always

fame,

CHAP. lame,

PHILOSOPHY.

i.

without any regard to the fpu

them applying

:

f

time taken up in

fo that greater or lefler intervals

between

the application of each of thefe powers will produce no dif Since therefore the alliance of ference at all in their effects.

time between the action of each power is of no confequence ; effect will ftill be the fame, though the

widiout doubt the

all be applied at the very fame inftant ; or al a though {ingle power fhould be applied equal in ftrength to the collective force of all thefe powers. Hence it plainly fol

powers fhould

lows,

that the degree of motion,

be put out of a

(late

of

reft

into

which any body

by any power,

will

will be proportio

A

nal to that power. double power will give twice the velo times the velocity, and fo on. three a treble The city, power

foregoing reafoning will equally take place, though the bo dy were not fuppofed to be at reft, when the powers began to

be applied to it ; provided the direction, in which the powers were applied, either confpired with the action of the body, or

was

directly oppofite to

it.

Therefore

if

any power be ap

and act upon the body either in plied to a moving body, the direction wherewith the body moves, fo as to accelerate the

body

;

or if

it

act directly oppofite to the

motion of the

in both thefe cafes the change of body, motion will be proportional to the power applied ; nay, the of the motion in one cafe, and the dimi fo as to retard

it

:

augmentation

will be equal to that degree of motion, into which the fame power would put the body, had it been at reft, when the power was applied.

nution thereof in the other,

i r.

FART

ii

E

Sir I

40

the effects

N E w T o N'S may

BooKL

be fo applied to a moving

motion of the body. And of fuch an oblique motion may be deduced from

as to aft

body,

A AC

a power

FARTHER,

11.

s

this obfervation

D with the

lono-

obliquely to the

;

that as all bodies are continually

earth,

we

fee that the vifible effects

power

are always the fame, in whatever direction the

acts:

and therefore the

visible effects

a-

moving

of the fame

power

of any power upon a

is appearance always body, which feems only to be at reft, the fame as the real effect would be upon a body truly at reft. Now fuppofe a body were moving along the line A B (in

to

fig. i.

)

the line

and the eye accompanied equidiftant from A B ;

CD

it

with an equal motion in

fo that

when

the

body

is

at A, the eye fhall be at C, and when the body is advanced to E in the line A B, the eye fhall be advanced to F in the line

C D,

the diftances

that here the

the line

PEG

to the eye to

A E and C F

being equal.

It

is

evident,

and ; body drawn from the eye through the body fhall feem be immoveable ; though as the body and eye will appear to the eye to be at reft

move forward together, this line fhall really alfo move ; when the body mail be advanced to H and the eye to

that

FEG

the line this line

fhall

be transferred into the fituation

fb

K,

KHL,

KHL being equidiftant from FEG. Now if the bo

dy when

E were

to receive an impulfe in the direction of while the eye is moving on from F to 1^ and carrying along with it the line FEG, the body will appear to the eye to move along this line FEG: for this is what has juft now been faid ; that while bodies are moving along with the earth, and the fpedator's eye partakes of the fame motion, the effect of any power upon the body will appear to be what

the line

at

FEG;

it

CHAP. it

would

when when

41

have been, had die body been truly at reft* power was applied. From hence it follows, that

really

the

where

PHILOSOPHY.

i.

the eye is advanced to K, the body will appear fomethen it is in the line K H L. Suppofe it appear in ;

M

from what has been premifed

manifeft,

M

paragraph, that the diftance H body would have run upon the line

this

at the beginning

of

equal to what the EG, during the time, is

wherein the eye has paffed from F to K, provided that the bo dy had been at reft, when acted upon in E. If it be farther ? asked, after what manner the body has moved from E to

M

through a ftraight line ; for it has been fhewn above in the explication of the firrt law of motion, that a mov I anfwer,

ing body, from the time

one continued

EN

XI. IF

HM

fince

body,

dy

is

will

it felf,

proceed on in

HM

be taken equal to

and

NM

N M be drawn

;

will be equidiftant

Therefore the effect of any power upon a moving that power acts obliquely to the motion of the

when is

to be

moving

come to E, line

to

equidiftant from E N,

is

from E H. body,

it is left

ftraight line.

EG,

determined in

this

manner.

along the ftraight line

AEB,

Suppofe the bo if

when

the

body

is

a power gives it an impulfe in the direction of the to find what courfe the body will afterwards take

we muft proceed thus. Take in E B any length E H, and in E G take fuch a length E N, that if the body had been at reft in E, the power applied to it would have caufed it to move over in

EN

in the

fame fpace of time, as it would have employed if the power had not acted at all upon it.

paiTmg over EH,

Then draw

HL equidiftant

from EG, and

G

NM

equidiftant

from

Sir I

42 from EB.

After

M, where

s

A Ac

this,

thefe

if

two

N E w T o N'S a line be

lines

BOOK I.

drawn from E

meet, the line

to the

EM will be the

point courfc into which the body will be put by the action of the

power upon 2.

3

fome

it

at E.

A MATHEMATICAL

.

particulars

reader

would here expert

more regular demonftrations

;

but as

I

in

do

not at prefent addrefs my felf to fuch, fo I hope, what I have now written will render my meaning evident enough to thofe,

who

are unacquainted with that kind of reafoning.

,.

Now

as

we

have been fhewing, that fome actual

of reft in neceftary either to put bodies out of a ftate to motion, or to change the motion, which they have once force

is

received

;

it is

proper here to obferve, that

this

quality in

bo

dies, whereby they prefervc their prefent ftate, with regard to motion or reft, till fome active force difturb them, is cal

iNERTiAEof matter and by this property, mat fluggim and unadlive of it felf, retains all the power imprefTed upon it, and cannot be made to ceafe from action, but led the vis

:

ter,

by the opposition of as great a power, as that which rlrft mov ed it. By the degree of this vis INERTIA E, or power of inac as we fhall henceforth call it, we tivity, primarily judge of the quantity of folid matter in each body ; for as this quality is inherent in all the bodies, upon which we can make trial,

any

we conclude it to be a property eflential to all matter and as we yet know no reafon to fuppofe, that bodies are compofed of different kinds of matter, we rather prefume, that ;

the matter of

all

bodies

is

the fame

j

and

that the degree of this

CHAP.

PHILOSOPHY.

i.

43

power of inactivity is in every body proportional to the folid matter in it. But although we have no quantity of the abfolute proof, that all the matter in the univerfe is uniform, this

and

poffeffes

we can with

this

power of inactivity

certainty

in the

fame degree; yet

compare together the

different degrees

power of inactivity in different bodies. Particularly this power is proportional to the weight of bodies, as Sir ISAAC NEWTON has demonftrated a However, notwithstanding that this power of in any body can be more certain inactivity of

this

.

ly

known, than the quantity of folid matter in it ; yet fince one is not proportional to the is no reafon to fufpect that

there

we (hall hereafter fpeak without heiitation of the quan

other,

of matter in bodies, power of inactivity.

tity

.

effects

to

we

THIS being eftablimed, we may now compare the of the fame power upon different bodies, as hither have mewn the effects of different powers upon the

fame body.

And

here

peculiar fenfe given to all

meafure of the degree of their

as the

that

is

to be faid

it

if

in

upon

we

philofophy,

this

word motion

limit the

to the

we may comprehend

head under one fhort precept

fame power, to whatever body it ways produce the fame degree of motion.

that the

is

;

applied, will al

But here motion

does not iignify the degree of celerity or velocity with which a body moves, in which fenfe only we have hitherto ufed it ;

but

it is

made

force with *

ufe of particularly in philofophy to lignify the as if two bodies A and B be-

which a body moves

Princ. Philof. L. II. prop. 24. corol. 7.

:

Sec

alfo B. II.

G

^

Ch.

5.

3. of this treatife.

ing

Sir I

44

s

AAc

N E w T o N'S

B OOK

I.

to (top A as ing in motion, twice the force would be required to ftop B, the motion of A would be efteemed double the

motion of

In

B.

moving

be diftinguifhed

fully to

;

bodies,

thefe

two

things are care

their velocity or celerity,

which

is

meafured by the fpace they pafs through during any determi nate portion of time ; and the quantity of their motion, or refiftance. the force, with which they will prefs againft any

Which

when

force,

different bodies

move with

the fame ve

in the proportional to the quantity of folid matter bodies ; but if the bodies are force is proportio equal, this nal to their refpeclive velocities, and in other cafes it is pro is

locity,

portional both to the quantity of folid matter in the body, alfo to its velocity. To inftance in two bodies A and B : if

and

A be

twice as great as B, and they have both the fame velocity, the fhall be double the motion of B ; and if the bo

motion of A

and the

dies be equal,

motion of

A

velocity of

A be

twice that of B,

mall likewife be double that of

B

;

but

if

the

A

be

twice as large as B, and move twice as fwift, the motion of A will be four times the motion of B ; and if A be twice laftly,

as

and move but half

large as B,

motion

fliall

TH

as faft,

the degree of thejr

be the fame.

the particular fenfe given to the word motion by philofophers, and in this fenfe of the word the fame pow er

is

always produces the fame quantity or degree of motion.

the fame it

i s

fhall

power

acl

upon two bodies A and

If

B, the velocities,

give to each of them, fhall be fo adjufted to the refpec-

tive bodies, that the

in each.

fame degree of motion

If A be twice as great as B,

its

be produced velocity fhall be half fhall

that

CHAP. that of

PHILOSOPHY.

i.

B

;

if

A

A

fhall

has three times as

much

folid

45

matter as B, the

be one third of the velocity of B ; and ge nerally the velocity given to A fhall bear the fame proportion to the velocity given to B, as the quantity of folid matter con

velocity

of

tained in the

body B

bears to the quantity of folid matter

con

tained in A.

THE If a

before.

reafon of

all this is

evident from what has gone B, which fhould bear

power were applied to

the fame proportion to the power applied to A, as the body B bears to A, the bodies B and A would both receive the fame velocity

;

it

and the

velocity,

which B

will receive

from

this

fame proportion to the velocity, which would receive from the action of the power applied to A, will bear the

power, as the

former of thefe powers bears to the

latter

that

:

is,

the velocity, which A receives from the power applied to it, will bear to the velocity, which B would receive from the fame power,

the fame proportion as the

body B

bears

to A.

FROM

1 8.

hence

we may now

the third pafs to

law of

where this diftinction between the velocity of a bo dy and its whole motion is farther neceflary to be regarded, as fhall immediately be fhewn ; after having firft illuftrated the

motion,

law by a familiar

meaning of

this

ther load be

drawn by

as

much

which

is

much

as

a horfe

as the horfe acts

;

If a ftone or o-

inftance.

the load re-acts

upon

the load

;

upon

the horley

for the harnefs,

between them, prefles againft the horfe ?s the load , and the progreffive motion of the againft

ftrained

horf;

ISAAC NEWTON'S

Sir

46 horfe forward

Kindred

much by

as

the load, as the motion

endeavour of the horfe that promoted by the fame the horfe put forth the ftrength, when loofened

of the load if

is,

is

BOOK!.

from the

:

is

load, he

would move himfelf forwards with

greater

fwiftnefs in proportion to the difference between the weight of his own body and the weight of himfelf and load to

gether.

19.

THIS inftance will

meaning of

cal explication let

reft,

the

afford

fome general notion of the

But to proceed to a more philofophiif a body in motion ftrike againft another at

this law. :

body

ftriking

be ever fo fmall,

yet (hall

it

com

municate fome degree of motion to the body it ftrikes againft, though the lefs that body be in comparifon of that it impin ges upon, and the lefs the velocity is, with which it moves, the fmaller will be the motion communicated. But whatever

degree of motion fhall lofe

it

gives to the refting body,

forementioned power the

two bodies

equal,

firft

j

therefore the

it is

body

evident from the time they meet, the {ingle motion of the

moved by in

motion by means of

motion

other with the fame force,

but

it

is

both the bodies are to be

inactivity retaining the

the fame

the neceffary confequence of the For fuppofe of inactivity in matter.

This

it felf.

firft

given

wherewith

it,

it

its

ftrikes

power of upon the

was acted upon

it

now

both the bodies being to be moved by that force, which before moved one only, the enfuing velocity will be the fame, as if the to one power, which was felf

:

applied

of the bodies, and put both ; whence it

it

appears,

into motion,

had been applied to

that they will proceed forwards,

with

CHAP.

PHILOSOPHY.

i.

with half the velocity, which the body that is, the body firft moved will have

firft

loft

in

47 motion had

half

:

motion,

its

have gained exactly as much. This rule the bodies after keep contiguous meeting ; as juft, provided if it were not for a certain caufe that would do, always they

and the other

will

is

and which muft now be explained. Bodies

often intervenes,

upon

ftriking againft each other,

naffer

an alteration

in their

having their parts prefled inwards by the ftroke, which for the moft part recoil again afterwards, the bodies endea figure,

vouring to recover their former fhape. This power, whereby bodies are inabled to regain their firft figure, is ufually called their elafticity, and when it acts, it forces the bodies from

each other,

and caufes them

this elafticity in

Now the effect of

to feparate.

the prefent cafe

is

fuch, that if the bodies are

fo as to recoil with as great a force as perfectly elaftic, they are bent with, that they recover their figure in the fame fpace

of time,

as has

been taken up in the alteration made in it by then this power will feparate the ;

their compreffion together

bodies as fwiftly,

on both

they before approached, and acting up upon the body firft in motion contrary to as

equally, the direction in which

in the direction

add

of

its

it

moves, and upon the other

motion,

it

will take

from the

as

much

firft,

and

of velocity fo that the power being ftrong enough to feparate them with as great a velocity, as they approached with, the firft will be quite ftopt, and that which was at reft, will receive all the motion of the to the other equal degrees

:

other.

If the bodies are elaftic in a lefs degree, the firft will

not lofe

all its

of the

firft,

motion, nor will the other acquire the motion but fall as much fhort of it, as the other retains, For.

Sir I

s

N E w T o N'S

AAc

BOOK I.

_

For of

this rule is

elafticity

never deviated from,

determines

motion

in

ty the

body

lofs in

the motion of this

that other tion, as

is

firft

(hall lofe

body

{hall

;

than half

its

veloci

in every cafe the yet

be transferred to the other,

the body always receiving by taken from the firft.

TH

though the degree

that

how much more

ftroke as

much mo

an

the cafe of a

body ftriking directly againft the reafoning here ufed is fully con and equal body firmed by experience. There are many other cafes of bodies but the mention of thefe one another impinging againft where we intend to be next the to fliall be referved go.

i

s is

at reft,

:

chapter,

more

particular

tion, than

we

and

diffufive in the proof of thefe laws

of mo

have been here.

CHAP. Farther proofs of the

IT.

LAw s

of

MoT

i

o N.

deduced the three

in the preceding chapter

HAVING from

laws of motion, delivered by our great philofopher, the moft obvious obfervations, that fuggeft them to us ;

now

intend to give more particular proofs of them, by re counting fome of the difcoveries which have been made in I

philofophy before

Sir

ISAAC NEWTON.

For

as

they were

by reafoning upon thofe laws fo the conformity of thefe difcoveries to experience makes them fo many proofs

all

collected

of the truth of the

;

principles,

from which they were derived. ^.

LET

CHAP.

PHILOSOPHY.

2,

49

LET

us begin with the fubjecl, which concluded the Although the body in motion be not equal to the body at reft, on which it ftrikes ; yet the motion after the ftroke is to be eftimated in the fame manner as above. 1.

laft

chapter.

Let A

B

(

in fig. 3

.)

be a body in motion towards another body is arrived at B, it cannot proceed

When A

lying at reft.

farther without putting

B

into

motion

and what motion

;

it

mo

gives to B, it muft lofe it felf, that the whole degree of tion of A and B together, if neither of the bodies be elaftic, mall be equal, after the meeting of the bodies, to the iingle

motion of been

A

before the ftroke.

{aid above,

it is

from what has

Therefore,

manifeft, that as foon as the

two bodies

they will move on together with a velocity, which will bear the fame proportion to the original velocity of A, as

are met,

body A

the

g.

bears to the

IF the

;

ter the ftroke,

fum of both

jdics are elaftic,

A muft

the bodies.

fo that

they mall feparate af

lofe a greater part

of

its

and

motion,

the fubfequent motion of B will be augmented by this elaftias much as the motion of is diminiflied A city, by it. The elafticity acting equally

between both the bodies,

municate to each the fame degree of motion feparate the bodies

the

;

it

that

will is,

com

it

will

by taking from the body A and adding to

body B

their tion,

different degrees of velocity, fo proportioned to refpedive quantities of matter, that the degree of mo

wherewith

gree of motion, therefore

,

A

feparates

from

wherewith B

B,

mall be equal to the de

feparates

from A.

It

follows

from A by the elafticity which the fame elafticity adds to B, the

that the velocity taken

bears to the velocity,

H

fame

Sir

ISAAC NEWTON'S

BOOK!

fame proportion, as B bears to A confequently the velocity, which the elafticity takes from A, will bear the fame propor tion to the whole velocity, wherewith this elafticity caufes the :

two bodies to feparate from each other, as the body B bears to and the velocity, which the fum of the two bodies A and B to the velocity, where bears the added to is B elafticity, ;

by

with the bodies feparate, the fame proportion, as the body A Thus is found, bears to the fum of the two bodies A and B.

how much

the elafticity takes from the velocity of A,

and

adds to the velocity of B ; provided the degree of elafticity be known, whereby to determine the whole velocity wherewith the bodies feparate from each other after the ftroke

a .

AFTER this manner is determined in every cafe the reof a body in motion ftriking againft another at reft. The fame principles will alfo determine the efTedts, when both fult

bodies are in motion.

LET two equal

y.

qual

bodies

Then

fwiftnels.

move

againft each other with e-

the force, with which each of

them

being equal when they ftrike ; each preffdirection with the fame energy, neither fliall

prefTes forwards,

ing in

its

own

furmount the other, but both be ftopt, if they be not elaftic : for if they be elaftic, they fhall from thence recover new moas don, and recede from each other, as if fwiftly they met, but more flowly , if lefs fo. In the if two bodies of ftrike unequal bignefs

they be perfedly

fame manner, each other, and a

How this

elaftic

;

their velocities be fo related,

Degree of elafticity

is

to be found by experiment, will be

againft that the velocity

fhewn below

in $ 74.

of

CHAP.

PHILOSOPHY.

2.

51

leffer body fhall exceed die velocity of the greater in the fame proportion, as the greater body exceeds the lelTer (for inftance, if one body contains twice the folid matter as the o-

of the

ther,

and moves but half

as faft)

two fuch bodies

will entire

each other's motion, and remain from the time of ly fupprefs their meeting fixed ; if, as before, they are not elaftic but, :

they are fo in the higheft degree, they fhall recede again, For this each with the fame velocity, wherewith they met.

if

elaftic

power,

as in the

preceding cafe, fhall renew their

and

both, fhall give the

fame

mo mo

prefling equally upon tion to both ; that is, fhall caufe the velocity, which die leffer body receives, to bear the fame proportion to the velocity,

tion,

which the greater leffer

:

receives,

as the greater

fo that the velocities fhall bear the

each other

after the ftroke, as before.

body bears to the fame proportion to

Therefore

if

the bodies,

perfectly elaftic, have the fum of their velocities after the ftroke equal to the fum of their velocities before the

by being ftroke, ty.

each body after the ftroke will receive its firft veloci the fame proportion will hold likewife between the

And

wherewith they go

off, though they are elaftic but only then the velocity of each will be lefs in proportion to the defect of elafticity.

velocities,

in a lefs degree

;

s.

wherewith the bodies meet, are not in the proportion here fuppofed ; but if one of the bodies, as A, has a fwifter velocity in comparifon to the velocity of the 6. I F the velocities^

then the effect of this excefs of ; velocity in the body A muft be joined to the effect now mentioned, after the manner of this following example. Let A be twice as great as B, and other

H

i

move

Sir

move with

NE

ISAAC

the fame fwiftnefs as B.

that degree of fwiftnefs,

vv

To

BOOK

N'S

I.

Here A moves with twice

which would anfwer

to the

foremen-

For A being double to B, if it moved tioned proportion. but with half the fwiftnefs, wherewith B advances, it has been

now

juft

fhewn,

that the

two bodies upon meeting would

they were not elaftic ; and if they were elaftic, that each recoil, fo as to caufe A to return with half would they the velocity, wherewith B would return. But it is evident ftop,

if

from hence, city,

if

that

B by encountring A

will

annul half

its

velo

the bodies be not elaftic; and the future motion of the

bodies will be the fame,

as

if

A had advanced

againft

B

at

with half the velocity here aftigned to it. If the bodies be elaftic, the velocity of A and B after the ftroke may be thus

reft

difcovered.

As

the

two bodies advance againft each other, is made up of the velo

the velocity, with which they meet, cities of both bodies added together. will feparate elafticity

them

again.

After die ftroke their

The

degree of

elafticity

what proportion the velocity, wherewith they muft bear to that, wherewith Divide feparate, they meet. this velocity, with which the bodies feparate into two will determine

parts,

that

one of the

fame propoition,

as

body A bears to B ; and afcribe the leffer part body A, and the greater part of the

the er

parts bear to the other the

body B.

Then

to the great velocity to the leffer take the part afcribed to A from the common

which A and B would have had after the ftroke, had not been elaftic ; and add die they part afcribed to B the fame common this means the true velocity,

velocity.

of A and

B

By

after the ftroke will

be

if

to

velocities

made known. 7, IF

CHAP. I F

7.

has laid

PHILOSOPHY.

2.

H

uYGENs the bodies are perfectly claftic, the great this rule for finding their motion after con-

down

Any ftraight line C D ( in fig. 4, y. ) being drawn, be divided in E, that CE bear the fame proportion to E D, as the fwiftnefs of A bore to the fwiftnefs of B before the Let the fame line C D be alfo divided in F, that C F ftroke.

courfe

1

.

let it

bear the fame proportion to

F D,

as the

body B bears

to the

being taken equal to F E, if the point G body falls within the line C D, both the bodies fhall recoil after the A.

Then F G

and the

ftroke,

will bear the

velocity,

wherewith the body A fhall return, velocity, wherewith B

fame proportion to the

but if the point G falls with as G C bears to G D C D, then the bodies after their concourfe fhall both proceed to move the fame way, and the velocity of A fhall bear to the velocity of B the fame proportion, that G C bears to G D, as before.

fhall return,

;

out the line

8. IF the body B had flood ftill, and received the impulfe of the other body A upon it ; the effect has been already ex And plained in the cafe, when the bodies are not elaftic.

when

the refult of their collision

is

found by

combining the effect of the elafticity with the other the fame manner as in the laft cafe.

effect, in

they are

elaftic,

9. WHEN the Hu Y GEN here s

before, 1

b

bodies are perfectly elaftic, the rule of to divide the line in E as ( fig. 6. )

CD

is

and to take E G equal to E D.

In oper. pofthum de

Motu

corpor.

ex

per-

I

b

And by

thefe points

In the above-cited place,

cuflion. prop. 9.

thus

Sir I

s

N E w T o N'S

AAc

BOOK

thus found, the motion of each body after the ftroke

is

I.

de

termined, as before. 10. IN the next place, fuppofe the bodies A and B were but A with a fwifter motion, fo

both moving the fame way, as to overtake B,

and

ftrike againft

when

cuflion or ftroke,

it.

The

of the per-

effect

the bodies arc not elaftic,

is

difcover-

ed by finding the common motion, which the two bodies would have after the ftroke, if B were at reft, and A were to with a velocity equal to the excels of the A above the velocity of B ; and by ad common velocity thus found the velocity of B.

advance againft

it

prefent velocity of

ding to

this

II* IF the bodies are

elaftic,

to be united with this other,

11.

WHEN

HuYGEN take in

it

s

a

is

to prolong

C E in the of A bears to

thus prolonged

which F G being taken equal

two bodies preceding

former

after the ftroke will

to

CD

(

is

cafes.

the bodies are perfectly elaftic,

in this cafe

as the greater velocity

after

the effect of the elafticity

as in the

the rule of

fig. 7.

)

and

to

fame proportion to E D, the lefler velocity of B ; F E, the velocities of the

be determined,

as in the

two

cafes.

Ig. THUS I have given the fum of what has been writ ten concerning the effects of percuifion, when two bodies freely in motion ftrike directly againft each other; and the refults here fet down, as the confequence of our reafoning *

In the place above -cited.

2

from

CHAP.

PHILOSOPHY.

2.

from the laws of motion, anfwer

A

mod exactly

to experience.

of experiments has been invented to make particular trial of thefe effects of percuflion with the greateft exactnefi. fet

But

muft defer thefe experiments,

I

nature of pendulums

a

I fliall

.

till I

therefore

have explained the proceed to de-

now

fome of the appearances, which are caufed

fq- ibe

in bodies

from the influence of the power of gravity united with the general laws of motion ; among which the motion of the

pendulum

will be included.

T H E moil fimple of thefe

appearances is, when bo In this cafe the body merely by their weight. increafes continually its velocity, during the whole time of its

14.

dies

fall,

fall

down

and that

in the very

fame proportion

as the

time increaf

For the power of gravity ads constantly on the body with and it has been obferved above the fame degree of ftrength es.

:

in the

firft

law of motion,

that a

body being once

in

motion

will perpetually prelerve that motion without the continuance of any external influence upon it: therefore, after a has

body

been once put in motion by the force of gravity, the body would continue that motion, though the power of gravity fhould ceafe to act any farther upon it ; but, if the power of gravity continues

ftill

to

draw the body down,

frefli

degrees

of motion muft continually be added to the body ; and the power of gravity acting at all times with the lame ftrength, equal degrees of portions of time.

motion

will

Thefe experiments

conftantly be added in equal

arc defcrihed in

THIS

Sir I

THIS

I $.

conclufion a

fhall find hereafter

fame ftrength

AAc

s

level

not indeed abfolutely true for we of the power of gravity is not :

is

at all diftances

from the center of the

lean; fenfible in

The weight of

any

earth.

bodies

is

But

which

to

diftance,

the very fame

the higheft towers or mountains, as upon the fo that in all the obfervations we can make,

upon

ground

BOOK I.

that the

,

nothing of this is in the we can convey bodies. to fenfe

N E w T o N'S

;

the forementioned proportion between the velocity of a fall it has been defcending, ob ing body and the time, in which

without any the

tains

1 6.

a

body

leaft

perceptible

FROM hence it follows, is

falls,

difference.

that the fpace, through

not proportional to the time of the

which

fall

;

for

a greater fpace will be in fame of time at the latter part of the over the pafied portion a fall, than at the beginning. Suppofe body let fall from the fince the

point

A

increafes

body

(

in fig.

tion of time

;

8

.

)

then

proceed from B to C; time of the

17.

fall

from A

velocity,

were to defcend from

I

fay,

B

in

any por were to

it

the fpace B C is greater than AB ; A to C being double the time

AC fhall be more than double of A B.

THE geometers have proved,

which bodies

to

from

fall

to B,

A

an equal portion of time

if in

Co that the

of the

its

that the fpaces, through

thus by their weight, are juft in a duplicate or two-fold proportion of the times, in which the body has

been

falling.

fall

That

is,

fame proportion to A B, ployed in falling from

if

we were

A

to C, Book

II.

D E in the which the body has im-

to take the line

as the time,

bears to the time of die Chap.

fall

5.

from

CHAP. from

PHILOSOPHY.

2.

A

to

B

;

then

AC

57

D E in

the fame proportion. through A C be twice the

will be to

In particular, if the time of the fall time of the fall through A B ; then D E will be twice

AC fall

twice

DE

through

AB

;

DE

;

;

or

AC

four times

A C had been

A B. But

thrice the time

if

A B, and

the time of the

of the

fall

through

D E would have been treble of A B, and A C treble of that is, A C would have been equal to nine times A B.

1 8. Ira body fall obliquely, it will approach the ground by (lower degrees, than when it falls perpendicularly. Suppofe two lines A B, A C in fig- 9. ) were drawn, one perpen then if a dicular, and the other oblique to the ground D E (

:

body were

to defcend in the flanting line

AC

becaufe the

;

power of gravity draws the body directly downwards, if the line A C fupporta the body from falling in that manner, it muft take off part of the effect of the power of gravity ; fb that in the time,

which would have been

fufficient for the

body to have fallen through the whole perpendicular line A B, the body fliall not have paffed in the line A C a length equal to A B confequently the line A C being longer than A B, ;

the

body mall moft

certainly take

A C, than it would down through A B.

through larly

19.

up more time

have done

THE geometers demonftrate,

in

falling

in

palling

perpendicu

that the time, in

which

defcend through the oblique ftraight line A C, bears the fame proportion to the time of its delcent through the

body

will

the perpendicular

And

in

AB,

as the

refpect to the velocity

,

line

it

fclf

AC

which the body T

bears to

AB.

will have ac-

quired

Sir I

s

AAc

N E w T o N'S

BOOK I. *

that the length of quired in the point C, they likewife prove, the time imployed in the defcent through A C fo compenfates

the diminution of the influence of gravity from the obliquity of this line, that though the force of the power of gravity on the obliquity of the line A C, yet the the is

body oppofed by time of the body's defcent mail be fo much prolonged, that the body mail acquire the very fame velocity in the point C, as it would have got at the point B by falling perpendicularly down. 10.

Ira body were

to defcend in a crooked line, the time

defcent cannot be determined in fo fimple a manner ; but the fame property, in relation to the velocity, is demon-

of

its

ftrated to take place in all cafcs:

body defcends, the

that

is,

in

whatever

line the

velocity will always be anfwerable to the

For inperpendicular height, from which the body has fell. the A were o. i ftance, fuppofe (in fig. ) hung by a body (Iring to the pin B.

the point

A

to

C

If this

body were

C perpendicularly under B,

in the arch of a circle.

let fall,

it

Then

will

till it

came

to

have moved from

the horizontal line

AD

the velocity of the body in C will be the fame, had fallen from the point D diredly down to C.

being drawn, as if

it

a I. Ira body be thrown perpendicularly upward with any force , the velocity, wherewith the body afcends, mail continually diminim, till at length it be wholly taken away; and from that time the body will begin to fall down again, and pafs over a fecond time in its defcent the line, wherein it afcended ; falling through this line with an increafing veloci in fuch a manner, that in ty every point thereof, through

which

CnAP.II which

PHILOSOPHY.

it falls, it

was ty which

have the very fame velocity, as it had in afcended and confequently fhall come

fhall

the fame place, when down into the place, at firft

59

it

;

whence it

afcended, with the veloci

firft

given to it. Thus if a body were thrown in the line A B (in fig. 1 1 ) with fuch a

perpendicularly up force, as that it fhould ftop at die point B, and there begin to fall again ; when it fhall have arrived in its defcent to any .

point as C in as that wherewith

this line

,

it

it

fhall

wherewith

it

was

have the fame velocity,

fhall there

pafled by

A

at the point

that

it

this

point

have gained firft

C

in

its

As

thrown upwards.

monftrated by the geometrical writers

afcent

and

;

great a velocity,

as

fo,

;

I

this

think,

is

it

as

dewill

by confidering only, that while the body defcends, the power of gravity muft act over again, in an invert ed order, all the influence it had on the body in its afcent ;

appear evident,

fo as to give again to the

which 11.

it

had taken away

AFTER

upwards

body the fame degrees of

velocity,

before.

the fame manner, if the

in the oblique ftraight line

CA

body were thrown from the fig. 9. )

(in

point C, with fuch a degree of velocity as juft to reach the own weight return again through the point A ; it fhall by its the fame line A C degrees, as it afcended. by

AND

laftly,

if

a body were thrown with any velocity

in a line continually incurvated upwards, the like effect will be produced upon its return to the point, whence it was

thrown. Suppofe for inftance, the body

hung

by a firing

A B.

Then

A

(

in fig. 1 1.

)

were

if this

body be impelled any

i

way,

I

60

Sir I

s

AAc

N E w T o N'S

BOOK

I.

a circle. Let it receive Rich way, it muft move in the arch of an impulfe, as {hall caufe it to move in the arch A C ; and let that the body impulfe be of fuch ftrength,

this

ried

weight

:

fhall

D,

as that

may

be car

overcome by its D, forthwith the that I here, returning from body fay come again into the point A with the fame velocity,

from

A

before

as far as

wherewith

it

began

to

its

motion

is

mo\v.

T

will be proper in this place to obferve concerning does not of power gravity, that its force upon any body of the it conti all the but that ; body fhape depend upon ..

I

the at

nues conftantly the fame without any variation in the fame body, whatever change be made in the figure of the body and :

body be divided into any number of pieces, all thofe fhall weigh juft the fame, as they did, when united pieces and if the body be of a uniform con together in one body

if

the

:

texture,

bulk.

the weight of each piece will be proportional to its This has given reafon to conclude, that the power of

upon bodies

gravity acts ter in fall

we

them.

Whence

in proportion to the quantity

it

fhould follow,

that

all

of mat

bodies muft

from equal heights in the fame fpace of time. And as evidently fee the contrary in feathers and fuch like fub-

ftances,

bodies ;

which it is

fall very flowly in comparifon of more folid reafonable to fuppofe, that fome other caufe con

make fo mariifeft a difference. This cairfe has been found by particular experiments to be the air. The experi ments for this purpofe are made thus. fet a, curs to

They

hollow

up

very

within which near the top they lodge a fea ther and fome very ponderous body, ufually a piece of gold,

tall

glafs;

this.

CHAP.

PHILOSOPHY.

2.

61

metal being the moft weighty of any body known to us. of the air contained within it, and by glafs they empty which the top of the glafs, a wire, paffes through moving they this

This

and it is al let the feather and the heavy body fall together ways found, that as the two bodies begin to defcend at the fame time, fo they accompany each other in the fall, and ;

come to the bottom at the very feme can judge. on,

it is

eye experiment can be depended that the effect of the power of gravity upon

Thus,

certain,,

each body

is

inftant, as near as the

as far as this

proportional to the quantity of folid matter, or to

power of inactivity in each body. For in the limited fenfe, which we have given above to the word motion, it has been fhewn, that the fame force gives to all bodies the fame the

degree of motion, and different forces communicate different degrees of motion proportional to the refpective powers \ In if the power of gravity were to act equally upon the and feather, upon the more iblid body, the folid body would defcend fo much flower than the feather, as to have no great er degree of motion than the feather but as both bodies de

this cafe,

:

fcend with equal fwiftnefs, the degree of motion in the folid body is greater than in the feather, bearing the fame propor tion to

it,

as

the quantity of matter in the folid body to the

Therefore the effect of quantity of matter in the feather. is greater than on the feather, in pro gravity on the folid body portion to the greater degree of motion communicated ; that is,

the

the effect of the

power of

fame proportion to a

Chap.

I.

its

gravity

effect

on the

on the

folid

feather,

25, 26, 27, compared with

r I

5,

<.

o

.

body

as the

bears

quanti-

NEWTON'S

AC

Sir Is A

6-2

BOOK!.

bears to the quantity of matter ty of matter in the folid body in the feather. Thus it is the proper deduction from this expe

riment, that the power of gravity ads not on the furface of bo bodies themfelves moft intimately, dies only, but penetrates the

and operates

alike

on every

particle

of matter in them.

with which the bodies

as the great quicknefs,

fall,

But

leaves

it

defcend abfolutely in fomething uncertain, whether they do the fame time, or only fo nearly together, that the difference in their fwift

perty of the

from

this

motion

experiment,

whofe motion

become on

is

fuch,

not difcernable to the eye ; this pro which has here been deduced

gravity, is

now

laid

a

;

down

confirmed by pendulums, minute difference would

farther

that a very

This will be farther difcourfed

fufficiently fenfible.

in another place

ciple

is

power of

but here

fhall

I

make

to explain the nature

ufe of the prin is called

of what

the center of gravity in bodies.

.

THE

center of gravity

is

that point,

by which

if

a

In body be fufpended, it /hall hang at reft in any fituation. a globe of a uniform texture the center of is the fame gravity

with the center of the globe ; for as the parts of the globe on every fide of its center are {imilarly difpofed, and the power of gravity acts alike on every part ; it is evident, that the parts of the globe on each fide of the center are drawn with force,

and therefore neither

fide can

yield to the other

;

the globe, if fupported at its center, muft of necefTity at reft. In like manner, if two equal bodies A and B 4

BookU. Chap.

5.

3.

equal but

hang (

in

CHAP.

PHILOSOPHY.

2.

1 3 ) be hung at the extremities of an inflexible f od C D which fhould have no weight ; thefe bodies, if the rod be at its middle E, fhall equiponderate y and the rod fupported For the bodies being equal and at remain without motion. the fame diftance from the point of fupport E> the power of .

fig.

$

-

gravity will act

upon each with equal

ftrength,

and

in all re-

under the fame circumftances ; therefore the weight of one cannot overcome the weight of the other. The weight fpecls

of A can no more furmount the weight of B, than the weight of B can furmount the weight of A. Again, fuppofe a bo in the form of a a texture as of uniform A B (in fig. 14.) dy roller,

or as

it is

more

ufually called a cylinder,

lying hori

If a ftraight line be drawn between C and D, the centers of the extreme circles of this cylinder ; and if this ftraight line, commonly called the axis of the cylinder, be divided into two equal parts in E : this point E will be the zontally.

The cylinder being a uni center of gravity of the cylinder. form figure, the parts on each fide the point E are equal, and fituated in a perfectly fimilar manner ; therefore this cylin der,

fupported at the point E, muft hang at reft, for the as the inflexible rod above-mentioned will remain

if

fame reafon

when fufpended its middle point. And that the force applied to the pcint E, which uphold the cylinder, muft be equal to the cylinder's

without motion, it is

would weight.

CD

Now

fuppofe two cylinders of equal thicknels AB fo that the two axis's

to be joined together at C B, F, and F G lie in one ftraight line.

r.nd

E

at

evident,

Let the

axis

E F be di two

vided into two equal parts at H, and the axis F G into

equal

*.-

Sir I

64.

equal parts at

upheld

at reft

s

Then

I.

by a

NEwTo

AAc

BOOK L

N'S

A B would

becaufe the cylinder

power applied

in

H

be

equal to the weight of

CD

would likewife be upheld cylinder, and the cylinder in I equal to the weight of this cylinder ; a by power applied die whole cylinder A D will be fupported by thefe two powers but the whole cylinder may likewife be fupported by a power this

:

applied to K, the middle point of the whole axis EG, provided that power be equal to the weight of the whole cylinder. It is evident therefore, that this power applied in K will produce the fame effect, as the is

two other powers applied

farther to be obferved,

that

HK

is

in

H and

equal to half

F G,

I.

It

and

K I equal to half E F ; for E K being equal to half E G, and E H muft be equal to half equal to half E F, the remainder the remainder F G ; fo likewife G K being equal to half G E, and G I equal to half G F, the remainder I K mull be equal to half the remainder E F. It follows therefore, that H K bears

HK

K I,

the fame proportion to

as

FG

bears to

E F.

Beiides,

I

my readers will perceive, and it is demonftrated in form by the geometers, that the whole body of the cylinder C bears the fame proportion to the whole of the believe,

D

linder it

body

A B,

as the axis

that in the

follows,

power applied applied at

F G bears to the

I,

at

as

ftrong

I,

enough

a

bears to

K H.

Now

fuppofe two firings

upwards, one from the point and to be laid hold on by two to hold

1

cy

But hence

.

at H and I, the fame proportion to the power

HL and I M extended other from

EF

two powers applied

H bears the

KI

axis

up the

cylinder

Sec Euclid's Element--, Boo': XII.

A B, and

H

and the

powers, one the other of

prop. 13.

ftrength

CHAP.2.

PHILOSOPHY.

to fupport the cylinder flrength fufficient

C D.

Here as thefe

two powers uphold the whole cylinder, and therefore pro duce an effedl, equal to what would have been produced by a power applied to the point

K of fufficient force to fuflain

the

manifefl, that if the cylinder be taken axis only being left, and from the point K a firing, the away, as K Nj be extended, which (hall be drawn down by a power

whole cylinder

:

it is

of the cylinder, this power fhall at equivalent to the weight two other the powers, as much as the cylinder afted againfl againft

upon But

them ; and confequently thefe three powers fhall be and hold the axis H I fixed between them.

a balance,

if thefe three

two powers applied

powers preferve a mutual balance, to the firings

HL

and

I

M

the

are a balance

the power applied to the firing H L bearing ; the fame proportion to the power applied to the firing I M, Hence it far as the diflance I K bears to the diflance K H.

to each other

ther appears,

that if an inflexible rod

AB

(in

fig. 15*.)

be

C

not in the middle thereof; and if fulpended by any point at A the end of the morter arm be hung a weight, and at B the end of die longer arm be alfo hung a weight lefs than and that the greater of thefe weights bears to the

the other,

as the longer arm of the rod bears then thefe two weights will equiponderate : for a power applied at C equal to both thefe weights will fup port without motion the rod thus charged; fince here no thing is changed from the preceding cafe but the fitua-

lefler the

fame proportion,

to the fhorter;

tion of the powers,

ry fides

of the

line,

which are now placed on the contra which they are fixed. Alfo for the

to

K

fame

66

Sir I

s

AAc

N E w T o N'S

BOOK

I.

reafon, if two weights A and B ( in fig. 1 6. ) were con nected together by an inflexible rod C D, drawn from C the center of gravity of A to D the center of gravity of B ; and

fame

the rod C D were to be fo divided in E, that the part D E bear the fame proportion to the other part C E, as the weight A bears to the weight B then this rod being fupported at E

if

:

uphold the weights, and keep them at reft without mo tion. This point E, by which the two bodies A and B will be

will

fupported, is called their common center of gravity. And if a greater number of bodies were joined together, the point, by which they could all be fupported, is called the common center

of gravity of them

all.

Suppofe ( in

fig.

17.) there were three

bodies A, B, C, whofe refpe6live centers of gravity were joined by the three lines D E, D F, E F the line D E being fo divided :

A

;

G

and B

is

;

DG

bear the fame proportion to G E, as B bears to the center of gravity common to the two bodies A

in G, that

that

is,

prefied as if if

a

power equal

to the weight of both the bo

G would

fupport them, and the point G is two weights A and B, as it would be, they were both hung together at that point. Therefore, a line be drawn from G to F, and divided in H, fo that G H

dies applied to

much by

the

proportion to H F, as the weight C bears to both the weights A and B, the point H will be the common center of of all the three weights ; for H would be gravity bear the fame

their

common center

werC hung together

of gravity,

if both the weights A and B and the point G is prelTed as much fituation, as it would be in that cafe.

at G,

their prefent by them in manner from the fame In the

common

center of thefe three weights.

CHAP.

PHILOSOPHY.

2.

67

weights, you might proceed to find the common center, if a fourth weight were added, and by a gradual progrefs might find the

common

center of gravity belonging to any

number

of weights whatever. .

As all this

tion laid

down

die obvious confequence of the propoficommon center of gravity of by the fame propofition the center of gra

is

for ailigning the

any two weights, vity of all figures

In a triangle,

found.

is

as

A B C (in

the center of gravity lies in the line drawn from the middle point of any one of the fides to the oppofite angle, as the line B D is drawn from D the middle of the line A C to 1 8. )

fig.

a

the oppofite angle B ; fo that if from the middle of either of the other fides, as from the point E in the fide A B, a line

be drawn, as

E C,

this line crofles the

vity

of the triangle

to the oppofite angle ; the point F, where other line B D, will be the center of gra b

Likewife

.

DF

is

equal to half F B, and

c

In a hemifphere, E F equal to half F C the center of the bafe the line if from .

D

and

as.

ABC

(

fig.

19.)

DB

be erected per line be fo divided in E, that

pendicular to that bafe, DE be equal to three fifths of B E, the point d . gravity of the hemifphere this

E

is

the center of

I T will be of ufe to obferve concerning the center of of bodies ; that fince a power applied to this center gravity alone can fupport a body againft the power of gravity , and a

Archimed de aequipond. prop. .

b Jbid. prop. e

!

1 1

.

prop. i. d

2.

Lucas Valerius

De

Idem L.

IJ. prop. 2.

ccntr. gravit. folid. L. I.

K

^

hold

68

Sir

hold

ISAAC NEWTON'S

it

fixed at reft

is

the fame,

;

BOOK!.

power of gravity on a whole power were to exert itfelf

the effed of the

as if that

body on the center of gravity only. Whence it follows, that, when the power of gravity a&s on a body fufpended by any point, if the body is fo fufpended, that the center of gravity of the will give motion to body can defcend ; the power of gravity that body,

otherwife not

:

or if a

number of

when any one

conne&ed

bodies are fb

put into motion, together, that, their of the manner fhall, being joined, receive by fuch motion, as fhall keep their common center of gravity at is

the reft

then the power of gravity fhall not be able to produce in thefe bodies, but in all other cafes it will. motion any Thus, if the body A B (in fig. 10, x I ) whofe center of gra vity is C, be hung on the point A, and the center C be per pendicularly under A (as in fig. 10. ) the weight of the bo dy will hold it ftill without motion, becaufe the center C reft

;

.

But if the body be removed in where the center C is not perpendi

cannot defcend. any lower. to any other fituation,

in the body by its fig. 11. ) cularly under A ( as weight will be put into motion towards the perpendicular fituation of its

center of gravity.

Alfo if two bodies A,

joined together by the rod tion,

and be fupported

center of gravity

CD

at the

common

lying in

point

to the

E>

two

B

(in

fig.

if this

bodies,

of the rod

CD defcending,

in

which the

be

fitua

point be the their

not put them into motion ; but if this point E common center of gravity, the bodies will move will

n.)

an horizontal

is

;

common

weight not their that part

center of

gravity is found. So in like manner, if thefe two bodies were connected together by any more complex contrivance ; yet if

CHAP. if

2.

PHILOSOPHY.

one of the bodies cannot move without

common

that their

other,

69

fo

moving the

center of gravity {hall

weight of the bodies will not put them in motion, it

the

reft,

otherwife

will.

ISHALL proceed in

18.

chanical powers. contrived for the

the next place to fpeak of the

me

Thefe are certain inftruments or machines, moving great weights with fmall force ; and

their effects are all deducible

from the obfervation

we have

They are ufually reckoned in number the lever, the wheel and axis, the pulley, the wedge,

juft been making. five

;

As plane. thefe inftruments have been of very ancient ufe, fb the cele feems to have been the firft, who difbrated and the fcrew ; to which fome add the inclined

ARCHIMEDES

covered the true reafon of their collected

from what

is

effects.

This,

related of him, that

I

think,

fbme

may be

expre/Iions,

which he ufed to denote the unlimited force of thefe in ftruments, were received as very extraordinary paradoxes-: whereas to thofe, who had underftood the caufe of their great force,

no

expreflions of that kind could have appeared

furprizing.

19. ALL the effects of thefe powers may be judged of by one rule, that, when two weights are applied to any of

this

thefe inftruments, the weights will equiponderate,

put into motion,

if,

when

their velocities will be reciprocally propor

And what is faid of weights, of any other forces be underftood neceility equally

tional to their refpedive weights.

muft of

equi-

Sir

70

ISAAC NEWTON'S

equivalent to weights, ftream of water, or the

BOOK!

fuch as the force of a man's arm, a like.

the meaning of this rule, the 30. BUT to comprehend be underftood by reciprocal to is reader muft know, what

proportion ftiruftly

;

as I

which can

;

I fhall

now endeavour

for I fhall

to explain, as di-

be obliged very frequently to

When any two things are fo rekted, fame proportion as the other, they are So if any number of men can perform directly proportional. in a determined fpace of time a certain quantity of any work, and twice the num fuppofe drain a fifh-pond, or the like make

that

ufe of this term.

one

increafes in the

;

men

can perform twice the quantity of the fame work, in the fame time ; and three times the number of men can ber of

perform

as

foon thrice the

work

;

here the

number of men

On and the quantity of the work are directly proportional. the other hand, when two things are fo related, that one decrcafes in the

fame proportion,

as the other increafes,

they

Thus if twice the fame work in half the time,

are faid to be reciprocally proportional.

number of men can perform the and three times the number of men can finifh the fame third part of the time then the number of men and

in a

;

the

We

time are reciprocally proportional. fhewed above a how to find the common center of gravity of two bodies, there the diftances of that vity

common

center from the centers of gra

of the two bodies are reciprocally proportional to the

fpective bodies.

For

CE

in fig. j 6. being in the

re-

fame pro-

*

25-

portion

CHAP.

PHILOSOPHY.

2. to

portion

proportion

B

ED,

as

than

ED,

A

bears to as

A

CE

;

is lefs

in

is

fo

7

much

1

greater in

proportion than B.

Now

this being underftood, the reafon of the rule gl. For if thefe two bodies were here ftated will eafily appear. put in motion, while the point E refted, the velocity, where

with

A would move, would

velocity,

bear the lame proportion to the as E C bears to E D. The

wherewith B would move,

velocity therefore of each body,

when

the

common

center

of gravity refts, is reciprocally proportional to the body. But we have fhewn above a that if two bodies are fo connected to ,

that the putting them in motion will not move their common center of gravity ; the weight of thofe bodies will Therefore in any of thefe not produce in them any motion.

gether,

mechanical engines,

if,

when

the bodies are put into motion,

their velocities are reciprocally proportional to their refpedive

weights,

main

whereby the

at reft

;

common

center of gravity

would

re

the bodies will not receive any motion from their

But this perhaps weight, that is, they will equiponderate. will be yet more clearly conceived by the particular defcription of each mechanical power.

31.

THE lever was firft named above.

This

is

a bar

made

The bar is ap and move great weights. one part to fome ftrong fupport ; as the bar A B ( in

ufe of to fuftain plied in fig.

13,

14..)

is

applied at the point

C

to the fupport D.

In

fome other

be part of the bar, as E, is applied the weight to fuftained or moved ; and in a third ano is place, asp, applied ther weight or equivalent force, which is to fuftain or move 27.

the

ISAAC

Sir

72

Now here,

the weight at E.

N2w if,

i

when

o N'S the ICVCT

houid be

and turned upon the point C, the oucity, wherewith the point F would move, bears the fame propor tion to the velocity, wherewith the point E would move, as the weight at E bears to the weight or force at F ; then the put in motion,

,

lever thus charged will have no propenfity to move either If the weight or other force at F be not fo great as to way.

bear

but

this

proportion,

if the force at

be furmountecL

above

on

a

when

,

the weight at

the forces at

different fides

E

will not be fuftained

E and F

of the fupport D.

ly manifeft in the other cafe,

are placed It will

F

;

1 3 .)

by continuing the bar B C in

CG

be equal

to the

power power at F were removed, the two G and E would counterpoize each other, as in if the

for then,

weights at the former cafe

be

(as in fig.

appear alfo equal

the other fide of the fig. 14. on fupport D, till to C F, and by hanging at G a weight equivalent at

;

greater than this, the weight at E will This is evident from what has been {aid

F be

and

evident, that the point F will up by the weight at G with the fame degree of as by the other power applied to F ; fince, if the :

it

is

lifted

force,

weight at E were removed, that at

CF

G would

a weight hung at

balance the lever,

F equal

the diftances

CG

to

and

being equal.

I F the two weights, or other powers, applied to the do not counterbalance each other ; a third power may be applied in any place propofed of the lever, which fhall

33.

lever

*

Pag. 65, 68.

hold

CHAP.

PHILOSOPHY.

2.

hold the whole in a juft counterpoize. Suppofe ( in fig.i 5-.) the two powers at E and F did not equiponderate, and it were a third power to the point G, that required to apply might be Find what power in F would fufficient to balance the lever. juft

counterbalance the power in

between

this

power and

E

then

;

which

the difference

if

actually applied at F, bear the fame proportion to the third power to be applied at bears to the lever will be coun ; G, as the diftance that,

CG

is

CF

terpoized by the help of this third power, as to act the fame way with the power in F, is

if

it

be fo applied

when that power

too fmall to counterbalance the power in E

;

but other-

wife the power in G muft be fo applied, as to act againft the power in F. In like manner, if a lever were charged with three, or any greater number of weights or other powers, which did not counterpoize each other, another power might be applied in any place propofed, which fhould bring the whole to a juft

And what

balance.

powers,

may

is

here faid concerning a plurality of

be equally applied to

all

the following cafes.

34. IF the lever fhould confift of two arms making an angle at the point

C

plied perpendicularly

(

as in fig.

16.} yet if the forces are ap the fame proportion will

to each arm,

hold between the forces applied, and the diftances of the cen

from the points to which they ter, whereon the lever refts, are applied. That is, the weight at E \vill be to the force in F in the fame proportion, as C F bears to C E. 3 j\

BUT

whenever the

liquely to the arm, to

forces applied to the lever act

which they

L

are applied

(

as in fig.

ob

17. ) then

Sir I

74.

s

N E w T o N'S

AAc

BOOK L

then the ftrength of the forces is to be eftimated by lines let fall from the center of the lever to the directions, wherein the

To

forces acl.

other force at

F

the weight or fig. i7> fame proportion to the weight

balance the levers in will bear the

at E, as the diftance

CE

bears to

CG

the perpendicular let

fall

from the point C upon the line, which denotes the direction for here, if the lever be wherein the force applied to F ads into motion, the power applied to F will begin to move in :

put

the direction of die line F G

;

and therefore

its firft

motion

will

be the fame, as the motion of the point G.

WHEN two weights hang upon a lever, and the point, the lever is fupported, is placed in the middle be which by tween the two weights, that the arms of the lever are both .

of equal length ; then this lever is particularly called a ba lance ; and equal weights equiponderate as in common fcalesWhen the point of fupport is not equally diftant from both weights, called

is

it i\

conftitutes that inftrument for weighing,

fteelyard.

Though both

fteelyard, the point, in the ally placed juft

hold the weights,

in

common

fcales,

which and the

on which the beam fame

ftraight line

but rather a

little

is hung, is not ufuwith the points, that

above

(

as in

fig,

18.

)

drawn from the point C, whereon the beam iufpended, to the points E and F, on which the weights are If the hung, do not make abfolutely one continued line. where the

lines

three points E, C,

and F were in one Straight line, thofe weights,

which equiponderated, when the beam hung horizontally, would alio equiponderate in any other Situation. But we fee in thefc inftruments,

when

they are charged with weights,

which

I.

':

Jfl

<>;*

r/;,.

.

M

.

CHAP.

PHILOSOPHY.

2.

which equiponderate with the beam hanging horizontally ; that, if the beam be inclined either way, the weight moft elevated furmounts the other, and defcends, caufing the beam to fwing,

This

till

by degrees it recovers its horizontal from the forementioned ftrudlure

effect arifes

inftruments are

this ftructure thefe

le\ ers

poiition. :

for by

compofed of two

which make an angle at the point of fupport ( as in 19, 30.) the firft of which reprefents the cafe of the

arms, fig.

common

balance,

the

where C E and

the fecond the cafe of the fteelyard.

CF

are equal

In

equal weights hung the points E and F are in an horizontal fituation. Suppofe the lines E G and F H to be perpendicular to the horizon, then they will denote the di

at

firft,

E and F

rections,

will equiponderate

,

when

,

wherein the forces applied to E and F act. There between the weights at E and F, which

fore the proportion

are to be judged of by perpendiculars, from C upon EG and FH fo that the the lines muft be C C K, I, weights being equal, equal alfo, But I believe my readers when the weights equiponderate. fhall equiponderate,

as

CI,

CK,

let fall

will eafily fee,

C I and C K

:

CE

that fince

will be equal,

and

when

CF

are equal, the lines

the points

E and F

are

ho

rizontally fituated.

57fig.

I F this lever

weigh the E,

be

fet

into

any other poiition

31.) then the weight, which other.

Here,

the perpendicular

fore the weights

CK

is

raifed

higheft,

(

as in

will out

the point F be raifed higher than will be longer tha'n C I and there if

would equiponderate, L 1

:

if

the weight at F

were

Sir I were

lefs

s

N E w T o N'S

AAc

than the weight at E.

to that atE

;

therefore

is

BOOK

But the weight

than greater,

is

neceflary

at

F

is

I.

equal

to counter

balance the weight at E , and confequently will outweigh and draw the beam of the lever down.

it,

I N like manner in the cafe of the fteelyard ( fig.g l. ) 3 8. the weights at E and F are fo proportioned, as to equipon derate, when the points E and F are horizontally fituated ; then in any other fituation of this lever the weight, which is

if

That is, if in the hori raifed higheft, will preponderate. zontal fituation of the points E and F the weight at F bears the fame proportion to the weight at E, as C I bears to C K ; then, if the point F be raifed higher than E ( as in fig. 31.) the weight at F fhall bear a greater proportion to the weight

atE, than ClbearstoCK. 39. FARTHER a lever may be hung upon an axis, and then the two arms of the lever need not be continuous, but where fixed to different parts of this axis ; as in fig. 3 3 ,

the axis

AB

this axis

one arm of the lever

is

fupported by

at the point D.

two

its

Now here,

extremities

A and B.

To

fixed at the point C, the other if a weight be hung at E, the

is

extremity of that arm, which is fixed to the axis at the point C ; and another weight be hung at F, the extremity of the arm, which is fixed on the axis at D ; then thefe weights will equiponderate, when the weight at proportion to the weight at F, as the

E bears the fame arm DF bears to

CE.

4' THIS

CHAP.

PHILOSOPHY.

2.

THIS

4.0.

and

to the axis, in the

the cafe,

is

fame plane

lie

if

as the

(

77

both the arms are perpendicular

geometers exprefs them Hives ) arms are fo fix

or, in other words, if the

;

ed perpendicularly upon the

axis,

that,

when one of them

the other (hall alfo be horizontal.

If ei horizontally, ther arm (land not perpendicular to the axis; then, in de termining the proportion between the weights, inftead of the lies

length of that arm, you muft ufc the perpendicular let fall upon the axis from the extremity of that arm. If the arms are not fo fixed as to become horizontal , at the fame time ; the is

method of

affigning the proportion between the weights

analogous to that made ufe of above in

an angle

FROM

4.1.

fy to

at the

make

wheel and

whereon they

point,

this cafe

of the lever

levers,

which make

are fup ported.

hung on an

axis, it

THIS

inftrument

is

a wheel fixed

on a

being fupported at each extremity fo round freely with the wheel, in the manner

two

ea-

the

axis.

roller

fig. 3

is

a tranfition to another mechanical power,

4, where

fupports.

AB

is

the wheel,

Now

CD

roller,

as

to

the

turn

reprefented in the roller, and E F its

fuppofe a weight

G hung

by a cord

wound round the roller, and another weight H hung by a cord wound about the wheel the that thefe contrary way :

weights

may

fupport each other, the weight

lame proportion to ler bears to the

t'ie

weight G,

H

muft bear the

as the thicknefs

of the rol

diameter of the wheel

SUPPO

AC

Sir Is A

78 43

.

SUPPOSE

dle of the roller

BOOK!

NEWTON'S

drawn through the mid and from the place of the roller, where

the line k I to be

;

the cord, on which the weight roller, as at ;//, let the line

G

begins to leave the

hangs,

mn be drawn perpendicularly to

/J/;

where the cord holding the weight

and from the point,

H begins to leave the wheel, as

at 0,

let

the line

mn

and

op be drawn lines of

This being done, the two arms of a lever fixed on the reprefent two

perpendicular to kl.

H

confequently the weight

will bear to the

mn

mn

weight

G

axis

&/;

the fame

the fame

bears bears to op. But pro to as the thicknefs of the roller bears to the dia portion ofy n is half the thicknefs of the roller, meter of the wheel ; for

proportion, as

m

and of half the diameter of the wheel. 44. round,

I F

the wheel be put into motion, and turned once on which the weight G hangs, be

that the cord,

wound once more round

the axis; then at the fame time the

whereon the weight H hangs, will be wound off from Therefore the velocity of the weight the wheel one circuit. cord,

G H,

fame proportion to the velocity of the weight circumference of the roller to the circumference of

will bear the as the

the wheel.

But the circumference of the

roller bears the

fame

proportion to the circumference of the wheel, as the thick nefs of the roller bears to the diameter of the wheel, confe quently the velocity of the weight G bears to the velocity of the weight the fame proportion, as the thicknefs of

H

the roller bears to the diameter of the wheel, which is the proportion that the weight H bears to the weight G. There fore as before in the lever,

fo here alfo the general rule laid

down

CHAP. down

PHILOSOPHY.

2.

above

is

verified, that the

would be

their velocities

79

weights equiponderate,

when

proportional to their

reciprocally

refpe&ive weights. I

45-.

N

like

on the fame

if

manner,

axis

two wheels of dif

and a weight hung on each ; the weights will equiponderate, if the weight hung on the greater wheel bear the lame proportion to the weight hung ferent fizes are fixed

on the

as the

leflcr,

(as in fig. 55-.)

diameter of the

letter

wheel bears to the

diameter of the greater. I

4,6.

T

is

ufual to join

many

wheels together in the fame

frame, which by the means of certain teeth, formed in the cir cumference of each wheel, {hall communicate motion to each other.

A machine of this nature a winch,

ed with

teeth,'

EF I,

fixed

which

on the fhall

is

reprefented in

fig. 3

6~.

Here

upon which is fixed a finall wheel D indent which move in the like teeth of a larger O wheel

A B C is

axis

move

MN.

on the

axis

which

after the

G H.

Let

in like

manner

Let

this axis

fame manner

P Q^ fixed on the

roller

carry another wheel wheel K L fixed

a greater

carry another fmall wheel O, turn about a larger wheel

fhall

R S, on which

that holds a weight, as T. tween the weight and a

T

this axis

a cord fhall be

Now the proportion power applied

to the

wound,

required be

winch

at

A

fumcient to fupport the weight, will moft eafily be eftimated, by computing the proportion, which the velocity of the point

A would bear to the velocity of the weight. If the winch be turned round, the point A will defcribe a circle a A V. Suppofe the wheel E F to have ten times the number of teeth, as the

So

Sir

the wheel

D;

ISAAC NEWTON'S

then the winch muft

round. carry the wheel E F once times the number of teeth, as I, ten times to carry the whtel quently the winch A BC mi to turn the

wheel

XL

'

If

<rn :

round ten times to

wheel K .el I

t]

has alfo ten

;

and confe-

-und an hundred times

n

once round.

L

muft turn round

round

'

BOOK!.

Lailly,

if

the wheel PQ^

wheel O, the winch muft turn about one thoufand times in order to turn the wheel PQj or the roller R S once round. Therefore here the point has ten times the

A muft

number of

have gone over the

teeth, as the

circle

AV

a thoufand times, in or

the weight T through a fpace equal to the circum whence it follows, that the power ference of the roller R S

der to

lift

:

applied

at

A

will balance the

weight T,

if

it

bear the fame

of the roller to one proportion to it, as the circumference ouirmd times the circle A V ; or the fame proportion as half the thicknefs of the roller bears to one thoufand times A B. Let 47. I SHALL now explain the effect of the pulley. Here it is evi a weight hang by a pulley, as in fig. g 7. dent, that the power A. by which the weight B is fupported,

muft be equal to the weight ; for the cord C D is equally ftrained between them and if the weight B move, the power A muft move with equal velocity. The pulley E has no other ;

effect,

than

than to permit the power A to act in another direction, muft have done, if it had been directly applied to fupport

it

the weight without the intervention of any fuch inftrument.

4,8.

AGAIN,

let

where the weight A

is

a weight be fupported, as in fig. 38; fixed to the pulley B, and the cord, by

which

CHAP:

PHILOSOPHY.

si

81

which the weight is upheld, is annexed by one extremity to a hook C> and at the other end is held by the power D. Here the weight is fupported by a cord doubled ; infomuch that although the cord were not ftrong enough to hold the weight If the thus doubled it might fupport it. fingle, yet being

end of the cord held by the power D were hung on the hook C, as well as the other end ; then, when both ends of the cord were

tied to the

hook,

it

is

evident,

that the

hook would

bear the whole weight ; and each end of the firing would bear againft die hook with die force of half the weight only, feeing both ends together bear with the force of the whole.

Hence

it is

evident, that,

the weight, the force,

when

which

power D holds one end of muft exert to fupport the

the

it

weight, muft be equal to juft half the weight. And the fame proportion between the weight and power might be collect ed from comparing the refpeclive velocities, with which they would move ; for it is evident, that the power muft move

through a {pace equal to twice the diftance of the pulley from the hook, in order to lift the pulley up to the hook. 4.9.

IT

is

when many

equally eaiy to eftimate the effecl,

combined together, as in of which the under fct of pulleys pulleys are

fig. 3 ,

9,

40

;

in the firft

and confequently the

held by fix firings ; and in the latter figure by five: therefore in the firft of thefe figures the to power fupport the weight, muft be one fixth part only of the weight, and in

weight

is

the latter figure the

power muft be one

M

fifth

part.

o.

THERE

THERE by

ISAAC NEWTON'S

Sir

82

are

which

pulleys,

BOOK I.

two other ways of fupporting a weight

I {hall

particularly

confider.

O N E of thefe ways is reprefented in fig. 41. Here the j- 1 weight being connected to the pulley B, a power equal to .

half the weight

mediately to

fupport the pulley C, if applied im Therefore the pulley C is drawn down

A would

it.

But if the pulley D with a force equal to half the weight A. half the force, with to be immediately fupported by

were

which the pulley C the pulley

C

is

drawn down,

this pulley

D

fo that if the

D will uphold

be upheld with a force

pulley equal to one fourth part of the weight A, that force will fup But, for the fame reafon as before, if the port the weight. power in E be equal to half the force neceffary to uphold the ;

pulley D ; this pulley, and confequently the weight A, will be upheld therefore, if the power in E be one eighth part of the weight A, it will fupport the weight. :

yi.

ANOTHER way

reprefented in fig.

of applying pulleys to a weight is explain the effect of pulleys thus

To

41.

applied, it will be proper to confider different weights hang ing, as in fig.4 3. Here, if the pov/er and weights balance each other, the power A is equal to the weight B ; the C is

weight

equal to twice the power A, or the weight B ; and for the fame reafon the weight D is equal to twice the weight C, or equal to four times the power A. It is evident therefore, that all the three weights B, C,

D

together are equal to feven times the

power A. But if thefe three weights were joined in one, they would produce the cafe of fig. 40 fo that in that figure the :

weight

PHILOSOPHY.

CHAP.2.

where there are three

weight A,

power

B. If theie

had been but two

pulleys, pulleys,

83

feveri

is

times the

the weight would there had ben four

have been three times the power ; and if the weight would have been fifteen times the power. pulleys,

THE

5-3.

this

is

is

The form

next to be confidcred.

fufficiently

(as in fig.

any weight will

wedge

inftrument

When

known.

it is

of

put under

44.) the force, with which the wedge

the weight, when drove under it by a blow upon the B, will bear the fame proportion to the force, where

lift

end A

with the blow would aft on the weight,

if

directly applied to

as the velocity, which the wedge receives from the blow, ; bears to the velocity, wherewith the weight is lifted by the

it

wedge. 5-4.

THE

fcrew

is

two ways of applying into a hole,

as in

the fifth mechanical power. inftrument. Sometimes it

this

fig. 4,5-,

where the fcrew

AB

There are is

fcrewed

is

fcrewed

Sometimes the fcrew through the plank C D. applied to where the thred of the the teeth of a wheel, as in fig. 4,6', is.

fcrew

AB

cafes,

if a bar, as

turns in the teeth of a wheel

A E, be

fixed to the

C D.

In both thefe

end A of the fcrew ; the

force,

wherewith the end B of the fcrew in

forced

down, and the

wheel

CD

in fig.

44

fig.

45-

is

wherewith the teeth of the

force,

bears the

are held,

fame proportion

power applied to the end E of the bar ; as the velocity, wherewith the end E will move, when the fcrew is turned, bears to the the end B of the fcrew in fig. velocity, wherewith

to the

4.5,

cr the teeth of the wheel

CD

M

-L

in fig.

46,

will be

moved.

5-7.

THI

ISAAC NEWTON'S

Sir

84

THE

-.

a weight with

inclined plane affords alfo a lefs

were required to

it

felf.

force,

than what

is

BOOK

I.

means of raifmg

equal to the weight it the globe A ( in fig.

raife

Suppofe from the ground B C up to the point, whofe perpendi If this globe be drawn cular height from the ground is E D. the flant D F, lefs force will be required to raife it, than along

4/7. )

if

it

were

lifted directly up.

Here

the force applied to the

if

to its weight, as E D bears globe bear the fame proportion only to F D, it will be fufficient to hold up the globe ; and there fore any addition to that force will put it in motion, and draw

up ; unlefs the globe, by preiTmg againft the plane, where This indeed on it lies, adhere in fome degree to the plane. it muft always do more or lefs, fince no plane can be made fo

it

abfolutely

fmooth

as to

have no inequalities at

all

;

nor yet

fb

not to yield in the lead to the prefTure of the Therefore the globe cannot be laid on fuch a plane,

as infinitely hard,

weight.

whereon it will flide with perfect freedom, but they muft in and this friction will fome meafure rub againft each other ;

make

neceflary to imploy a certain degree of force more than what is neceflary to fupport the globe, in order to give

it

it

But as all the mechanical powers are fubject any motion. fome degree or other to the like impediment from friction fhall here only mew what force would be neceflary to fu-

in I

ftain the globe,

ing any

if it

friction at

drawn by the force,

the cord

could

G

lie

And

upon the plane without

cauf-

fay, that if the globe were F ; and H, lying parallel to the plane

all.

I

wherewith the cord

D

is

pulled,

proportion to the weight of the globe,

as

bear

the

fame

ED bears to DF; this

CHAP. 2

PHILOSOPHY.

.

the globe.

this force will fuftain

I

let

fay,

and

I,

let

DE

the globe A, the globe. globe A will

GH

be continued on, and turned the weight K be hung to itif this weight bears the fame proportion to as bears to DP, the weight will {upport

proof of this,

over the pulley

Now

the cord

85

In order to the makinot?

I

think

lie

in

very manifeft, that the center of the line with the cord H G. Let

it is

one continued

M

L be the center of the globe, and the center of gravity of the weight K. In the firft place let the weight hang fo, that a line drawn from L to fhall lie and I fay, horizontally ; if the globe be moved either up or down the plane DF, the

M

weight will fo move along with it, that the center of gravity to both the weights fhall continue in this line L M,

common

and therefore fully,

fhall in

no

and make will fully believe,

prove

this

more

my

readers,

will

i

D'S

they

ELEMENTS,

;

who

make no

in themfelves fb evident, that are wholly ftrangers to geometri

difficulty

of admitting them. This

the globe be moved up, till its center be the center of gravity of the weight K be N fhall be equal to G L. Draw fo that G

being premifed, at G, then will

N

who has read E u c L

comprehend; and are

cal writings,

funk to

To

:

are fuch, as any perfon,

I

cafe defcend.

depart a little from the method of this treatife, ufe of a mathematical propofition or two but

I fhall

let

M

M

N

M

L in O ; then I fay, that O is the common crofting the line center of gravity of the two weights in this their new iitua-

M

tion. Let G P be drawn perpendicular to L ; then G L will bear the fame proportion to G P, as D F bears to D E ; and AT will bear the fame being equal to G L, proportion

N

MN

to-

86 to

Sir

G P,

tion to

as

DF

O G,

ISAAC NEWTON'S

bears to

as

D E.

But

M N bears to G P

;

N O bears

BOOK!.

the fame propor O will bear

confequently

N

In the laft die fame proportion to OG, as DF bears to DE. fame the bears the weight of the globe A proportion to place,

the other weight K, as the fame proportion to

DF

DE

bears to

OG, Whence

as the

;

therefore

NO

weight of the globe

bears

A bears

it follows, that, when the center A is in G, and the center of gravity of the weight N, O will be the center of gravity common to both

to the weight K.

of the globe K.

is

in

After the fame manner, if the globe had been the weights. caufed to defcend, the common center of gravity would have Since therefore no motion of L. been found in this line

M

the globe either

defcend,

it is

the weights

$6,

I

way

will

manifeft,

A and K

make

the

common

from what has been

center of gravity faid above, that

counterpoize each other.

SHALL now coniider the cafe of pendulums. A is made by hanging a weight to a line, fo that it

pendulum

may fwing backwards and forwards. This motion the geo meters have very carefully considered, becaufe it is the mod commodious inftrument of any

for the exacl

measurement of

time.

HAVE

a

obferved already , that if a body hanging perpendicularly by a firing, as the body A (in rig. 4,8.) hangs by the firing A B, be put fo into motion, as to be made to a5-7.

I

fcend up the circular arch

AC;

then as foon as

it

has arrived

at

CHAP.

PHILOSOPHY.

2.

at the highcft point,

to

which the motion,

87

that the

body has

received, will carry it ; it will immediately begin to defcend, and at A will receive again as [ ree of motion, as it '

had

at firft.

A D,

the arch

This motion therefore will carry the body up as high as it afccnded before in the arch A C.

Confequently in again at the arch

A

out end

its

its

its

return th

Ji

original velocity,

A C as high

as at firft

;

reciprocal motion.

the arch

D A it will acquire

and advance a iecond time up by this means continuing with It is true

indeed,

that in fact

every pendulum, which we can put in motion, will gradual lefTen its fwing, and at length ftop, unlefs there be fome ly

power conftantly applied to it, whereby its motion fhall be renewed but this arifes from the reiiftance, which the body meets with both from the air, and the ftring by which it is hung for as the air will give fome obftruction to the progress fo alfo the ftring, whereon of the body moving through it ;

:

;

the body hangs, will be a farther impediment ; for this ftring muft either flide on the pin, whereon it hangs, or it muft bend

motion of the weight ; degree of friction, and in the to the

refiftance to

its

inflection.

in the firft there

muft be fome

latter the ftring will

However,

make fome

if all reiiftance

could

be removed, the motion of a pendulum would be perpetual,

5*8.

tice

BUT

of in

this

body moves

fir ft property, I fhall take no that the motion, is, greater arch the pendulous the though greater time it takes up through,

to proceed,

the

:

the length of time does not increafe in fo great a proportion as the arch. Thus if C D be a greater arch, and E F a leffer> where C A is equal to A D, and E A equal to A F ; the body,

whe

88

Sir I

s

N E w T o N'S

AAc

BOOK I.

arch C D, fhall take up in fwings through the greater than in Twinging from E time a to D from C longer fwing to F, when it moves only in rlv.it leiTer arch ; or the time in which the body let fall from C will defcend through the arch

when

it

its

C A is greater than the time, in which the arch EA, when let fall from E.

it

will defcend through

But the

firft

of thefe

times will not hold the fame proportion to the latter, as the which will appear firft arch C A bears to the other arch E A ;

Let

thus.

C G and E H

remarked above

CA

a ,

be two horizontal

that the

body

lines.

in falling

will acquire as great a velocity at the point A,

have gained by falling directly falling through the arch

ly that velocity,

H A.

which

Therefore,

C A,

when

EA

it

has been

It

through the arch as

down through G A

would

it

and

;

the

in

A on

will acquire in the point would have got in falling it

through

body defcends through the great

mall gain a greater velocity, than when it pafonly through the lefler ; fo that this greater velocity will in fame degree compenfate the greater length of the arch. er arch

it

fes

5-9.

THE

incrcafe of velocity,

which the body acquires

from a greater height, has fuch an effect, that, if lines be drawn from A to C and E, the ftraight body would fall through the longer ftraight line C A juft in the fame time,

in tailing

through the fhorter ftraight line E A. ed by the geometers, who prove, that (fig. 49.) be placed in a

as

This if

any

is

demonftrat-

circle, as

perpendicular fituation;

ABCD a

body

obliquely through every line, as A B drawn from the loweft point A in the circle to any other point in die circumfliall fall

a

20.

ference

CHAP.

PHILOSOPHY.

2.

ference juft

in the

fame time,

as

89

would be imployed by the

body in falling perpendicularly down through the diameter CA. But the time in whieh the body will defcend through die arch, is different from the time, which it would take up in falling

through the

line

A B.

60. IT has been thought by feme, that becaufe in very correfpondent ftraight line differs but little

fnial 1 arches this

from the arch ftraight line

itfelf;

therefore the defcent

would be performed

fame time

this

through

in fuch fmall arches

nearly fo that

as through the arches themfelves were to fwing in fmall arches, half the time pendulum of a fingle fwing would be nearly equal to the time, in which

in the if

:

a

body would

perpendicularly through twice the length That is, the whole time of the fwing, ac cording to this opinion, will be four fold the time required for the body to fall through half the length of the pendu

a

fall

of the pendulum.

becaufe the time of the body's falling down twice the length of the pendulum is half the time required for the fall through one quarter of this fpace, that is through half the

lum

;

However there is here a miftake for pendulum's length. the whole time of the fwing, when the pendulum moves ;

through fmall arches, bears to the time required for a body to fall down through half the length of the pendulum

very

nearly the fame proportion, as the circumference of a circle bears to its diameter , that is very nearly the proportion of 3

5*

$ to II

If the

3,

or

pendulum

little

more than

the proportion of

3

to I.

takes fo great a fwing, as to pafs over an arch

equal to one fixth part of the whole circumference of the

N

circle.

circle,

this

ISAAC NEWTON'S

Sir

po will

it

fwing

1 1

proportion to have

y times, while

fwings in fo large an arch, If fwings in an hundred. circle,

fhall

it

fwing in

~

not

of the

it

fwung 117 times

lofe

it

lofes

BOOK!.

ought according to ;

fo that,

fomething

lefs

when

it

than two

l

only of the above one vibration in 160. If it

circle,

it

fwing through

fhall lofe

it

about one vibration in

fwing be confined to 4^ of the whole circle, it 690. fhall lofe very little more than one fwing in 1600. And if it take no greater a fwing than through ^ of the whole cir If

cle,

it

its

fhall

not lofe one fwing in y8oo.

N

o w it follows from hence, that, when 61 pendulums fwing in fmall arches, there is very nearly a conftant propor tion obferved between the time of their fwing, and the time, .

in

which a body would

half their length.

fall

And we

perpendicularly down through have declared above, that the

which bodies fall, are in a two fold fpaces, through propor a tion of the times, which they take up in There falling . fore in pendulums of different lengths, hfmall arches, the lengths of the

fwinging throng in a two fold or

pendulums are

duplicate proportion of the times, they take in fwinging ; fo that a pendulum of four times the length of another fhall

up twice the time in each fwing, one of nine times length will make one fwing only for three fwings of Ihorter, and fo on. take

6^.

THIS

the the

proportion in the fwings of different pendu but in large ones alfo, ;

lums not only holds in fmall arches "7.

provided

CHAP.

2.

PHILOSOPHY.

91

be fuch, as the geometers call fnnilar ; that provided they if the arches bear the fame is, proportion to the whole cir cumferences of their refpedive circles. Suppofe ( in fig. 48. )

A B, C D

Let the arch E F be defcribto be two pendulums. ed by the motion of the pendulum A B, and the arch G H be defcribed by the pendulum CD ; and let the arch E F bear the fame proportion to the whole circumference, which

would be formed by turning the pendulum A B about the point A,

as the

arch

GH

quite round bears to the whole cir

cumference, that would be formed by turning the pendu

lum

CD quite round the point C.

Then

I fay,

the propor

which the length of the pendulum AB bears to the length of the pendulum CD, will be two fold of the propor tion, which the time taken up in the defcription of the arch E F bears to the time employed in the defcription of the arch

tion,

GH. .

THUS pendulums,

which fwing

in very fmall arches,

are nearly an equal meafure of time. But as they are not fuch an equal meafure to geometrical exactnefs ; the mathematicians

have found out a method of caufing a pendulum fo to fwing, that, if its motion were not obftrudted by any refinance, it

would always perform each fwing it

in the

fame time, whether

moved through

a greater, or a lefler fpace. This was the great u Y G E N s, and is as follows.

difcovered by on the ftraight line

H

AB

(

in fig.

49.

)

let

the circle

CDE

firft

Up

be fo

Then let placed, as to touch the ftraight line in the point C. this circle roll as a coachthe line AB, along upon ftraight wheel

rolls

along upon the ground.

N

2,

It

is

evident,

that,

as

foon

Sir I

s

N

A A c

K vv

To

BOOK

N'S

I,

foon as ever the circle begins to move, the point C in the cir cle will be lifted off from the ftraight line AB; and in the

motion of the

circle will dcfcribe a

CFGH.

the line reprefented by

crooked courfc, which

Here the

CH

part

is

of the

H

included between the two extremities C and ftraight line will be equal to the whole circumference of the line

CFGH

of the

CDE; andifCH

circle

at the point parts

pendicular

of the let fall

down

C H, CDE.

to

circle

and the

this line I

Now

be divided into two equal I K be drawn per

ftraight line

K

will

be equal to the diameter body were to be

in this line if a

from the point H, and were to be carried by

its

weight

HG K, as far as the point K, which the loweft the line CFGH; and if from any other point G a

the line

point of

body were which

I,

falls

is

to be let

from G,

fall

takes up,

as the

in the

fame manner

will take juft the

which

K, body a pendulum can be fo hung,

falls

;

this

body,

fame time

in

coming

to

from H.

Therefore

if

that the ball fhall

move

in the

AG FE, all its fwings, whether long or fhort, will be per formed in the fame time ; for the time, in which the ball line

will defcend to the point K,

whole fwing.

is always half the time of the of a pendulum will be made to line by the following means. Let K I ( in fig,

But the

ball

fwing in this 5-1.) be prolonged upwards to L,

Then

let

the line

LMH equal and

till

IL

like to

is

equal to IK.

KH be applied,

as

in the figure between the points L and H, fo that the point which in this line anfwers to the point in the line

LMH

KH

H

be applied to the point L, and the point anfwering to the point K fliall be Alfo let fuch applied to the point H. another line L N C be applied between L and C in the fame /hall

manner,

CHAP.

PHILOSOPHY.

2.

93

being made

if

LNC,

pendulum fwings

This preparation ; pendulum be a length, that the ball thereof fuch of L hung ihall reach to K ; and if the firing mall continually bend a-

manner.

a

at the point

HML

the lines

gainft to and fro

the line

64.

by

;

and

means the

this

as the

ball {hall conftantly

keep in

C K H.

Now

in this

pendulum,

as all the

fwings, whether

long orfhort, will be performed in the fame time; fo the time of each will exactly bear the fame proportion to the time re quired for a body to fall perpendicularly down, through half the length of the pendulum, that is from I to K, as the cir cumference of a circle bears to its diameter.

IT may from hence be underftood in fome meafure, when pendulums fwing in circular arches, the times of why, their fwings are nearly equal,

if

the arches are fmall, though

thofe arches be of very unequal lengths ; for if with the febe defcribed, this arch midiameter LKthe circular arch

OKP

in the lower part

of

it

will differ very

little

from the

line

CKH. 66. IT

may

not be amifs here to remark,

will fall in this line

point, as Q^or

CKH

(fig. 5*3.)

R in a fhorter fpace

or through any other line whatever, thefe

two

C

that a

to

of time, than

through the ftraight line drawn from

tween

from

body any other

if it

moved

C

to the other point ; that can be drawn be

points.

3

67.

BUT

Sir

94. 67.

dulum

now

BUT

as I

ISAAC

N E w T o N'S

BOOK I.

have obferved, that the time, which a pen

takes in Twinging, depends fomething concerning the

fay

upon way,

its

in

length

which

I

;

this

(hall

length

If the whole ball of the of the pendulum is to be eftimated. into one point, this length, by could be crouded pendulum which the motion of the pendulum is to be computed, would

But the ball of the pen be the length of the firing or rod. dulum muft have a fenfible magnitude,, and the feveral parts of

this ball will

not

the

pendulum

locity.

fwings,

move with

which are

for thole parts, is

the fame degree of fwiftnefs ; from the point, whereon

fartheft

fufpended, muft move with the greater! ve know the time in which the pendulum

Therefore to it

is

neceflary to find that point of the ball, which as if the whole ball

moves with the fame degree of velocity, were to be contracted into that point. 68.

THIS

point

is

not the center of gravity, as

I fhall

now

Suppofe the pendulum AB (in fig. 5*4. ) compofed of an inflexible rod A C and ball C B, to be fixed on the point A, and lifted up into an horizontal fituation.

endeavour to mew.

Here if the rod were not fixed to the point A, the body C B would defcend directly with the whole force of its weight ; and each part of the body would move down with the lame degree of

fwiftnefs.

But when the rod

is

fixed at the point

body muft fall after another manner ; for the of the body muft move with different degrees of A, the

parts

velocity,

parts more remote from A defcending with a fwifter modon, than the parts nearer to A ; fo that the body will ret.-ive a kind of But it has rolling motion while it defends.

the

been

CHAP.

PHILOSOPHY.

2.

effect of gravity upon any bo the fame, as if the whole force were exerted on the bo

been obferved above, that the is

dy

of gravity \ Since therefore the power of gravity dy's center in drawing down the body muft alfo communicate to it the

motion juft defcribed

rolling

;

it

feems evident, that the cen

of gravity of the body cannot be drawn down as fwiftly, when the power of gravity has no other effect to produce

ter as

If there on the body, than merely to draw it downward. whole matter of the body CB could be crouded into

fore the its

center of gravity, fo that being united into one point, this motion here mentioned might give no hindrance to

rolling its

defcent

;

the point, whole matter ot the farther

would defcend fafter, than it can now which now defcends as faft, as if the body C B were crouded into it, will be

this center

And

do.

removed from the point A, than the center of

gravity

of the body CB. fuppofe the pendulum A B (in fig. yy.) to. hang obliquely. Here the power of gravity will operate lels upon the ball of the pendulum, than before but the lineDE

69.

AGAIN,

:

being drawn the

pendulum

now

it is

if the

to ftand perpendicular to the rod the force of gravity upon the

fo, as ;

in this fituation, will

body were

D E,

to glide

AC

of

body CB, produce the fame effect, as

down an

inclined plane in the po-

But here the motion of the body, when the

fition

of

rod

fixed to the point A, will not be equal to the uninter

is

rupted defcent of the body

down

this

plane

;

for the

bod

*

Sir I

96

s

A A c JS E

will here alfo receive the

wToNs 7

fame kind of rotation

BOOK in

its

I.

motion,

motion of the center of gravity will in like manner be retarded ; and the point, which here defcends with that degree of fwiftnefs, which the body would

as before

;

fo that the

have, if not hindered by being fixed to the point A ; that is, which defcends as fall:, as if the whole body were the point,

crouded into

it,

will be as far

removed from the point

A, as

before.

70. THIS point, by which the length of the pendulum is And the to be eflimated, is called the center of ofcillation. mathematicians have laid

down

to find this center in all bodies.

general directions, If the globe

AB

(

in

whereby fig. 5*6.

)

be hung by the firing C D, whofe weight need not be re Let the garded, the center of ofcillation is found thus.

D be continued through the through the center of the globe is evident. Suppofe E to be this center of the globe ; and take die line G ot fuch a length, that it fhall bear the fame ftraight line

drawn from C

globe to

That

F.

it

will

to

pafs

E D bears E C. Then E H being of G, the point H fhall be the center of of If the weight of the rod C D -is too confiderable

proportion to E D, as

made

equal to

cillation

a .

to

-

f

CD

I, that DI be equal fame proportion to C I, as the weight ot the globe A B to the weight of the rod C D. Then having found H, the center of ofcillation of the globe, as

to be neglecled, divide to part of C D ; and take ^,

before,

divide

I

a

K in

L,

in (fig. 5*7)

K

in the

fo that

Hu^cn. Horohg,

oicilL:.

I

L

ihall

pjg. 141,

bear the fame pro-

142.

portion

CHAP.

2.

PHILOSOPHY.

97

to L H, as the line C H bears to K ; and portion the center of ofcillation of the whole pendulum.

THIS computation

71.

L

fhall

made upon fuppofition,that

is

center of ofcillation of the rod

be

the

C D, if that were to fwing alone

without any other weight annexed, would be the point I. And this point would be the true center of ofcillation, (b far If any one of the rod is not to be regarded. chufes to take into confideration the thicknefs of the rod, he

as the thicknefs

muft place the center of the point the point

ofcillation thereof fo

much below

that eight times the diflance of the center from I, I fhall bear the fame proportion to the thicknefs of

the rod, as the thicknefs of the rod bears to

its

length

CD

a .

71. IT has been obferved above, that when a pendulum fwings in an arch of a circle, as here in fig. y8, the pendu

lum A B

fwings in the circular arch

rizontal line, as

E F, from

to the line

let fall,

A G, which

ing to the point G,

ferve,

ofcillation

in the

the

acquire in

com

any body would ac from F to G. Now this is to be

which is defcribed by the cen

of the pendulum.

pendulum

falls,

I fhall

here farther ob-

E G be drawn from

the point, to the loweft point of the arch ; the velocity, which the

that if the ftraight line

whence

will

will be the fame, as

quire in falling directly down underftood of the circular arch,

of

perpendicular to the horizon :

is

which the pendulum

then the velocity,

ter

if you draw an ho whence die pendulum is

CD;

the place

fame or in equal pendulums 1

.See

Hugen. Kcrolog,

O.'cilkrt.

O

p. 14^.

pendulum

Sir I

s

A AC

N E w T o N'S

BooKl.

to this line that is, if acquires in G,is proportional the pendulum, after it has defcended from E to G, be taken G be back to H, and let fall from thence, and the line :

pendulum

H

the velocity, which acquire in pendulum fame the bear fhall from defcent G by H, proportion to the velocity, which it acquires in falling from E to G, as the bears to the ftraight line E G. ftraight line H G

drawn

the

;

fliall

its

73

We may now proceed to thofe experiments

.

percuflion

of

bodies,

made with pendulums.

I

upon

the

obferved above might be

This expedient for examining the firft propofed by our late great

of percuiTion was

effecls

architect

Two

which

SirCnRiSTOPHERWREN. And it is as as A and B (in fig. 5-9.) either equal

follows,

or une

balls,

hung by two firings from two points C and D, fo the balls hang down without motion, that, they fliall other L and the firings be parallel. touch each Here if juft one of thefe balls be removed to any diftance from its perpen qual,

are

when

dicular fituation, gainft the other

and then

let fall to

defcend and

ftrike a-

by the laft preceding paragraph it will be known, with what velocity this ball /hall return into its firft perpendicular fituation, and confequently with what force it fliall ftrike againft the other ball ; and by the height to which ;

other ball afcends after the ftroke,

this

nicated to this ball will be difcovered.

the

For

velocity

commu

inftancc,

let

the

A

be taken up to E, and from thence be let fall to ftrike againft B, pafting over in its defcent the circular arch E F.

ball

By lar

this

impulfe arch HG.

B fly up to G, moving through the circu Then El and GK being drawn horizontally,

let

the

CHAP.

2.

the ball

A

PHILOSOPHY. will ftrike againft

99

B with the

velocity, which it down from I ; and the ball

would acquire in falling directly B has received a velocity, wherewith, if it had been thrown it would have afcended directly upward, up to K. Likewife lines be drawn from E to F and from H to G, if the ftraight velocity of A,

wherewith

it ftrikes, will bear the fame pro which B has received by the blow, as

portion to the velocity, die ftraight line

EF

its

ftroke,

H G.

In the

A afcends

after the

bears to the ftraight line

fame manner by noting the place remaining velocity

to

may

which

be compared with that,

ftruck againft B. Thus may be experimented the effects of the body A ftriking againft B at reft. If both

wherewith

it

the bodies are lifted up, and fo let fall as to meet and impinge the coming of both into their againft each other juft upon fituation ; by obferving the places into which perpendicular

they move

after the ftroke,

all thefe cafes

may

the effects of their percuflion in

be found in the fame manner as before.

SirlsAAcNEWTON has defcribed thefe experiments

74.

and has fhewn how

;

improve them to a greater exactnefs by for the reiiftance, which the air allowance making gives to But as this reiiftance is exceeding the motion of the balls to

a

.

and the manner of allowing

for it is delivered by himneed not enlarge upon it here. I mail rather fpeak to a difcovery, which he made by thefe ex periments upon the elafticity of bodies. It has been explained

fmall,

felf in

very plain terms,

I

above

b

bodies ftrike,

,

that

when two

a

Princip.

if

b

Philof. pag. 22.

O

z

they be not

Chap,

i,

elaftic,

29.

they

ICQ

ISAAC NEWTON'S

Sir

BOOK!.

they remain contiguous after the ftroke ; but that if they are elaftic, they feparate, and that the degree of their

elafticity

determines the proportion between the celerity wherewith Now they feparate, and the celerity wherewith they meet.

our author found, that the degree of elaflicity appeared in the fame bodies always the lame, with whatever degree of that is, the celerity wherewith they fe; always bore the fame proportion to the celerity wherewith they met fo that the elaftic power in all the bo

force they ftruck

parated,

:

he made

dies,

trial

upon, exerted

portion to the compreffing force.

it

felf in

one conftant pro

Our author made

trial

of wool bound up very compact, and found the which they receded, to bear about the with celerity propor tion of y to 9 to the celerity wherewith they met ; and in fteel he found nearly the fame proportion ; in cork the elafti with

balls

was fomething lefs ; but in glafs much greater ; for the wherewith balls of that material feparated after percuflion, he found to bear the proportion of I f to 1 6 to the city

celerity,

celerity

75-.

wherewith they met I

SHALL

rmifti

my

a .

difcourfe

on pendulums, with

this farther

obfervation only, that the center of ofcillation is alfo the center of another force. If a body be fixed to any

and being put

in

motion turns round

the body, if ; uninterrupted by the power of gravity or any other means, will continue perpetually to move about with the. fame point,

ble motion.

Now

the force, 8

it

equa with which fuch a body

Princip. Philof. pag. 25.

4

moves,

CHAP.

2.

moves,

is

PHILOSOPHY.

101

united in the point, which in relation to the is called the center of ofcillation. Let the

all

power of gravity cylinder A B the point E. the cylinder

C D (in fig. 60. ) whofe axis is E F, be fixed to And fuppofing the point E to be that on which

found in the

axis

is

be that center

:

fufpended, let the center of ofcillation be E F, as has been explained above a Let G then I fay, that the force, wherewith this cy .

linder turns round the point E, is fo united in the point G, that a fufficient force applied in that point fhall ftop die motion of the cylinder, in fuch a manner, that the cylinder fhould im mediately remain without motion, though it were to be loof-

ened from the point E at the fame inftant, that the impedi ment was applied to G whereas, if this impediment had been of the axis, the cylinder would applied to any other point :

turn

upon

the point, where the

impediment was applied.

the impediment had been applied between E and G, linder would fo turn on the point, where the

If

the cy

impediment was applied, that the end B C would continue to move on the fame way it moved before along with the whole cylinder ; but if the impediment were applied to the axis farther off from.

E than G, the end A D of the cylinder would ftart out of its that way in which the cylinder moved. From prefent place of ofcillation, it is alfo called the this property of the center center of percuflion. That excellent mathematician, Dr.BRooK TAYLOR, has farther improved this doctrine concerning die center of percuffion, by fhewing, that if through this point a line, as G HI> be drawn perpendicular to EF, and lying

G

n

102

ISAAC NEWTON'S

Sir

in the courfe of die body's

ed to any point of

motion

this line will

BOOK!.

a fufficient

;

have the fame

we

power effect,

appli as the

before fhewed die

like power applied G center of percuflion within the body on its axis ; by this means we may find this center on the furtace of the body alfo, for ll

to

be where

it will

fo that as

:

this line

HI

crofles that furface.

76. I SHALL now proceed to the laft kind of motion, to be treated on in this place, and ihew what line the power of gravity will caufe a

wards by any

body

when

to defcribe,

This was

force.

firft

it

is

thrown

for

difcovered by the great

GALILEO, and

is the principle, upon which engineers the fhot of great guns. But as in this cafe bo dies defcribe in their motion one of thofe lines, which in geo

fhould

direcl:

metry are called conic

feclions

;

it

is

neceflary here to pre-

In which I fliall be the mife a defcription of thofe lines. more particular, becaufe the knowledge of them is not only neceflary for the prefent purpofe, but will be alfo required hereafter in

77.

fome of the principal

THE

were the

firft lines

ftraight line

parts of this treatife.

considered by the ancient geometers

and the

circle.

Of

thefe

they compof-

various figures, of which they demon ftrated many proper and refolved divers problems them. ties, Thefe

ed

concerning problems they attempted always to refolve by the defcribing For inftance, let a ABCD ftraight lines and circles. fquare

( fig.

6 1.) be

propofed, 4

and

let it

be required to

make ano-

See Method. Increment, prop. 25.

ther

CHAP.

PHILOSOPHY.

2.

103

ther fquare in any aiTigned proportion to this. Prolong one bear the fame fide, as D A, of this fquare to E, till

AE

propor

new fquare is to bear to the fquare A C. If the oppofite fide B C of the fquare A C be alfo prolonged to F, till B F be equal to A E, and E F be afterwards drawn, will eafily conceive, that the figure ABFE I fuppofe my readers will bear to the fquare A B C D the fame proportion, as the line AE bears to the line AD. Therefore the figure ABFE will be equal to the new fquare, which is to be found, but is not the fide A E is not of the fame length it felf a fquare, becaufe But to find a fquare equal to the figure with the fide E F. A D,

tion to

ABFE you

as the

muft proceed

Divide the

thus.

line

D E into two

and to the center G with the inter equal parts in the point G, val G D defcribe the circle D H E I ; then prolong the line A B, till it

meets the circle in K ; and

fquare

will

ABCD 78.

make the

the fame proportion, as the line

I

only here

fquare

AKLM, which

be equal to the figure ABFE, and bear to the fquare

AE

bears to

AD.

SHALL not proceed to the proof of this, having fet it down as a fpecimen of the method of refolv-

the defcription of ftraight lines ing geometrical problems by But there are fome problems, which cannot be and circles. refolved drawing ftraight lines or circles upon a pkine. For

by

the

management

therefore of thefe they took into confideraand of the folid figures they found that,

tion folid figures,

which

is

called a cone, to be the

moft ufefuL

79

Sir

o'

ISAAC NEWTON'S

BOOK

79. A CONE is thus defined by EUCLIDE in a ments of geometry If to the ftraight line A B (in .

I.

his ele fig. 61.)

A C, be drawn perpendicular, and the two extremities B and C be joined by a third ftraight line compofing the triangle A C B ( for fo every figure is called, another ftraight

which

line, as

included under three ftraight lines

is

:

)

then the two

A and B being held fixed, as two centers, and the trian gle A C B being turned round upon the line A B, as on an axis the line A C will defcribe a circle, and the figure A C B will defcribe a cone, of the form reprefented by the figure BCDEF points

;

6%.

( fig.

)

in

which the circle CDEF and B the vertex.

is

ufually called the

bafe of the cone,

N

o w by this figure may feveral problems be rcfolved, cannot which by the fimple defcription of ftraight lines and circles upon a plane. Suppofe for inftance, it were required

80.

to

make

to

fome other cube named.

ers,

a cube,

that a

much

cube

celebrated

which

is

iliould bear I

any aiTigned proportion need not here inform my read

the figure of a dye. This problem was the ancients, and was once inforced

among

This problem by the command of an oracle. may be per formed by a cone thus. Firft make a cone from a triangle & whofe fide AC fhall be half the length of the fide BC ^

the plane A B C D ( fig. 6 4. ) let the line E F be exhibited equal in length to the fide of the cube propofed and let the line FG be drawn perpendicular to EF, and of fuch a length, that it bear the fame proportion to E F, as the

Then on

a

Lib. XI. Dcf.

cube

CHAP.

PHILOSOPHY.

2.

cube to be fought

is

105

required to bear to the cube propofed.

Through the points E, F, and G let the circle F H I be defcribed. Then let the line E F be prolonged beyond F to K, that F K be equal to F E, and

let

the triangle F

KL, having

all its

fides

equal to each other, be hung down perpendi from the After this, let another plane plane A B C D. cularly N O P be extended through die point L, fo as to be equi-

F K,

K L, L F

M

diftant

from the former plane A B C D, and

the line

QL R

E F K.

All this being thus prepared,

be drawn

fo, as

in this plane let

to be equidiftant let

from the

line

fuch a cone, as was

M

above directed to be made, be fo applied to the plane N O P, that it touch this plane upon the line QJl, and that the vertex of the cone be applied to the point L. This cone, by cutting through the firfl plane A B C D, will crofs the circle F H I be And if from the point S, where the furface fore defcribed. of

this

cone

interfects the circle,

to be equidiftant from the line to the fide of the cube fought

the line S

EF :

;

T

the line F

that

is,

be drawn

fo, as

T will

be equal if there be two cubes

or dyes formed, the fide of one being equal to E F, and the fide of the other equal to F T ; the former of thefe cubes fhall bear the fame proportion to the latter, as the line E F bears to

FG.

8 1. INDEED this placing a cone to cut through a plane is But when not a practicable method of refolving problems. the geometers had difcovered this ufe of the cone, they ap of the lines, which plied themfelves to condder the nature will be produced by the interfedion of the furface of a cone

P

and

1

06

Sir I

and a plane

;

s

N E w T o N'S

AAc

BOOK I.

enabled both to reduce whereby they might be and alfo to render their

thefe kinds of folutions to practice,

demonftrations concife and elegant.

WH

E N E v E R the plane, which cuts the cone, is equifrom another plane, that touches the cone on the fide; which is the cafe of the prefent figure ; ) the line, wherein

8 ^.

diftant (

the plane cuts the furface of the cone, But if the plane, which cuts the cone,

is

called a parabola.

be fo inclined to

this

through the cone (as in fig. 6f.) fuch a plane by cutting the cone produces the figure called an ellipfis, in which we fhall hereafter mew the earth and other, that

it

will

pafs quite

other planets to move round the fun. If the plane, which cuts the cone, recline the other way (as in fig.<5<5. ) fo as not to be parallel to any plane, whereon the cone can to cut quite through the cone ; fuch a plane mall the cone a third kind of line, which is called an

lie,

nor yet

produce in

hyperbola. the parabola, wherein bodies, that are thrown obliquely, will be carried by the force of gravity ; as I mall here proceed to mew, after having firft

But

it is

directed plane,

83.

C D be

the

firft

of thefe

my readers how

lines

to defcribe this fort of line

by which the form of

T o any ftraight fo

named

line

it

may

AB

(fig.

applied, as to ftand againft

upon a

be feen.

67.)

let

a

ftraight ruler

it

perpendicularly. Upon the edge of this ruler let another ruler E F be fo placed, as to move along upon the edge of the firft ruler C D, and keep al it. This being fo difpofed, let any be taken in the line AB, and let a firing equal

ways perpendicular to point,

as G,

in

CHAP.

PHILOSOPHY.

2.

EF

in length to the ruler

107

be fattened by one end to the point

G, and by the other to the extremity F of the ruler E F. if the firing be held down to the ruler EF by a pin H,

Then as

is

in the figure ; the point of this pin, while the reprefented ruler EF moves on the ruler C D, fhall defcribe the line IKL>

which

will

be one part of the curve

we were here to teach manner on the other the other part I to half the line

in

THE

84.

and the point

64, the

fig.

ABCD

line

AI

called the focus.

is

defcription

rulers in the like

A B, we may CG

line

MIL will

defcribe

be equal

be that very

in that figure cuts the cone.

G

is

whofe

If the diftance

this line.

wherein the plane

line,

line,

and by applying the

fide of the line

M of EF

:

called the axis of die parabola

MIL,

N o w by comparing the effects of gravity upon foiling

85*.

what

bodies, with

meters,

it

is

is

demonftrated of

proved,

carried forward in

figure by the geo thrown body obliquely is lines, the axis whereof is per this

that every

one of thefe

pendicular to the horizon.

86. THE geometers demon ftrate, that if a line be drawn to touch a parabola in any point, as the line A B (infig.6'8.) touches the parabola lines

then

C D, whofe axis is YZ,

in the

point E; andfeveral

H I, K L be drawn parallel to the axis of the parabola the line F G will be to H I in the duplicate proportion of

F G,

:

E F to E H, and F G to K L in the duplicate proportion of E F to E K likewife H I to K L. in the duplicate proportion of E H to EK. What is to be imderfcood by duplicate or tv P ;

08

1

Sir I

N E w T o N'S

A Ac

s

BOOK

I.

a

has been already explained Accordingly I the fame pro bear to be taken if line the mean here, that the fame bear will to HT as bears to EF, EH, portion .

proportion,

M

EH

proportion to

FG,

as

M bears to EF

the lame proportion to the fame proportion to

E K, F G,

as as

;

and

if the line

N bears

E K bears to E F, K L will bear N bears to E F ; or if the line

bear the fame proportion to EK, as EK bears to EH, will bear the fame proportion to HI, as O bears to EH.

O

KL

fo

87. THIS property is eflential to the parabola, being connected with the nature of the figure, that every line

pofTeiTing

88. (

this

Now

in fig. 69.

body,

)

property

is

to be called

if left to it felf,

it

name.

would move on with a uniform

Suppofe the eye of a fpe&ator to juft under the point A ; and let us

motion along with the

eye along the line C D parallel on with the fame velo

B ; and

that the eye mould move wherewith the body would

were to be

mo

A B.

at the point C the earth to be fo put into imagine as to body, carry the fpe&ator's

be placed

city,

this

fuppofe a body to be thrown from the point A towards B in the direction of the line A B. This

tion through this line

to A

by

proceed in the line

left

to

move without any

gravitation towards the earth.

A B,

difturbance from

In this cafe

if

the

if its

body mov

ed on without being drawn towards the earth , it would ap But if the power of gra pear to the fpeclator to be at reft. vity exerted it felf on the body, it would appear to the fpea

Chap.

2.

17.

*

dlator

CHAP.

PHILOSOPHY.

2.

ctator to

fall

directly

wherein the body by

moved from A

down.

own

its

Suppofe

109

at die diftance

progreflive motion

of time,

would have

fhould appear to the fpectator to have fallen through a length equal to E F then the body at the end of this time will actually have arrived at the point F. to E,

it

:

of time, wherein the body would have

If in the fpace

mov

progreflive morion from A to G, it would have ap : peared to the fpectator to have fallen down the fpace G then the body at the end of this greater interval of time

ed by

its

H

Now

will be arrived at the point H. that,

has here been

the line pafles

faid, it will follow, that this line

;

is

A F H I be from what

one of thofe,

have been defcribing under the name of the parabo For the diftances E F, G H, through which the body is

which la.

if

through which the body actually I

feen to

times

fall,

a ;

will increafe in the duplicate proportion of the lines A E, A G will be proportional to the

but the

times wherein they

would have been

motion of the body progreflive

:

defcribed by the fingle

will be in the duplicate proportion of the lines

the line

AFHI

E F, G H A F, A G j and

therefore the lines

polIeHes the property of the parabola.

89. IF the earth be not fuppofld to move along with the For the body be body, the cafe will be a little different. ing conftantly drawn directly towards the center of the earth, the body in its motion will be drawn in a direction a little ob lique to that, wherein

it

tion, as before fuppofed.

h<j drawn by the earth in mo But the diftance to the center of the

would

See above Ch. z.

17.

earth

no

Sir I

s

N E w T o N'S

AAc

BOOK I.

earth bears fo vaft a proportion to the greateft length, to which we can throw bodies, that this obliquity does not merit any the fequel of this difcourfe it may indeed be what line the body being thrown thus would be

From

regard. collected,

found to

defcribe, allowance being

the earth's adtion \

but has no ufe in to confidcr the

90. thus

THE

This

this

body

is

for this obliquity of

the difcovery of Sir

Here

place. as

made

moving

it is

I

s.

N E w T ON

;

abundantly fufficient

in a parabola.

which a projected body defcribes, being methods have been deduced from practical

line,

known,

hence for directing the mot of great guns to ftrike any ob This work was firit attempted by GALILEO, defired.

ject

improved by his fcholar TORRICELLI; been rendred more complete by the great

and foon

after farther

but has

lately

is an unfpeakable lofs to be required to throw a body

Mr. COTES, whofe immature death mathematical learning.

If

it

from the point A ( in fig. 70. ) through the points A, B draw the

fo as to ftrike die

ftraight line

point

C D, and

B

;

erect

AR perpendicular to the horizon, and cf four times the height, from which a body muft fall to acquire the velo wherewith the body is intended to be thrown. Through city,

the line

the points A and E defcribe a circle, that mall touch the line Then from the point B draw the line C D in the point A. B F perpendicular to the horizon, interfering the circle in the ancl H. This being done, if the points G directly towards either of thefe points G or

on the point B

;

but with

this difference,

FromB

H.

L'h. 3.

body be projected H,

that,

it ftiall fall i( it

up

be thrown in

CHAP.

m

PHILOSOPHY.

2.

in the direction

A G,

it

mall fooner arrive at B, than

in the direction

projected in the direction B, will bear the

AG

When

A H.

the time,

;

fame proportion

it

the

will take

to the time,

body

up

in

were

if it

is

projected

arriving at

wherein

it

would

down through one fourth part of A E, as A G bears to But when the body is thrown in the direction of half A E. A H, the time of its palling to B will bear the fame proportion

fall

to the time, wherein

of

A E,

as

AH

it

would

bears to half

fall

through one fourth part

A E.

91. IF the line A I be drawn fo as to divide the angle un der EAD in the middle, and the line IK be drawn perpen dicular to the horizon ; this line will touch the circle in the

point

and

I,

if

the

body be thrown

in the direction

A I,

it

upon the point K: and this point K is the farthefl in the line A D, which the body can be made to ftrike, point

will fall

without mcreafing

.

moves,

THE may

the parabola

velocity,

A.

velocity.

wherewith the body every where

be found thus.

AB

(fig.

horizon, and equal fall

its

71.)

Suppofe the body to move in Erecl:

AC

perpendicular to the

from which a body muft to acquire the velocity, wherewith the body fets out from If you take any points as D and E in the parabola, and

draw body

to the height,

D F and E G parallel to the horizon the velocity of the in D will be equal to what a body will acquire in falling

down by

;

its

own weight through C F, and

in

E

the velocity

would be acquired in falling through CG. Thus the body moves flowed at the higheft point H of the parabola ; and at equal diftances from this point will will be the fame,

as

move

ii2

Sir I

s

N E w T o N'S

AA c

BOOK

L

move with

equal fwiftnefs, and defcend from that higheft point through the line H B altogether like to the line A H in which it afcended ; abating only the refinance of the air, which is not here confidered. If the line HI be drawn from the higheft point to

i

tion

of

the direction

parallel

when

70, equal to

A G, and

93.

H

BG in fig. AH

THUS

I

body

is

AI

will be equal projected in the direc

to the horizon,

the

when the body is thrown A D be drawn horizontally.

of B H,

provided

in

have recounted the principal difcoveries,

which had been made concerning the motion of bodies by Sir I s A A c N E w T o N'S predeceflbrs ; all thefe difcoveries, by being found to agree with experience, contributing to eftablifh the laws of motion, from whence they were deduced.

what I had to fay upon thofe and conclude this chapter with a few words concern ing the distinction which ought to be made between abfolute and relative motion. For fome have thought fit to confound them together ; becaufe they obferve the laws of motion to take place here on the earth, which is in motion, after the fame I fhall therefore here finifli

laws

;

manner

as if

it

were

at reft.

But

Sir

ISAAC

NEWTON

has

been careful to diftinguifh between the relative and abfolute consideration both of motion and time 3 The aftronomers .

anciently found it necefTary to make this diftinction in time. Time confidered in it felf pafies on equably without relation to

any thing external, being the proper meafure of the continu ance and duration of all things. But it is moft frequently con ceived of by us under a relative view to fome fucceilion in *

Prin. Philof. pag. 7,

&c.

fenfible

CHAP.

PHILOSOPHY.

2.

fenfible things,

fion of the thoughts in

we

receive our

more

idea of time, but

firft

for the thoughts

fure thereof;

113

we take cognizance. The fuccefour own minds is that, from whence

of which

is

a very uncertain mea-

of fome

men

flow on

much

than the thoughts of others ; nor does the fame The motions of the perfon think equally quick at all times. heavenly bodies are more regular ; and the eminent divifion fwiftly,

of time into night and day, made by the fun, leads us to rneafure our time by the motion of that luminary nor do we in the affairs of life concern our felves with any inequality, :

which there may be in that motion ; but the fpace of time which comprehends a day and night is rather fuppofed to be

However aftronomers

always the fame.

anciently found

thefe fpaces of time not to be always of the fame length, have taught how to compute their differences.

Now

when

and the

equated as to be rendered perfectly equal, is And therefore the true meafure of duration, the other not. time,

this latter,

other,

no

fo

which

which

is

is

abfolutely true time,

only apparent.

And

we

as

between apparent time,

differs

from the

ordinarily

make

as meaflired

by the fun, and the true ; fo we often do not diftinguim in our ufiiand the apparent or relative al difcourfe between the real, diflinclion

motion of bodies

mould in

;

for the other.

but ufe the fame words for one, as we Though all things about us are really

motion with the earth ;

as this

motion

is

not

vifible,

we

fpeak of the motion of every thing we fee, as if our felves and the earth flood flill. And even in other cafes, where we difcern the

motion of bodies, we often fpeak of them not in whole motion we fee, but with regard to other

relation to the

bodies

Sir

114. bodies, to

which they

ing on a table

are contiguous.

when

;

NEWTON'S

ISA AC

If

BOOK!

any body were

that table fhall be carried along,

ly

we

upon the table, or perhaps abfolutely, that However philofophers muft not reject all the body diftinction between true and apparent motions, any more than aftronomers do the diftinction between true and vulgar time ; fay the

refts

body is

for there

is

at reft.

as real a difference

between them,

Suppofe by the following confederation. the univerfe to have their courfes flopped,

as will

all

appear

the bodies of

and reduced

to

Then fuppofe their prefent motions to be again perfect reft. reftored ; this cannot be done without an actual impreffion

made upon fome of them left ftill

untouched, remain at

wrought upon,

at

leaft.

If any of

them be

they will retain their former ftate, that is, reft ; but the other bodies, which are

have changed their former ftate of reft, Let us now fuppofe the to be annihilated, this will make no al

will

for the contrary ftate of motion.

bodies

left at reft

teration in the ftate of the

moving bodies; but the

effect

of the impreiTion, whicli was made upon them, will ftill This fLews the motion they received to be an abfubfift. folute thing, and to have no neceffary dependence

upon

which the body

the relation

other body

faid to

be in motion has to any

a .

94. BESIDES abfolute and relative motion are diftinguimOne effect of motion is, that bodies, by their Effect.

able

when moved round any

center or axis,

* See Newton, princip. philof. pag-9-

lin.

acquire a certain 30.

powejy

PHILOSOPHY.

CnAp.2.

115

power, by which they forcibly prefs themfelves from that cen As when a body is whirled about in a ter or axis of motion. the body prefies againft the fling, and is ready to fly fling, And this power is prcpcrout as foon as liberty is given it. tional to the true, not relative motion of the body round fuch

lowing inftance

a

If a

.

N

s A A c E w T o N gives the fol or fuch like veflel near full of wa pail

Of this

a center or axis.

Sir I

be fufpended by a firing of fufficient length, and be turn ed about till the firing be hard twifted. If then as foon as the

ter

and water in

veflel

it

are

become

(till

and

at reft, the veflel

be

nimbly turned about the contrary way the firing was twilled, the vefTel by the firings untwifting it felf fliall continue its mo And when the veflel firft begins to turn, the

tion a long time.

water in

till

tion, felf.

it

fhall receive little or

but by degrees

veflel,

at lafl

it

fhall

fliall

nothing of the motion of the communication of mo

receive a

move round

as fwiftly as the veflel it

Now the definition of motion, which DESCARTES has

given us upon lative,

is

this

:

this

principle of

vicinity

to other bodies,

with

and are confidered

it,

making

all

motion meerly re

a removal of any body from its which were in immediate contact

that motion,

is

as at reft

b

And

.

if this

be

com

pared with what he foon after fays, that there is nothing real or pofitive in the body moved, for the fake of which we afcribe

motion to

it,

which

is

not to be found as well in the c

contiguous bodies, which are confideri'd as at reft ; it will follow from thence, that we may confider the vefiel as at reft Princip. PhiloC- p.ig. 10. Des Cart. Princ. Plvlof.Part. II.

Rcnat.

I

c

Ibii.

30.

25.

and

T 1

6

Sir Is

and the water

as

NE

AAc

moving

in

it

:

the veflel has the greatefl motion,

and

to turn,

lofes this relative

vv

BOOK I

T o N'S

and the water

when

in

the veflel

refpedt of

firfl

motion more and more,

begins till

at

But now, when the veflel firfl: begins length quite to turn, the farface of the water remains fmooth and flat, as before the veflel began to move ; but as the motion of the ceafes.

it

veflel

communicates by degrees motion

to the water,

the fur-

the water fub-

face of the water will be obferved to change,

and rifing at the edges: which elevation caufed by the parts of it prefling from the axis, about ; and therefore this force of receding from

fiding in the middle

of the water

is

they move the axis of motion depends not upon the relative motion of the water within the veflel, but on its abfolute motion ; for it is leafr.,

when

95-.

of

when

that relative

that relative

THUS

motion

is

motion leaft,

the true caufe of

is

and

greatefl:,

or none at

greatefl^

all.

what appears

in the furface

water cannot be afligned, without considering the So alfo in the fyfbem of the water's motion within the veflel. this

world, in order to find out the caufe of the planetary mo which be tions, we muft know more of the real motions,

long to each planet, than is abfolutely neceflary for the ufes If the aftronomer fhould of aftronomy. fuppofe the earth to ftand

ftill,

he could

afcribe fuch

motions to the

celeftial

bo

mould anfwer all the appearances though he would not account for them in fo fimple a manner, as by attributing dies,

as

motion to the

;

earth.

But the motion of the earth muft of

neceflity be considered, before the real caufes,

the planetary fyftem,

can be difcovered.

which aduate

.

CHA

p,

,

CHAP.

PHILOSOPHY.

3-

CHAP. Of

117

HI.

CENTRIPETAL FORCES.

have juft been defcribing in the preceding chapter the effects produced on a body in motion, from ifc> being continually acted upon by a power always equal in a But bodies ftrength, and operating in parallel directions

WE

.

be acted upon by powers, which in different places fhall have different degrees of force, and whofe feveral directions

may

(hall

The

be varioufly inclined to each other.

rnoft fim-

to direction is, when the power is ple of thefe in refpect This is one center. to the cafe of truly pointed constantly

whofe effects we defcribed in the foregoing chap though the center of that power is fb far removed, that the fubject then before us is moft conveniently to be coniider-

that power, ter;

wherein we have placed it But Sir I s A A c confidered very particularly this other cafe of powers, which are conflantly directed to the fame center. It is upon this foundation, that all his difcoveries in the ryftem

ed in the

:

light,

NEWTON has

of the world are

raifed.

And

therefore,

as this

fubject bears

very great a fhare in the philofophy, of which I am difcourfing, I think it proper in this place to take a fhort view fo

of fome of the general me. to apply

them

effects

of thefe powers,

before

we

particularly to the fyftem of the -world, '

.85, S.T.

2;

THESE

1 1

8

Sir I

THE

s

AAc

N E WT o N'S

s

F

I.

NEWTON

are by Sir I s A A c effect is to caufe the body,

powers or forces called centripetal ; and their firft 1.

BOOK

on

which they aft, to quit the ftraight courfe, wherein it would and to defcribe an incurvated line, proceed if undifturbed, towards the center of the force. bent be which fliall It is

always not neceflary, that fuch a power fliould caufe the body The body may continue to recede that center.

to approach from the center of the power, notwithftandhig its being drawn muft always belong to its by the power ; but this property

motion, that the' line, in which it moves, will continually be concave towards the center, to which die power is directed.

Suppofe

A

(

in fig.

71.

)

to be the center of a force.

Let a

body in B be moving in the direction of the ftraight line B C, in which line it would continue to move, if undiihirbed ; but being attracted by the centripetal force towards A, die body muft neceilarily depart from this line B C, and being drawn into the curve line B D, muft pafs between the lines A B and

B C. It is evident therefore, that the body in B being gra dually turned off from die ftraight line B C, it will at firft be convex toward the line BC, and confequently concave to wards the point A : for thefe centripetal powers are fuppofed to be in ftrength proportional to the power of gravity, and, like that, not to be able after the manner of an impulfe to turn

the body fenfibly out of its courfe into a different one in an inftant, but to take up fome fpace of time in producing a vifi-

That the curve will always continue to have its In the line B C near concavity towards A may thus appear. to B take any point as E, from which the line EF G may be fo ble effect.

drawn

PHILOSOPHY.

CHAP.

3.

drawn,

as to

when

the

touch the curve

body

is

come to F,

mediately to be fufpended,

nue to move

in a curve line,

line

BD

in

continuing this line

its

FG

Now

power were im would no longer conti but being left to it felf would courfe and that ftraight courfe

if the

:

motion

up as F.

centripetal

the body

forthwith reaffume a ftraight ; would be in the line F G for that line the body's

fome point

at the point F.

is

in the direction of

But the centripetal force

energy, the body will be gradually drawn from keep in the line F D, and make that line

fo as to

near the point F to be convex toward F G, and concave toward A. After the fame manner the body may be followed on in its

courfe through the line B D, and every part of that line be to be concave toward the point A,

fhewn

THIS then is the conftant character belonging to thofe 3 motions, which are carried on by centripetal forces ; that the line, wherein the body moves, is throughout concave towards .

the center of the force.

In refpect to the fuccefTive diftances

of the body from the center there is no general rule to be laid down ; for the diftance of the body from the center may ei ther increafe, or decreafe, or even keep always the fame. The point A ( in fig. 73.) being the center of a centripetal force, let a body at B fet out in the direction of the ftraight line

BC

It will be~ perpendicular to the line A B drawn from A to B. that is line there in the no other B C fo eafily conceived, point

near to A, as the point B ; that A B is the fhorteft of all the lines, which can be drawn from A to any part of the line B C ; all

other

lines,

as

being longer than

AD, A B.

A E, drawn from A to the line B C Hence it follows, that the body fet-

or

ting

i2o

Sir

ting out from B,

NEWTON'S

ISA AC if it

moved

in the line

B C,

it

BOOK!. would recede

more and more from the point A. Now as the operation of a centripetal force is to draw a body towards the center of if fuch a force act the force upon a retting body, it mufl :

neceffarily put

move towards

that

body

fo into motion, as to caufe

the center of the force

:

if

the

it

to

body w ere of r

the centripetal force felf moving towards that center, would accelerate that motion, and caufe it to move fafter down: but if the body were in fuch a motion, as being left to itfelf it would recede from this center, it is not necefit

firy,

that the action of a centripetal power upon it fhould compel the body to approach the center, from

immediately

which

it

would otherwife have receded

is

not without

if it

;

caufe the

the centripetal body to recede

power more ilowly from that center, than otherwife it would have Thus in the cafe before us, the fmalleft centripetal done. power, if it act on the body, will force it out of the line B C, and caufe it to pafs in a bent line between B C and the point A,

effect,

been before explained. has advanced to the line

When

as has

ftance,

tripetal force difcovers

of the

line

it

;

for in-

to crofs the line

AD

fome-

Now fuppofe at F. alfo be longer than A B.

AD

being

it

A B, A F may power may indeed be than A B or it may be

longer than fhorter

D*.

the body,

the effect of the cen

by having removed the body out

B C, and brought

where between A and

tripetal

felf

A D,

AF

The cen

fo

ftrong,

fo

evenly balanced with the

that

fhall

be

progreflive motion of the body, that A F and A B fhall be juft and in this laft cafe, when the centripetal force is of equal that ftrength, as conftantly to draw the as much toward :

body

the

CHAP.

PHILOSOPHY.

3.

121

the center, as the progrefTive motion would carry it off, the body will defcribe a circle about the center A, this center of

the force being alfo the center of the circle.

I F

4,.

B C per out in another line B G more in

the body, inftead of fetting out in the line

pendicular to

A B, had

clined towards the line

then as the body,

if it

fet

A B, moving in the curve line BH ; were to continue its motion in the line

B G, would for fome time approach petal force would caufe it to make that center.

But

if

the center

A

;

the centri

greater advances toward the body were to fet out in the line B I re

way from

the perpendicular B C, and were to be drawn by the centripetal force into the curve line B K ; the clined the other

body, notwithftanding any centripetal force, would for fome time recede from the center ; fince fome part at lead of the curve line B K lies between the line B I and the perpendicular EC.

THus

5-.

far

we

have explained fuch But as thefe forces

every centripetal force.

effects,

may

as attend

be very diffe

rent in regard to the different degrees of ftrength, where with they acl upon bodies in different places; I mall now pro

ceed to

make mention

in general of

fome of the

differences

attending thefe centripetal motions. 6. cafe.

A

(

To

reaftume the confederation of the

laft

mentioned

Suppofe a centripetal power directed toward the point in fig. adl on a body in B, which is moving in 74.. ) to

the direction of the ftraight line B C, the line B C reclining off from A B. If from A the ftraight lines AD, A E, A F are

R

drawn

Sir Is A

122 drawn

at

pleafure to die line

ed beyond B to G,

G C more

it

NE w TON'S

AC

CB

;

the line

C B being prolong

AD

inclined to die line

appears that

obliquely, than

AB

is

BOOK!.

is

inclined to

AE

it,

is

inclin

To

and A F more than A E.

ed more obliquely than A D,

{peak more correctly, the angle under A D G is lels than that under A B G, the angle under AEG lefs than that under AD G, and the angle under AEG lefs than that under AEG.

Now Then

fuppofe the body to move in the curve line it is here likewife evident, that die line

BHIK.

BHIK

ing concave towards A, and convex towards the line it is more and more turned off from the line B C ;

be

B C, fo

H

H

that in the point the line A will be lefs obliquely inclin ed to the curve line BHIK, than the fame line A D is inclin

H

ed to B C

D

at the

at the point I the inclination of the point line A I to the curve line will be more different from the in ;

clination of the fame line

and

AIE

to the line

B C,

at the point

K and

F the difference of inclination and in both the inclination at the curve

in the points

E;

will be

will be than at the line B C, But the oblique, ftraight ftraight line A B is lefs obliquely inclined to B G, than A D is inclined frill

greater

;

lefs

towards

DG

:

therefore although the line

ly inclined towards the curve

inclined towards at

H may

DG

;

yet

H B,

it is

AH

be

lefs

than the fame line

poflible,

oblique

A H D is

that the inclination

be more oblique, than the inclination at B. The in H may indeed be lefs oblique than the other, or

clination at

This depends upon the they may be both the fame. degree of ftrength, wherewith the force exerts it centripetal

felf,

during the paffage of the body from B to H.

manner

the inclinations at

I

and

K depend

After the fame

entirely

on the de gree

CHAP.

body

PHILOSOPHY.

3.

of ftrength, wherewith the centripetal force ads on the if the in its pallage from H to K centripetal force be :

weak enough, to the

H and at

at

body

force

tripetal

may

clinations equal,

be

lefs

ticularly

a certain

A H and A I drawn from

the lines

is

be of that ftrength or

if

the center

A

be more obliquely inclined to inclined towards B G. The cen

I iliall

AB

the curve, than the line

will

123

ftronger,

oblique than at B.

as to

render

all

the inclinations at

Sir I

s

AAc

thefe in I

and

fhewn, that if the centripetal power decreafes manner with the increafe of diftance, a body

defcribe fuch a curve line,

that

all

K

N E w T o N has par

the lines

after

may

drawn from the

body fhall be equally inclined to that curve line \ do not here enter into any particulars, my prefent inten

center to the

But

I

tion being only to mew, that it is poffible for a body to be acted by a force continually drawing it down towards a

upon and yet

center,

that center

;

that the

for here as

body

long

continue to recede from

fhall

as the lines

AH, A I, &c drawn

from the center A to the body do not become lefs oblique to the curve, in which the body moves ; fo long fhall thofe lines and confequently the body fhall more perpetually increafe, and more recede from the center. 7.

BUT we may

obferve farther,

power, while the body increafes retain fufficient ftrength to

center to the

curve

;

then

to

body

if this

make

become

that if the centripetal

diftance

its

the lines

from the

center,

drawn from the

at length lefs oblique to the

diminution of the obliquity continue, '

Princip. Philof.

Lib.

R

I.

x

till

prop. 9.

at

Sir I at laft the line

s

NE

A Ac

drawn from

vv

To

BOOK I.

N'S

the center to the

body

fhall ceafe

to be obliquely inclined to the curve, and fhall become per fhall no longer pendicular thereto ; from this inftant the body

recede from the center, again defcend,

and

which

but in

its

following motion it fhall curve line in all refpects

(hall defcribe a

has defcribed already ; provided the at the fame diftance from the centripetal power, every where So we obferved in the fame acts with the center, ftrength. like to that,

it

preceding chapter, that,

came

when

the motion of a projectile be no longer afcend-

the horizon, the projectile parallel to

ed, but forthwith directed

its

in a line altogether like that, 8.

THIS

return of the

courfe

wherein

downwards, defcending it had before afcended a

.

body may be proved by the

fol

lowing proportion that if the body in any place, fuppofe at I, were to be ftopt, and be thrown directly backward with the :

velocity,

wherewith

it

was moving forward

in that point

I

;

then the body, by the action of the centripetal force upon it, would move back again over the path I H B, in which it had before advanced forward, and

would

arrive again at the point

B in the fame fpace of time, as was taken up in its pafTage from B to I ; the velocity of die body at its return to the point

B being point.

would

the fame, as that wherewith

To

it firft fet

give a full demonftration of

require that ufe of mathematics,

out from that

this

which

proportion, I here pur-

pofe to avoid ; but, I believe, it will appear in great meafure evident from the following confederations. S 92.

9, SUP-

PHILOSOPHY. SUPPOSE

o.

that a

(in fig. 75*.)

body were

125 carried after

the following manner through the bent figure A of' the ftraight lines AB, BC, CD, DE, EF.

BCDEF,

compofed let it be moving uniform

in the line

At B

velocity.

fome

rected toward

in the ftraight line fo

long

point it,

B

it

in

fhall

its

let

point,

the

A B,

be

left

body

as G,

No\v whereas

of the figure. as

A B, from A towards

this

it

felf ;

any

receive an impulfe di

taken within the concavity body, when once moving

will continue to

to

Firft

B, with

move on

in this line,

but being difturbed at the

motion by the impulfe, which there ads upon A B into fome other ftraight

will be turned out of this line

it

wherein

will afterwards continue to

move, as long as it impulfe have ftrength Then let the fufficient to turn the body into the line B C. move on undifturbed from B to C, but at C let it receive

line,

mail be

left

it

to

itfelf.

Therefore

let this

body

another impulfe pointed toward the fame point G, and of fuf At D let ficient ftrength to turn the body into the line CD.

a third impulfe, directed like the body into the line DE. And at E

reft to let

the point G, turn the

another impulfe, direct

ed likewife to the point G, turn the body into the

Now,

I

be ftopt, velocity,

E F.

line

EF moving and turned back again in this line with the fame as that wherewith it was moving forward in this line ; fay,

if

the body while

in the

line

then by the repetition of the former impulfe at E the body will be turned into the line E D, and move in it from E to D with the fame velocity as before

it

moved with from D

to

E

;

by

the repetition of the impulfe at D, when the body fhall have returned to that point, it will be turned into the line

DC

;

and by the

repetition

of the other impulfes

at

C and B die.

126 the

Sir

body

the

the brought back ngain into

will be

wherewith

velocity,

I o.

ISAAC NEWTON'S it firft

moved

BOOK!

line

B

with

A,

in that line.

Let D E and F B be conti prove as follows. In DE thus continued take at plealure the

THIS!

nued beyond E. length E H, and

let H I be fo drawn, as to be equidiftant from Then, by what has been written upon the fecond law of motion a it follows, that after the impulfe on

the line

G E.

,

move through El in the fame time, as it would have imployed in moving from E to H, with the ve In FE prolonged take which it had in the line DE. locity E K equal to E I, and draw K L equidiftant from G E. Then, becaufe the body is thrown back in the line F E with the lame the body in

E

it

wherewith

velocity as that

when

will

it

went forward

in that line

;

if,

were permitted to go in the fame time, as it it would E K on, ftraight pafs through took up in palling through E I, when it went forward in the the body was returned to E,

it

line E F. But, if at the body's return to the point E, fuch an impulfe directed toward the point D were to be given it, where by it fhould be turned into the line D E ; I fay, that the

impulfe neceilary to produce this effect muft be equal to that, which turned the body out of the line D E into E F ;

and

that the velocity,

the line

through K L and

E D,

is

with which the body will return into

the fame, as that wherewith

this line

from

D to

E.

Becaufe E K

is

it

moved E I, and

before

equal to

H I, being each equidiftant from G E, are by confe-quence equidiftant irom each other ; it follows, that the two * Ch.

II.

22.

trian-

CHAP.

PHILOSOPHY.

3.

triangular figures to each other.

them

were writing

are altogether like and equal to mathematicians, I

to

:

fuch,

fo I

think this aflertion will be evident enough without

a proof in form it

E H and K E L

might fome proportions in the elements of EUCLID a but as I do not here addrefs my felf to the proof of this

refer

for

I

If I

127

as a

muft

at leaft I

;

defire

my

readers to receive

But thefe two triangu each other and equal ; as E K

proportion true in geometry.

being altogether like equal to El, fo EL is equal to EH, and KL equal to HI. Now the body after its return to E being turned out of the line F E into E D by an impulfe ading upon it in E, after the man lar figures

is

ner above expreiled this

impulfe,

the

;

as will

body

carry

it

will receive fuch a

velocity

through E L in the fame time,

by

as it

would have imployed in paf ling through E K, if it had gone on in that line undifturbed. And it has already been obferved, that the time, in which the body would pafs over E K with the velocity wherewith it returns, is equal to the time took up in going forward from E to I ; that is, equal to the

it

which

time,

in

locity,

wherewith

in

it

would have gone through E H with it

which the body

the line

E D,

is

moved from

will pafs

the fame,

as

D to E.

the ve

Therefore the time,

through E L after its return into would have been taken up by

body in pafling through E H with the velocity, where Since therefore with the body firft moved in the line DE. E L and E H are equal, the body returns into the line D E with the

the velocity, which it had before in that line. the fecond impulle in E is equal to the firft. Viz. L.

I.

prop. 30, 29,

&

26,

Again

I

By what

fay,

has

,

128

Sir I

s

AAc

N E w T o N'S

BOOK

I.

faid on the fecond law of motion concerning the effect of a oblique impulfes , it will be underftood, that the impulfe in E, the whereby body was turned out of the line D E into the line

been

E F, is ok fuch ftrength, that if the body had been at reft, when this impulfe had acted upon it, this impulfe would have -communicated fo much motion to the body, as would have carried

it

through a length equal to

H I,

in the time wherein

body would have pafled from E to H, or in die time wherein it paffed from E to I. In the fame manner, on the re the

turn of the body, the impulfe in E, whereby the body is turn is of fuch ftrength, that if it

ed out of the line F E into E D, .had acted on the body at reft, to

move through

it

would have can fed

a length equal to

K L,

in the

the body fame time, as

the body would imploy in palling through E K with the velo wherewith it returns in the line F E. Therefore die fe city, cond impulfe, had it acted on the body at reft, would have caufed

it

to

move through

fpace of time,

as

a length equal to

through a length equal to

H I,

were the

is

KL and HI

equal to the

II.

THUS

velocity,

by the

in the

are equal

:

in

fame

paiTino-

impulfe to act on the effects of the firft and

the body when at reft. That is, fecond impulfe on the body when at for

KL

would be taken up by the body iirft

reft

would be

the fame

confequcntly the fecond impulfe

firft.

it

the

repetition

body be returned through

FE with

the

moved forward we have (hewn how of the impulfe, which afted on it at E, the

wherewith

it

;

Ch.

II.

^1,22.

body

CHAP.

PHILOSOPHY.

3.

129

body will return again into the line DE with the velocity, which it had before in that line. By the fame procefs of reabe proved, that, when the body is returned the impulfe, which before acted on the body at that point, will throw the body into the line D C with the ve it firft had in that line ; and the other impulfes locity, which

foning

it

may

back to D,

being fuccelTively repeated, the body will at length be brought back again into the line B A with the velocity, wherewith it fet

out in that

THu

1 1.

ed order

all

s

line.

by acting over again in an invert on die body, bring it back again

thefe impulfes,

their operation

And through the path, in which it had proceeded forward. this obtains whatever be the the number of ftraight equally, whereof this curve figure is compofed. Now by a me thod of reafoning, which Sir I s A A c NEWTON mikes great ufe of, and which he introduced into geometry, thereby

lines,

a

we might make a transition ; of a number of ftraight lines to a compofed one continued a number of feof and from curvature, figure

greatly inriching that fcience

from

this figure

parate impulfes repeated at diftinct intervals to a continual and fhew, that, becaufe what has been centripetal force,

here advanced holds universally true, whatever be the is lines, whereof the curve figure

ACF

ber of ftraight

num com

pofed, and howfoever frequently the impulfes at the angles of this figure are repeated ; therefore the iame will ftill remain true, although this figure fliould be converted into one o! a continued curvature, and thefe diftinct impulfes fliould be *

viz.

His doftrine of prime and ultimate

ratios.

S

changed

Sir I

130

s

AAc

N E w T o N'S

BOOK

I.

changed into a continual centripetal force. But as the explain ing this method of reafoning is foreign to my prefent defign ; fo I

hope

my

readers,

what has been

after

in receiving the propofition laid difficulty

faid,

will find

down above

:

no

that, if

H

I the body, which has moved through the curve line B (in fig. it is come to I, be thrown when to fromB I, diredtly back 74.)

with the fame velocity as that, wherewith it proceeded forward, the centripetal force, by ading over again all its operation on the body, fhall bring the body back again in the line I B

H

and

as the

motion of the body

in

its

:

B to I was eve the line drawn from the

courie from

ry where in fuch a manner oblique to center to the body, that the centripetal

power acled

in

fome

degree againft the body's motion, and gradually diminished it ; fo in the return of the body, the centripetal power will every where draw the body forward, and accelerate its motion

by

the fame degrees, as before

it

retarded

it.

THIS being agreed, fuppofe the body in K to have the A K no longer obliquely inclined to its motion. In this cafe, if the body be turned back, in the manner we have been con1 3

.

line

fidering,

But

if it

it

mutt be directed back perpendicularly to AK.

had proceeded forward,

it

ed in a direction perpendicular to ther

it

move from

defcribe the

turned back

this

point

will

;

likewife have

mov

confeqyently, whe or forward, it muft

K backward

fame kind of courfe. it

would

AK

Therefore fince by being line KI H B ; if it be per

go over again the

mitted to go forward, the line K L, be altogether fimilar to the line

which

it fliall

defcribe,

KH B.

will

4

IN

CHAP.

IN

.

motion, in fig.

PHILOSOPHY.

3.

if

like

the line, wherein the

76.) down toward

body and the

131

manner we may determine the nature of the body

the line

fets

BA

If the centripetal

center.

creafes in flrength, as the

body

out, be inclined (as

drawn between

the

much

in-

power

fo

approaches, that

it

can bend

the path, in which the body moves, to that degree, as to caufe all the lines as A H, A I, A K to remain no lefs oblique to the motion of the body, than A B is oblique to B C ; the body

mall continually more and more approach the center. But if the centripetal power increafes in fo much lefs a degree, as to permit the line drawn from the center to the body, as it ac companies the body in its motion, at length to become more and more erecl; to the curve wherein the body moves, and in

the end, fuppofe at K, to become perpendicular thereto ; from that time the body fhall rife again. This is evident from what

has been faid above y becaufe for the very fame reafon here alfo the body fhall proceed from the point K to defcribe a line alto -

gether fimilar to the line, in which it has moved from B to K. Thus, as it was obferved of the pendulum in the preceding chap ter

a ,

that

lar to

all

the time

the horizon,

it

approaches towards being perpen<iicuas foon as it ; but,

it

more and more defcends

come into that perpendicular Situation, it immediately rifes again by the fame degrees, as it defcended by before : fo here the body more and more approaches the center all the time it

is

is

moving from B

to

K

;

but thence forward

center again by the fame degrees, as

it

it

rifes

from die

approached by before.

57-

S

x

i

.

IF

Sir I

132 I it

5-.

I F (in fig-77-)

A AC

s

the line

has been obferved above

a ,

N E w T o N'S

BOOK!.

B C be perpendicular to A B then ;

that the centripetal

power may

be fo balanced with the progreflive motion of the body, that the body may keep moving round the center A constantly at the fame diftance ; as a body does, when whirled about any point, to

be too

a firing. If the centripetal power it istyed by to produce this effect, the motion of the body become oblique to the line drawn from itfelf to

which

weak

will

prefently the center, after the

manner of the firft of the two cafes, which we have been considering. If the centripetal power be ftronger, than what is required to carry the body in a cir cle,

the motion of the

cond of the

we

cafes,

body

will prefently fall in

with the

fe-

have been confidering.

of

with the

the centripetal power change change that the body, after its motion has become oblique diftance, to the line drawn from itfelf to the center, friall again become 1 6.

fo

I F

perpendicular thereto ; which we have fhewn to be poiTible in both the cafes treated of above ; then the body fhall in its fubfequent motion return again to the diftance of AB, from that diftance take a courfe fimilar to the former

:

and

and

thus, if the body move in a fpace free from all reiiftance, which has been here all along fuppofed ; it (hall continue in a perpetual motion about the center, defcending and afcend-

If the body fetting out from B ( in B C perpendicular to A B, defcribe the line D fhall be oblique to the line A D, but in E

ing alternately therefrom. fig-78.) in the line

B DE, which

in

fhall

J

L'

CHAP.

flrdl again

center

A

;

EFG

line

PHILOSOPHY.

3.

133

become erect to AE drawn from the body in E to the then ironi this point E the body ilia 11 defcribe the altogether like to the line BDK, and at G fhall be

But likewife the fame diftance from A, as it was at B. mall be erect to the body's motion. Therefore the body fhall proceed to defcribe from G the line G H I altoge ther fimilar to the line G I E, and at I have the fame diftance at the line

AG

7

from the

center, as

it

had

at

E

;

and

alfo

have die line

AI

crc .!

following motion muft be in the line I K L fimilar to I H G, and the diftance A L equal to A G. Thus the body will go on in a perpetual round without ceafing, al to

its

motion

:

fo that

its

and contracting

ternately inlarging

its

diftance

from the

center,.

17. I F it fo happen, that the point E fall upon the line B A continued beyond A ; then the point G will fall on B, I on E, and L alfo on B ; fo that the body will defcribe in this cafe a

round the center A, like the line fimple curve line in

79, and from E fig.

which to

it

will continually revolve

B without

B DEE

in

from B to E

end;..

1 8. IF AE in fig. 78 fhould happen to be perpendicular A B, in this cafe alfo a fimple line will be defcribed for the point G will fall on the line B A prolonged beyond A, the point I on the line AE prolonged beyond A, arid the point L

to

on B

;

:

BEG I

fo that the in

fig.

body

80,

are equally diftant

will defcribe a line like the curve line

which the oppolite points B and G from A, and the oppofite points E and I in

are alfo equally diftant

from the fame point A,

ISAAC NEWTON'S

Sir

34

)

BOOK!.

line defcribed will have a more 19. IN other cafes the

complex

have endeavoured to fhew

how

a conftantly attracted towards center,

may

THUS we

10.

while

figure.

it is

a body, notwith-

from

it falling progreflive motion keep to that center ; but defcribe about it an endlefs circuit,

Handing by

down

felf

its

fometimes approaching toward that center, times as

much

BUT

11.

and

at ether

receding from the fame.

we

here

have fuppofed, that the centripetal power

of equal ftrength every where at the fame diftarice from the And this is the cafe of that centripetal power, which center.

is

will hereafter be

fhewn

to be the caufe, that keeps the planets on in a perpetual be a

But body may kept round a center, although the centripetal power have Indeed a body may by a centripetal force not this property.

in their courfes. circuit

be kept moving in any curve line whatever, that fhall have its the center of the force. concavity turned every where towards ,

To

make

this

evident

I fhall firft

propofe the cafe of a

body moving through the incurvated figure ABCDE (in fig. 8 1 .) which is compofed of the ftraight lines A B, B C, C D, D E, and

EA;

the motion being carried on in the following manner. firft move in the line A B with any uniform velo

Let the body

When it is arrived at the point B, let it receive an impulfe diredled toward any point F taken within the figure ; and let the impulfe be of that ftrength as to turn the body out

city.

of

CHAP. of

PHILOSOPHY.

3.

AB

the line

pulfe,

At C

into the line

left to itfelf, will

while

The body

B C.

135 after this irru

continue moving in the line B C.

body receive another impulfe directed towards the fame point F, of fuch ftrength, as to turn the body from At D let the body by another the line B C into the line CD, the

let

impulfe, directed likewife to the point F, be turned out of the And at E let another impulfe, directed to line C D into D E.

ward the point F, turn the body from the line D E into E AThus we fee how a body may be carried through the figure

ABCDE by

certain impulfes directed always toward die fame intervals, by their acting on the body at

center, only

proper

and with due degrees of

ftrength,

BUT

farther, when the body is come to the point A, if there receive another impulfe directed like the reft toward the a degree of ftrength as to turn the point F, and of fuch body into the line A B, wherein, it firft moved ; I fay that the body .

it

fhall return into this line

Let

G

;

with the fame velocity, as it had at firft.

A B be prolonged beyond B at pleafure, fuppofe to G let G H be drawn, which if produced fhould

and from

from B F, or, according to the always continue equidiftant let G H be drawn Then more ufual parallel to B F. phrafe,

it

from what has been

appears,

motion

a

from B

to G,

,

faid

that in the time, wherein the

means of will carry

had

it

not received a

that impulfe it

it

upon the fecond law of body would have moved

new

impulfe in B,

will have acquired a velocity,

from B to H.

by the which

After the fame manner, if C I be

Sir I

s

N E w T o N'S

A A c

BOOK L

IK be drawn equidiflant from or pa have moved from C to K with the body which it has in the line C D, in the fame time, as it velocity, would have employed in moving from C to I with the velocity, it had in the line B C. Therefore fince C I and B H are equal, the body will move through C K in the fmic time, as it would taken equal to BH, and rallel to

CF

;

the

will

have taken up in moving from B to G with the original velo it moved Again, DL through the line AB. city, wherewith to drawn D F ; for and taken to L K C parallel being equal

M

DM

with the fame reafon as before the body will move through the velocity, which it has in the line D E, in the fame time, as

it

would imploy

locity.

NO to

In the

ia(1-

in

moving through B G with if

place,

be drawn parallel to

original ve

be taken equal to DM, and likewife if AP be taken equal

EF;

E O, and P (^be drawn

its

EN

parallel to

AF

:

then the body with

the velocity, wherewith it returns into the line A B, will pafs through A Qjn the fame time, as it would have imployed in

G

with

pafling through B this follows directly from

its

original velocity.

what has above been

Now as all

delivered, con

cerning the efrect of oblique impulfes imprefled upon bodies that it can be in motion ; fo we muft here obierve farther,

proved by geometry, that A Q. will always be equal to EG. proof of this I am obliged, from the nature of my pre-

The fent

dehgn, to omit

granted,

it

follows,

;

but

this

that the

geometrical proportion being into the line

body has returned

the velocity, which it had, when it firft moved in that line; for the velocity, with which it returns into the line

A B with

AB>

will carry

it

over the line

3

A ^in

the fame time, as

would

k

e

CHAP.

PHILOSOPHY.

3.

have been taken up in

its

137

pafling over an equal line

B G with

the original velocity.

THu

s we have found how a body may be carried round A B C D E by the action of certain impulfes upon it^ which fhould all be pointed toward one center. And we likewife fee, that when the body is brought back again to the

1 5-.

,

the figure

whence

point,

it firft fet

pulfe fufficient to

ed

at firfr,

its

turn

it

out

;

if it there

meet with an im-

again into the line, wherein

original velocity will be again reftored

;

it

mov

and by

the repetition of the fame impulfes, the body will be carried Therefore if thefe impulfes, which again in the fame round.

on die body at the points B, C, D, E, and A, continue al ways the fame, the body will make round this figure innu

act

merable revolutions.

1 6. THE

which we have here made ufe

proof,

of,

holds the

any number of ftraight lines, whereof the figure A B D fhould be compofed ; and therefore by the method of reafoning

fame

in

referred to above

been

faid

upon

a

we

are to conclude,

this rectilinear

figure,

that

will

what has here

remain

true, if this

figure were changed into one of a continued curvature, and

inftead of difHnct impulfes acting by intervals at the angles oi force. this have figure, we had a continual centripetal

We

therefore fhewn,

ABC

that a

body may be carried round in any 81.) which rtiall every where be

curve figure ( fig. concave towards any one point as D,

3

T

by the continual

action

cf

Sir I

138

s

AAc

N E w T o N'S

BOOK I.

of a centripetal power directed to that point, and when it is returned to the point, from whence it fet out, it fhall recover it departed from that point. again the velocity, with wrrich it fhould return that It is not indeed again always neceflary,

into

its firft

courfe

figure as the line if the

for the curve line

ABC DBF

may have fome

in fig. 83.

In

out from B in the direction

fet

body

;

BCD,

through the line

till it

this

curve

fuch line,

B F, and moved

returned to B;

here the

body

would not enter again into the line BCD, becaufe the two and B C of the curve line make an angle at the point parts B D

B fo that die centripetal power, which, at the point B could turn the body from the line B F into the curve, will not be able to turn the body into the line B C from the direction, in :

which

it

given the

a 7.

returns to the point B ; a forceable impulfe body in the point B to produce that effect.

I F at

the point B,

whence the body

fets

muft be

out, the curve

8x

then the body, up ; ) ( fig. on its arrival again at B, may return into its former courle, and thus make an endlefs circuit about the center of the cen line return into

tripetal

1.8.

it

felf

as in

power.

WHAT has here been faid,

fure enable

my

readers to

form a

I

hope, will in fome meaof the nature of

juft idea

thcfe centripetal motions.

0,9.

I

HAVE

not attempted to fliew,

what kind of centripetal ly,

force

is

any curve

This

is

line

propofed.

how to find particular

neceflary to carry a body in to be deduced from the de gree

CHAP.

PHILOSOPHY.

3.

139

which the figure has in each point of it, grec of curvature, and requires a long and complex mathematical reafoning. However I (liall fpeak a little to the firft proportion, which Sir

NEWT ON

ISA AC

when

a

lays

down is

for this

found moving

purpofe. By this in a curve line, it

body whether the body be kept in its courfe by a power always pointed toward the fame center ; and if it be fo, The proportion is this that if where that center is placed.

proportion, may be known,

:

drawn from fome

fixed point to the body, and re to that point, it be carried united one extream maining by with the round then, if the power, ; whereby

a line be

body

along

the body is kept in its courfe, be always pointed to this fixed will move over equal fpaces in equal point as a center, this line of time. Suppofe a body were moving through the portions curve line A B C D (in fig. 84.) and paffed over the arches A B,

BC,

CD in

equal portions of time; then if a point, as E, can

be found, from whence the line E A being drawn to the body in A, and accompanying the body in its motion, it {hall make the fpaces

E A B, E B C, and E C D

over which

equal,

it

paf-

fes, while the body defcribes the arches A B, B C, and C D : and if this hold the fame in all other arches, both great a ad fmall, of the curve line A BCD, that thefe foaces are always

equal, this line

30.

where the times are equal ; by a

power

then

always pointed to

E

is

the

body kept

in

as a center.

THE principle, upon which SirlsAAcNEwroN has

demonftrated prehend.

this,

requires but fmall skill in geometry to com

I ihall therefore

take the liberty to clofe the pre-

T

^

icnt

1

Sir I

40

fent chapter with

s

N E w T o N'S

AAc

BOOK L

an explication of it ; becaufe fucli an exam of our author's method of ap

notion ple will give the cleared

to thefe philofophical fubjeds. plying mathematical reafoning 5 I

A

(

.

in

H E reafons thus. to fig. 85-.)

had moved

for

Suppofe a body fet out from the point

move

in the ftraight line

ibme time

in that line,

it

AB

;

and

after

it

were to receive an

Let it receive that imimpulfe directed to fome point as C. turned into the line D E ; and let pulfe at D j arid thereby be the body after pafling from

D. Sir

Then ISAAC

CAD

and

this

D

impulfe take the fame length of time in

to E,

as

it

imployed

the ftraight lines

in the pailing

C A, CD, and C E

NEWTON proves, CDE are equal.

that the

from A

to

being drawn,

and triangular

fpaces

This he does in the following

manner.

fince

LET EFbe drawn

parallel to C D. Then, from what has a it is evident, that upon the fecond law of motion the body was moving in die line A B, when it received

31.

been

faid

,

the impulfe in the direction

DC;

it

will

have moved

after

impulfe through the line D E in the fame time, as it would have taken up in moving through D F, provided it had re ceived no difturbance in D. But the time of the body's mov

that

ing from D to E is fuppofed to be equal to the time of its mov ing through A D ; therefore the time, which the body would have imployed in D F, had it not been di-

moving through

fhirbed in D,

AD

:

is

equal to the time, wherein

confequently

DF *

is

Ch.

it

equal in length to \. fcft.

moved through

AD;

for if the

is,:i.

body

CHAP.

PHILOSOPHY.

3.

body had gone on to move through the it

A D and D F

Now C F

are equal, the triangular fpace

to the triangular fpacc C A D. to C D, it is proved parallel

CED CED 3 3

is is

.

all

equal to the triangle equal to the triangle

Farther,

C D F is equal EF being

i

:

if the

of

the line

*

A F T E R the lame manner,

parts

being drawn,

E u c L D, that therefore CFD C A D. by

in

parts thereof

and have pafled over equal

that line in equal portions of time. iince

A B without

line

would have moved through

terruption, with the lame velocity,

141

body

the trianglethe triangle

receive at

E ano

ther impulfe directed toward the point C, and be turned by if it move afterwards from E to that ; impulfe into the line

EG

G in the lame Ipace of time, as was taken up by

D to E, C E G is

equal to

two former line

A to D C D E.

or from

G H,

to C,

will

;

its

motion from

C G being drawn, the triangle third impulfe at G directed as the

then

A

whereby the body mail be turned into the

have alfo the like

effect

with the

reft.

If the

body move over G H in the fame time, as it took up in mov ing over EG, the triangle CGH will be equal to the triangle

C E G.

Laftly, if the

directed

toward

C

body

at

into the line

pulfe directed alfo to

C

H be turned by a frefh impulfe H I, and at I by another im

be turned into the line

body move over each of the

lines

H I,

and

I

I

K K

;

and

in the

if

the

fame

in moving over each of the preceding and GH then each of the triangles AD, DE, EG, CHI, and C I K will be equal to each of the preceding. Like-

time,

as

it

imployed

lines

:

Elem.

Book

I.

p. 37.

wife

i

Sir I

42

A Ac

s

N E w T o N'S

BOOK

I.

which the body moves over A D E, is the time of its moving over E G H, and to the time

wife as the time,

in

equal to of its moving over

HIK

the fpace

manner is

CEGH,

as the time,

in

equal to the time of

CADEG .

will

;

the fpace

CADE

and to the fpace

will be equal to

CHIK.

In the fame

which the body moved over A DEC

its

moving over G H

be equal to the fpace

I

K,

fo the fpace

C G H I K.

FROM this principle Sir I s A A c N E w T o N dernonftrates

method of arguing introduced by him into geometry, whereof we have before a taken notice by making according to the principles of that the proportion mentioned above, by that

,

method a

from this incurvated figure compofed of to a figure of continued curvature j and by that fmce equal fpaces are defcribed in equal times

tranfition

ftraight lines,

{hewing,

in this piefent figure

compofed of ftraight

lines,

the fame re

between the fpaces defcribed and the times of their dein a figure of one continued fcription will alfo have place lation

curvature.

of

it ;

He

alfo

and proves,

ally defcribed

;

the

deduces from thr.t

body

direded to the center,

at

this

proportion the reverfe

whenever equal fpaces are continu is adled upon by a centripetal which the ipaces terminate.

force

CHA

P.

CHAP.

JP

4.'

H I L O S O P H Y. CHAP.

Of the

143

IV.

RESISTANCE

of

FLUIDS.

which keeps the to know, whe empty and void, or fil

the caufe can be difcovered,

BEFORE

in

motion, it planets ther the fpace, wherein they led with

is

neceffary

move, any quantity of matter.

is

firft

It has been a prevailing opinion, that all fpace contains in it matter of fome kind or other ; fo that where no fenftble matter is found, there was

yet a fubtle fluid fubftance by which the fpace was filled up ; In order to exa even fo as to make an abfolute plenitude. has largely confimine this opinion, Sir I s A A c dered the effects of fluids upon bodies moving in them.

NEWTON

a.

In the

THESE firft

effects

place he

the refiftance,

he has reduced under thefe three heads,

mews how

which bodies

to determine in

fuffer,

what manner

when moving

in a fluid,

gradually increafes in proportion to the fpace, they defcribe in any fluid ; to the velocity, with which they defcribe it ;

and to the time they have been in motion. Under the fecond head he confiders what degree of refiftance different bodies moving in the fame fluid undergo, according to the different proportion between the denfity of the fluid and the denfity of the body. The denfities of bodies, whether fluid or folid, are meafured by the quantity of matter, which is comprehended under the fame magnitude j that body being

the

S* r

144

ISAAC NEWTON'S

BOOK!.

the moft denfc or compact, which under die fame bulk con or which weighs tains the greateft quantity of folid matter,

the weight of every body being obferved above to be a Thus water is to the quantity of matter in it proportional more denfe than cork or wood, iron more denfe than water,

moft,

.

N

The third particular Sir I s. E w T o N iron. coniiders concerning the refiftance of fluids is the influence, which the diverfity of figure in the refifted body has upon its and gold than

refiftance. .

Fo

.

3

R the

more

perfect illuftration of the

firft

he diftinclly fhews the relation between

heads,

all

of thefe

the parti

The culars fpecified upon three different fuppofitions. fame body be refifted more or lefs in the is, that the

firft

fimple proportion to its velocity ; fo that if its velocity be doubled, The fecond is of the its refiftance fliall become threefold.

of the velo-

refiftance incrcafmg in the duplicate proportion city

fo that,

;

ftance

fliall

velocity of a

if the

be rendered four times

trebled, nine times as great as at

body be doubled, ;

firft.

and

if

the

But what

its refi

velocity be is to be un-

derftood by duplicate proportion has been already explain

ed

b .

The

third fappofition

that the refiftance increafes

is,

in the (ingle proportion partly

of the velocity,

and

partly in

the duplicate proportion thereof. 4.

two

I

N

all

refpefts,

thefe

fuppofitions, either as

bodies are confidered under

moving,

*

Ch

i

fc

14..

Ch

and oppofing themfelves * felea. 17.

againft

CHAP.

4.

PHILOSOPHY.

145

fluid by that power alone, which is effcntial to againft the them, of reiifting to the change of their ftate from reft to

motion, or from motion to reft, which we have above cal power of inactivity ; or clfe, as defending or nfcending, and fo having the power of gravity combined witJi led their

Thus our author has fliewn in all thole in what manner bodies are refifted in an uniform fluid, when they move with the aforelaid progreilive motion ; and what the refiftance is, when they afcend or that other power.

three fuppofitions, a

defcend perpendicularly obliquely, and the it is

locity,

form

fliewn

b

And

.

if

a

body afcend or defcend

be fmgly proportional to the ve the body is refifted in a fluid of an uni

refiftance

how

and what

c

which is de , termined by the meafurement of the hyperbola, and ap no to other than that be firft considered in line, pears par d ticular by Dr. B A R R o w , which is now known denflty,

line

it

will delcribe

commonly

by the name of the logarithmical iition

curve.

In the fuppo-

that the refiftance increafes in the

tion of the velocity,

duplicate propor our author has not given us the line

which would be delcribed

in

an uniform

fluid

;

but has in-

ftead thereof difcufled a problem, which is in fome fort the reverfe ; to find the denlity of the fluid at all altitudes, by

which any given curve line may be defcribed ; which pro blem is fo treated by him, as to be applicable to any kind of e refiftance whatever But here not unmindful of practice, .

he a

fliews that a Newt. IV. p.

body

Princ. L. II. prop. 2 3

;

b',

9; 13, 14.

;

in a fluid of uniform denfity, like the

5, 6, 7

;

1

1

,

12. e

Newton.

Princ. Lib.

II.

prop. 10.

c

Prop. 4,

V

air,

Sir I

AAc

s

will defcrfbe a line,

air,

that

N E w T o N'S

BOOK L

which approaches towards an hy

motion will be nearer to that curve

line perbola than to the parabola. And confequent upon this remark, he fhews how to determine this hyperbola by experiment, and refolves the chief of thofe problems relating to proje briefly* ;

its

3 are in ufe in the art of gunnery, in this curve ; others have done in the parabola b , c inventions have been explained at large above .

which

ctiles,

as

is,

TORRICEL.LI and

whofe

OUR

f.

lar fort

author has alfo handled diftinctly that particu

of motion, which

is

d

defcribed by

has likewife confidered fome few cafes

pendulums ; and of bodies movin^ in

round a center, to which they are impelled by a centripetal force, in order to give an idea of thofe kinds of

refitting fluids

motions

e .

6. T H E treating of the refiftance of pendulums has en him an opportunity of inferring into another part of his work fome fpeculations upon die motions of them with out refinance, which have a very peculiar elegance ; where

them as moved by a gravitation acting in the law, which he fhews to belong to the earth below its

in he treats of

furface

force

f

performing in

;

this

kind of gravitation, where the

H

proportional to the diftance from the center, all that u Y G E N s had before done in the common fuppofition of

its

being uniform, and acting in parallel lines

a

*!

is

Newton.

Princ. Lib II

T

*?? 8y,&c.

Ch. 2

* Ifcwt. Princ

L

prop

10. in fchoj.

L. II. fcft 4.

I

U grayium { E II

fcft.f.

^

g.

S

B

Lib.

-

I.

u ch 6 / fc$. 10

7-

<>f this

7.

HUY-

PHILOSOPHY.

CHAP.4-'

HuYGEN

7.

s

end of

at the

H7

of the caufe of

his treatife

a

informs us, that he likewife had carried his fpecuof the refiftance in lations on the firft of thefe fuppofitions,

gravity

fluids being proportional to the velocity of the body, as far as But finding by experiment that the fecond was our author.

more conformable to nature, he afterwards made fbme proin that, till he was not being able to execute to his grefs flopt, by wifli what related to the perpendicular defcent of bodies ; not obferving that the meafurement of the curve line, he made ufe of to explain it by, depended on die hyperbola. Which overfight

may

well be pardoned in that great man,

confi-

dering that our author had not been pleafed at that time to communicate to die publick his admirable difcourfe of the

QUADRATURE Or MEASUREMENT OF CURVE

LINES,

With which he

has fince obliged the world: for without the ufe of that it is I think no treatife, injury even to our author's unparal leled abilities to believe,

it

would not have been

himfelf to have fucceeded fo happily in of his writings. parts

WH

8.

were

in

AT

HuYGEN

s

this

eafy for

and many other

found by experiment, that bodies of their ve

refitted in the duplicate reality proportion b

agrees with the reafoning of our author , who diftinguifhes the refinance, which fluids give to bodies by the tena city of their parts, and the fridlion between them and the bo locity,

dy, from that, which

*

from the power of inactivity, witli of fluids are endued like all particles

arifes

which the c^nftituent

b

pc]aPdan:eur,pag. 169, and the foDowing.

V

|

1

Newton.

Princ. L. 11.

prop

4. fcho].

other

Sir

148

ISAAC NEWTON'S

BOOK

I.

other portions of matter, by which power the particles of fluids like other bodies make refinance againft being put into motion,

9.

THE

refinance,

which

arifes

from the

friction

of the

fluid, muft be very inconfiderafollows from the which the and refinance, ble; tenacity of the parts of fluids, is not ufually very great, and does not

body againft the parts of the

depend much upon the for as the parts

velocity of the

body

in the fluid

;

of the fluid adhere together with a certain

degree of force, the refiftancc, which the body receives from much depend upon the velocity, with which

thence, cannot the

body moves ; but

like the

power of gravity,

be proportional to the time of

may

its

find farther explained by Sir

acting.

SOPHICAL TRANSACTIONS,

which moft

N

$71.

fluids give to bodies,

inactivity in the parts

of the

by

The arifes

and

effect

muft

NEWTON himfelf

ISAAC

in the poftfcript to a difcourfe publifhed

its

This the reader

me

in

THE PHILO

principal refinance,

from the power of

this

depends upon the with which the body moves, on a double account. In the firft place, the quantity of the fluid moved out of fluids,

velocity,

place by the

moving body

in

any determinate fpace of time

proportional to the velocity, wherewith the body moves; and in the next place, the velocity with which each particle of the fluid is moved, will alfo be proportional to the velocity of the body therefore fince the refinance, which makes is

:

any body

againft being put into motion, is proportional both to the quan of matter moved and the velocity it is moved with ; the tity refinance, which a fluid gives on this account, will be in-

doubly

creafed with the increafe of the

velocity in the

moving body; that

CHAP. that

PHILOSOPHY.

4.

149

the refiftance will be in a two-fold or duplicate propor wherewith the body moves through the

is,

tion of the velocity, fluid.

FARTHER

10.

moft manifeft,

it is

that this latter kind

of refiftance increafing with the increafe of velocity, ever* in a greater degree than the velocity it felf increafes, the fwifter the

body moves, the of reftftance will bear to this ance

may be till

city, this,

fo

proportion the other fpecies this part of the refift

lefs

nay that

:

much augmented by

a due increafe of velo

the former refiftances fhall bear a

rience fhews, that

no other

refiftance,

lefs

And

than any that might be afligned.

proportion to indeed expe

than what

arifes

from

power of inactivity in the parts of the fluid, is of mo ment, when the body moves with any confiderable fwiftnefs. the

THERE

11.

befides thefe yet another ipecies of refift are elaftic. fluids, as, like our air,

is

ance, found only in fuch to Elafticity belongs this lefs

no

fluid

known

of property any quantity

air

1 fpace by a forcible preffure,

prefting

power

is

removed,

The

former dimenfions.

air

it

to us befide the

may and

air.

as

foon as the com-

will fpring out again to

we

By

be contracted into a

breath

is

held to

its

its

prefent

And as this in by the weight of the air above us. cumbent weight, by the motion of the winds, or other caufdenfity

frequently varied

es,

is

fo

when

this

weight

is

(

than at other times.

To

it felf

ii

by

its

fpring,

which appears by the barometer;) we breath a more denfc air

greateft,

what degree the air would expand preffure were removed, is not

all.

known,

Sir I

s

AAc

NEwTo

BOOK L

N'S

yet into how narrow a compafs it is capable Mr. BOYLE found it by experiment of being comprefled. both of expanflon and compreflion to fuch a degree, capable

known, nor

that he could caufe a quantity of air to expand it felf over a than the fpace to fpace fome hundred thoufand times greater, a But I {hall which he could confine the fame quantity b in the air hereafter this I am more of treat fully fpring now only to confider what refinance to the motion of bodies .

.

arifes

from

it.

BUT

II.

what manner

before our author /Lews in

this

caufe of refiftance operates, he propofes a method, by which fluids may be rendered claftic, demonftrating that if their particles

which

be provided with a power of repelling each other, exert it felf with degrees of ftrength recipro

friall

cally proportional to

the diflances between the centers of

the particles ; that then fuch fluids will obferve the fame rule in being comprefled, as our air does, which is this, that the fpace, into which it yields upon compreflion, is recipro c The term cally proportional to the comprefling weight .

d reciprocally proportional has been explained above . And if the centrifugal force of the particles acted by other laws, fuch

fluids

would

yield in a different

manner

to compreflion

c .

13. WHETHER the particles of the air be endued with fuch a power, by which they can act upon each other out of contact, cur author does not determine ; but leaves that 1

the *>

See his Tract on the admirable raiifaclion of

Book

r

4

air.

II.

Ch.6.

e

Princ.ph;lof. Lib. If. prop. 11.

Book

I.

Ch

z.

30

Princ. philof. LID. II. pr p. 25. in fchol.

3

to

CHAP.

PH I L O S O

.'

to future examination,

P

H Y.

and to be difcufled by

philofophers.

Only he takes occafion from hence to confider the refift ance in claftic fluids, under this notion; making remarks, as he

pafles along,

upon the

differences,

which

will arife, if their

be derived from any other fountain a And this, I elafticity think, muft be confefled to be done by him with great judg .

for this

ment;

is

far the

moft reafonable account, which has

been given of this furprizing power, as muft without doubt be freely

acknowledged by any one, who

been framed

;

in the leaft eonfiders

the other conjectures, which have and alfo how little reafon there is to deny to

the infufficiency of

all

bodies other powers, by which they may act upon each other at a diftance, as well as that of gravity ; which we fhall here

fhew to be a property univerfally belonging to all the b bodies of the univerfe, and to all their parts Nay we actu in a the loadftone very apparent repelling, as well asfind ally after

.

an

attractive

But of this more

power.

in the conclufion

of

this difcourfe.

14.

BY

thefe fteps our author leads the

the refiftance, to bodies thus.

by

which the their

air

and fuch

which ; power of the

elafticity

If the elaftic

way

to explain

like fluids will give

refiftance

fluid

he explains

were to be va

ried fo, as to be always in the duplicate proportion of the of the refifted velocity body, it is fhewn that then the refiftance derived

from the

would

elafticity,

duplicate proportion of the velocity y -

3 Princ. philof. Lib. II, prop. 33. coroll.

in fo fc

|

Lib.ll.

increaie in the

much

that the

Ch.f.

whole

Sir I whole ly

NE

AAc

would be

refiftance

which

that (mall part,

body and the

s

in that

arifes

\v

To

proportion, exceptii g on

from the

power of the fame

truth continue the fame, if the velocity of the

the whole refinance, will decreafe in a

lels

it

follows,

fluid

does in

moving body be

the refinance from the elafticity,

diminifhed,

between the

friction

From whence

parts of the fluid.

that becaufe the elaftic

BOOK I.

N'S

and

therefore

proportion, than the

duplicate of the velocity; and if the velocity be increafed, the refinance from the elafticity will increale in a lels proportion,

than the duplicate of the velocity, that

than the refinance parts

of the

made by

And from

fluid.

the

is

in a lels

power of

foundation

this

proporti*-

of

inz(

is

railed

i..e

-of

t!

of a property of this refinance, given by the elafcicity in com mon with the others from the tenacity and friction of the parts

of the fluid

;

that the velocity

may

be increafed,

t

;

;l

this

refinance from the fluid's elafticity fhail bear no confidcrable proportion to that, which is produced by the pov.cr of inacti vity thereof

a

From whence our

.

author draws

this

conclu-

fion; that the reiiftance of a body, which moveo very fwiftas if the fluid were ly in an elaftic fluid, is near the lame,

not

; provided the elafticity arifes from the centrifugal of the of the medium, as before power parts e.vpained, cipeciif the ally velocity be fo great, that this

claftic

fliall

want time

to exert

that in the proof of

it

all this

pofition of this centrifugal if the elafticity be caufed

felf

b .

But

it

centrifugal power is to be obicrvcd,

our author proceeds upon the fup-

power

in the

by the expanfion of the

Ibid.

Prop. 33. coroll.i.

|

fie

fluid

;

but

parts in die

k Ibid, ccro"; 3.

manner

CHAP 4

PHILOSOPHY.

:

manner of wool comprefied, and and

their

by which

fucli like bodies,

the parts of the fluid will be in together,

153

fome meafure entangled

motion be obftrud:ed,

the fluid will

be in a manner tenacious, and give a refiftance upon that ac count over and above what depends upon its elafticity on a

ly

and the

;

refiftance derived

judged of in the manner before I ^. ry

;

I

T

which

is is

from that caufe

is

to

be

down.

fct

now

time to pafs to the fecond part of this theo-i to ailign the meafure of refiftance, according

to the proportion between the denfity of the body and the What is here to be underftood by the denfity of the fluid. b For this purpofe word denfity has been explained above .

as

our author before coniidered two diftind: cafes ot bodies

moving

in

mediums

die fluid by their

;

one when they oppofed themfelves to and another inactivity only,

power of

afcending or defcending their weight was com^ fo likewife, the fluids them bined with that other power

when by

:

be regarded under a double capacity; either at reft, and difpofed freely without retheir having parts

felves are to as

ftraint

,

weight,

or as being compreffed together by or any other caufe.

16. IN the

firft cafe,

if the

difingaged from one another, ty to

move

that if

parts

fo that

their

own

of the fluid be wholly each particle

is

at liber

ways without any impediment, it is fhewn, a globe move in Rich a fluid, and the globe and all

k

ViJ, ibid.coroll. 6.

\

X

In

$2.

tides

Sir

tides of the fluid are as the

bound fame

NE

ISAAC

endued with

To

\v

N'S

BOOK I

perfect elafticity

;

fo that

globe impinges upon the particles of it, they {hall off and feparate themfelves from the globe, with the

velocity,

the refinance, locity fuffers,

of the globe, third parts of

with which the globe ftrikes upon them ; then which the globe moving with any known ve is

to be thus determined.

wherein

the time, its

own

From

the

velocity

would move over two

it

diameter with that velocity, will be as the denfity of the fluid bears

known. And fuch proportion

to the denfity of the globe, the fame the reflftance given to the globe will bear to the force, which acting, like the power

of gravity, on the globe without intermiflion during the {pace of time now mentioned, would generate in the globe the

fame degre of motion, as that wherewith a But if neither the globe nor the fluid .

be

fluid

elaftic

fo that the

,

particles,

moves

in the

particles

of the

it

when

the globe

them, do not rebound from it, then the b reflftance will be but half fo much Again, if die par ticles of the fluid and the globe are imperfectly elaftic, fo ftrikes againft

.

from the globe with part only of that velocity wherewith the globe impinges upon them ; then the refiftance will be a mean between the two preced ing cafes, approaching nearer to the fir ft or fecond, accor that the particles will fpring

ding

as the

17.

elafticity

THE

elafticity,

cles of the fluid, 1 '-

is

is

more or which

lefi

is

c .

here afcribed to the parti

not that power of repelling one another,

Princ. philof. Lib.II. Prop.

?

/.

I

c

Id.

[bid.

4

when

CHAP. 4 when

PHILOSOPHY.

.

out of contact,

whole

tioned, the

an

be rendred

as

elaflicity only,

may many folid

whenever any

their figure,

elaftic

men

been

as has before

by which,

fluid

155

;

but fuch

bodies have of recovering

forcible

change

made in it, by Which elafticity

is

the impulfe of another body or otherwife. a has been explained above at large .

TH

1 8.

by

dy,

i

s is

die cafe of difcontinued fluids,

prefling againft their

in fluids

which are comprefled,

moved out of

place by the

behind the body, and left

is

fluid

particles,

while the fpace behind the body

itfelf,

fill

vacant, the refinance

which

but half as

fhall

much

refifted

body

all

them

before

But empty. of them re

parts

immediately

which

is ft ill lefs ;

be free from

is left

fo that the

that fpace,

where the bo

drives

for a globe in

elafticity,

retire

in the other cafe-

fuch a

will be refifted

as the leaft refiftance in the

former cafe

b-

But by elafticity I now mean that power, which renders the whole fluid fo ; of w hich if die comprefled fluid be poflefled, r

in the

manner of the

air,

then the refiftance will be greater

than by the foregoing rule ; for the fluid being capable in fome degree of condenfation, it will refemble fo far the cafe of unc But, as has been before related, comprefled fluids ference is moft confiderable in flow motions. .

this dif

IN the next place our author is particular in deter mining the degrees of refiftance accompanying bodies of different figures ; which is the laft of the three heads, we 19.

3

h.

i.

(j

19.

coroll. r. |

ic.philof.Lib.II.Prop.38,

compared with

X

of prop.;>-.

L.II.

I

x

Lem.

j.'lchol. pag. 341.

divided

Sir I

s

AAc

N E w T o N'S

BOOK I. And

divided the whole difcourfe of refiftance into.

in this

dilquifition he finds a very furprizing and unthought-of dif He proves, ference, between free and compreffed fluids.

that in the former kind, a globe fuffers but half the refift ance, which the cylinder, that circumfcribes the globe, will a But in the lat do, if it move in the direction of its axis .

he proves,

ter

b

And

and cylinder are

that the globe

refifted a-

that let the fhape of bodies be ever fo different, yet if the greateft fections of the bodies perpendicular to the axis of their motion be equal, the like

.

in general,

bodies will be refifted equally

PURSUANT

ao.

c .

to the difference found between the re-

and cylinder in rare and uncompreffed our author gives us the refult of fome other inquiries cf the fame nature. Thus of all the fruftums of a cone,

fiftance of the globe fluids,

that can be defcribed altitude,

will its

he fhews

be the d

axis

.

upon the fame

how

and with the fame which of all others

bafe

to find that,

when moving in the direction of from hence he draws an eafy method of al

leaft refifted,

And

tering the figure of any fpheroidical folid, city

ed

fo

that its capa be enlarged, and yet the refiftance of it diminiiha note which, he thinks may not be ufelefs to

may

e :

fhip-

He concludes with determining the folid, which wights. will be refifted the leaft that is poffible, in thefe difcontinued fluids

f .

Lib. II. '<

Fr P- 34^ Lem. 7 .p.34,.

Scho], to

Lcm.7.

I

* e

J..

^

Prop. 34. fchol. ibid. Ibid.

3.1.

THAT

CHAP.

PHILOSOPHY.

4.

THAT

a I.

r

57-

may here he undcrftood by readers unac with mathematical terms, I mall explain. what I quainted mean by a fruftum of a cone, and a fphcroidical folid. I

A

A

cone has been defined above.

when

fruftum

part of the cone next the vertex

tion parallel to the bafe

of the cone,

is

is

cut

what remains,

away by

as in fig. 8 6.

a fec-

A fpheroid

is produced from an ellipfis, as a fphcre or globe is made from a circle. If a circle turn round on its diameter, it de-

fcribes by its motion a fphere; fo it an has been defined above, and will be

hereafter

a

(which figure

eliipfis

more

fully explained

be turned round either upon the longeft can be drawn through the middle of

)

fhorteft line, that

-

v

it,

there will be defcribed a kind of oblong or flat fphere, as Both thefe figures are called ipheroids, and any in fig. 87. folid

refcmbling thefe

.

IF

it

I

here

call

fhould be asked,

fpheroidicaL

how

the

facilitating a fhip's

motion,

when

method of

altering

can contribute to the

fpheroidical bodies, here mentioned, I

juft

above affirmed,

the figure of bodies, which move in a comprefTed fluid not elaftic, has no relation to the augmentation or di minution of the refiftance; the reply is, that what was

that

there fpoken relates to bodies deep

immerged

into fuch flu

but not of thofe, which (wim upon the furface of them; for in this latter cafe the fluid, by the appulfe of the an

ids,

terior parts

furface,

of the body,

raifed

is

and behind the body Book

II,

is

Ch.

above the

level

of the

funk fomewhat below; i.

;

$4.

that

Sir

ISAAC NEWTON'S

BOOK!.

that by this inequality in the fuperficies of the fluid, that is higher than part of it, which at the head of the body the fluid behind,

will

manner of difcontinued

fome meafure after the analogous to what was be

in

refift a

fluids

,

happen in the air through its elafticity, b And the furrounded on every fide by it be though body as far as the thefe caufes extends, the figure of the of power fore obferved to

.

for it is evident, that the moving body affects its refiftance the parts of the fluid, figure, which preffes leaft directly againft and fo raifes leaft the furface of a fluid not elaftic, and leaft ;

comprefies one that .

is

will

elaftic,

be

leaft refifted.

THE way dfcbUefting the difference of the refiftance

in rare fluids,

which

from the

arifes

diverfity

of figure, is of the fluid

'by considering the different effedl of the particles

upon the body moving againft them, according to the diffe rent obliquity of the feveral parts of the body upon which they refpectively ftrike ; as it is known, that any body im pinging againft a plane obliquely, ftrikes with a lefs force, than if it fell upon it perpendicularly ; and the greater the obliquity if

thing,

a 4.

is,

the

the weaker

body be

THAT

of a body and thus. fluid, a

there its

is

And

the force.

is

at reft,

is

the fame

no connexion between the

c

it

.

figure

refiftance in

compreffed fluids, is proved (infig.88.) to be a canal, having fuch a

Suppofe A B C D water for inftancc, running through

Vid. Newt.princ. in fchol. to

tib.II. pzg. 341.

it

and the plane move againft

Lcm.

7,

b

of j

c j

Scft.

17.

of

it

this

with an equable

chapter.

see Princ.philof.Lib.il, prop. 34.

v

"locity

;

CHAP.

PHILOSOPHY.

4.

and let any body E, by being placed in the axis ; It is evi of the canal, hinder the paflfage of the water. dent, that the figure of the fore part of this body will

velocity

have

little

the whole

influence in obftrudting the water's motion, but impediment will arife from the fpace taken up

by the body, by which it diminishes the bore of the ca a But pro nal, and ftraightens the paflage of the water portional to the obftruftion of the water's motion, will be .

b Now fuppole upon the body E of the canal to be clofed, and the water in it reft ; the body E to move, Ib that the parts

the force of the water

both orifices to

remain

at

of the water

may

pals

they did before ; ffure of the water as

by

it is

.

it

with the lame degree of velocity,

beyond contradiction, that the

upon the body,

that

pref-

the refiftance

is,

the lame ; and there gives to its motion, will remain c fore will have little connexion with the figure of the body .

it

1$.

BY

a

method of realbning drawn from the fame foun

determined the meafure of refiftance thefe compreffed fluids give to bodies, in reference to the proportion between This mall be the denfity of the body and that of the fluid.

tain

is

explained particularly in

my comment on

Sir I

s.

N E w T o N'S

mathematical principles of natural philofophy ; but is not a proper fubjecl to be infifted on farther in this place.

WE have

now gone through all the parts of this There remains nothing more, but in few words to mention the experiments, which our author has made, both 16.

theory.

a

Vid. Princ.philof.Lib.

II.

Lem.j-. p. 314.

b (

Lcmm.

6.

r |

Ibid,

v \v

;

Sir

ISAAC NEWTON'S

BOOK!.

bodies foiling perpendicularly through water, and the b \ and with pendulums : all which agree with the theory. In the cafe of falling bodies, the times of their fall determin

air

ed by the theory come out the fame,

as

by obfervation, to a

in the pendulums, the rod, by which furprizing exactnefs ; the ball of the pendulum hangs, fufTers refiftance as well as

die ball, and the motion of the ball being reciprocal, it com municates fuch a motion to the fluid, as increafo die refift

ance;

but the deviation from the theory is no more, than may reafonably follow from thefe caufes.

2.7.

B Y diis theory of the refiftance of fluids, and thele ex

periments, our author decides the queftion fo long agitated among natural philofophers, whether all fpacc is abfolutely The Ariftotelians and Cartefians both aflert full of matter. this plenitude

;

the Atomifts have maintained the contrary.

-Our author has chofe to determine this queftion by >f refiftance, as Hiall be explained in the

his

theory

following chapter.

* NewtPrinc,

Lib. Il.prop. 40. in fchol.

* \

Lib. II. in fchol. port prop. 3 1.

OOK

CHAP.

i.

PHILOSOPHY.

BOOK

II.

CONCERNING THE

SYSTEM

of the C

That

the Planets

H A

move

P.

WORLD, I.

in a fpace

empty of

all fenfible matter,

HAVE firft

now gone through

part of

my defign,

the

and have ex

plained, as far as the nature of

undertaking would permit, Sir I

s

AAc

NEWTON

my

what

has delivered

general concerning die motion It follows now to of bodies. {peak

in

of the

difcoveries,

he has made

in the fyftem of the

Y

world

;

and

1

62

Sir I

s

AAc

N E w T o N'S

BOOK II.

and to fhew from him what caufe keeps the heavenly bo But it will be neceffary for the life of

dies in their courfes.

fuch, as are not skilled in aftronomy, to premife a brief defcription

of the planetary fyftem.

THIS

1.

the middle

In difpofed in the following manner. him fix globes con fun. About the placed Thefe are the primary planets; that which

fyftem is

tinually roll. is

is

is called Mercury, the next Venus, our earth, the next beyond is Mars, after and the outermofl of all Saturn. Befides thefe

neareft to the fun

next to

him

this

Jupiter,

is

there are difcovered in this fyftem ten other bodies, which move about fome of thefe primary planets in the fame

Thefe are called move round the fun. The moft fecondary planets. confpicuous of them is the moon, which moves round our earth four bodies move in manner,

as

they

;

manner round Jupiter ; and five round Saturn. Thofe which move about Jupiter and Saturn, are ufually called fatellites; and cannot any of them be feen without a telike

It

lefcope.

is

not impoflible, but there

may

be more

fe

condary planets, befide thefe ; though our infbuments have not yet difcovered any other. This difpofition of the planetary or folar fyftem

is

reprefented in

fig.

89.

THE

fame planet is not always equally diftant from But the middle diftance of Mercury is between of the diftance of the earth from the fun ; Venus

the fun. '-

is

and

}

diftant

earth

;

from the fun almoft

~

the middle diftance of Mars

of the diftance of the is

fomething more than half

B

r>,

/.

CHAP.

PHILOSOPHY.

i.

much

half as

as the diftance

again,

middle diftance exceeds middle diftance

the

;

3

Jupiter's

of

diftance

the

part of this diftance ; Saturn's fcarce more than 9-; times the diftance

is

between the earth and fun the earth

times

of the earth

and

by between

earth,

five

r<J

and fun

but the middle diftance between

;

about 1177o times the fun's femidi-

is

'

ameter.

4. eaft

;

ALL

in

eft

thefe planets

move one way, from weft

and of the primary finiiliing

of Saturn

falls

planets

round the

courfe

its

the moft remote

The

fun.

fhort only fixteen days

is

to

long-

period

of 19 years and

The period of Jupiter is twelve years wanting aThe period of Mars falls fhort of two years bout yo days. about by 43 days. The revolution of the earth conftitutes

a half.

Venus performs her period

the year.

and mercury y.

in

in

about zi 4^ days,

days.

courfe of each planet lies throughout in one in which the fun is placed ; but they do move in the fame plane, though the different planes,

all

flat (urface,

which they move,

crofs each other in

each other in

They

all crois

fun

becaufe the fun

;

88

THE

plane or

not

in about

lies in

lines,

which

very frnall angles. pafs through the

the plane of each orbit.

inclination of the feveral orbits to each other fig.

90.

The

line,

in

is

which the plane of any

the plane of the earth's motion, of that orbit.

Y

is

l

This

reprefented in orbit croiles

called the line of the nodes

6.

EACH

Sir Is

EACH

6.

we

planet

NEWTON'S BOOK II.

A AC

moves round the fun

in the line,

have mentioned above a under the name of

I fhall

how

mew more

here

there faid to

how

form

it

it

is

particularly

produced

to defcribe.

in the cone.

which ;

which I

have

now mew

I fhall

Fix upon any plane two

a plane.

upon

how

ellipfis

pins,

A and B in fig. 9 1 To thefe tye a firing A C B of any Then apply a third pin D fo to the ftring, as to hold length.

as at

.

ftrained ; and in that manner carrying this pin about, the If through the points A, point of it will defcribe an ellipfis. B the ftraight line be drawn, to be terminated at it

EABF

the

ellipfis

in the

E and

points

F,

this

is

the longeft line

of any, that can be drawn within the figure, and is call ed the greater axis of the ellipfis. The line GH, drawn perpendicular to

this

axis

middle of

it,

and B are

called focus's.

is

EF,

fo as to pafs

called the leffer axis.

through the

The two

points

A

Now

the fun in a line of this

each planet moves round kind, fo that the fun is found in

focus. Suppofe A to be the Then E place of the fun. the point, wherein the planet will be neareft of all to the The point E is call fun, and at F it will be mofl remote.

one

is

In G ed the perihelion of the planet, and F the aphelion. and H the planet is faid to be in its middle or mean diftance;,

AG

becaufe the diftance

tween

AE the

leaft,

and

or

AF

AH

is

truly the

the greateft diftance.

middle be In

fig.

91.

how

the greater axis of each orbit is iltuated in reprefented the of reft. The refpecl proportion between the greateft and leaft diftances of the planet from the fun is very different

is

in the different planets. Book

i.

ch.z

In Saturn the proportion of the i8 lt

greateft

no -x

CHAP.

PHILOSOPHY.

i.

165

to the leafl is fomething lefs, than the propor greateft diftance tion of 9 to 8 ; but much nearer to this, than to the propor

o

In Jupiter this proportion is a little greater, In Mars it exceeds the proportion of 10. In the earth it is about the proportion of go to iy.

tion of I

to

than that of

6

to

5*.

9.

1 1 to

And in Mercury it is near to that of 70 to 69. comes not a great deal fhort of the proportion of 3 to In Venus

7.

EACH

the line

of thefe planets

fo

moves through

its

ellipfis,

it

i.

that

drawn from

the planet in

its

the fun to the planet, by accompanying motion, will defcribe about the fun equal {pa

ces in equal times, after the centripetal forces

a .

manner fpoke of in the chapter of

There

is

alfo a certain relation

between

the greater axis's of thefe ellipfis's, and the times, in which Which the planets perform their revolutions through them. relation be expreffed thus. Let the period

may

of one planet be denoted by the letter A, the greater axis of its orbit by D ; let the period

A

D

B

of another planet be denoted by B, and the Then greater axis of this planet's orbit by E.

C

E F

G

C

be taken to bear the fame proportion to B, as B bears to A ; likewife if F be taken to bear the fame pro and G taken to bear the fame ; portion to E, as E bears to if

D

proportion likewife to F, as E bears to D ; then the fame proportion to C> as D bears to G. 8.

THE

primary,

fecondary planets

much

in the

move round

fame manner 1

Book

I.

Ch,j.

as the

A

{hall bear

their refpective

primary do round

29.

the

1

66

Sir I

s

AAc

N E w T o N'S

But the motions of thefe

the fun.

And

a

fhall

BOOK II.

be more fully ex

befides the planets, another fort of bodies, which in all probability move round the fun ; I mean the comets. The farther defcription of which bodies

plained hereafter

there

on

.

without

all fo

number

is

this

fyftem the fixed

remote from

ble of contriving

which we

particularly

h

JAR

Thefe are

is,

where they are to be

leave to the place,

I alfo

treated

9.

.

any means

us, that

we

ftars

are placed.

feeni almoft

incapa

to eftimate their diftance. Their

Befides two or three thoufand, exceeding great. fee with the naked eye, telefcopes open to our view

vaft

numbers

are,

we

ftill

;

and the

difcover

farther

improved thefe inftruments Without doubt thefe

more and more.

are luminous globes, like our fun, and ranged through the wide extent of fpace ; each of which, it is to be fuppofed, perform the fame office, as our fun, affording light and heat

to certain planets moving about them. are not to be purfued in this place.

10.

SHALL

therefore

now

thefe conjectures

proceed to the particular de-

no chapter, and mew, that there is the move. in the where fpace lodged planets

fign of ter

I

But

11.

this

THAT

fuch matter,

is

ienfible

mat

they fuffer no fenfible reiiftance from any evident from the agreement between the obfer-

vations of aftronomers in different ages, with regard to the their time, in which the planets have been found to

perform

1

Ch.

3.

of

this prclent

book.

b

Ch.4.

periods.

CHAP.

PHILOSOPHY.

i.

i6 7

was the opinion of DESCARTES a , that the be kept in their courfes by the means of a fluid planets might which matter, continually circulating round fhould carry But

periods.

it

There is one appearance that the planets along with it. to favour this opinion ; which is, that the fun turns feem may The round its own axis the fame way, as the planets move. earth alfo turns

round

moves round the

its

axis the

fame way,

as the

moon

And

the planet Jupiter turns upon its axis the fame It way, as his fatellites revolve round him. might therefore be fuppofed, that if the whole planetary region

were

with a fluid matter, the fun, by turning round on axis, might communicate motion firft to that part of

filled

own

its

earth.

which was contiguous, and by degrees propagate After the fame the like motion to the parts more remote. manner the earth might communicate motion to- this fluid, to the fluid,

adiftance fufficient to carry round the moon, and Jupiter com Sir I s A A c municate the like to the diftance of its fatellites.

NEWTON has particularly of fuch a motion

as this

b ;

examined what might be the refult and he finds, that the velocities,

with which the parts of this fluid will move in different diftances from the center of the motion, will not agree with the

motion obferved in different planets time of one intire circulation of the :

for inftance,

that the

wherein Jupiter fhould fwim, would bear a greater proportion to the time of one intire circulation of the fluid, where the earth is ; than the fluid,

But he of the earth. period of Jupiter bears to the period c a in fuch circulate that the cannot alfo proves , fluid, planet 3

b

In Princ. philof.part. Philof. princ. mathem.

Scfchol. Lib. II.

prop.

2.

c

Ibid,

prop fj. fc

1

68

NEWTON'S

ISA AC

Sir

BOOK II.

fo as to keep long in the fame courfe, unlefs the planet and the contiguous fluid are of the fame deniity, and the planet be carried along with the fame degree of motion, as the fluid.

There

is

alfo

another remark

made upon

motion by our

this

fome

vivifying force will be continual a The fun in par ly neceflary at the center of the motion ticular, by communicating motion to the ambient fluid, will

author; which

is,

that

.

lofe

from

it

felf as

fome acting motion continually. unlefs

much

motion, as

of motion would continue if the fluid till

there

it

imparts to the fluid

;

in the fun to renew its principle refide If the fluid be infinite, this gradual lofs

were limited,

till

the whole fhould

this lofs

would remain no

b

op ; and of motion would continue, ft

fwifter a revolution in the fun,

than in the utmoft part of the fluid ; fo that the whole would turn together about the axis of the fun, like one folid lobe

c .

T

farther to be obferved, that as the planets do not round the fun ; there is a greater difr.ance between their orbits in fome places, than in others. For

II.

move

I

is

in perfect circles

inftance, the diftance

between the

orbit of

Mars and Venus

is

near half as great again in one part of their orbits, as in die Now here the fluid, in which the earth oppofite place.

fhould fwim, mutt

move with

a lefs rapid motion, where greater interval between the contiguous orbits ; but the contrary, where the fpace is ftraitefr, the earth moves

there

on more

is

this

flowly, than

where

Philof, princ. prop, j-z, coroll4. b Ibid.

wideft

it is

c J|

d .

Cor oil. n. See ibid.fchol.

port prop.

5-3

.

13,

FARTHER

CHAP.

PHILOSOPHY.

i.

FARTHER,

Ig.

if this

our globe of earth

169

fwam

in a fluid

of equal denfity with the earth it felf, that is, in a fluid more denfe than water ; all bodies put in motion here upon the where earth's furface muft fuffer a great refiftance from it ; as,

by

Sir I

s

AAc

NEWTON'S

experiments mentioned in the

fell perpendicularly down of the refiftance, felt about ~o the air, only through part which bodies fufFered that fell in like manner through water.

bodies, that

preceding chapter,

14..

Sir Is A

AC

NEWTON

applies thefe experiments yet

and examines by them the general queftion concern abfolute the plenitude of fpace. According to the Ariftoteing full without any the lea ft vacuities whate was all lians, fpace ver. DESCARTES embraced the fame opinion, and therefore farther,

fuppofed a fubtile fluid matter, which fhould pervade

and adequately

dies,

fill

up

their pores.

all

The Atomical

bo

philo-

who fuppofe all bodies both fluid and folid to be compofed of very minute but folid atoms, aflert that no fluid, how

fophers,

fubtile foever the particles or

atoms whereof

it

is

compofed

can ever caufe an abfolute plenitude ; becaufe it impoflible that any body can pafs through die fluid with

fhould be, is

out putting the particles of rate ally

it

into fuch a motion, as to fepa-

from one another, and fo perpetu part, to caufe fmall vacuities ; by which thefe Atomifh endea them,

at leaft in

vour to prove, matter,

is

that a

vacuum, or fome fpace empty of

abfolutely neceflary to be in nature.

Sir I

s

NEWTON objects againft the filling of fpace with fuch a tile fluid,

that all bodies in

fub

motion muft be unineafurably

Z

all

AAc

re-

fifted

by a fluid through which fifled

NEWTON'S

A AC

Sir Is

170

fo denfe, as abfolutely to it

is

that this objection

And

fpread.

fill

left it

up

BOOK II. all

the

fpace,

fhould be thought,

might be evaded by afcribing to this fluid as might remove all ad-

fuch very minute and fmooth parts, heiion or friction between them,

would be

which

loft,

whereby all refiftance might otherwife give to bo I s A A c EwT oN proves, in the

this fluid

N

dies moving in it ; Sir manner above related, that

fluids refift

from the power of

and that water and the inactivity of their particles ; on fift almoft this account fo that in this entirely :

fluid,

however minute and lubricated the

compofe water,

it,

it

might be ;

would

whereas fuch a

refift

yet

if

water,

it

which

particles,

much

as

water does

;

and

parts are abfolutely clofe toge

ther without any intervening fpaces,

more denfe than

fubtile

the whole fluid was as denfe as

very near as

whole

fluid,

air re-

muft

muft be a great deal more than water in

refift

proportion to its greater deniity ; unlefs we will fuppofe the matter, of which this fluid is compofed, not to be endued

with the fame degree of

inactivity as other matter.

But

if

you deprive any fubftance of the property fo univerfally be longing to all other matter, without impropriety of fpeech it

can fcarce be called by 15*.

this

name.

SirlsAAcNEWTON made alfo an experiment to try in

particular, flftance.

whether the internal parts of bodies fuffered any

re-

And the refult did indeed appear to favour fome fmall

degree of refiftance; but fo very little, as to leave it doubtful, a effect did not arife from fome other latent caufe .

whether the

*

Princ. ph'lof. pa?. 316, 317,

CHAP.

CHAP.

PHILOSOPHY.

2.

CHAP.

171

II.

caufe, which keeps in motion the primary planets.

Concerning the

the planets

SINCE from

refiftance

;

motion, would

once

in

end,

if left to

move they,

in a void fpace

move on

themfelves.

and are

like all other bodies,

And

in a ftraight line

free

when

without

now

to be explained carries them round the fun. it

is

what kind of action upon them Here I {Kail treat of the primary

planets only, and difcourle of the fecondary apart in the next chapter. It has been

now declared, that thefe primary planets move fo about the fun, that a line extended from the fun to the planet, will,

juft

by accompanying the planet in its motion, pafs over equal {pa a And this one property in the ces in equal portions of time motion of the planets proves, that they are continually acted .

on by a power therefore

is

directed perpetually to the fun as a center. This which keeps the

one property of the caufe,

planets in their courfes, that center is the fun.

z.

AGAIN,

it is

a centripetal power,

whofe

in the chapter upo:i centripetal forces

it

was obferv'd, that if the ftrength of the centripetal power was fuitably accommodated every where to the motion of

any body round a

center, Ch.

i.

the body might be carried in b

7.

Z

Book

^

I.

Ch.

3.

an/

ISAAC NEWTON'S

Sir

172

BOOK

II.

fhould be every any bent line whatever, whofe concavity where turned towards the center of the force. It was far that the ftrength of the centripetal force,

ther remarked,

was to be collected from the nature of the

in each place,

Now

3

wherein the body moved moves in an ellipfis, and the lun .

line,

Sir I

s

AAc

NEWTON

fince each planet

placed in one focus ; deduces from hence, that the ftrength is

of this power is reciprocally in the duplicate proportion of the This is deduced from the properties, diftance from the fun.

which the geometers have difcovered

in the ellipfis.

The pro-

of the reafoning is not proper to be enlarged upon here but I fhall endeavour to explain what is meant by the recipro cal duplicate proportion. Each of the term s reciprocal pro cefs

portion,

and duplicate proportion, has been already defined

Their fenfe when thus united

is

b .

Suppofe the planet about the fun in S.

as follows.

moved in the orbit ABC (in fig. 93. ) Then, when it is faid, that the centripetal power, which ads on the planet in A, bears to the power acting on it in B a propor which

tion,

diftance S in

A

is

A

the reciprocal of the duplicate proportion of the SB; it is meant that the power

to the diftance

bears to the

power

in

B

the duplicate of the proportion

The

of the diftance S B to the diftance S A.

may

plicate proportion

lows.

Suppofe

be explained

reciprocal

by numbers

alfo

feveral diftances to bear to

du

as fol

each other propor

by the numbers i, i, 3, 4, y that is, let the fecond diftance be double the firft, the third be three times,

tions expreiTed

;

and the

the fourth four times, Book

I.

Ch.

3.

29.

fifth five

t Ibid.

times as great as the

Ch.

:.

30, 17.

firft.

CHAP.

PHILOSOPHY.

2.

Multiply each of thefe numbers by

firft.

plied by I produces

by

makes

3

and

i

multi

i multiplied by i produces 4, 3 makes 16, and y by y gives xy. This

ftill

4 by 4

9,

it felf,

173

I,

being done, the fractions ~,

~, ~,

-^,

will

respectively exprefs

the proportion, which the centripetal power in each of the following diftances bears to the power at the firft diftance for :

in the fecond diftance, petal

power

will be

diftance

firft

which

is

double the

firft,

one fourth part only of the power

at the third diftance the

;

the centri

power

v/ill

at the

be one

ninth part only of the firft power ; at the fourth diftance, the power will be but one fixtcenth part of the firft ; and at the fifth diftance., one twenty fifth part of the

3

.

THu

power -the

s is

firft

power.

found the proportion, in which this centripetal from the fun increafes, within

decreafes, as the diftance

compafs of one

planet's

motion.

How

it

comes

to

pa(s,

that the planet can be carried about the fun by this centripetal power in a continual round, fometimes riling from the fun,

then defcending again as low, and from thence be carried up again as far remote as before, alternately riling and falling

without end ; appears from what has been written above con cerning centripetal forces: for the orbits of the planets re ferable in fhape the curve line propofed in

on

thefe forces

1

7 of the chapter

a .

4. B u T farther, in order to know whether this centripetal force extends in the fame proportion throughout, and confe-

quently whether

all

the planets are influenced by the very fame Book

I.

Ch.;;

wer.

1

Sir I s

74

A AC

NEwTo

thus. powei, our author proceeds

He

BOOK II.

N'S

inquires

what

relation

there ought to be between the periods of the different planets, the fame power decreafing they were acted upon by

provided and he finds, throughout in the forementioned proportion ; that have cafe would in this of each that the period very rela a tion to the greater axis of its orbit, as I have declared above to be found in the planets

And

this

puts

it

by the obfervations of aftronomers.

beyond queftion, that the

different planets are

the fun, in the fame proportion to their diflanpreffed towards And thence ces, as one planet is in its feveral diftances. in the laft place

it is juftly concluded, that there is fuch a the fun in the forefaid towards power acting proportion at all

diftances

y.

calls

from

THIS

it.

wife the

when referred to the planets, our when to the fan attractive he gives

power,

centripetal,

name of gravity,

becaufe he finds

earth, as will appear hereafter

b .

By

it

like-

it

to be of the

fame

which

nature with that power of gravity,

all

author

j

thefe

is

obferved in our

names he

defigns

only to fignify a power endued with the properties before mentioned ; but by no means would he have it underflood, as it

thefe

names

referred

any way

in one place where he ufes the ons us expreisly againft

to the cauie of

it.

In particular

name

of attraction, he cauti implying any thing but a power di recting a body to a center without any reference to the caufe

of

or ariimg it, whether refiding in that center, c external impulie

from any

.

Ch.i.7.

k

Ckp.f.S.

Princ.pg. 60.

6.

BUT

C;up.2.

PHILOSOPHY.

175

B u T now, in thefe demonftrations fome

very minute in in the motion of the are equalities planets ncgleded which is done with a great deal of judgment ; for whatever be their 6.

;

caufe, the effects are very inconiiderable, they being fo exceed ing fmall, that fome aftronomers have thought fit wholly to pafs them by a However the excellency of this philofophy, when in the hands of fo great a geometer as our author, is fuch, that .

able to trace the lead variations of tilings

it is

up to

their caufes.

The all

only inequalities, which have been obferved common to the planets, are the motion of the aphelion and the nodes

The

tranfverfe axis of each orbit does not always remain fix but moves about the fun with a very ilow progreiTive motion nor do the planets keep conftantly the fame plane,

ed,

:

but change them, and the lines in which thofe planes interfeel each other by infenlible degrees. The firft of thefe

which

the motion of the aphelion, may be ac by fuppofing the gravitation of the planets to wards the fun to differ a little from the forementioned re

inequalities,

counted

is

for,

ciprocal duplicate proportion of the diftances ; but the fecond, which is the motion of the nodes, cannot be account

ed

for

by any power directed towards the fun

for

;

no fuch

can give the planet any lateral impulfe to divert it from the into any new plane, but of necelTity muft plane of its motion be derived from fome other center. Where that power is lodged,

Now

remains to be difcovered.

it

is

proved,

as

be explained in the following chapter, that the three primary planets Saturn, Jupiter, and the earth, which have

fhall

{atellites

revolving about them, *

are

endued with

a

power of

Street, in Aftron. Carolin.

caufing

Sir Is A

\-j6

NEWTON'S

AC

BooKlL

caufmg bodies, in particular thofe latellites, to gravitate to wards them with a force, which is reciprocally in the duplicate and the planets are in all reproportion of their diftances; which they come under our examination, fo fimilar but they have alike, that there is no reafon to queftion,

Ipccls, in

and

the fame property.

all

thefe planets

Though

it

be fufficient for the prefent

proved of Jupiter and Saturn only ; for contain much greater quantities of matter than

purpofe to have

it

and proportionally exceed the others in power it the influence of thefe two planets being allowed, the

reft,

come

how the planets for each of the planets

vident

a .

is

But evi-

to fhift continually their planes: in a different plane, the

moving

action of Jupiter and Saturn upon the reft will be oblique to the planes of their motion ; and therefore will gradually draw

them

into

on the

The fame action of thefe two planets up caufe likewiie a progreffive motion of the fo that there will be no neceflity of having recourfe new

ones.

reft will

aphelion ; to the other caufe for this motion, b'

which was before hinted

of the planets towards the fun differing from the exact reciprocal duplicate proportion of the diftan

at

}

ces.

viz, the gravitation

And

in the laft place, the action

of Jupiter and Saturn

upon each other will produce in their motions the fame ine All this produces in the reft. fame manner, as the fun produces the fame kind of inequalities and many others in the motion of the

qualities, is

as their joint action

effected in the

moon and beft

the other fecondary planets

apprehended by what 3

Sec Chap. f.

9,

fhall

cc.

;

and therefore

will be

be faid in the next chapter. b

In the foregoing page.

Thole

CHAP.

PHILOSOPHY.

2.

177

Thofe other irregularities in the motion of the fecondary have place likewife here ; but are too minute to be planets obfervable : becaufe they are produced and rectified alternate ly,

for the

moft part

in the time

of a {ingle revolution

;

whereas the motion of the aphelion and nodes, which conti become fenfible in a long feries of years. Yet nually increafe,

fome of

thefe other inequalities are difcernible in Jupiter

Saturn, in Saturn chiefly- for

when Jupiter, who moves

and

fafter

than Saturn, approaches near to a conjunction with him, his action upon Saturn will a little retard the motion of that pla net, and by the reciprocal action of Saturn he will himfelf be accelerated.

After conjunction, Jupiter will again accelerate likewife retarded in the fame degree, as before

Saturn, and be

the

firft

was

retarded and the latter accelerated.

Whatever

inequalities befides are produced in the motion of Saturn by the action of Jupiter upon that planet, will be fufficiently rec

by placing the focus of Saturn's ellipfis, which fhould otherwife be in the fun, in the common center of gravity of

tified,

And all the inequalities in the mo the fun and Jupiter. tion of Jupiter, caufed by Saturn's action upon him, are much of Saturn's motion a lefs confiderable than the irregularities .

7.

THIS

one principle therefore of the planets having a towards

as well as the fun, to caufe bodies to gravitate

power, them, which

is proved by the motion of the fecondary pla nets to obtain in fact, explains all the irregularities relating to the planets ever obferved by aftronomers.

4

See

Newton.

Princ. Lib. III. prop. 13^

Aa

8. Sir

Sir

178 8. Sir

ISAAC

ISAAC NEWTON'S NEWTON

BOOK II

after this proceeds to

make an

aftronomy by applying this theory to the far For as we have here obfervof their motions. ther correction to pofTefs a principle of gravitation, as well as ed the in

improvement

planets

the fun

;

fo

it

will

be explained

is

at large hereafter,

that the

which makes action and reaction

third law of motion,

to be applied in this cafe

a

;

and

equal, that the fun does not only

each planet, but is it felf alfo attracted by them ; die wherewith the planet is acted on, bearing to the force, wherewith the fun it felf is acted on at the fame time, the which the quantity of matter in the fun bears to proportion, attract

force,

the quantity of matter in the planet.

From

the action be

tween the lun and planet being thus mutual Sir ISAAC NEWTON proves that the fun and planet will defcribe about their

common center of gravity fimilar ellipiis's and then that ;

the tranfrerfe axis of the

ellipfis

defcribed thus about the

able fun, will bear to the tranfverfe axis of the

ellipfis,

movewhich,

would be

defcribed about the fun at reft in the fame time, the fame proportion as the quantity of folid matter in the fun and

planet together bears to the firft of two mean proportionals be tween this quantity and the quantity of matter in die fun only b.

9.

ABOVE, where

I

fhe wed

how

to find a cube,

that

c any proportion to another cube , the lines F T and T S are two mean proportionals between E F and F G ;

fliould bear

and counting from E F, F T is called the firft, and F S the fecond of thofe means, In numbers thefe mean proportionals Chap,

f,

10.

k

Princ.Lib.I. prop. (Jo.

Book

I,

Chap.

i.

So.

are

CHAp. 2

PHILOSOPHY.

;

are thus found.

Suppofe

A and B two

numbers,

j

and

required to find C the firft, and D the fecond of the two mean proportionals between them. Firft multiply A by it felf, and the product multiply

by B ; then metic

is

C will

it

be

A C B

>

be the number which in arith

called the <:ubic root of this laft product

number C being

the

79

multiplied by

it felf,

;

that

is,

and the product

again multiplied by the fame number C, will produce the In like manner D is the cubic product above mentioned. root of the product of B multiplied by it felf, and the pro duce of that multiplication multiplied again by A. i

o.

IT

will be asked, perhaps,

how

this correction

can be

when

the caufe of the motions of the planets was before found by fuppoftng the fun the center of the power, which acted upon them for according to the prefent correc

admitted,

:

tion this

power appears

rather to be directed to their

common

But whereas the fun was at firft conclu center of gravity. ded to be the center, to which the power acting on the planets

was directed, becaufe the fpaces defcribed round the fun in equal times were found to be equal ; fo Sir I s A A c NEWTON proves, that if the fun and planet move round their common center of gravity, yet to an eye placed in the planet, the fpa ces,

which

will

appear to be defcribed about the fun, will have

the fame relation to the times of their defcription, as the real fpaces would have, if the fun were at reft \ I farther aflerted, ;t.

fuppofing the planets to :

move round

the fun at

reft,

Pi inc. philof. Lib. I. prop. 5-8. coroll. 3.

Aa

%

j.

i

So

Sir I

s

AAc

N E w T o N'S

BOOK IL where

fhould attracted by a power, which every with degrees of ftrength reciprocally in the duplicate of the diftances ; then the periods of the planets proportion

and to be

a&

muft obferve the fame relation to their diftances, as aftronomers find them to do. But here it muft not be fuppofed, that the obfervations of aftronomers abfolutely agree without any the leaft difference ; and the prefent correction will not caufe a deviation from any one aftronomer's obfervations, fo much For in Jupiter, where this as they differ from one another. th correction is greateft, it hardly amounts to the jooo part

of the whole II.

axis.

UPON this head

equalities

I

made by our

a reflection

think

it

not improper to mention

excellent author

in the planets motions

;

upon thefe fmall in which contains under it a

the eternity of the very ftrong philofophical argument againft It is this, that thefe inequalities muft continually inworld.

by flow degrees, till they render at length the prefent a And frame of nature unfit for the purpofes, it now ferves a more convincing proof cannot be defired againft the pre

creafe

.

fent conftitution's

having exifted from eternity than this, it to an end. I am

that a certain period of years will bring

thought of our author has been reprefented even and as no lefs than cafting a reflection upon the wifdom of the author of nature, for framing a perinV

aware

this

as impious,

But I think fo bold an aflertion ought to have For if this remark been made with fingular caution. upon the increafing irregularities of the heavenly motions able work.

a

4

Newt,

Optics, pag. 378.

be

CHAP.

PHILOSOPHY.

3.

be true in fod,

upon

as

the aflerter,

it

really

is,

the imputation mufl return from the divine

that this does dctracl:

wifdom. Certainly we cannot pretend to know all the omnifcient Creator's purpofes in making this world, and therefore cannot undertake to determine how long he de-

And it is fufficient, if it endure figned it fhould laft. the time intended the author. The body of every ani by mal (hews the unlimited wifdom of its author no lefs, nay

in

many

and

-yet

refpects

we

fee,

than the larger frame of nature ; they are all defigned to laft but a fmall

more,

fpace of time. 1 1. nets

;

There need nothing more be faid of the primary pla the motions of the fecondary fhall be next confidered.

CHAP. Of the

motion of the

III.

MOON and

the other

SECONDARY PLANETS.

THE

excellency of this philofophy fufficiently appears its extending in the manner, which has been re

from

lated,

to the minuteft circumftances of the primary planets

motions

;

fuccefs of

which it

no proportion

motions of the fecondary

;

for

to the vaft it

not only

the irregularities, by which their motions were to be difturbed, but has difcovered others fo complicat

accounts for

known

neverthelefs bears

in the all

ed, that aftronomers were never able to diftinguim them,

reduce them under proper heads

;

and

but thefe were only to be found

1

82

Sir

found out from

ISAAC

their caufes,

HE w TON'S

which

this

BooKlL

philofophy

has brought

and has fhewn the dependence of thcfe inequalities fuch caufes in fo perfect a manner, that we not only learn upon from thence in general, what thofe inequalities are, but are

to light,

N

EwT oN compute the degree of them. Of this Sir I s. moreover found means given feveral fpecimens, and has to reduce the moon's motion fo completely to rule, that he

;

ible to

lias

framed a theory, from which the place of that planet may at all times be computed, very nearly or altogether as ex

lias

actly, as the places

of the primary planets themfelves, which is the greateft aftronomers could ever effect.

much beyond what 1. is,

THE

firft

thing demonftrated of thefe fecondary planets drawn towards their refpective primary in the

that they are

fame manner as the primary planets are That each fecondary planet is kept in

attracted by die fun. its orbit by a

power

pointed towards the center of the primary planet,

about

which the fecondary revolves; and that the power, by which the fecondaries of the fame primary are influenced, bears the fame

relation to the diftance

from the primary,

as the

power,

by which the primary planets are guided, does in regard to a the diftance from the fun This is proved in the fatellites of and becaufe Saturn, Jupiter they move in circles, as far as we .

can obferve,

about their

refpective primary with an equable courfe, the refpeclive primary being the center of each or bit: and by comparing the times, in which die different fa-

Jtcllites

of the fame primary perform their periods, diey are *

Ncv/ton. Princ.Lib.

III. prop. ;.

found

CHAP.

PHILOSOPHY.

3.

18

found to obferve the fame relation to the distances from as the

primary,

mean

diftances

circles

primary planets obllrve in refpect of

from the

fua*.

Here

thefe bodies

with an equable motion, each

qual parts ot line ly the

its

fatcllite

orbit in equal portions of time

drawn from

thi

tlu

moving

in.

pailes over ;

<.

confequent-

the center of the orbit, that

is,

from

the primary planet, to the fitellitc, will pafs over equal fpaces along with the latellite in equal portions of time; which proves the power, by which each fatellite is held in its orbit, b to be pointed towards the It is alfo maprimary as a center nifeft that the which carries a centripetal po\ver, body in a circle concentrical with the power, acts upon the body at all .

NEWTON

times with the fame ftrength. But Sir I s A A c demonftrates that, when bodies are carried in different circles by directed to the centers of thofe circles, then centripetal powers '

the degrees ot ftrength of thofe powers are to be compared coniidering the relation between the times, in. which the bo dies

c perform their periods through thoie circles ; and in par he ftiews, that if the periodical times bear that relation^

ticular

which

I

have juft

now afierted

the

itellites

of the lame

pri

mary to obferve; then the centripetal powers are reciprocally in the duplicate proportion of the femidiameters of the circl or in that proportion to the diftances of the bodies from the 1 Hence it follows that in the planets Jupiter and centers' . S?tvru, the power in each decreafes with the incentripetal

en.

*

:

New

of diftance, in the fame proportion as the centripetal on.^rinc.Lib.III. pa.jpo.jpl. com-

paicd wi;

Book

Ch.

3.

Princ, philof. Lib,

I,

prop. 4,

Ibid, cr

;

i.

19.

pow

Sir I

s

N E w T o N'S

AAc

BOOK II.

power appertaining to the fun decreafes with the increafe of diftance. I do not here mean that this proportion of the cen powers holds between the power of Jupiter at any di compared with the power of Saturn at any other di ftance ; but only in the change of ftrcngth of the power be

tripetal

ftance

longing to the fame planet at different diftances from him. Moreover what is here difcovered of the planets Jupiter and Saturn by means of the different fatellites, which revolve round each of them, appears in the earth by the mcon alone ; becaufe fhe is found to move round the earth in an ellipfis af ter the

fame manner

as the

primary planets do about the fun ;

.excepting only fome (mall irregularities in her motion, the caufe of which will be particularly explained in what follows, it will appear, that they are no objection againft the earth's acting on the moon in the fame manner as the fun acts on the primary planets ; that is, as the other

whereby

primary

Certain planets Jupiter and Saturn act upon their fatellites. fince thefe irregularities can be otherwife accounted for, we ly

ought not to depart from that

rule of induction fo neceffary that to like bodies like properties are to be at where no reafon to the contrary appears. can

in philofophy, tributed,

We

not therefore but afcribe to the earth the fame kind of action

upon

the

moon,

as the other

turn have upon their

fatellites

primary planets Jupiter and Sa which is known to be very ;

exactly in the proportion affigned by the method of comparjng the periodical times and diftances of all the fatellites. which

move about

the fame planet

;

this

abundantly compenfating

our not being near enough to obferve the exact figure of their orbits. For if die little deviation of the moon's orbit from

CHAP.

PHILOSOPHY.

3:

185

orbit

from a true permanent ellipfis arofe from the action of the

earth

upon the moon not being

cate .proportion of the diftance,

in the exact reciprocal dupli

were another

moon to

revolve

about the earth, the proportion between the periodical times this

new moon, and

tion

from the mentioned proportion

BY

3.

the

the prefent,

would

' '.

difcover the devia

much more

manifeftly.

number of fatellites, which move round

and Saturn, the power of each of thefe o great diverfity

of diftance

;

planets

for the diftance

is

ITR

of the outermost

each of thefe planets exceeds feveral times the dift ance of the innermoft. In Jupiter the aftronomers have ufually

fatellite in

placed the innermoft

fatellite at

a diftance from the center of

y| of the femidiameters of Jupiter's performs its revolution in about i day

that planet equal to about

body, and

this fatellite

lS~

The

hours.

about

3

next

fatellite,

which

revolves

round Jupiter in

hours, they place at the diftance from Jupiter To the third laof that planet's femidiameters.

days I

g

-J

of about 9 tellite, which performs

its period nearly in 7 days g ; hours, about 1 4, j femidiameters. of diftance the But they aflign the outermoft fatellite they remove to if^ femidiameters, and

this fatellite

makes

its

In Saturn there

is ftill

feveral fatellites.

By

a

~ period in about 1 6 days 1 6 hours a greater diverfity in the diftance of the .

the obfervations of die late

celebrated aftronomer in France,

known

who

firft

fatellites,

except one

about

of Saturn's femidiameters from

4>[

a

Newt.

CAss

difcovered

before, the innermoft his center,

i

N

all

is

i,

a

thefe

diftant

and

re-

Princ. philof. LiKIII. pag. 390.

Bb

volves

1

86

Sir I

s

volves round in about I day is

diftant about

N E w T o N'S

AAc

^^

J

-

hours.

The

y ^ femidiameters, and makes

4 days

j

i

next

fatellite

period in aremoved to the dift-

bout i days 17-* Jiours. The tliird is ance of about 8 femidiameters, and performs near

BOOK II.

{

hours.

The

fourth

fatellite

its

its

revolution in

difcovered

firft

by the great HUYGENS, is near 18- femidiameters, and moves round Saturn in about 1 5- days a 1 1 hours. The outermoft is diftant ?6 femidiameters, and makes its revolution in about

a

Befides thefe fatellites, there days 7* hours to die Saturn another belongs planet body of a very fingular kind. This is a mining, broad, and flat ring, which encom-

79

.

The diameter of the outermoft pafles the planet round. verge of this ring is more than double the diameter of Saturn. HUYGENS, who firft defcribcd this ring, makes the whole diameter thereof to bear to the diameter of Saturn the pro portion of 9 to 4. The late reverend Mr. POUND makes the proportion fomething greater,

viz.

that of 7 to 3.

The

di-

ftances of the fatellites of this planet Saturn are compared by A s s i N i to the diameter of the ring. His numbers I have

C

reduced to thofe above, according to Mr. P o u N D'S propor between the diameters of Saturn and of his ring. As o

tion

this ring

appears to adhere

no \vhere

to Saturn, fo the dift-

ance of Saturn from the inner edge of the ring feems rather The diftances, whicli greater than the breadth of the ring. have here been given, of the feveral fatellites, both for Jupiter may be more depended on in relation to the

and Saturn, proportion,

which thofe belonging Newt.

to the

fame primary planet

Princ. philof. Lib. Ill, pag. 391,

bear

CHAP.

PHILOSOPHY.

3.

187

bear one to another, than in refpecl: to the very numbers, that have been here fet down, by reafon of the difficulty there is in meafuring to the greateft exaclnefs the diameters of the pri

mary

planets

to treat

be explained hereafter,

as will

;

a

of telefcopes

By

.

when we come

the obfervations of the foremen-

tioned Mr. POUND, in Jupiter the diftance of the innermofl fatellite fhould rather be about 6 femidiameters, of thefecond 9-',

of the third

ij",

and of the outermoft ^6

turn the diftance of the innermoft

fatellite

4,

^

-

b

and

',

in Sa

femidiameters>

of the next 6;> of the third 8;, of the fourth ^o-^ and of the c fifth However the proportion between the diftances 5*9 .

of the

fatellites

we

the only thing necef-

is

are here upon.

B u T moreover

4.

fame primary

in the

fary to the point

the force, wherewith the earth afts in

confirmed from the following confideration, yet more exprefly than by the preceding analogical It will reafoning. appear, that if the power of the earth, by

different diftances,

which

it

retains the

is

moon in

her orbit, be fuppofed to aft at

all

between the earth and moon, according to the forementioned rule ; this power will be fufficient to produce up

diftances

on bodies, near the furface of the earth, all the effects afcribed This is difcovered by the fol to the principle of gravity. lowing method.

B

the

a

circle,

of which

left to it felf

Book

III.

Let

BCD

moon,

to

Ch.4,

A

A

is

in fig. 94.

the center.

move with k

(

reprefent the earth,

If the

the velocity,

Nc.vt, Princ. philof.

)

which

the moon's orbit,

it

differs little

moon

from

B were

has in the point B,

Lib. III. pag. 391.

Bb x

in

e

Ibic*.

it

pag: 392.

would

Sir ISA would

leave the orbit,

B E, which

NEWTON'S

AC

and proceed

right

forward in the

Suppofe the

touches the orbit in B.

BooKlL line

moon would

this condition move from B to E in the fpace of one mi nute of time. By the action of the earth upon the moon, where by it is retained in its orbit, the moon will really be found at the

upon

end of this minute

in the point F,

from whence a

ftraight line

make the fpace B F A in the circle equal to the the time wherein triangular fpace B E A ; fo that the moon in it would have moved from B to E, if left to it felf, has been impelled towards the earth from E to F. And when the time of the moon's palling from B to F is fmall, as here it is only one minute, the diftance between E and F fcarce differs from the fpace, through which the moon would defcend in the fame time, if it were to fall directly down from B toward A drawn

to A fhall

without any other motion. A B the di'ftance of the earth and is about 60 of the earth's femidiameters, and the moon

moon

completes her revolution round the earth in about 17 days 7 hours and 4,3 minutes: therefore the fpace EFwill here be

found by computation to be about 16-3 feet. Confequently, power, by which the moon is retained in its orbit, be

if the

near the furface of the earth greater, than at the distance of the moon in the duplicate proportion of that diftance ; the

number of feet, earth

a body would defcend near the furface of the upon it in one minute of

by the action of this power

to 16- multiplied twice into the num equal to ^So yo. But how fafk bodies fall near a die fuiface of the earth may be known by the pendulum ; and

time,

would be equal

ber 60, that

is,

See

Book

I.

Ch.

i.

60^64.

by

CHAP.

PHILOSOPHY.

3.

by the exacteft experiments they are found to defcend the fpace of i6{ feetjb a fecond of time; and the fpaces defcribed by falling bodies

of their

a

fall

,

being in the duplicate proportion of the times the number of feet, a body would defcribe in it?,

near the furface of the earth in one minute of time, will-

fall

be equal to 1 6 J twice multiplied by 60, the fame as would' be caufed by the power which acts upon the moon.

IN

y.

this

whereas

reft,

pofed

it

to

computation the earth is fuppofed to be at would have been more exact to have fup-

it

move,

as well

the

as

moon,

about their

com

mon

center of gravity ; as will eafily be underftood, by what has been faid in the preceding chapter, where it was fliewn, is fubjected to the like motion about the com center of gravity of it felf and the planets. The ac tion of the fun upon the moon, which is to be explained in what follows, is likewife here neglected: and Sir ISAAC-

that the fun

mon

NEWTON

{hews,

if

you take

in

both thefe .considerations,

the prefent computation will beft agree to- a fomewhat greater diftance of the moon and earth, viz. to 6o{ femidiameters

of the earth, which diftance

.is

more conformable to

agronomical observationsis.

6.

THESE

computations afford an additional proof, that

the action of the earth obferves the diftance,

which

was rcafonable

is

here contended

to conclude fo

*

Book

I.

fame proportion to the for.

Before

I

laid,

it

by induction from the pla-

Ch.2.

.

17.

.

nets

,

Sir

190 nets

ISAAC NEWTON'S

and Saturn; bccaufc they

Jupiter

BOOK

act in that

II.

manner.

now

the fame thing will be evident by drawing no other confequence from what is fcen in thofe planets, than that the

Silt

power, by which the primary planets act on their fecondary, is extended from the primary through the whole interval be fo that it would ad: in every part of the intermediate is fo far from In {pace. Jupiter and Saturn this power being confined to a finall extent of diflance, that it not only reaches

tween,

to feveral fatellites at very different diftances, but alfo from one planet to the other, nay even through the whole plane a Confequently there is no appearance of reafon, tary lyftem .

why

power fhould not

this

act at all diitances, even at the

very furfaces of thefe planets as well as farther off. But from hence it follows, that the power, which retains the moon in her orbit,

is

the fame, as caufes bodies near the furface of

For iince the power, by which the the earth to gravitate. earth acts on the moon, will caufe bodies near the furface

of the earth

to defcend

to do,

certain

it

is

befides; becaufe if

with

fwifter.

Now

that the

power

in the earth,

tends

to the

moon, and

7.

the velocity they are found

from

all

this

it

is

at

length very

which we

call

evident,

gravity,

ex

decreafes in the duplicate pro of the increafe of the diftance from the earth.

up

portion

all

no other power can act upon them it did, they muft of neceiTity deicend

THIS

finifhes the

difcoveries

made

the primary planets upon their fecondary. * See Ch.

in the action of

The

next thing

!!.. to

CHAP. to be this

PHILOSOPHY.

3.

fhewn

purpofe

that the fun acts

is,

it is

upon them

to be obferved, that if to the

191

likewife

:

for

motion of the

whereby it would be carried round its primary at be fuperadded the fame motion both in regard to

fatellite,

reft,

velocity and direction, as the primary it felf has, it will defcribe about the primary the fame orbit, with as great

caufe

The primary was indeed at reft. law of motion, which makes a

as if the

regularity,

of

this is

body near the

that

furface

of

the earth,

when

let

fall,

to

defcend perpendicularly, though the earth be in fo fwift a motion, that if the falling body did not partake of it, its

defcent

would be remarkably oblique; and that a bo defcribes in the moft regular manner the fame whether projected in the direction, in which the

dy projected

parabola, earth moves, or in the oppofite direction, if the project a From this we learn , that ing force be the fame .

if

the

fatellite

gularity,

moved about

befides

of

its

its primary with perfect re motion about the primary, it would

the

motion of

its primary; have the with which the primary is car velocity, ried about the fun; and be impelled with the fame velo

participate

all

fame progreflive the city as

primary towards the fun, in a direction

parallel

And on the contrary, the to that impulfe of its primary. want of either of thefe, in particular of the impulfe to

mo

wards the fun, will occafion great inequalities in the tion of the fecondary planet. The inequalities, which would arife from the abfence of this impulfe towards the fun are The

fecond of the laws of motion hid dov/n ia

Book

I.

Ch.

i.

fo

1

Sir Is A

9.2

NEWTON'S

AC

BooKlL

by the regularity, which appears in the mo tion of the fecondary planets, it is proved, that the fun com municates, the fame velocity to them by its adtion, as it gives at the fame diftance. For Sir I s A A c to their E wfo -great, that

N

primary

T O.N informs any of the

more

or

upon examination he found, that if of Jupiter were attracted by the fun

that

us,

fatellites

than Jupiter himfelf at the fame diftance, the inftead of being concentrical to

lefs,

orbit of that fatellite,

muft have

Ju

center at a greater or lefs diftance, than the center of Jupiter from the fun, nearly in the fubduplicate proportion of the difference between the fun's a&ion piter,

its

upon

the

and upon Jupiter ; and therefore

fatellite,

~

were attracted by the fun but than Jupiter is at the fame diftance, lite

orbit

of that

no Jupiter

fatellite

would be

than a

lefs

fifth

diftant

if

any

fatel

part more or leis, the center of the

from the center of

part of the diftance of the outa

fatellite from Jupiter ; which is alraoft the whole diftance of the innermoft fatellite. By the like argument

crmoft the

fatellites

as Saturn

much 8.

dary

it

of Saturn gravitate towards the fun, the fame diftance j

felf at

as

much

and the moon

as

as the earth.

THUS

is

planets, as

diftance

:

but

it

proved, that the fun ads upon the fecon much as upon the primary at the fame

was found

adlion of the fun

upon

in

bodies

the is

plicate proportion of the diftance Newton.

;

chapter, that the reciprocally in the du laft

therefore die fecondary

Princ. philof. Lib.III. prop. 6. pag. 4(11.

planets

CHAP.

PHILOSOPHY.

3.

fometimes nearer planets being

to

193

the fun than the pri

and fometimes more remote, they are not alway acted upon in the fame degree with their primary, but

mary,

when

nearer to the fun, are attracted more, and

ther diflant, are attracted

SOME

9.

the

moon,

if

when

arife various

motion of the fecondary planets

in the

ties

Hence

lefs.

far

inequali

*.

of thefe inequalities would take place, though undifturbed by the fun, would have moved in

a circle concentrical to the earth, and in the plane of the earth's

motion

;

depend on the

others

elliptical figure,,

lique fituation of the moon's orbit.

moon

One of the

and the ob firft

kind

is,

caufed fb to move, as not to defcribe equal Ipaces in equal times, but is continually accelerated, as fhe pafles from the quarter to the new or full, and is retarded that the

is

again by the like degrees in returning from the Here we consider not fo to the next quarter. folute,

as the

10.

THE

guifh thefe fun,

A

apparent motion of the principles

moon

in

new and full much the ab-

refpect to us.

of aftronomy teach how to diftinLet S (in fig. 9 5-.) reprefent the

two motions.

the earth

moving

in

its

orbit

orbit, the place of the

moon

moved from A

Becaufe

to

I.

H. it

B C,

DEFG

the moon's

Suppofe the earth to have has been fhewn, that the

moon

of the earth ; and partakes of all the progreflive motion likewife that the fun attracts both the earth and moon equal

when they are at the fame diftance from it, or that the mean action of the fun upon the moon is equal to its action

ly,

2

Newton's Princ.

philof. Lib. III.

C

c

prop. 22, 23.

upon

1

Sir I

94

upon

the earth

we mu ft

:

rying about with earth

is

AAG

s

wife be removed from

though the

its

now

II.

to

I,

;

fo

when

that

the

the moon's orbit mall like-

former fituation into that denoted

if the moon be mould Ol O, parallel to HA, moon would really have moved from H to O, yet

by were found

it

A

BOOK

therefore confider the earth as car

the moon's orbit

it

removed from

KLMN.

N E w T o N*S

But

the earth being in I,

fo that

in

would not have appeared

have moved

at all,

to a fpedlator

becaufe the earth has

upon the

moved

as

earth to

much it

felf ; fo that the moon would ftill appear in the fame place with refpect to the fixed ftars. But if the moon be obferved in P, it will then appear to have moved, its apparent motion

And if the angle being meafured by the angle under O I P. lefs than the angle under HAS, the moon will have approached nearer to its conjunction with the fun.

under PIS be

II.

To

inequality

the fun,

come now

in the

to the explication of the

moon's motion

:

let

S (in

A the earth, B C D E the moon's orbit, C

moon, when

in the latter quarter.

fame diftance from the

mentioned

fig. p<5.)

reprefent the place of the

Here it will be nearly

fun, as the earth

is.

In

at the

this cale there

fore they will both be equally attracted, the earth in the dire Whence as the S, and the moon in the direction C S.

ction

A

earth in

moving round the run

ward

fo the

it,

moon

is

continually defcending to

muft in any equal por and therefore the pofition of

in this fituation

tion of time defcend as

much

;

AC in refpect of AS, and the change, which the moon's motion produces in the angle under CAS, will not be

the line

altered by the fun.

11.

BUT

CHAP

PHILOSOPHY.

3.

BUT now

J^.

as

foon as ever the

moon

is

advanced from

the quarter toward the new or conjunction, fuppofe to G, the action of the fun upon it will have a different effect. Here,

were the rection

fun's action

upon

the

moon

GH

to be applied in the di on the moon were

if its action parallel to A S, action on the earth, no change

would be wrought equal to its fun the the on motion of the moon round the by apparent earth. But the moon receiving a greater impulfe in G than the earth receives in A, were the fun to act in the direction

GH,

DAG,

would

it

yet

accelerate the defcription of the fpace G A to decreafe farter,

than otherwife

it

would.

The

fun's action will

upon account of the obliquity of which the

means

D

and caufe the angle under

is

drawn by two

G toward moon muft

therefore the

have

this effect

direction to that,

in

For the moon by

this

forces oblique to each other,

one

earth attracts the

drawing from

its

moon.

G

A, the other from

toward H> neceffarily be impelled toward D.

Again, becaufe the fun does not act in the direction G H pa rallel to S A, but in the direction GS oblique to it, the fun's action

on the moon will by rea/bn of this obliquity farther con moon's acceleration. Suppofe the earth in any

tribute to the

fhort fpace of time attracted by the fun

which touches the the fame time

and

would have moved from A the point

I

it,

Then the

earth's orbit in A.

would have moved if

moon,

to

I,

if

not

C E, moon in

being in the ftraight line

Suppofe the

in her orbit

befides have partook of all the progreilive

earth.

to

;

from G

to K,

motion of the

KL be drawn parallel to A I, if

and taken equal not attracted by the fun, would be found

C

c

a

in

ISAAC NEWTON'S

Sir

196

BOOK II.

But the earth by the fun's action is removed from in the line were moved down to

in L.

M

it

pofe

IMN

I.

Sup-

parallel

moon were

attfaded but as much, and in here fuppofed to be attraded> trie fame direction, as the earth fame time in the line LO, the fo as to have defcended during

and

to S A,

if

the

is

A S, down

alfo to

parallel

as far as P,

till

L P were

equal

PMN

would be equal to that IM, the angle under under LIN, that is, the moon will appear advanced no far ther forward, than if neither it nor the earth had been fubject

to

to the fun's action.

But

action of die fun

upon

whereas the

I

;

upon

the fuppofition, that the earth were equal ; more than the earth, did

moon and

acted upon draw the moon in the

would draw

M

is

the

moon being

the fun's action it

this

it

down

fo far as to

line L O to A S, parallel make L P greater than

PMN

will be rendred lefs, whereby the angle under LIN. But moreover, as the fun draws the

than that under

earth in a direction oblique to in

its

moon

orbit is

I

N, the earth will be found

M

fomewhat

attracted by

than the earth

is

fhort of the point however the ; the fun ftill more out of the line L 0,

out of the line

I

N

;

therefore this obli

quity of the fun's action will yet farther diminifh the angle

under

PMN.

13.

THUS

from the

fun,

fun producing

the

moon

at the

point

whereby her motion

is

G

receives

accelerated.

animpulfe

And

the

every place between the quarter and the conjunction, the moon will move from the quarter with a motion continually more and more accelerated ; and this effect in

therefore by acquiring from time to time additional degrees of

CHAP.

PHILOSOPHY.

3.

of velocity in

its

197

the fpaces, which arc dcfcribed in

orbit,

equal times by the line drawn from the earth to the moon, will not be every where equal, but thofe toward the conjunction

toward the quarter.

will be greater, than thofe

But

now

in

the moon's paffagejrom the conjunction D to the next quarter the fun's action will again retard the moon, till at the next

quarter in

E

it

be reftored to the

firft

velocity,

which

had

it

in C.

AGAIN

.

as the

moon moves from E

poiition to the fun in B,

of the fun's action upon earth, action.

Here

to the full or

op-

again accelerated, the deficiency the moon, from what it has upon the it is

producing here the fame effect as before the excefs of its Confider the moon in Q^ moving from E towards B.

if

moon were

the

attracted by the fun in a direction:

parallel to AS, yet being acted on lefs than the earth, as the earth defcends toward the fun, the moon will in fome

meafure be

left

behind.

Therefore Q^F being drawn pa

a fpectator on the earth would fee the moon as if attracted from the point Q^ in the direction

rallel to S B,

move,

Q^F with a degree of force equal to that, whereby the fun's action on the moon falls fhort of its action on the earth. But the obliquity of the fun's action has alfo here an effect. In the time the earth would have moved from A to I without the influence of the fun,

let

the

moon

have moved in

its

orbit

from

Q^to R. Drawing therefore R T parallel to A I, and equal to the fame, for the like reafon as before, the moon by the motion of its

orbit,

and

if

not at

all

attracted

therefore^ if attracted in

by the fun, mult be found in

a direction parallel to S A,

T;

would be

Sir

198

be in the line

moon lefs

ISAAC NEWTON'S

TV

parallel

to

AS

;

fuppofe in

BOOK W.

in (^ being farther off the fun than the earth,

attracted,

that

is,

T\V

will

be

lefs

than

II.

But the it

will be

IM, and

if

the

XMW

SM

be prolonged toward X, the angle under Thus by the fun's adlion will be lefs than that under XIT. line

the moon's pafTage from the quarter to the full would be ac celerated, if the fun were to act on the earth and moon in a direction parallel to AS: and the obliquity of the fun's ac For the action tion will dill more increafe this acceleration.

of the fun on the moon is oblique to the line S A the whole time of the moon's paffage from Q, to T, and will carry the moon out of the line TV toward the earth. Here I fup pofe the time of the moon's paffage from it

fhall

a

little

Q to T fb ihort, that

not pafs beyond the line S A. The earth alfo will come T as was faid before. From thefe fhort of the line I N ,

caufes the angle under

XMW

will be

ftill

farther lelTened.

T

H E moon in paffmg from the oppofition B to the I }\ next quarter will be retarded again by the fame degrees, as Becaufe it is accelerated before its appulfe to the oppofition. this

action of the fun,

which

rated,

moon's paffage from the to be extraordinarily accele

in the

caufes quarter to the oppofition

it

and diminimes the angle, which meafures

its

diftance

from the oppofition ; will make the moon flacken its pace af terwards, and retard the augmentation of the fame angle in its is,

it

the oppofition to the following quarter ; that paffage from from increafing fo faft, as otherwife will prevent that angle would. And thus the moon, by the fun's action upon it, is

twice accelerated and twice reftored to

its firft

velocity, every circuit

PHILOSOPHY.

CHAP.

3.

circuit

makes round the

it

motion about the earth

THE

16.

is

earth.

This inequality of the moon's

called by aftronomers

next effect of the fun upon the

the orbit of the gives

moon

199 its

variation.

moon

is,,

that

in the quarters a greater

it

de

it would receive from the action of gree of curvature, than the earth alone ; and on the contrary in the conjunction and

oppofition the orbit

is

lefs inflected.

WHEN

the moon is in conjunction with the fun in 17. the point D, the fun attracting the moon more forcibly than it does the earth, tke moon by that means is impelled lefs to

ward the is

lefs

it

for the power, by

j

the earth, pelled toward

from a

would be, and fo the orbit which the moon is im being that, by which it is inflected

earth, than otherwife

incurvated

rectilinear courfe, the lefs that

Again, when

will be inflected.

tion in B, farther

the

power

moon

is

is,

the

lefs it

in the oppofi

removed from the fun than the earth

is ;

follows then, though the earth and moon are both conti to the fun, that is, are drawn by the fun nually defcending toward it felf out of the place they would otherwife move

it

into,

yet the

earth

;

moon

defcends with

infomuch that the moon

lefs

in

velocity than the

any given fpace of

of oppofition will have paffing the point than otherwife it would have the earth, approached in of the earth will its orbit that done, is, refpect

time from

its

lefs

ap

proach nearer to a ftraight the

moon

is

from the fun

in as

line.

In the

laft

place,

when

quarter in F, and equally diftant the earth, we obferved before, that

the

the

200

Sir I SA A c

moon would

the earth and

ward the

N E w T o N'S

fo

fun,

as

BOOK

defcend with equal pace to

make no change by

to

II.

that defcent

but the length of the line FA mutt of neceffity be mortned. Therefore the moon in moving from F toward the conjunction with the fun will be impelled more toward the earth by the fun's action, than it would have been

in the angle under F

AS

;

by the earth alone, if neither the earth nor moon had been acted on by the fun ; fo that by this additional impulfe the orbit

is

rendred more curve,

The fame 1 8.

ANOTHER

we

this

have

effect

now

than

it

would otherwife

be.

be produced in the other quarter.

effect will alfo

of the fun's action, confequent upon

explained,

is,

that

though the moon un-

difturbed by the fun might move in a circle having the earth for its center ; by the fun's action, if the earth were to be the very middle or center of the moon's orbit, yet the be nearer the earth at the new and full, than

in

moon would

In this probably will at firfl appear fome in the quarters. the moon mould come neareft to the earth? difficulty, that

where

it is

leaft attracted to

Which

attracted.

and be

it,

fartheft off

when moft

yet will appear evidently to follow

from

that very caufe, by confidering what was laft mewn, that the orbit of the moon in the conjunction and oppofition is ren

dred the it

if

lefs

lefs

curve will

;

the

would move the

the line,

of the

moon

is,

moon

into,

moon were

difturbance

for the lefs curve the orbit

to

have defcended from the place without the action of the earth. Now

move from any

from that

action,

which would touch

its

fince

place without farther it

would proceed in it would

orbit in that place,

recede

CHAP.

PHILOSOPHY.

3.

201

tecede continually from the earth ; and therefore if the power of the earth upon the moon, be (ufficient to retain it at the fame diftance,

diminution oi that power will caufe

this

But on the the diftance to increafe, though in a lefs degree. other hand in the quarters, the moon, being preffed more to wards the earth than by the

made

earth's fingle action,

will

be

palling from the conjunction or oppofition to the quarters the moon afcends from the earth, and in pafTing from the quarters to the conjunction to

approach

it

;

fo that in

and oppodtion it defcends again, becoming nearer the other. laft mentioned places than in

ALL

19. earth

thefe forementioned inequalities are of different

according O as the fun

degrees, ' O

greater

;

in thefe

when

is

the earth

more is

or

lefs

diftant

neareft the fun,

when it is fartheft off. For in the quarters, the moon is to the fun, the greater is the addition to

from the

and

lefs

nearer the the earth's

power of the fun ; and in the conjun upon ction and oppofition, the difference between the fun's action

action

it

by the

upon the earth and upon the moon

is

likewife fo

much

the

greater.

10.

THIS

difference in the diftance

and the fun produces a tion fun,

For the

farther effect

cauflnor o the orbit to dilate

: *

and become it is

fein,

moon,

greater,

proved by

by which in the

Sir I it

s

than

AAc

between the earth

upon the moon's

mo

when lels remote from the when at a farther diftance.

NEWTON,

diminimes the

conjunction or oppofition,

D

d

that the action of

earth's is

power over the about twice as great

202

ISAAC

Sir

N E w T o N'S

BOOK II.

by the fun in the power of the earth

to the earth's action great, as the addition a

quarters upon the

fo that

;

moon

upon

the whole,

the

diminished by the fun, and therefore is molt diminifhed, when the action of the fun is ftrongeft but is

:

approach to the fun has its influence leffenby the moon being lefs attracted will gradually recede from

as the earth

ed,

the earth

;

by degrees

its

and its

as the earth in its recefs

former power,

from the fun recovers

the orbit of the

moon

mull: a-

Two confequences follow from hence the gain contract. moon will be moft remote from the earth, when the earth is :

and alfo will take up a longer time in per ; revolution through the dilated orbit, than through contracted.

neareft the fun

forming the

its

more

THESE

fun would produce in the without moon, moon, being acted on unequally by the defcribe a would fun, perfect circle about the earth, and in die plane of the earth's motion ; but though neither of thefe

II.

if

irregularities the

the

the moon, yet the foremppofitions obtain in the motion of mentioned inequalities will take place, only with fome diffe

rence in refpect to the degree of them

moving fo.

in this

For

manner

as the

moon

is

fubject to

defcribes,

;

but the

iome other

moon by

not

inequalities al

inftead of a circle concentri-

with the earth in one focus, that It can neither will be fubjected to various changes. ellipiis fi the fame nor pofition, yet the fame preferve conftantly

cal to the earth,

gure

;

an

ellipiis,

and becaufe the plane of Newton.

this

ellipfis

is

not the fame

Princ. Lib.I. prop. 66. coroll, 7,

with

CHAP.

PHILOSOPHY.

3.

with that of the earth's in the in

moon

which

it

orbit, the fituation

203

of the plane, where

moves, will continually change ; neither the line the plane of the earth's orbit, nor the

interfects

inclination of the planes to each other, will remain for

All thefe alterations offer themfelves

time the fame.

any

now to

be explained. I

SHALL

firft

confider the changes which are

in the plane of the moon's orbit. in the fame plane with the earth,

made

The moon the fun

is

not moving feldom in the

plane of the moon's orbit, viz. only when the line made by the common interfection of the two planes , if produced)

through die fun, as is reprefented in fig. 97. where S denotes the fun ; T the earth ; A T B the earth's orbit dewill pafs

fcribed

upon

the plane of this fcheme

CDEF

;

the moon's

CDE

being raifed above, and the part C F E Here the line C E> depreffed under the plane of this fcheme. in which the plane of this fcheme, that is, the plane of the orbit,

the part

earth's orbit

and the plane of the moon's

orbit interfedt each

When other, being continued pafTes through the fun in S. is directed in the of fun action the this the plane happens, of the moon's

orbit,

and cannot draw the moon out of this

appear to any one that fliall confider for fuppofe die moon in G> and let a the prefent fcheme Straight line be drawn from G to S, the fun clrr.ws the moon plane,

as will evidently :

in the direction of this line

from G toward

S

:

but

this line lies

in the plane of the orbit ; and if it be prolonged from S G, the continuation of it will lie on the plane C D E ;

plane

itfelf, if fufficiently

extended, will pafs

Dd

i

beyond for the

through the fun.

But

NEWT GIN'S

ISAAC

Sir

204

BOOK II.

the plane of the fun's aclion to this caufe of the orbit will change. plane continually

But

to

in other cafes the obliquity

a3

SUPPOSE

.

in the

firft

place,

the line, in

which the

t

.

interfecl each other, to be perpendicular to the line planes the earth and fun. Let T (in fig. 9 8,9 9, 1 oo, I o I .) which

joins

the earth ; S the fun ; the plane of this fcheme the the earth's motion, in which both the fun and earth of plane Let A C be perpendicular to S T, which joins the are

reprefent

placed. earth and fun

and

;

To

T

the center

the circle

let

the line

A C be

A B C D.

defcribe the circle

And in the AECF, one

deprelTed

Now

.

(in fig.

98.

)

:

below

fuppofe the

plane of the moon's orbit half of which will

AEC

this

the other half

fcheme,

it,

moon

to fet forth

in the direction of the plane

will be continually

the fun

which the plane

interfects the

be elevated above the plane of

AF C as much

that, in

plane of the earth's motion. defcribe in the plane of the earth's motion

of the moon's orbit

from the point A Here me

AEC.

drawn out of

for this plane

AEC,

if

this plane by the aclion of extended, will not pafs through

it ; fo that the fun, by drawing the moon it felf, will force it toward continually more and more direclly from that plane towards the plane of the earth's motion, in

the fun, but above

which

it felt is

;

caufing

it

to defcribe the line

A K G H I, which

convex to the plane AEC, and concave to the plane of the earth's motion. But here this power of the iun, which

will be

is

faid to

draw the moon toward

the plane of the earth's

motion, muft be underftood principally of

fo

much

only of the

CHAP.

PHILOSOPHY

3.

the fun's action,

upon the moon,

as

it

2c

exceeds the action of the

For fuppofe the preceding figure to he lame upon the earth. viewed hy the eye, placed in the plane o that fcheme, and ii>

C T A on the iide of: A, the plane A B C D will appear as the ftraight line D T B, (in fig. I o l.) arid the plane A E C F as an other ftraight line F E ; and the curve line A K G H I under the the line

form of the

line

T K G H I. Now it

is

that the earth

plain,

and

moon

being both attracted by the fun, if the fun's action up on both was equally ftrong, the earth T, and With it the plane

AECF

or line F

TE

in this fcheme,

would be

carried

toward

the fun with as great a pace as the moon, and therefore the moon not drawn out of it by the fun's action, excepting

only from the fmall obliquity of the direction of this action upon the moon to that of the fun's action upon the earth, which arifes from the moon's being out of the plane of the

motion, and is not very confiderable ; but the action of the fun upon the moon being greater than upon the earth, all the time the moon is nearer to the fun than the earth is, earth's

it

will be

drawn from the plane AEC or the line TE by and made to defcribe the curve line AGI or

that excefs,

But

TGI.

fidering the

it is

the cuftom of aftronomers,

moon

as

moving

inflead of con-

in fuch a curve line,

to refer

motion continually to the plane, which touches the true line wherein it moves, at the point where at any time the

its

moon is

then its

is.

Thus when

the

moon

is

confidered as being in the plane eilaies to

motion

earth,

and

move

;

and when

in the point

referred to the plane, touches the line

is

in the point A, its motion in whofe direction it

A E C,

which

AKGHI

K

pafies

in the

(

in fig. 99.

)

through the

point K>

Thus be.

20 6

Sir I

s

A Ac

N E w T o N'S

BOOK II.

moon in pafling from A to I will continually change the In what manner this change proceeds, plane of her motion. I mall now particularly explain.

the

.

LET the plane, which touches the line AKI in the point

interfecl K. (in fig. o, 9.)

the plane of the earth's orbit in the line

L T M. Then, becaufe the line A K I is concave to the plane A B C, it falls wholly between that plane, and the plane which touches it in K fo that the plane M K L will cut the plane AEC, ;

before

it

meets with the plane of the earth's motion ; fuppofe

Y T, and the point A will fall between K and L. With a femidiameter equal to T Y or T L defcribe the femicircle L Y M. Now to a fpedator on the earth the moon, when in A, will appear to move in the circle A E C F, and, when in The K, will appear to be moving in the iemicircle L Y M. in the line

earth's

motion

to a fpectator in that plane.

is

performed in the plane of

on the

We

of the fun to the

this

and

fcheme,

earth the fan will appear always moving may therefore refer the apparent motion

circle

A B C D,

defcribed in this plane about

But the pointc where this circle, in which the fun feems to move, interfe<ts the circle in which the moon is feen at any time to move, are called the nodes of the moon's

the earth.

orbit at that thru.

When

the

moon

is

feen

moving

in the cir

the points A and C are the nodes of the orbit ; are when me appears in Lie cmicircle L Y M, then L and it from what has been here nodes. the faid, appears, that while the moon has moved from A to K, one of the

cle

AEC D,

M

4

Now

nodes has been carried from A to L, and the other as much C to M. But the motion from A to L, and from C to

from

4,

M,

is

CHAP. M, is

.PHILOSOPHY.

3.

backward

is

the other

motion of the moon, which and from thence toward C.

in regard to the

way from A

FARTHER

.

207

to K,

the angle,

which the

plane,

wherein the

any time appears, makes with the plane of the earth's motion, is called the inclination of the moon's orbit at that

moon

at

And

time.

tion of the

me

was

in

line of the

I

orbit,

A

;

now proceed to fhcw, when the moon is in K,

mall

or, that the

moon's motion

that this inclina lefs

is

L Y M, which

plane

makes a

than

when

touches the

angle with the or with the circle A B C D, than plane of the earth's motion The femicircle L Y the plane A E C makes with the fame. in K,

lefs

M

interfects the femicircle

AEC

Y

in

and the arch A Y

;

is

lels

than L Y, and both together lefs than half a circle. But it is demonftrated by the writers on that part of aftronomy, which is called the doctrine of the fphere, that as here,

when

a triangle is made, and AL, AY, YL, the angleis than the greater angle under

three arches of circles

by under YAB without the

triangle

AY, Y L taken together do two arches make a com the two angles will be equal but if the two femicircle, plete arches taken together exceed a femicircle, the inner angle un Here therefore the two der Y L A is greater than the other

YLA not

within,

amount

if

the

two

arches

to a femicircle

;

if

the

;

*.

arches

angle

A Y and L Y together being lefs than a femicircle, the But under AL Y is lefs, than the angle under BAE.

from the doctrine of the fphere it gle under A L Y is equal to that, a Menclai Sphaeric. Lib. I.

is

in

alfo evident,

that the

an

which the plane of the

prop. 10,

cii

AAC NEWTON'S

Sir Is

208 drcle

L Y K M,

GHI

in K,

is

that

the plane

is,

tion of the former plane

SUPPOSE now

i*j.

which touches the

line

AK

inclined to the plane of the earth's motion ABC; under B A E is equal to that, in which the plane

and the angle A EC is inclined to the fame

G

BooKlL

is

lefs

the

Therefore the inclina

plane.

than the inclination of the

moon

latter.

to be advanced to the point

100.) and in this point to be diftant from its node a quarter part of the whole circle ; or in other words, to be And in this cafe the in the midway between its two nodes. (in fig.

nodes will have receded yet more, and the inclination of the for orbit be ftill more diminished (uppofe the line AKGHI :

to be touched in the point G by a plane palling through the let the interfection of this earth T plane with the plane of :

the earth's motion be the line \V terfection with the plane

T O,

and the

line

TP

its

in-

LKM.

In this plane let the circle be defcribed with the femidiameter TP or cutting in P. the line A K G I is convex the other circle L K

NT

NGO

M

Now

LKM, which touches it in K and therefore the N G O, which touches in G, will interfedl the other

to the plane

plane

;

it

touching plane between G and K; that is, the point P will fall between thofe two points, and the plane continued to the plane of the earth's motion will pafs beyond the places of the nodes, points N and O, or is

in G,

will

will be farther

from A and

have moved farther backward.

of the plane

C

than

L fo that the when the moon ;

L and M,

that

is,

Befides, the inclination

NGO

to the plane of the earth's motion ABC than the inclination of the plane I K to the fame ; for here alfo the two arches LP and NP taken together are lefs O is lefs,

,

M

than

CHAP.

PHILOSOPHY.

3.

209

than a femicircle, each of thefe arches being lefs than a quar ter of a circle ; as appears, becaufe G N, the diftance of the

moon part

G from

in

of a

its

node N,

is

here fuppofed to be a quarter

circle.

18. AFTER the

moon is parted beyond G,

the cafe

altered

is

;

then theie arches will be greater than quarters of the circle, which means the inclination will be again increafed tho' by the nodes ftill go on to move the fame way. Suppo/e the for

,

moon

in

H, (in

rig.

A KG I

the line

i

o I.

in H,

)

and that the plane, which touches

intcrfecls the

plane of the earth's

mo

and the plane NGO in the line TV> and befides that the circle QJi R be defcribed in that plane ; then, for the fame reafon as before, the point V will fall be tion in the line

Q^TR,

H

and G, and the plane R V Q^ will pafs beyond the plane O V N, caufing the points Q^and R to fall farther from A and C than N and O. But the arches N V, V (^ are

tween laft

each greater than a quarter of a circle, N V the lean: of them being greater than G N, which is a quarter of a circle ; and

N

V and V Q^ together exceed a fethe will be greater, ; confequently angle under B than that under B V.

therefore the

two arches

QV

micircle

N

19. IN the

laft

place,

when

the

moon

is

by

this attra

drawn at length into the plane of the earth's motion, the node will have receded yet more, and the incli nation be fo much increafed, as to become fomcwhat more ction of the fun,

than at

firft

planes,

which touch

:

for the line it,

AKGI-II being convex

the pait

HI

will

E

c

wholly

to

fall

all

the

between the

N E w T o N'S

210

Sir I

the plane (VV

R and the plane A B C

s

AAc

BOOK II.

fo that the point

;

will

I

fall

W

will be far between B and R and drawing I T W, the point ther removed from A than (^. But it is evident, that the plane, ;

which in the

in the line

der

HIB

I

I,

will cut the plane

T \V,

and be

palled into L,

N and

node which was

Q^,

which was

comes

at firft in

is

30.

in the angle

at laft into the point

W

as the

;

O and R to I but the angle under H I B, the inclination of the orbit to the plane of the manifeftly not lefs than the angle under E C B or :

is

but rather fomething greater.

THUS

the

moon

in the cafe before us,

while

it

from the plane of the earth's motion in the quarter, comes again into the fame plane, has the nodes of its fes

continually is

un

in A, after having

now

ecliptic,

EAB,

fame firft

C has pafled fuccciTivcly from thence

through the points M,

which

of the

inclined to the

fo that the node,

;

and touches the line AG I earth's motion ABCD

through the earth T,

pailes

point

moved backward, and

at firft diminifhed, viz.

till it

the inclination of

comes

to

G in

fig.

its

paftill it

orbit

orbit

loo, which

is

conjunction with the fun, but afterwards is increafed again almoft by the fame degrees, till upon the moon's arrival again to the plane of the earth's motion, the inclina near to

its

reftored to fomething more than its firft though the difference is not very great, becaufe

tion of the orbit

magnitude, the points

I

is

and C are not

far diftant

from each other

* Vid. Ncivt, Princ. Lib. I. prop. 66.

V

coroll. 10.

gj.

AFTER

CHAP.

PHILOSOPHY.

3.

211

if the moon had depart 31. AFTER the fame manner, ed from the quarter in C, it fhould have defcribed the curve

line

CXW

between the planes

(in fig. 98.)

AFC and ADC,

which would be convex to the former ot thofe concave to the latter

fo that,

;

here

planes,

and

alfo, the nodes fhould

inclination of the orbit gradually continually recede, and the diminifli more and more, till the moon arrived near its oppo-

fun in

fition to the

fhould again increafe,

X

;

but from that time the inclination

till it

became a

little

greater than at

This will eafily appear, by confidering, that

firfl.

as the action

of

moon, by exceeding its action upon the earth, drew it out of the plane A E C towards the fun, while the moon

the fun

the

upon

A to I ; fo, during its paflage from C to W, the fun than the earth, being all that time farther from the will be attracted lefs ; and the earth, together with the

paffed from

moon it

as it were be drawn from the moon, in plane AECF, will fuch fort, that the path the moon defcribes fhall appear from the earth, as it did in the former cafe by the moon's being

drawn away. 31.

THESE

are the changes,

which the nodes and the

in

moon's orbit undergo, when the nodes are in but when the nodes by their motion, and the

clination of the

the quarters

;

motion of the fun together, come to be fituatcd between the quarter and conjunction or oppofition, their motion and the

change made

in the inclination of the orbit are

fomewhat dif

ferent.

E

e

i

.

LET

212

Sir I

AGCH

LET

33.

s

N E w T o N'S

AAc (

in fig. i

o3

.

)

BOOK II.

be a circle defcribed in the

T for its center. plane of the earth's motion, having the earth in Let the point oppofitc to the fun be A, and the point G a fourth Let the nodes of the moon's part of the circle diftant from A. orbit be fituated in the line B T D, and B the node, falling be tween A, the place where the moon would be in the full) and G the place where the moon would be in the quarter. in which the moon effays to Suppofe B E D F to be the plane,

move, when

B

in

more

is

attracted

lefs

fun fo

faft as

it

proceeds from the point B. Bccaufe the moon from the fun than the earth, it fhall be

diftant

and

by the fun, the earth

:

fhall

not defcend towards the it

confequently

fhall quit the plane

B E D F, which we fuppofe to accompany the earth, and defcribe the line B I K convex thereto, till fuch time as it comes to the point K, where it will be in the quarter: but from thenceforth being more attracted than the earth, the moon

change its courfe, and the following part of the path or BGD, defcribes fhall be concave to the plane and fhaJl continue concave to the plane BGD, till it croffes

fhall

BED

it

Now

I that plane in L, juft as in the preceding cafe. fay, while the moon is pa/ling from B to K, the nodes, contrary to what was found in the foregoing cafe, will proceed for a

ward, or move the fame way \vith the moon ; and fame time the inclination of the orbit will increafe b

at the

.

34.

M

I

N

* VLd.

WHEN

the

moon

is

in the point

the earth T, pafs through Newt.

Princ. Lib. Ill

prop 30

p.

440.

I,

let

the plane

and touch the path of the fc

Ibid. Lib, I.

prop. 66.

coroll. to.

moon

}

CHAP. moon

in

M T N, BIK

is

HILOSOPH

P

3.

Y.

213

cutting the plane of the earth's mourn in the in the line T O. I

I,

and the plane B E D

convex to the plane BED, which touches it l-i B, mufl crols the plane DEB, before it niLUs

NIM

plane

plane CGB

and therefore the pclnt wards G, and the node of the moon's from B to is moved forward. ;

M

3$*.

plane

I

SAY

farther,

M will

full

from B

i

t

!

to

orbit being tranflated

the angle under

OMG,

M O N makes with the plane B G C,

is

which the

greater than the

BOD

makes with the angle under O B G, which the plane fame. This appears from what has been already explained f becaufe the arches B O, O are each lefs than the quarter of :

M

and therefore taken both together are

a circle,

lels

than a k

micirckle. the moon is come to the point K in the nodes will be advanced yet farther forward, the inclination of the orbit alfo more augmented. Hi

36. its

AGAIN, when

quarter,

and

therto the moon's

motion has been referred to the

plane,,

which paiTmg through die earth touches the path ct the moon in the point, where the moon is, according to what was afTerted nodes,

that

at it

is

here in the point

the beginning of this difcourfe upon the the cuftom of aftronomers fo to do. But

K no

ry, feeing the line

K

is

fuch plane can be found ; on the contra of the moon's motion on one fide the point

convex to the plane B E D,

K3

but will cut the line B

KL

and on the other

fide con-

through the points T and in that point. Therefore inftead

rave to the fame, no plane can

pals

Sir I

214.

s

A Ac

N E w T o N'S

BOOK

II.

of fuch a touching plane, we muft here make life of what is with which the line BKL fhall equivalent, the plane P K (i,

make

a

does as cuts

it,

lefs

for this plane angle than with any other plane ; fince it fo line B K in the point K,

were touch the

it

no other plane can be drawn fo, as to pafs be BK and the plane.PKQ; But now it is evi to the point P, or the node, is removed from

that

tween the

line

dent, that

M

wards G, that

moved

has

farther

is, yet likewife as 'manifefr., that the angle

clination of the

moon's orbit

the angle under

IMG,

37. the

AFTER

moon

the

in the

forward

under

and

;

K P G, is

point K,

it

is

or the in

greater than

for the reafon fo often affigned.

moon

has parted the quarter, the path of A G C H, the nodes, as

being concave to the plane

in the preceding cafe,

fhall recede,

till

the

moon

arrives at

the point L ; which mews, that considering the whole time of the moon's palling from B to L, at the end of that time the nodes fhall be found to have receded, or to be placed back-

warder,

in

when

moon

the

parting

the

moon

is

in L, than

when

it

was

For

in B.

takes a longer time in parting from K to L, than from B to K ; and therefore the nodes continue to

recede a longer time, than they moved forwards; fo that their recefs muft furmount their advance.

3 8.

IN the fame manner, while the moon

K to L, the moon comes

is

in

its

partage

from

inclination of the orbit fhall diminifh,

the

to

part

R

,

of a

circle

the point,

difbnt from

its

in

which

node

;

and from that time the inclination

it

is

till

one quarter

fuppofe in the point fhall

again increafe. Since

CHAP.

PHILOSOPHY.

3.

215

Since therefore the inclination of the orbit increafes,

moon

while

parting from B to K, and diminishes itfelf again only, while the moon is parting from K to R, and then augments again, till the moon arrive iti L; while the moon is

the

is

from B to L, the inclination of the orbit is much more palling increafed than diminifhed, and will be diftinguifhably greater, when the moon is come to L, than when it fet out from B. 3 9. IN like manner, while the moon is parting from L on the other fide the plane A G C H, the node fhall advance for ward, as long as the moon is between the point L and the next

quarter ; but afterwards it fhall recede, till the moon come to pafs the plane A G C again in the point V, between B and A and bccaufe the time between the moon's parting from

H

:

L

to the next quarter

is lefs,

than the time between that quar

and the moon's coming to the point V, the node fhall have more receded than advanced ; fo that the point V will

ter

L is to C. moon is in V,

be nearer to A, than orbit,

when

the

So

alfo the inclination

will be greater, than

of the

when

the

moon was at L for this inclination increafes all the time the moon is between L and the next quarter it decreafes only while the moon is parting from this quarter to the mid way ;

;

between the two nodes,

and from thence

increafes again

ring the whole partage through the other half of the die next node.

40.

THUS we

have traced the

moon from

and thereby

will

to.

her node in

the quarter, and (hewn, that at every period of the

uodes will have receded,

du

way

moon

the

have approached toward

Sir Is A

2i6 .var J a

NE WTON'S

conjunction with the fun.

much forwarded by

he

AC

But

this

BOOK

II.

conjunction will

the vifiblc motion of the fun

itfelf.

fchcmc the fun will appear to move from S to from S to W, ward W. Suppofe it appeared to have moved while the moon's node has receded from B to V, then drawing the line T X, the arch V X will reprefent the difbnce of the In the

laft

W

drawn between

line is

V whereas moon was in

in

the

;

when

the nodes from the fun,

BA

the

that diftance, reprefcnted This vifible motion of the fun is

the arch B.

moon when much

of tru- node ; for the fun appears to revolve greater, than that near 1 9 years in mak quite round each year, Luid the node is V. e have alfo fccn, that when the node ing o one revolution.

was

in the quadrature,

creafed, tion,

till

the

according to

terwards

the inclination of the moon's orbit de-

moon came

again increafed, o

it

to the conjunction,

which node

it

till it

fet

out from

became

;

at the

or oppoft-

but that af next node

ra-

When

the node is once re ther greater than at the former. moved from the quarter nearer to a conjunction with the fun, the inclination of the moon's orbit, when the moon comes into the node,

preceding

;

is

more

feniibly greater, than

the inclination of the orbit

by

it

was

this

in the

node

means more

and more increafing till the node comes into conjunction with the fun ; at which time it has been fhewn above, that the fun has no power to change the plane of the moon's motion and confequently has no effect either on the nodes, or on the in ;

clination of the orbit.

41. As foon as the nodes, by the action of the fun, are out of conjunction toward the other quarters, they begin

I

again

CHAP.

PHILOSOPHY.

3.

217

again to recede as before ; but the inclination of the orbit in the appulfe of the moon to each fucceeding node is lefs than till the nodes come again into the quar Let A (in fig. 104.) reappear as follows. one of the moon's nodes placed between the point prefcnt Let the plane A D E pafs of oppofition B and the quarter

at the

preceding,

This

ters.

will

C

through the earth T, and touch the path of the moon in A. be the path of the moon in her paflagc Let the line A F G from A to H, where fhe crofles again die plane of the earth's

H

'

motion. This line will be convex toward the plane

moon comes

the

this,

this

between

while

G and

where fhe

H, the fame

All the time this line

plane.

A DE,

to G,

the nodes will recede; it is

concave to that plane.

A D E,

till

in the quarter ; and after line will be concave toward

is

is

convex toward the plane

and on the contrary proceed, All this will eafily be con

But ceived from what has been before fo largely explained. the moon is longer in pafling from A to G, than from GtoH ; therefore the nodes recede a longer time, than they proceed ; the whole, when the moon is arrived at

confequently upon

H, the nodes will have receded, that is, the point H will fall between B and E. The inclination of the orbit will dccreafe, till

the

moon

A and H.

arrived to the point F, in the middle between Through the paflage between F and G the incli is

nation will incrcafe, but decreafe again in the remaining part of the paflage from G to H, and confequently at H muft be The like effeds, both in rcfpccl to the nock lefs than at A.

and

will take place in the following the other fide of the plane A B F C,

inclination of the orbit,

the paflage of

from H,

till it

moon on

comes over that plane again F f

in

I.

41.

THUS

2

1

8

Sir I

4/1.

THUS

s

N E w T o N'S

AAc

the inclination of the orbit

is

BOOK II. when

greateft,

the line drawn between the moon's nodes will pafs through the fun ; and Icaft, when this line lies in the quarters, efpecial-

moon

ly if the

at the

fame time be in conjunction with the In the

fun, or in the oppofition.

have no motion, in and have receded :

when the

all others,

of thefe cafes the nodes

firft

the nodes will each

this regreftive

nodes are in the quarters

;

motion

month

will be greateft,

for in that cafe the nodes

have no progreflive motion during the whole month, but in all other cafes the nodes do at fome times proceed forward, viz.

whenever the mcon

node which

is

lels

between

is

diftant

either quarter,

and the

from that quarter than a fourth

part of a circle.

IT now remains only to explain the irregularities in which follow from the elliptical figure

4,3.

the moon's motion,

of the

orbit.

chapter

it

By what

appears,

has been faid at the beginning of this power of the earth on the moon

that the

acts in the reciprocal duplicate proportion

therefore the

moon,

if

round the earth

in a true ellipfis,

the earth to the

moon would

of time. portions

of the diftance :

move drawn from

undifturbed by the fun, would

That

and the

line

over equal fpaces in equal defcription of the fpaces is

pafs

this

It has alfo by the fun, has been already declared. the of orbit is changed each been fhewn, that the figaire O O

altered

'

month full,

;

that the

moon

and more remote

out the fun.

is

nearer the earth at the

in the quarters,

Now we mull

and confider the

effect,

pals

than

it

new and

would be with

by thefe monthly changes, will have in the differ

which the fun

ent

PHILOSOPHY.

CHAP. 3.

.219

ent fituations of the axis of the orbit in refpect of that lu

minary.

44..

the

THE

moon

is

action of the fun varies the force,

drawn toward the

force of the earth

new and

full

is

earth

by the fun ; at the and in the interme

directly increafed

the fame

is

diminifhed

diate places the influence of the earth

fometimes lefTened by the fun.

;

is

wherewith

in the quarters the

;

fometimes aided, and

In thefe intermediate places

between the quarters and the conjunction or opposition, the fun's action is fo oblique to the action of the earth on the moon, as to produce that alternate acceleration and re tardment of the moon's motion, which I obferved above

But befides

to be (tiled the variation.

by which the earth be

attracts the

at full liberty to act

acted not at action,

all

And

whereby

it

will

not

as if the

fun

itfelf,

with the fame force,

on the moon.

the power,

this effect,

moon toward

this effect

of the fun's

corroborates or weakens the action of the

here only to be confidered. And by this influence of the fun it comes to pafs, that the power, by which the moon is impelled toward the earth, is not perfectly in the re earth,

is

ciprocal duplicate proportion of die diftance. the moon will not defcribe a perfect ellipfis.

,

wherein the moon's orbit will fids in the xlicular to ellipfis,

the line

after the

and

at

its

from an

differ

drawn from

moon this

greateft diftance

fet

drawn from from the

F

f

con-

perpenIn an

out in the direction itfelf

earth,

x

is

the earth.

itfelf to

fhould have

line

particular,

ellipfis,

where the motion of the moon

places,

perpendicular to

Confequently

One

its

to the earth,

motion would again

22O

ISAAC NEWTON'S

Sir

BoonlL

line drawn between icagain become perpendicular to this felf and the earth, and the moon be at its neareft diftance

when it fhould have performed half its pe half of its period its mo performing the other become tion would again perpendicular to the foremention-

from the riod

ed

earth,

after

;

line,

and the moon return

and have recovered again in

its

real

its

into the place

whence

greateft diftance.

it fet

out,

But the moon,

motion, after fetting out as before, fometimes makes half a revolution, before its motion comes again

more than

to be perpendicular to the line drawn from itfelf to the earth, and then performs is at its neareft diftance ;

and the moon

more than another

half of an intire revolution before

tion can a fecond time recover

the line

drawn from

arrive again to

times the

its

moon

the

moon

from the

greateft diftance

will defcend to

its

mo

perpendicular direction to to the earth, and the moon

its

earth.

At

other

neareft diftance, before

its

it

made

half a revolution, and recover again its greateft di The place, ftance, before it has made an intire revolution.

has

where the moon

is

at

its

greateft diftance

from the

earth,

is

call

ed the moon's apogeon, and the place of the leaft diftance the perigeon. This change of the place, where the moon [ucceflively comes to its greateft diftance from the earth, is In what manner the fun called the motion of the apogeon.

caufes the

45-.

apogeon to move,

OUR

I

mall

author fhews, that

now endeavour to

if

the

moon were

explain, attract

ed toward the earth by a compofition of two powers, one of which were reciprocally in the duplicate proportion of the

diftance

from the

earth,

and the other

reciprocally in

CHAP. in the

PHILOSOPHY.

.

22;

of the lame diftance

triplicate proportion

then,

;

by the moon would not be in an ellipsis, yet the moon's motion might be reality perfectly explained by an ellipfis, whofe axis fhould be made to move though the

line defcribed

round the earth ;

motion being

this

nomers expreis themfelves, that

is,

in

confcquence, as aftro-

the fame

way

as the

moon

moves, if the moon be attracted by the fum of the two powers \ but the axis muft move in antecedence, or the con itfelf

trary

if

way,

moon

the

What

powers.

is

be acted on by the difference of thefe

meant by duplicate proportion has been

often explained ; namely, that if three magnitudes, as A, B, and C, are fo related, that the fecond B bears the fame pro as the firft A bears to the fecond portion to the third C, then the proportion of the firft A to the third C, is the

B,

duplicate of the proportion of the firft A to the fecond B. if a fourth magnitude, as D, be aflumed, to which C

Now

fame proportion as A bears to B, and B to C, then the proportion of A to D is the triplicate of the pro portion of A to B. fhall bear the

THE this cafe

fuppofe the diftance

way of

T

thus.

is

moon

from the

reprefenting the denoting the earth

in the point A,

earth,

moving

moon's motion in (

in fig. i

o 5", I o 6.

)

apogeon, or greateft in the direction per its

AF

pendicular to A B, and acted upon from the earth by two fuch forces as have been named. By that power alone,

which

is

reciprocally in the

moon

duplicate proportion of the from the point A with a

fet

out

proper degree of velocity,

the

diftance,

if

the

ellipfis

A MB may

be de

222

Sir Is

AAC NEWTON'S

BooKlI.

But if the moon be acted upon by the fum of the forementioned powers, and the velocity of the moon in the a point A be augmented in a certain proportion ; or if that

fcribed.

velocity be diminished in a certain proportion,

and the moon

be adled upon by the difference of thofe powers; in both thefe cafes the line AE, which fhall be defcribed by the be that, moon, is thus to be determined. Let the point

M

which the moon would have arrived in any given fpace of time, had it moved in the ellipfis A Draw B. T, and likewife C T D in fuch fort, that the angle under ATM fhall bear the fame proportion to the angle under A T C, as into

M

M

M

the velocity, with which the ellipfis A B muft have been de fcribed, bears to the difference between this velocity, and the velocity,

with which the

moon muft

in order to defcribe the path A E. ken toward the moon ( as in fig. I

ed by the fum of the powers ;

fet

out from the point A A T C be ta

Let the angle

o y.

)

if

the

moon

but the contrary

be attract

way

(

as in

if Then let the line be fig. 106'.) by their difference. moved into the pofition C D, and the ellipfis A B into the fit-nation C be tranflated to L : then D, fo that the point

AB

M

M

N

the point

L

fhall fall

upon

the path of the

moon A E.

47. THE angular motion of the line A T, wereby it is removed into the iituation C T, reprefents the motion of the ; by the means of which the motion of the moon be might fully explicated by the ellipfis A MB, if the action of the fun upon it was directed to the center of the earth, and

apogeon

*

What this proportion

i

,

maybe known from

Coroll. ^

prop 44. Lib.I.Princ.

philof.

Newton.

red-

CHAP.

PHILOSOPHY.

3.

reciprocally in the triplicate proportion of the

from

it.

But that not being

the regular

manner now

fo,

223

moon's diftance

the apogeon will not

move

in

defcribed.

However, it is to be obfervedhere, that in the firft of the two preceding cafes, where the apogeon moves forward, the whole centripetal power with the decreafe of diftance,

increafes farter,

than

if

the

power were reciprocally in the duplicate proportion of the diftance ; becaufe one part only is in that proportion, intire

and the other

whole power,

part,

which

added

is

to this to

make up

the

increafes fafter with the decreafe of diftance.

On the other hand, when the centripetal power is the differ ence between thefe two, it increafes lefs with the decreafe of the diftance, than if it were limply in the reciprocal dupli cate proportion of the diftance.

Therefore

plain the moon's motion by an ellipfis for aftronomical ufes to be done, and

of the

(

as

if is

we

chufe to ex

moft convenient

by reafon of the fmall

power, the doing fo will not be attended with any feniible error;) we may collect in general, that when the power, by which the moon is attracted to the earth, effect

fun's

by varying the diftance, increafes in a greater than in the du of the diftance diminifhed, a motion in con-

plicate proportion

fequence muft be afcribed to the apogeon

but that

;

attraction increafes in a lefs proportion than that

apogeon muft have given to then obferved by Sir obtains,

when

and the

latter,

in the

firft

I

s.

moon

the

when

*

is

firft

is

of thefe cafes

in the conjunction and oppofition ; moon is in the quarters : fo that

moves according

Princ. Phil.

the

named, the

a motion in antecedence \ It

N E w T o N, that the

the

the apogeon

it

when

Newt.

to the order of

Lib. I. prop. 4f. Coroll. i.

tl

-%

figns;

figns

N E w T o N'S

ISAAC

Sir

224.

in the other, the contrary

;

a

way

BOOK

II.

But, as was faid before,

.

the difturbance given to the action of the earth by the fun in the conjunction and oppofition being near twice as great as b in the quarters , the apogeon will advance with a greater velocity than recede,

lution of the

moon

48. IT

fhewn

when

and the the

is

AB

the line fun,

moon

regreflive

is

.

in the next place by our author, that coincides with that, which joins the earth

the progreflive motion of the apogeon, in the conjunclion or oppofition,

more than

in the quadratures

iion of the line

makes

in the compafs of a whole revo c be carried in confcquence

and

will

AB

d .

On

the contrary,

in

any other

when

iitua-

the line

right angles with that, which joins the earth motion will be more considerable c

the retrograde

when

exceeds the

and

AB fun,

nay is exceed the progremVe ; fo that in this cafe the apogeon in the compafs of an intire revolution of Yet from the confithe moon is carried in antecedence.

found

,

fo great as to

derations in the laft paragraph the progreffive motion ex fo that in the whole the mean motion of ;

ceeds the other the apogeon find.

is

Moreover,

in

ccnfequence, the line

according

A B changes

its

as

aftronomers

fituation with that,

joins the earth and fun, by fuch flow degrees, that the in the motion of the apogeon ariiing from this are much greater than what arifes from laft confederation,

which

inequalities

the other a

r .

Pr. Phil Newt.r.ibJ. prop. 66. Coi oil. 7 (9 of rh's chapter. Phil Nat.Pr.Muth Lib I. prop. 6 5 cor .8. .

-

T!

'V.

Corol

8.

Ibid.

Ibid.

40. FAR-

CHAP.

3.

PHILOSOPHY.

49. FARTHER, this unfteady motion in the apogcon is at tended with another inequality in the motion of the moon, that it

cannot be explained at

ellipfis

all

times by the fame

ellipfis.

The

by aftronomcrs an eccentric orbit. which the two axis's crofs, is called the center of

in

is

general

called

The point, in the figure ; becaufe all lines drawn through this point within the ellipfis, from fide to fide, are divided in the middle by

this

But the center, about which the heavenly bodies lying out of this center of the figure in one focus,

point.

revolve,

thefe orbits are faid to be eccentric

;

and where the diftance of

die focus from this center bears the greateft proportion to the whole axis,, that orbit is called the moft eccentric and ill :

fuch an orbit the diftance from the focus to the remoter ex tremity of the axis bears the greateft proportion to the di ftance of the nearer extremity. whenever the apo-

Now

geon of the moon moves in confequence, the moon's motion muft be referred to an orbit more eccentric, than what the

moon would defcribe, if the whole power, by which the moon was acled on in its pafling from the apogeon, changed according to the reciprocal duplicate proportion of the di ftance from the earth, and by that means the moon did de fcribe

an immoveable

in antecedence,

orbit

lefs

ellipiis

;

and when the apogeon moves muft be referred to an

the moon's motion

eccentric.

In the

firft

of the two figures o

laft re-

ferred to, the true place of the moon L falls without the orbit B, to which its motion is referred : whence the orbit ALE,

AM

in the point A, truly defcribed by the moon, is lefs incurvated than is the orbit A B is more ob B ; therefore the orbit A

M

long,

and

differs farther

M

from a

circle,

Gg

than the

ellipfis

would,

whofe

'226

Sir

whofc curvature

N E u T o N'S

ISAAC in

A were

BOOK II.

r

equal to that of the line

ALB,

the proportion of the diftance of the earth T from the center oi the ellipfis to its axis will be greater in the elA MB, than in the other ; but that other is the lipfis

that

is,

ellipnV,

which the moon would defcribe, if the power acting upon it in the point A were altered in the reciprocal duplicate pro In the fecond figure, when the portion of the diflance. apogeon recedes, the place of the moon L falls within the

A M B,

orbit

and therefore

the immoveable orbit truth of this

evident

is

;

from the apogeon,

diflance,

is lefs

eccentric, than defcribe.

The

when

the apogeon moves for the moon is influenced in its de~

for,

ward, the power, by which fcent

that orbit

which the moon (hould

increafes fafter

with the decreafe of

than in the duplicate proportion of the diftance

;

and confequently the moon being drawn more forcibly to ward the earth, it will defcend nearer to it. On the other hand,

when

moon

increafes

the apogeon recedes, the power acting on the with the decreafe of diftance in lefs than the

duplicate proportion of the diftance ; and therefore the moon is lefs impelled toward the earth, and will not defcend fo low. j-o.

Now

apogeon

A

is

fuppofe in the in the fouation,

firft

of thefe figures, that the it is approaching toward

where

the conjunction or oppofition of the fun. In this cafe the proof the apogeon is more and more accelerated. greflive motion

Here fuppofe

that the

moon,

after

having defcended from A

through the orbit A E as far as F, where diftance from the earth, afcends caufe the motion of the apogeon

it is

again up here

is

come

to

its

neareft

the line F G.

Be-

continually more and more

CHAP,

PHILOSOPHY.

3.

227

more accelerating, the caufe of its motion is conftantly up that is, the power, whereby the moon is on the increafe ;

drawn in the

to the earth, will decreafe with the increafe of diftancr,

moon's afcent from

wherewith

it

F, in a greater proportion

than that

increafed with the "decreafe of diftance in the i

moon's defcent to er

F.

moon will afcend high A T, from whence it defcended there of the greateft diftance of the moon to And when the moon defends again, the

Confequently the

than to the diftance

fore the proportion the leaft is increafed.

power

will yet

than in the

more

;

increafe with the decreaie of diftance,

it dccreafed with the augmentation of diftance; the moon therefore muft defcend nearer to the earth than it did before, and the proportion of the greateft Thus as long diftance to the leaft yet be more increafed. as the apogeon is advancing toward the conjunction or oppo-

laft

afcent

the proportion of the greateft diftance of the the earth to the leaft will continually increafe from

moon

fition,

the elliptical orbit, to will be rendered

which the moon's motion

more and more

is

;

and

referred,

eccentric.

As foon as the apogeon is pafTed the conjunction 5*1. with the fun or the oppofition, the progreflive motion thereof abates, and with it the proportion of the greateft diftance of the

moon from the earth to the leaft diftance will alfo dimiand when the apogeon becomes regrcilive, the diminu

nifh;

farther continued on, till tion of this proportion will be ftill the apogeon comes into the quarter ; from thence this pro and the eccentricity of the orbit will increafe again. portion,

Thus

the orbit of the

moon

is

moft eccentric, when the apox geon

Gg

228

Sir

ISAAC NEWTON'S

BooKlL

geon is in conjunction with the fun, or in oppofition and leaft of all when the apogeon is in the quarters. yi.

THESE

changes in the nodes,

to

it,

in the inclination of

the orbit to the plane of the earth's motion, in the apogeon, and in the eccentricity, are varied like the other inequalities in the

motion of the moon, by the different diftance of the

earth from the fun; being greateft, when their caufe eft, that is, when the earth is neareft to the fun.

is

great-

the beginning of this chapter, that Sir I s A A c computed the very quantity of many of the That acceleration of the moon's mo moon's inequalities.

f3

.

I faid at

NEWTON tion,

has

which

is

called the variation,

when

greateft,

removes

moon

out of the place, in which it would otherwife be a In the phrafe found, fomething more than half a degree a the whole circuit of of aftronomers, degree is -^ part of the

.

the

moon

from the

or any planet fun,

If the

would have

moon, without difturbance

defcribed a circle concentrical to

the earth, the fun will caufe the

moon

to

approach nearer

to the earth in the conjunction and oppofltion, than in the b had quarters, nearly in the proportion of 6 9 to7o .

We

occaiion to mention above, that the nodes perform their pe riod in almoft 19 years. This the aftronomers found by obfervation

;

and our author's computations

aflign to

them

fame period c The inclination of the moon's orbit when kaft, is an angle about 1 part of that angle, which conftitutes the

.

'Ncwt,

b Ibid.

Princ. Lib. III. prop. 29,

4,

prep. 18.

Ibid.

prop. jr.

CHAP.

PHILOSOPHY.

3.

a perpendicular

and the difference between the

;

leaft inclination

of the orbit

computation to be about this alfo

is

,-a

is

grcateft

ISAAC

NEWTON

and

determined by our author's

of the lead inclination

a

And

.

to the obfervations of aftronomers. agreeable o

motion of the apogeon, Sir

229

and the changes

in the

The

eccentricity,

The apogeon

has not computed.

performs its revolution in about eight years and ten months. When the moon's orbit is mod eccentric, the greateft diflance of the

moon from

the earth bears to the leaft di-

ftance nearly the proportion of 8 to leaft eccentric,

II

this

proportion

is

7

;

when

the orbit

is

hardly fb great as that of

to j I.

.

Sir

ISAAC

NEWTON

fhews

farther,

how, by com

paring the periods of the motion of the fatellites, which re volve round Jupiter and Saturn, with the period of our moon round the earth, and the periods of thofe planets round the fun with the period of our earth's motion, the inequalities

in the

motion of thofe

ly in

in the orbits this

fatellites

may

be derived

moon's motion ; excepting on inequalities regard to that motion of the axis of the orbit, which

from the

in the

moon makes of thofe

diftance,

the motion of the

fatellites,

appearing

as far as little

apogeon

;

for the

can be difcerned by us

or nothing eccentric,

at

this

motion, as deduced from the moon, muft be dirmnimsd, b

Newt.Princ. pag,

45-9.

C H A PC

Sir Is A

230

AC

NEWTON'S

CHAP.

BOOK

II.

IV.

COMETS.

Of

die former of the two preceding chapters the powers have been explained, which keep in motion thofe celeftial bodies, whofe courfes had been well determined by the

IN

In the laft chapter we have fhewn, how thofe powers have been applied by our author to the making a more perfect difcovery of the motion of thofe bodies, the

aftronomers.

which were but imperfectly underftood for which we have been defcribing

courfes of

;

fome of the inequalities, in the

In

this

moon's motion, were unknown to the aftronomers. we are to treat of a third fpecies of the hea

chapter true motion of which was not at all ap venly bodies, the before our author writ ; in fo much, that here

prehended

NEWTON

has not only explained the caufes of ISAAC the motion of thefe bodies, but has performed alfo the part

Sir

of an aftronomer, 1.

THAT

by difcovering what their motions

thefe bodies are not meteors in

manifeftj

becaufe they

as the fun

and

their inquiries

the

moon

;

which they

The

liars.

and

moved

fet in

as

to prove

is

air,

by

in

their ob-

far in the etherial fpaces

but they had no true notion defcribed,

our

the fame manner,

aftronomers had gone fo far

concerning them,

that they

fervations,

rife

are.

The moft

at all

beyond of the path,

prevailing opinion

.

before

our

CHAP.

PHILOSOPH V.

4.

231

our author was, that they moved in ftraight lines what part of the heavens was not determined.

but in

;

D E CAR s

TES' removed them far beyond the fphere of Saturn, as finding the ftraight motion attributed to them, incotlfiftent with the vortical fluid, by which he explains the motions of the planets,

as

we have above

related

b

But

.

Sir I

s

A A c

NEWTON

diftinclly proves from aftronomical obfervation, that the comets pafs through the region of the planets, and

are moftly invifible at a

lefs

diftance, than that of Jupiter

c .

AND

from hence rinding the comets to be evidentthe within ly fphere of the fun's action, he concludes they muft neceflarily move about the fun, as the planets do d .

.

.

move

The

but

not neceflary that planets which is influenced the fhould move fun, by every body, in that particular kind of line. However our author proves, in ellipfiYs

;

power of the fun being

that the

it

is

reciprocally in the duplicate

the diftance, every body acted on by the fun proportion of

muft

dion

down,

either fall directly

of which

;

lines I

or

move

in

fome conic

fe-

have above obferved, that there arc e

If a parabola, and hyperbola which defcends toward the fun as low as the orbit

three fpecies,

the

body, of any planet,

figure, leaft.

*

k

move with body

In Princ. philof. part.

Chap.

a fwifter

motion than the pla

an orbit of a more oblong than that of the planet, and have a longer axis at The velocity of the body may be fo great, that it

net does, that

*

.

ellipfis,

i.

Newton.

3.

will defcribe

I

41.

ii.

Princ. philof,

Lib, III.

Lemra.

4-

'

pag. 478. d Princ. philof. Lib. III. prop. 40.

Book

I.

chap.

2.

8. ihal!

2

3

ISAAC

Sir

2

N E w T o N'S

BOOK II.

move in a parabola, and having once palled about the fun, mall alccnd for ever without returning any more

lhall

:

but the fun will be placed in the focus of

With a

But

hyperbola. in elliptical

greater the

flill

velocity

is

it

orbits,

body

will

this

parabola.

move

in

an

mod

probable, that the comets move though of a very oblong, or in the

fuch as phrafe of aftronomers, of a very eccentric form, in fig. 107, where S is the fun, C the co is reprefented met, and ABDE its orbit, wherein the diftance of S

and

D

far

exceeds that of S and A.

Whence

it

is,

that

they fometimes are found at a moderate diftance from the and appear within the planetary regions ; at other fun, times they afcend to vafl diftances, bit

do move

far beyond the vejy or become invifible. That the comets manner is proved by our author, from com

and

of Saturn,

in this

fo

which aftronomers had Thefe computations were perform ed by Sir I s A A c NEWTON himfelf upon the comet, which appeared toward the latter end of the year 1680, and at a the beginning of the year but the learned ; putations

built

upon the

made on many

Dr.

following

HA L LEY

in this,

are

obfervations,

comets.

profecuted the like computations more at large and alfo in many other comets b Which .

made upon

propofitions highly

paralleled genius,

by any one not

fuch

as

computations

worthy of our author's un-

could fcarce have been difcovered

poflerTed of the utmoft force cf invention;

Princ. philof. Lib. III.

r. ^99, ;oo.

b

lyj. pag- foo

4.

THOSE

CHAP.

PHILOSOPHY.

4.

THOSP. computations depend upon

4.

233 this

principle,

of the comets is fo eccentricity of the orbits that if they are really elliptical, yet they approach great, in that part ot ib near to them, where

that

the

they

parabolas

come under our

*

without fenfible error

FAG

parabola ry

little

that they may be taken for fuch as in the preceding figure the

view,

:

from the

it about A ve Upon which ground

the lower part of

differs in

ellipfis

D E A B.

our great author teaches a method of finding by three or>

made upon any comet

fervations

neareft agrees with

Now

5*.

leaft

room

orbit

its

what confirms for

doubt

puted

in the orbits,

ailigns

them,

is,

the

parabola,

which

b .

this

whole theory beyond the

that the places of the comets

com

which the method here mentioned

agree to the obfervations of aftronomers with

the fame degree of exa&nefs, as the computations of the do , and this in comets, primary planets places ufually c whofe motions are very extraordinary .

6.

OUR

author afterwards fhews

how

to

make

ufe of

the parabola, that fhall be obany fmall deviation from the orbits of the comets are whether determine "to ferved, elliptical

or not,

and

fo to difcover if the

fame comet

re

d

And upon examining the co turns at certain periods rnet in 1680, by the rule laid down for this purpofe, he .

finds

its

orbit to agree

Princ.Philof. Lib.III.prop.4o. b

Ibid. prop.

41.

more

exactly c

I

d

to an ellipfis than

Ibici.pag fn. Ibid prop. 4:.

Hh

to

2

to

ISAAC

Sir

34 a

N E w T o N'S

BOOK II.

though the ellipfis be fo very eccentric, comet cannot perform its period through it in the

parabola,

that the

H

fpace of 5*00 years Upon this Dr. ALLEY obferved, that mention is made in hiftory of a comet , with the like eminent tail as this , having appeared three feveral 1

.

times before;

death of

the

flrft

of which appearances was each appearance was

at the

JULIUS CESAR, and

at the

He there diftance of 5-7 f years from the next preceding. fore computed the motion of this comet in fuch an ellip

tic

orbit,

as

would

require this

number of

years for the

body to revolve through it; and thefe computations agree yet more perfectly with the obfervations made on this co b met, than any parabolical orbit will do .

7. THE comparing together different appearances of the fame comet, is the only way to difcover certainly the true form of the orbit tor it is impoiTible to determine with ex:

aftnefs the figure of an orbit fo exceedingly eccentric, from lingle obfervations taken in one part of it ; and there

fore Sir ISAAC

upon

NEWTON

c

the fuppoiition that

propofes to compare the orbits, they are parabolical, of fuch

comets bit

in

as appear at different times ; for it the fame or be found to be defcribed by a comet at different times,

all

fcribes

probability it.

And

it

will be

the

fame

comet which de-

here he remarks from Dr.

HALLE y,

that

the fame orbit very nearly agrees to two appearances of comet about the fpace of 75- years diftance a ; fo that Newt. Princ.philor edit. 1^.464,46;-. *

Ibid. edit. 3.

p

5-01,

joz.

c I

I

Ibid pa

Ibid. pag.

if

CHAP.

PHILOSOPHY.

4.

235

two appearances were

of the fame -comet, really the tranfverfe axis of the orbit of the comet would be near

if thofe

1

8 times the axis of the earth's orbit;

when

at

ed not

from the

greateft diftance

its

than

lefs

g $

fun,

and the comet, will be remov

times as far as the middle diftance

of the earth. 8.

AND

this

comet

7 5-

feems to be the fhorteft period of any of it will be farther confirmed, if the fame

But

the comets.

fliould return a

years.

However

it

third time after another period of not to be expected, that comets

is

preferve the fame

fliould

the planets ;

makes them

from the action of the

IT

regularity in

their periods,

as

becaufe the great eccentricity of their orbits liable to differ very confiderable alterations planets,

and other comets, upon them.

prevent too great disturbances in their motions from thefe caufes, as our author obferves, 9.

is

therefore to

that while the planets revolve all of them nearly in the fame plane, the comets are difpofed in very different oneSj and diftributed over all parts of the heavens ; that,

when

from the

in their greateft diftance

fun,

and moving

they might be removed as far as poffible out of the a reach of each other's action The fame end is likewife floweft,

.

anfwered in thofe comets, which by moving floweft in the aphelion, or remoteft diftance from the fun, defcend

farther

nearefl

to

by placing the aphelion of thefe from the fun b

it,

greateft height

at

the

.

1

Newt.Princ.

'

philof. p.j-zj.

1

1

h x

Ibid,

10.

OUR

236

Sir Is A

NEWTON'S

AC

.*

BOOK

II. i-

OUR

his principles to ex IO. philofophcr being led by the comets, in the manner now re plain the motions of his thoughts lated, takes occafion from thence to give us

upon the

their nature

and

For which end he proves in folid and com neccffarily be

ufe.

place, that they

firft

mud

no means any fort of vapour or light pact bodies, and by becaufe at fubftance exhaled from the planets or ftars the near diftance, to which fome comets approach the fun, :

could not be, but the immenfe heat, to which they are and fcatter any expofed, fhould inftantaneoufly difpcrfe a In particular the foremenfuch light volatile fubftance it

.

tioned comet of

1680

defcended fo near the fun, as to come within a fixth part of the fun's diameter from the iurface of

In which fituation

it.

it

rnuft have been ex-

appears by computation, to a degree of heat the heat of the fun upon our earth no lels than exceeding 28000 times ; and therefore might have contracted a de as

poled,

gree of heat xooo times greater, than that of red hot b iron Now a fubftance, which could endure fo intcnfe .

a

muft needs be

heat, without being difperfed in vapor,

firm

and

II.

folid.

IT

fubftances,

the fun rnets,

minim

c .

is

{hewn

like wife,

that the comets are opake

fhining by a reflected light, borrowed from This is proved from the obfervation, that co

diough they are approaching the earth, yet diin luftre, if at the fame time they recede from lliipag fcS,

b

Ibid.

<

Ibid. pag.

484.

the

CHAP. the fun

and on the contrary

;

daily in

though

PHILOSOPHY.

4.

found to encreafe

they advance towards the fun, the fame time they move from the earth J .

THE

II.

are

when

brightnefs, at

,

237

comets therefore

refpe^s refcmble the opake bodies, and both re volve about the fun in conic fe&ions. But farther the in thefc

planets;

that both are durable

comets,

like

our

The

fphere.

air

earth

we

,

an

atmo-

called the earth's

atmo-

furrounded

are

breath

is

by

fphere; and it is moft probable, that all the other planets are inverted with the like fluid. Indeed here a difference is found between the planets and comets. The atmofpheres of the planets are of fo fine and fubtile a fubftance, as hardly to be difcerned at any diftaace, by reafon of the

fmall quantity of light which they reflect, except only in In him there is fome little appearance the planet Mars. of fuch a fubftance fur-rounding him, as ftars which have

covered by him are

been

faid

to look

fomewhat dim a

body comes under them, as if their he is near, were obftru&ed when by his atrnofphere. light, But the atmofpheres which funmind the comets are fo fmall ipace before his

grofs

and

are alfo

round,

as

to

reflec-t light very copioufly. They greater in proportion to the body they furthan thofe of the planets, if we may judge of

thick,

much

the reft from our air

;

for

it

has been obferved of comets,,

that the bright light appearing in the middle *

IbiJ.pag. 482,

of them, which

48 3

is

&

2

Sir

from the

reflected

part of

1 s

A

AC

folid

N E w T o N'S

body,

is

BOOK

II.

fcarce a ninth or tenth

the whole comet,

13. I fpeak only of the heads of the comets, the mofl: lucid part of which is fiirroimded by a fainter light, the mo ft lucid part being ufuully not above a ninth or tentli

Their tails are an appear part of the whole in breadth ance very peculiar, nothing of the fame nature appertain ing in the leaft degree to any other of the celeftial bo '.

dies. Of that appearance there are feveral opinions ; our author reduces them to three \ The two firft, which he l

propofes, are rejected by him firft is, that they arife

The

;

but the third he approves. a beam of light tran

from

mitted through the head of the comet, in like manner as a ftream of light is difcerned, when the fun {Lines into a

darkened room through a fmall Sir

ISAAC

NEWTON

obferves,

This opinion, as the authors of it implies hole.

wholly unskilled in the principles of optics; for that ftream of light, feen in a darken'd room, arifes from the refle ction of the fun

the air

;

beams by the duft and motes

for the rays

floating in

of light thernfelves are not feen, but

by their being reflected to the eye from Tome fubftance, upon which they fall'. The ne.vr opinion examined by our author lagiris

in

its

is

DE

that of the celebrated

s

rhefe tails to be the light of the

paflagc to

prefentation

;

Ibid, pag.

comet

who

refracted

and thence affording an oblong

us,

as the light of" ^81.

CARTES,

*

Jbib.

r

fic

pag.;o 9

c ,

re-

fun does, when, refracted Sec the fore-cited place,

by

CHAP.

PHILOSOPHY.

4.

by the prifm

in that

noted experiment, which will have a book of this difcourfe a But this

great {hare in the third

opinion

is

at

.

once overturned from

that the planets could be

ly,

239

than the comets

this

no more

consideration on

from

free

this

re

ought to have larger or brighter tails, than they, becaufe the light of the planets is ftrongeft. However our author has thought proper to add

fraction

fome

;

nay

farther objections againft this opinion

:

for inflance,

thefe tails are not variegated with colours,

that

as

the

is

image produced by the prifm, and which is infcparable from that unequal refraction, which produces that

difpro-

And

portioned length of the image.

befides,

when

the

pafTage from dirlerent comets to the earth defcribes the fame path through the heavens, the refraction light in

of

its

fhould of neceiTity be in

it

contrary to obfervation

this

is

the

i8th day

of

December,

all ;

refpects the fame.

for

the

comet

in

and a former comet

But

1680 in the

the ipth day of December, appear'd in the fame place of the heavens, that is, were feen adjacent to the fame fixed ftars, the earth likewife being in the fame

year

1 5*7 7,

tail of the latter comet de place at both times; yet the viated from the opposition to the iun a little to the north

ward,

and the

tail

of the former comet declined from the

oppofition of the fun five times as

much fouthward

b .

14. THERE are fome other falfe opinions, though Ich regarded than thefe, which have been advanced upon this: a Ibid

andCartef. Princ.Phil. part.

3,

i34,8cc.

l

Vid. I fail. Nat. princ. Math. p.

j-i

i.

Sir I

240

s

AAc

N E w T o N'S

BOOK

II.

Thefe our excellent author panes over, haftenwhat lie takes to be the true caufe of this

argument.

ing to explain,

He thinks it is certainly owing to Reams and appearance. from the body, and grofs atmoiphere of exhaled vapours the comets, by the heat of the fun ; becaufe all' the ap to pearances agree peilcdly the comet but fmall, while

fentiment.

this is

Ihe

tails

defcending to the fun,

are

but

as foon as ever enlarge themfelves to an immenfe. degree, the comet has pafled its perihelion ; which fhews the tail to depend upon the degree of heat, which the comet re

from the

ceives

And

fun.

that the intenfe heat to

which

when

neareft the fun, are expofed, fhould exhale from them a very copious vapour, is a moft reaibnable fupthat in thofe free and poiition- efpecially \{ we coniider, ft earns will more eafily afccnd, than here empty regions

comets,

upon

the furface of the earth,

and hindered from air

:

we

as

of the

air,

ftances will

riling

where they are fuppreiled

by the weight of the incumbent

by experiments made in vdlels exhaufted where upon removal of the air feveral fubfume and djfcharge ileams plentilulJy, which

find

emit none in the open

air.

The

tails

of comets,

like fuch

a vapour, are always in the plane of the comet's orbit, and except that the upper part thereof oppofite to the fun, inclines towards the parts, which the comet has left its

by

refembling perfectly the fmoak of a burning coal, which, if the coal remain fixed, afcends from it perpendi

motion

;

'

cularly

y

but, if the coal be in

motion, afcends obliquely,

And befides, the inclining from the motion of the coal. to tails of comets be this fmoak in another may compared 3

refpedl:,

CHAP.

PHILOSOPHY.

4.

th^m nrp denfer nnH than on the concave.

that both of

refpetf:,

on the convex

fide,

241

miw

r n,Q-

The

different

appearance of the head of the comet, after it has pa ft its perihelion, from what it had before, confirms greatly this for fmoke raifed opinion of their tails by a ftrong heat is blacker and groffer, than when raifed by a lefs; and ac :

cordingly the heads of comets, at the fame diftance from the fun, are observed lefs bright and filming after the peri helion,

1

5".

than before,

THE

as if

obfcured by fuch a grofi fmoke.

obfervations of

HEX

ELI us upon the atmo-

fpheres of comets frill farther illuftrate the fame; who re lates, that the atmofpheres, efpecially that part of them next the fun, are remarkably contracted when near the fun, and dilated again afterwards.

16.

To

give a

more

full

idea of thefe

tails,

a rule

is

down by our author, whereby to determine at any time, when the vapour in the extremity of the tail firil

laid

rofe

from the head of the comet.

By this rule it is found, does not confift of a fleeting vapour, diilipated foon after it is raifed, but is of long continuance ; that almofl all the vapour, which rofe about the time cf that the tail

the perihelion from the

comet

of

1680, continued

to ac

company it, afcending by degrees, being fucceeded conftantly by freiri matter, which rendered the tail contigu ous to the comet.

From

this

computation the

tails

are

i.

found to

va participate of another property of afcending

pours, that,

they are

when

they

aicmd with

leaft incurvated.

the greateft velocity,

li

17.

THE

Sir I

242

N E w T o N'S

AAc

s

BOOK IL

Tut

only nhje^inn flint rnn ho made againft this of explaining, how a fufficient raifed from the atmofphere of a can be of vapour quantity 17.

is

opinion

comet

to

the difficulty

fill

through which their tails This our author removes by the

thofe vaft fpaces,

are fometimes extended.

following computation a has been faid before ,

of the earth, where above; than a

lefs

is

it

is

air

being an

elaftic fluid,

prefled

I

as

furface

upon by the whole earth, where it

from the

air

has

have obferved, that the denfity

to the comprefling our author computes to what degree muft be expanded, according to this rule, at

reciprocally proportional

From hence

weight. rarity

is

air

more denfe here near the

at a diftance

weight incumbent.

of the

of

it is

our

:

the air

an height equal to a femidiameter of the earth and he finds, that a globe of fuch air, as we breath here on the furface oF :

be one inch only in diameter,if

the earth,

which

expanded

to the degree of rarity,

fhall

which the

air

it

were

muft have

now mentioned, would fill all the planetary the very fphere of Saturn, and far beyond. to even regions Now fince the air at a greater height will be ftill imat the height

menfly more

rarified,

and the

furface of the

atmofpheres

ufually about ten times the diftance center of the comet, as the furface of the comet it

of comets

the

tails

is

are yet vaftly farther

from the felf,

and

removed from the center of

the comet; the vapour, which compofes thofe tails, may ve to be fo expanded, as that a moderate ry well be allowed quantity of matter may fill all that fpace, they are feen to take up. Though indeed the atmofpheres of comets being Book

I.

Ch.

4.

ii.

very

PHILOSOPHY.

CHAP.!-

243

very grofs, they will hardly be rarificd in their tails to fo great a degree, as our air under the

fame circumflances

; efpecially fince they may be fomething condenfed, as well by their gra vitation to the fun, as that the parts will gravitate to one ano ther ; which will hereafter be fhewn to be the univerfal

pro

perty of light

all

matter \

The

only fcruple

left is,

how

fo

much

can be reflected from a vapour fo rare, as this computa For the removal of which our author obferves,

tion implies.

moft refulgent of thefe tails hardly appear brighter, than a beam of the fun's light tranfmitted into a darkened room through a hole of a fingle inch diameter ; and that that the

the (mailed fixed ftars are vifible through

them without any

fenfible diminution of their luftre.

1 8. is

ALL

thefe considerations put

the true nature of the

it

beyond doubt, what There has in

of comets.

tails

deed nothing been faid, which will account for the irregular in which thofe tails are fometimes reported to have

figures,

appeared; but fince none of thofe appearances have ever been recorded by aftronomers, who on the contrary afcribe the

fame likenefs to the

judgment

ing clouds,

comets

19. led Sir

by interven

way contiguous

to the

b .

THE

of

difcuffion

ISAAC b

f,

of all comets, our author with great

or to parts of the milky

to their ufe, -Ch.

tails

refers all thofe to accidental refradlions

All thefe

NEWTON which

I

arguments are

this

into

appearance in comets has

fome

(peculations

cannot but extreamly laid

down

in Philof.

I

i

i

relating

admire,

as

Nat.Princ.Lib.IH. from p. 709, to $-17.

reprefenting

Sir

244

ISAAC NEWTON'S

BOOK II

the tvprefenting in the ftrongeft light imaginable of author of the nature, great providence

iive

exten-

who,

the furnifhing this globe of earth, and without doubt the reft of the planets, fo abundantly with eve for the fupport and continuance of the ry thing neceflary numerous races of plants and animals, they are flocked has over and above provided a numerous train of with, befides

comets,

exceeding the number of the planets,

far

to re-

gradual decay, which a For fince the our author's opinion concerning them comets are fubjec"l to fuch unequal degrees of heat, being lify

continually, and

reftore

their

is

.

fometimes burnt with the moft intenfe degree of

it,

at

other times fcarce receiving any fenfible influence frcm the

fun; it can hardly be fuppofed, they are defigned for any Now the tails, which they fuch conftant ufe, as the planets. emit, like

all

other kinds of vapour, dilate themfelves

as

and by confequence are gradually difperfed and through all the planetary regions, and thence can

they afcend, fcattered

not but be gathered up by the planets, their orbs:

as they pafs through having a power to caufe all bodies towards them, as will in the fequel of this

for the planets

to gravitate difcourfe be flievvn

b ;

drawn in procefs which happens to

thefe vapours will be

of time into this or the other planet,

upon diem. And by entering the atmofpheres of the earth and other planets, they may well be fuppofed to contribute to the renovation of the face of things, in par

adl ftrongeft

ticular to fupply the

diminution caufed in the humid parts

PWof. Nat.Priac.

Lib. III. p.

fif

.

l

CJi.f,

by

CHAP.

PHILOSOPHY.

4.

245

by vegetation and putrefaction. For vegetables are ed by moifture, and by putreraclicn are turned

nouriflvin great

and an earthy fubfhnce always fubiides in fermenting liquors by which means the dry parts of the planets muft continually increafe, and the fluids di-

part into dry earth;

;

nay in a fufficient length of time be exhaufted, not fupplied by fome fuch means. It is farther our great author's opinion, that the moft fubtile and adive of minifli, if

parts

upon which the life of things chiefly depends, is derived to us, and fupplied by the comets. So far are they from portending any hurt or mifchief to us, which

our

air,

the natural fears of

men are fo apt to fugged from the ap uncommon and aftonifhing.

pearance of any thing

10.

THAT

the

tails

of comets have fome fuch impor

tant ufe feems reafonable, if

we

confider, that thofe bodies

thofe fumes merely by their near approach to the fun ; but are framed of a texture, which difpofes them in a particular manner to fume in that fort for the

do not fend out

:

without emitting any fuch fteam, is more than half the year at a lefs diftance from the fun, than the comet earth,

of

1

6 64 and 166 f approached

the comets of

it,

when

neareft

;

likewife

I6S^ and 1683

never approached the fun much above a feventh part nearer than Venus, and were more than half as far again from the fun as Mercury ; yet afl

thefe emitted

a I. 3

FROM

680 our

tails,

the very near approach of the comet of author draws another fpeculation ; for if the

Sir

14.6

ISAAC

N E w T o N'S

BOOK II.

Inn have an atmofpherc about it, the comet mentioned teems to have defcended near enough to the fun to enter

within

If fo,

it.

the refinance

it

muft have been fomething retarded by and confequently in its

it

would meet with,

next defcent to the fun will

fall

nearer than

now

;

by

meet with a greater refiftance, and The event of which muft be, that be again more retarded. at length it will impinge upon the fun's furface, and thereby

which means

it

will

fupply any decreafe, which may have happened by fo long And fomething like this an emiilion of light, or otherwife.

our author conjectures may be the cafe of thofe fixed ftars which by an additional increafe of their luftre have for a certain time

out of

fight.

become There

vifible to us, is

though ufually they are ftars, which

indeed a kind of fixed

here appear and difappear at regular and equal intervals fome more fteady caufe muft be fought for ; perhaps thefe a ftars turn round their own axis's, as our fun does , and have :

fome

part

of their body more luminous

than the other,

when

is

they are feen,

the moft lucid part

whereby and when the darker part

us,

is

turned toward

next to

us,

they

vanifh out of fight, 'Li.

WHETHER

the fun does really diminifh, as has been

here fuggefted, is difficult to prove ; yet that it either does >fo, or that the earth increafes, if not both, is rendered pro A L L E Y'S obfervation b , that bable from Dr. by

H

SeeCh.

i.

comparing

11.

k Ncwt.Pr'nc. PhiloH -pag. fif, ccuat of all the ftars of both thefe

5-16.

y\nac-

have appeared within the laft ifo years may be feen in the PhiiofophicaJ tranfa<5tions, vol. *j.

kind.',

wh.ch

numb. 34$.

the

CHAP.

PHILOSOPHY.

5.

247

the proportion, which the periodical time of the moon bore to that of the fun in former times, with the proportion be the moon is found to be tween them at (bmething prefent,

But if the fun diminifh, accelerated in refpect of the fun. the periods of the primary planets will be lengthened ; and if the earth be encreafed, the period of the moon will be fhortened it

:

as

will appear

fhall be (hewn, that the

the refult of the fame

by the next chapter, wherein power of the fun and earth is

power being lodg'd

and

that this principle of

dies

is

producing gravitation in other bo

to the folid matter in each body. proportional

CHAP.

O

in all their parts,

the

BO

DIES

V.

of the S

UN

and

PLANETS. author, after having di (covered that the celeftial' motions are performed by a force extended from the

OUR

iun and primary planets, follows this power into the deepthofe bodies themfelves, and proves the fame

eft receffes ot

to

accompany the

fmalleft particle,

of which they are

com-

pofed.

^.

PREPARATIVE

hereto

lie

{hews

firft,

that each of the

heavenly bodies attracts the reft, and all bodies, with fuck different degrees of force, us that the forc<" of the fame at-

Sir

ISAAC

N E w T o N'S

BOOK II.

others exadly in proportion to is exerted on a in the body attraded of matter quantity

trading body Jin.-

.

g

OF

.

this

the

firft

proof he brings

is

from experiments

upon the earth. The power by which the moon with that is influenced was above fhewn to be the fame, on the furface of the earth, which we call gra here power

made

here

Now

b

one of the effeds of the principle of gravity bodies defcend by this force from the fame height Which has been long taken notice of; in equal times. methods having been invented to mew that the

vity

.

that

is,

all

particular

only caufe,

why fome

bodies were obferved to

fame height fooner than

others,

we have above

related

air.

This

was the c ;

fall

from the

refiftance of the

and proved from hence,

that fince bodies refift to any change of their ftate from reft to motion, or from motion to reft, in proportion to the

contained in them ; the power that can quantity of matter move different quantities of matter equally, muft be pro The only objedion here is, that to the quantity. portional

can hardly be made certain, whether this proportion in the effect of gravity on different bodies holds perfedly ex-

it

ad

or not from thefe experiments ; by reafon that the which bodies fall, prevents our being great fwiftnefs, with able to determine the times of their defcent with all the

cxadnefs

requifite.

Therefore to

remedy

this

inconveni

ence, our author fubftitutes another more certain experi ment in the room of thefe made upon falling bodies. PenNewt.

Princ. Philof Nat. Lib. III. prop. 6.

b

Ch.

A<

3.

6.

'

Bcok I.Ch.i.

i.j.

dulums

CHAP.

PHILOSOPHY.

5.

249

are caufcd to vibrate by the lame principle, as makes the power of gravity putting them in ; But it the ball of any as well as the Other.

dulums

mo

bodies defcend tion,

pendu

lum, of the fame length with another, were more or lefs attra&ed in proportion to the quantity of folid matter in the

ball,,

that

mud accordingly move farter or Now die vibrations of pendulums

pendulum

flower than the other.

continue for a great length of time, and the number of make may eafily be determined with

vibrations they

out

fufpicion of

error

fo that

;

this

extended to what exactnefs one afTures us

thor

that

,

fubftances, as gold,

experiment

pleafes

he examined in

filver,

may

be

and our au

:

this

feveral

way

lead, glafs, fand, common fait, in all which he found not the

wood, water, and wheat ; leaft deviation from the proportion mentioned, though he

made

the experiment in fuch a manner,

that in bodies of

the fame weight a difference in the quantity of their mat ter lefs than a thoufandth part of the whole would have a

It appears therefore, that all bodies are the by power of gravity here, near the furface of the earth, with the fame degree of fwiftnefs.

difcovered

made

it

felf

.

to defcend

We

have above obferved

fell

Moreover

be

after the rate

of

I

6\

fecond of time from the beginning of their

feet in the firft fall.

this defcent to

it

was

alfo obferved,

that if

any body, which were

here at the furface of the earth after this rate,

to be conveyed

up

to the height Newt.

of the moon,

it

would

Princ. Lib. III. prop. 6,

Kk

defcend

2

Sir

$o

N E w T o N'S

ISAAC

BOOK II.

defcend from thence juft with the fame degree of veloci as that with which the moon is attracted toward the ty, earth

and therefore the power of the earth upon the moon

;

bears the fame proportion to the power it would have upon thofe bodies at the fame diftance, as the quantity of mat ter

in the

moon

THUS

4. that the

bears to the quantity in thofe bodies.

down is proved earth on of the every body it power the afiertion laid

in the earth, attracts

is,

at

the fame diftance from the earth, proportional to the quan As to the fun, it of folid matter in the body acted on. tity

has been fhewn,

that the

power of the

fun's action

upon

the fame primary planet is reciprocally in the duplicate pro the diftance ; and that the power of the fun portion of decreafes throughout in the (a me proportion, the motion of comets traverfing the whole planetary region teftiries. This if that were removed from the fun to any planet proves,

any other diftance whatever, the degree of its acceleration toward the fun would yet remain reciprocally in die du plicate proportion of

its

diftance.

But

it

has likewife been

fhewn, that the degree of acceleration, which the fun gives to every one of the planets, is reciprocally in the duplicate All which com proportion of their refpective diftances. it out of doubt, that the power of pared together puts the fun other,

upon any planet, removed into the place of any would give it the fame velocity of defcent, as it

gives that other

upon

;

and confequently, that the fun's action fame diftance would be pro

different planets at the

portional to the quantity of matter in each.

It

has farther

been

CHAP.

PHJLO SOPHY.

5.

been (hewn, that the fun

attracts the primary planets, and rcfpeHve fecondary, when at the fame diftance, fo as to communicate to both the fame degree of velocity ; and therefore the force, wherewith the fun acts on the fe

their

bears the (lime proportion to the force, condary planet, wherewith at the fame diftance it attracts the primary, as

the quantity of folid matter in the fecondary planet bears to the quantity of matter in the primary.

THIS

f.

property therefore

is

proved of both kinds of

planets, in refpect of the fun. Therefore the run pofieffes the quality found in the earth, of acting on bodies with a de

gree of force proportional to the quantity of matter in the body, which receives the influence. 6.

THAT

the

power of

attraction,

with which the other

planets are endued, fhould difrer from that of the earth, can hardly be fuppofed, if we coniider the fimilitude between

thofe bodies

and

;

proved from the

that

it

does not in this refpect,

is

farther

of Saturn and Jupiter, which are at tracted by their refpective primary according to the fame law, that

is,

in the

fatellites

lame proportion to

their diftances, as the

prima

by the fun fo that what has been concluded of the fun in relation to the primary planets, may be juftly

ry are attracted

:

concluded of thefe primary in refpect of their fecondary, and in confequence of that, in regard likewife to all other bodic^, viz.

that they will attract every

quantity of folid matter

it

body

in proportion to

tl

contains.

Kk

x

7.

HENCE

2

Sir I

$2

HEN cE

7.

it

NE

AAC

S

TO

VV

BOOK II.

N*S

that this attraction extends itfelf

follows,

and that body no portion of matter whatever is exempted from the influ ence of thofe bodies, to which we have proved this attra to every particle of matter in the attracted

ctive

to belong.

power

8.

:

BEFORE we

that this attractive

proceed farther, we may here remark, power both of the fun and planets now

of the fame nature in all ; for it acts in appears to be quite each in the fame proportion to the diftance, and in the fame

manner

alike

acts

upon every particle of and other planets

therefore in the fun

power

erent nature from this

power

AND

is

This

not of a

dif-

which has been al which we call gravity a

in the earth

ready {hewn to be the fame with that,

matter.

;

.

open the way to prove, that the at in the fun and tracting power lodged planets, belongs likeand that their refpective powers vvife to every part of them 9.

this lays

:

upon ter,

the fame

of which

body are proportional to the quantity of mat they are compofed ; for inftance, that the force

with which the earth

attracts the

which the fun would

attract

it

moon, at the

is

to the force,

fame diftance,

quantity of folid matter contained in the earth, b contained in the fun tity

with as the

to the quan

.

TO.

THE

firft

quence from the 11.

?.<>;

of thefe aflertions

latter.

And h

Newt.

before

is

a very evident confeto the proof,

we proceed

Princ.philof Lib. III. prop. 7. cor.

i.

it

CHAP. it

muft

PHILOSOPHY.

5.

hrft be fliewn, that the third

law of motion,

makes action and rea&ion equal, holds The moft remarkable attractive powers. ii:

which

in thefe attractive force,

next to the

by which the loadftone attracts iron. a loadftone were laid upon water, and fupported by

power of gravity,

Now

253

is

that,

fome proper fubftance, as wood or cork, fwim ; and if a piece of iron were caufed water in like manner: attract the iron,

fo that it

might fwim upon the

to

foon as the loadftone begins to

as

move toward the ftone, and move toward the iron when they meet,

the iron fhall

the ftone fhall alfo

;

they fhall flop each other, and remain fixed together with This mews, that the velocities, where out any motion.

with they meet, are reciprocally proportional to the quan and that by the ftone's at tities of folid matter in each ; tracting O the iron,' the ftone itfelf receives as in the ftrict philofophic ienfe

nicates to the iron effect

:

for

of that word a ,

much as

it

motion,'

commu

has been declared above to be

it

an

of the percuffion of two bodies,

that if they meet proportional to the refpective

with velocities reciprocally bodies, they fhall be ftopped by the concourfe, unlefs their

them into frefh motion; but if they meet elafticity put with any other velocities, they {hall retain fome motion after

b

meeting

fubftances

.

Amber,

glafs,

by rubbing a power,

acquire

having been remarkable, electrical.

By 5ee

this

Book

fealing-v/ax,

I.

particularly in amber,

.power they Ch.i.

and many other which from its

i

will

Ilid.

is

fome time

tor

called after

,

rubbing

Sir I

s

A Ac

rubbing attract light bodies, die fphere of their activity. found, that

if

portion by a

dy whereon it.

Both

in

K

t;

vv

To

that (hall

On

BOOK II.

N"S

be brought within

the other hand Mr.

BOYLE

amber be hung in a perpendicular fhall be drawn itfelf toward the bo

a piece of

ftring,

it

was rubbed, if the loadftone and

it

afcribe the ally

power

that

body bj brought near

in electrical bodies

to the particular body,

we

ufu-

whofe pre-

The load find neceffary for producing the effect. but in ftone and any piece of iron will draw each other, frnce

two

we

pieces of iron

we

no fuch

eftect

is

ordinarily obferved

;

there

power the power of the load ftone though near a loadftone two pieces of iron will alIn like manner the rubbing of am fo draw each other. fore

call

this attractive

:

ber,

glafs,

or any fuch body,

till it

is

grown warm, being

neceiYary to caufe any action between thofe bodies and other fubftances, we afcribe the electrical power to thofe bodies.

But in

all

thefe cafes

and not extend the

we

it

we would

fenfe of our

fpeak more correctly,

exprefiions

beyond what

we

can only fay that the neighbourhood of a load ftone and a piece ot iron is attended with a power, where fee

;

by the loadftone and the iron are drawn toward each other ; and the rubbing ot electrical bodies gives rife to a power, whereby thofe bodies and other fubftances tracted. gravity,

are

mutually at

Thus we mu ft alfo underftand in the power of that die two bodies are mutually made to approach

When the fun draws any by the action of that power. and the motion, planet, that planet alfo draws the fun ;

.vhich the planet receives

to the motion,

from the fun, bears the fame prowhich the fun it felf receives, as the

CHAP.

PHILOSOPHY.

5.

255

the quantity of fclid matter in the fun bears to the quan of folid matter in the planet. Hitherto, for brevity tity fake in ipeaking of thefe forces, we have generally afcribed to the body, which is leaft moved ; as when we

them

the power, which exerts itfelf between the fun and any planet, the attractive power of the fun ; but to fpeak more correctly, we fhould rather call this power in called

any

cafe the force,

which

acts

between the fun and

earth,

be

tween the fun and Jupiter, between the earth and moon, &c. for both the bodies are moved by the power acting be tween them, in the fame manner, as when two bodies are tied together

or otherwife,

by a rope, if that rope fhrink by being wet, and thereby caufe the bodies to approach, by

drawing both, gree of motion, ties

this

as

will communicate to both the fame de and caufe them to approach with veloci

it

to the refpective bodies. From reciprocally proportional mutual action between the fun and planet it follows,

has been obferved above

do each move Let

A

(

about their

% that common

the fun

and planet

center

of gravity.

108. ) reprefent the fun, B a planet, C their If thefe bodies were once at center of gravity.

in fig.

common

their mutual attraction they would directly ap each other with fuch velocities, that their common proach center of gravity would remain at reft, and the two bodies reft,

by

would at length meet in that point. If the planet B were to receive an impulfe, as in the direction of the line DK, bodies from falling together ; this would prevent the two Chap, i

8,

but

ISA

Sir

A c

N E w T o N'S

BOOK II.

common center of gravity would be put into tion in the direction of the line Cl equidiftant from

but their

;

In

planet

would

NEWTON

ISA AC

this cafe Sir

round

defcribe

1

proves

their

',

that the fun

common

mo BE. and

center of gra

while that center would proceed with an vity fimilar orbits, uniform motion in the line C F ; and fo the fyftem of the

two bodies would move on with the center of

gravity with In order to keep the fyftem in the fame place, necellary, that when the planet received its impulfe in

out end. it

is

the direction BE,

the fun fhould alfo receive fuch an

im

pulfe the

C

vity

contrary way, as might keep the center of gra without motion ; for if thefe began once to move

without giving any motion to their common center of gra that center would always remain fixed. vity, II.

BY

this

may

be underftood in what manner the a-

dion between the fun and

we

have fhewn above

planets is mutual. that the power, which

h ,

But

farther,

ads between

the fun and primary planets,

is altogether of the fame na which ads between the earth and the bo dies at its furface, or between the earth and its parts, and with that which acts between the primary planets and their

ture with that,

fecondary; therefore all thefe actions muft be afcribcd to c the fame caufe Again, it has been already proved, that in different planets the force of the fun's action upon each at .

the fame diftance lid

would be proportional

matter in the planet "

Ncwt.Princ. Lib.

I.

prop.

<5*.

J ;

to the

quantity of fo-

therefore the readion of each b

8.

<

Sec Introd.

13

d

planet ~4,r

on

CHAP.

PHILOSOPHY.

5.

on the fun

257

fame diftance, or the motion, which the fun

at the

planet, would alfb be proportional to the quantity of matter in the planet ; that is, thefe pla nets at the fame diftance would act on the fame body with

would

receive

from each

degrees of ftrength proportional to the quantity of folid ter in each.

ed,

mat

iz. IN the next place, from what has been now prov our great author has deduced this farther confequence,

no

lefs furprizing than elegant ; that each of the particles, out of which the bodies of the fun and planets are framed,

power of gravitation by the fame law, and in the fame proportion to the diftance, as the great bodies exert their

which they compofe.

For

this

purpofe

he

demon-

firft

that if a globe were compounded of particles, which will attract the particles of any other body reciprocally in the duplicate proportion of their diftances, the whole ftrates,

globe will attract the fame in the reciprocal duplicate pro portion of their diftances from the center of the globe; a And provided the globe be of uniform denfity throughout from this our author deduces the reverfe, that if a globe acts .

upon diftant bodies by the law juft now fpeciiied, and the power of the globe is derived from its being compofed of at tractive

particles

fame proportion

down

at large 8

Newt.

;

b .

each of thofe particles will attract after the The manner of deducing this is not fet

by our author, but

Princ. philof. Lib. I.

prop 74.

L

1

is

as follows.

t

The

globe

is

Jbid.coroll. 3.

fuppofed

Sir

ISA AC

NEWTON'S

BOOK It

fuppofed to act upon the particles of a body without it con_ of their diftanftantly in the reciprocal duplicate proportion ces

from

its

the globe,

center ;

and

on which

therefore at the

fide foever the

fame diftance from

body be placed,

the

Now becaufe, if the parti globe will act equally upon it. of is which the cles, globe compofed, acted upon thofe with out in the reciprocal duplicate proportion of their diftances, the whole globe would acl: upon them in the fame manner as does ; therefore, if the particles of the globe have not all

it

of them that property, fome muft act ftronger than in that and if this be the con proportion, while others act weaker dition of the globe, it is plain, that when the body attracted :

is

in fuch a fituation in refpect of the globe, that the greater

number of the ftrongeft particles are neareil to it, the body will be more forcibly attracted than when by turning the globe about, the greater quantity of weak particles fhould ;

be neareft, though the diftance of the body fhould remain the fame from the center of the globe. Which to what was at firft remarked, that the globe on it acts with the fame ftrength at the fame diftance.

is

contrary of

all fides

Whence

appears, that no other conftitution of the globe can agree to

it it.

13. FROM thefe proportions it is farther collected, that the particles of one globe attract all the particles of an other in the proportion fo often mentioned, the attracting

if all i

globe will act upon the other in the fame proportion to the diftance between the center of the globe which attracts, and the center of that which

is

attracted

a :

and

farther,

that this

Lib. I. Prop. 7 f, and Lib. III. prop. 8.

proportion

CHAP.

PHILOSOPHY.

5.

proportion holds true,

compofed of denfe

though

diflimilar parts,

259

either or both the globes be fome rarer and fome more

that all the in the fame parts globe from the center be homogeneous a And b if both the attract each other All which globes place ;

provided only,

equally diftant alfo, it

.

.

beyond contradiction, that this proportion obtains with as cxactnefs near and contiguous to the furface of attra

much

as at greater diftances

cting globes,

14.

THUS our

from them.

author, without the

explaining the caufe of gravity, has

pompous pretence of made one very important

toward it, by fhewing that this power in the great bodies of the univerfe, is derived from the fame power being lodg ed in every particle of the matter which compofes them: and ftep

confequently, that this property is no lefs than univerfal to all matter whatever, though the power be too minute to pro

duce any converfe,

viiible effects

their action

by

on the fmall

bodies,

on each other c

.

wherewith

In the fixed

we

ftars

we have no particular proof that they have this pow for we find no apperance to demonftrate that they ei

indeed er

;

or are acted upon by it. But fince this power found to belong to all bodies, whereon we can make obfervadon ; and we fee that it is not to be altered by any ther act,

is

form of

bodies, but always accompanies them without diminution, remaining ever pro every mape to the portional quantity of folid matter in each ; fuch a

change

in the

in

power mutt without doubt belong Lib.

I.

Prop

7

<5.

b

<

Ibid, cor .f.

L

1

^

all matter. univerfally to Vid

Lib.III. Prop. 7.

corol

i.

I

.

THIS

260

Sir Is A

THIS

If.

recommends

therefore felf

it

no

AC is

NEWTON'S

the universal law of matter

lefs

for

its

creat O

than for the furprizing difcoveries

plicity,

we

this

learn

principle body will have

upon

BOOK II.

plainnefs 1 it

;

which

and fm>-

leads us

to.

By

weight, which the fame the furlaces of the iun and of dilifferent

we can judge of the compoplanets; and by the iamc fition of thofe celeftial bodies, and know the denfity of verie

each

which

;

is

formed of the moft compact,

and which of

Let the adverfarics of this philofowhether loading this principle with the

the moft rare fubftance.

phy

reflect here,

an occult quality, or perpetual miracle, or appellation of any other reproachful name, be fufficient .o dillliade us from cultivating

it

;

iince this quality,

which they

call occult, leads

knowledge of fuch things, that it would have been re no lefs than madnefs for any one, before they had been puted

to the

difcovered, even to have conjedlured that our faculties fhould ever have reached fo far.

SEE how

1 6.

all

this

ing principles ing about them.

perform

from

By

from the forego which have fatellites mov

naturally follows

in thofe planets,

in which compared with

the times,

their revolutions,

thefe fatellites their diftances

the proportion between the with which one primary attracts his fatellites, and the force with which any other attracts his will be known ; their refpective primary,

power,

and the proportion of the power with which any planet attracts its fecondary, to the power with which it attracts a

body

at

its

furface

is

found,

by comparing the diftance of

the fecondary planet from the center of the primary,

to

the

PHILOSOPHY.

C.iAp.5.

261

diftance of the primary planet's furface from the fanv is deduced the between the

e

and from hence

proportion power the furface of one planet, to the gravity upon the furface of another. By the like method of comparing

of gravity

upon

the periodical time of a primary planet about the fun, with the revolution of a fatellite about its primary, may be found the proportion of gravity, or of the weight of any body up

on the furface of the

fun, to the gravity, or to the

the fame body upon the furface of the planet, about the fatellite.

weight of

which

carries

BY thefe kinds of computation it is found, that the of the fame body upon the furface of the fun will weight be about 13 times as great, as here upon the furface of the 17.

earth ter

;

;

about 10- times

and near

1 8.

1

THE

upon the furface of Jupi a upon the furface of Saturn

great, as

quantity of matter,

fun contains

which compofes each of

is

1067 times as much matter as Jupiter Jupi much as the earth, and i\ times as much The diameter of the fun is about 91 times, ;

ter 1 5-8-5

times as

as Saturn

b .

about 9 times, and that Jupiter times the diameter of the earth.

that of

7

.

proportional to the power it has upon a at a given diftance. By this means it is found, that the

thefe bodies,

body

as

9 times as great, as

*

Newt.

Princ. Lib. III. prop. 8. coroll.

i.

*

of Saturn about

Ibid, coroll. i.

io,

B

v

Sir

6-2

ISAAC

N E w x o N'S

BOOK

II.

19. BY making a comparifon between the quantity of matter in thefe bodies and their magnitudes, to be found

from

their diameters,

deduced

tlieir

refpective denfities are readily

the denfity of every body being meafured by the of matter contained under the fame bulk, as has quantity been above remarked a . Thus the earth is found 4^ times ,

more denfe than

Jupiter

;

Saturn has between

~

and

-

of the

denfity of Jupiter ; but the fun has one fourth part only of b the denfity of the earth From which this obfervation is drawn .

by our author ; that the fun is rarified by its great heat, and that of the three planets named, the more denfe is nearer the fun as was highly reafonable to than the more rare expect, the ;

denfeft bodies requiring the greatefl heat to agitate and put their parts In motion ; as on the contrary, the planets which are more r are, would be rendered unfit for their office,

by

the intenfe hc,:t to which the denfer are expofed. Thus the waters of our feas, it removed to the diftance of Saturn from

the fun,

would remain perpetually frozen would conftantly boil

the fun as Mercury,

ao.

THE

denfities

and

;

if as

near

c .

of the three planets Mercury,

Venus,

and Mars, which have no fatellites, cannot be expreily ailianed ; but from what is found in the others, it is very proba ble, that

they alfo are of fuch different degrees of denfity,

that liniverfally the planet

which

is

nearer! to the fun,

is

formed of the moft compact fubftance. BockI.Ch_4.i.

b

Newt.

Pjinc. Lib. III. prop- ?. corolLj.

d. coro'J

4.

CHAP.

CHAP.

PHILOSOPHY.

6.

CHAP. Of

FLUID PARTS PLANETS.

the

THIS

VI.

globe, that

we

inhabit,

is

of the

compofed of two

parts

;

the folid earth, which affords us a foundation to dwell

upon

;

and the

feas

and other

of what

moon,

is

that furnifh rains

waters,

vapours neceffary to render the earth requisite for the fupport

though but a fecondary

fruitful,

of

planet,

life. is

and

and productive

And

that the

compofed

in like

manner, is generally thought, from the different degrees of the parts of that planet, light which appear on its furface ;

which

dim

being fuppofed to be fluid, and to imbibe the fun's rays, while the folid parts reflect them more Some indeed do not allow this to be a conclusive copioufly. reflect a

argument the moon's :

light,

but whether furface

we can

from the

diftinguifh the fluid part of

reft or

not ;

yet

it is

moft proba

two fuch

different parts, and with ftill great er reafon we may afcribe the like to the other primary planets, The earth is alfo which yet more nearly refemble our earth. ble that there are

encompafled by another fluid the air, and we have before re marked, that probably the reft of the planets are furrounded Thefe fluid parts in particular engage our au by the like. thor's attention,

both by reafon of fome remarkable appear

ances peculiar to them, and likewife of fome effects th have upon the whole bodies to which they belong, a.

F

L.

ij

i

D

s

,

Sir Is A

264

FLUIDS

a.

NE w TON'S

AC

have been already treated of

to the effect they have refpccl:

them

a ;

now we muft

ration of the

confider

power of

gravity

upon them

in

BOOK II, general, with

folid bodies

upon them.

By

like all other bodies, in

they are rendered weighty, to the quantity of matter, which

is

moving

in reference to the this

in

ope

power

proportion

contained in them.

And

the upper parts prefs upon the lower any quantity of a fluid

in as

much,

as

it

fhould

lie.

on another, whereon any folid body would prefs But there is an effect of the preffure of fluids on

the bottom of the veffel, wherein they are contained, which I The force fupported by the bot

fhall particularly explain.

tom of fuch

a veffel

not {imply the weight of the quantity but is equal to the weight of that which would be contained in a veffel of

is

of the fluid in the veffel,

quantity of the fluid, the fame bottom and of equal width throughout, when this veffel is filled up to the fame height, as that to which the vef fel

propofed

veffel

is

ABCD

filled.

Suppofe water were contained in the

(in fig. 1 09.) filled

up

to

E F. Here

it is

evident,

that if a part of the bottom, as G H, which is directly under any part of the fpace E F, be coniidered feparately ; it will ap at once, that this part fuftains the weight of as much of

pear the fluid, as (lands perpendicularly over it up to the height of EF ; that is, the two perpendiculars G I and H K being drawn,

the part G H of the bottom will fuftain the whole weight of the fluid included between thefe two perpendiculars. Again, I every other part of the bottom equally broad with this, fay,

will fuftain as great a preffure. .

Let the part

LM

be of the

Ch.4.

fame

CHAP,

PHILOSOPHY.

6.

fame breadth with GH.

26$

Here the perpendiculars

M N being drawn,

LOand

the quantity of water contained between thefe perpendiculars is not fo great, as that contained between

M

the perpendiculars G I and H K ; yet, I fay, the preflure on L will be equal to that on G H. This will appear by the fol lowing considerations. It is evident, that if the part of the

between

veflel

O and N were

removed,

the water

would im

mediately flow out, and the furface EF would fubftde ; for all parts of the water being equally heavy, it muft foon form itfelf to

a level furface,

tains

does not prevent.

it,

the form of the vefTel,

if

vented from rifing by the fide feft,

that

it

muft

which con

Therefore fince the water

prefs againft

is

pre

N O of the veflel it is maniN O with fome degree of force. ,

In other words, the water between the perpendiculars L O and N endeavours to extend itfelf with a certain degree of force;

M or

more

ter length.

tween

this

But fince

N O and L M,

prefles upon this, and column of water into a grea column of water is fuftained be

ambient water

correctly, the

endeavours to force

or pillar

this

each of thefe parts of the

veflel will

be

equally prefled againft by the power, wherewith this column bears this force endeavours to extend. Confequently

LM

over and above the weight of the

column of water between

L O and M N. To know what this expanfive force is, let the part O N of the veflel be removed, and the perpendiculars L O and

MN

over

NO let water be rilled between thefe perpendiculars up to

be prolonged

;

then by means of fome pipe fixed

P Qan equal height with E F. Here the water between the per (^ is of an equal height with the highpendiculars LP and

M

eft

part of the water

in the veflel

;

therefore the water in the

Mm

vcilel

266

Sir I

ve (Tel cannot by

water in raifc the

this

its

s

NE

AAc

preflure fubfide

column

water in the

force

vv it

To up

becaufe,

;

BOOK

N'S

higher,

if it

II.

nor can the

fhould,

veflel to a greater height

it

would

than

itfelf.

But it follows from hence, that the weight of water contained balance to the force, wherewith between P O and Q>T is a juft

the

column between L O and

M N endeavours

to extend. So

LM

of the bottom, which fuftains both this force and the weight of the water between L O and N, is preffed upon by a force equal to the united weight of the water the part

M

between L O and M N, and the weight of the water between P O and Q^N ; that is, it is prefled on by a force equal to the

MQ

And weight of all the water contained between LP and this weight is equal to that of the water contained between

G I and H K, which bottom B C,

is

Now

of the bottom. it

is

evident,

that if another veflel

RSTV

be

RV

equal to the bottom B C, and be whole height of one and the fame breadth ;

formed with a bottom throughout

H

the weight fuftained by the part G this being true of every part of the

its

when

this veflel is rilled

veflel

ABCD

is

filled,

with water to the lame height, the bottoms of thefe

two

as

the

veflels fhall

If the veflel be broader be prefled upon with equal force. at the top than at the bottom, it is evident, that the bottom will bear the preflure of fo much of the fluid, as is perpen

dicularly over

it,

and the

fides

of the

veflel will

fupport the

This property of fluids is a corollary from a propofia tion of our author ; from whence alfo he deduces the ef

reft.

fects

of the preflure of fluids on bodies refting in them. * Lib. II. prop. 20. cor. a.

Thefe

CHAP. Thefe

PHILOSOPHY.

6.

are,

that

any body

the bottom of the veflel,

and

in the fluid will

267

heavier than a fluid will fink to

wherein the fluid

weigh

as

much

as

its

is

own

contained,

weight ex

ceeds the weight of an equal quantity of the fluid ; any body uncompreflible of the (lime denfity with the fluid, will reft any where in the fluid without fuffering the leaft change ei ther in

its

place or figure from the preflure of fuch a fluid,

but will remain as undifturbed as the parts of the fluid themfelves ; but every body of lefs denfity than the fluid will

fwim on its furface, a part only being received within the Which part will be equal in bulk to a quantity of the fluid. fluid,

dy

dy

whofe weight is equal to the weight of the whole bo by this means the parts of the fluid under the bo

for

;

will furTer as great a preflure as

fluid as

3

.

much below

IN the next

any other

parts of the

the furface as thefe.

place,

in relation to the air,

bove made mention, that the

we

have a-

furrounding the earth being an elaftic fluid, the power of gravity will have this effect on it, to make the lower parts near the furface of the earth air

more compact and compreflTed together by the weight of than the higher parts, which are prefand therefore fufed upon by a lels quantity of the air,

the air incumbent,

ftain a lefs

a

weight

thor has laid

.

It

has been alfo obferved, that our au

down

a rule for computing the exact degree of denfity in the air at all heights from the earth h But there is a farther effect from the air's being comprefled by .

Chap.

4.

b Ibid.

17.

Mm

i

the

268

Sir

ISAAC NEWTON'S which he has

the power of gravity,

The

air

being

mulous body

elaftic

of found as

it

which

its

will fpread

to a great diftance.

for that fenfation

:

is

from the body that

This

is

the efficient caufe

produced by the

air, which, As this organ of hearing. fuccefs fo our author's great

ftrikes againft the

vibrates,

fubject is

them

diftindtly confidered.

of compreflion, any tre motion to the air, and excite

in a (late

will propagate

therein vibrations,

occafions

and

BOOK II.

was extremely

difficult,

fiirprizing.

4.

OuR

author's doctrine

upon

this

head

I fhall

endea

But preliminary thereto vour to explain fomewhat at large. muft be fhewn, what he has delivered in general of preffure propagated through fluids ; and alfo what he has fet

down

relating to that wave-like motion,

on the into

furface of water,

it,

5-.

agitated by throwing any thing or by the reciprocal motion of the finger, &c.

CONCERNING

fpread through line,

which appears up

when

but alfo

Of which propofed

:

fluids,

laterally,

the

firft,

it is

proved, that preflure

is

not only right forward in a flreight with aim oft the fame eafe and force.

a very obvious exemplification by experiment is that is, to agitate the furface of water by the re

of the finger forwards and backwards only ; ciprocal motion for though the finger have no circular motion given it, yet the waves excited in the water will diffufe themfelves on each

hand of the finger.

Nor

direction of the motion,

is

what we obferve

and foon furround the

in founds unlike to this,

which

not proceed in ftraight lines only, but are heard though a i

mountain

CHAP.

PHILOSOPHY.

6.

and when they enter a room in any they fpread themfelves into every corner ; not by reflection from the walls, as fome have imagined, but asmountain intervene,

part of

it,

far as the fenfe

can judge, diredtly from the place where they

enter.

6.

How

water,

may

the waves are excited in the furface of ftagnant be thus conceived. Suppofe in any place, the

water raifed above the

reft in

form of a fmall hillock

that

;

water will immediately fubfide, and raife the circumambient water above the level of the parts more remote, to which the

motion cannot be communicated under longer time. And again, the water in fubfiding will acquire, like all falling bo dies, a force, which will carry it below the level furface, till at length the prefTure rife

again,

of the ambient water prevailing,

and even with a

force like to that

it

wherewith

it

will

de-

But in fcended, which will carry it again above the level the mean time the ambient water before raifed will fubfide,

and in fo doing, will as this did, finking below the level ; not only raife the water, which firft fubiided, but alfo the wa So that now befide the firft hillock, ter next without itfelf.

we mall have a ring invefting it, at fome diftance raifed above the plain furface likewife ; and between them the water willbe funk below the reft of the furface. After this, the firft hil lock,

and the new made annular

rifing,

will defcend

;

raifing

the water between them, which was before deprefied, and likeof the furfacc without. Thus will thefc wife the adjacent part

annular waves be fucceflively fpread more and more, as the hillock fubfiding

For,

produces one ring, and that ring fub~ fidin

,

ISAAC

Sir

270

N E w T o N'S

BOOK TL

fo the hil fiding raifcs again the hillock, and a fccond ring ; lock and fecond ring fubiiding together raife the rlrft ring, and a third ; then this firft and third ring iubfiding together and fo raife the firft hillock, the fecond ring, and a fourth j

Now

on

it is decontinually, till the motion by degrees ceafes. in the defcend afcend and manner thefe that monftrated, rings of a pendulum ; defcending with a motion continually acce

they become even with the plain furface of the flu half the fpace they defcend ; and then being re tarded again by the fame degrees as thofe, whereby they were lerated,

till

which

id,

is

accelerated,

till

they are deprefled below the plain furface, as raifed above it and that this augmen

much as they were before

:

and diminution of

by the fame of a pendulum vibrating in a cycloid, and whofe length fhould be a fourth part of the diftance between and farther, that a new ring is any two adjacent waves tation

their velocity proceeds

as that

degrees,

:

produced every time a pendulum, whofe length the former, rnits

that

is,

equal to the interval

is

four times

between the fum-

of two waves, makes one ofcillation or fwing

a .

7- THIS now opens the way for underflanding the mo tion confequent upon the tremors of the air, excited

by

which we muft conceive

the vibrations of fonorous bodies:

to be performed in the following manner. 8.

ries

LET

of the

other.

I

A, B, C, D, F, F, G,

particles

KL

of the

H

air,

a mufical chord,

(

in fig. 1 1 o.

)

reprefent a fe-

at equal diftances

which

* Vid,Newt. Princ. Lib.

I {hall

from each

ufe for the trc-

II. prop. 45.

mulous

CHAP.

PHILOSOPHY.

6.

mulous and fbnorous body, ple I

as

may

be.

and L, and

Suppofe forcibly

to

this

drawn

make

the

271

conception as fim-

chord flrctched upon the points into the fituation

I

K L,

fo that

: to the particle A in its middle point K and let the chord from this fituation begin to recoil, preiling againfl the particle A, which will thereby be put into motion

it

become contiguous

B

towards

:

but the particles A, B,

C

the

being equidiftant,

power, by which B avoids A, is equal to, and balan ced by the power, by which it avoids C therefore the elaftic force, by which B is repelled from A, will not put B into any elaftic

;

degree of motion, till A is by die motion of the chord brought than B is to C : but as foon as that is done, die

nearer to B, particle

B

proach C,

,

moved towards C ; and being made to ap in the next place move that ; which will up

will be

will

on that advance, put

D

likewife into motion,

and

therefore the particle A being moved by the chord, of the air B, C, D, &c. will

lowing moved.

fo

on

the fol

fucceflively be

particles

ward

the point K of the chord moves for with an accelerated velocity, fo that the particle A fhall

move

againft

it,

Farther,

if

B with an advancing

pace,

and gain ground of

approaching nearer and nearer continually;

more upon

B, and give

A by approach

a greater velocity as the reafon that diftance between the particles likewife, by diminifhes, the elaftic power, by which they fly each other, ing will prefs

increafes.

Hence

the particle B,

it

as well as A,

will

have

its

motion gradually accelerated, and by that means will more and more approach to C. And from the fame caufe C will

more and more approach D ; and fo of the reft. Suppofe now, fince the agitation of thefe particles has been hewn to be

Sir I

72 be

s

N E w T o N'S

AAc

and to follow one another,

iuccefilve,

moteft particle moved, while the chord curve fituation I K L into that of a ftreight

F the

which remains unaftected,

firft

point of being put into motion. A, B, C, D, E, F, G, when the point

BOOK II.

that is

E be

the re-

moving from as I

line,

though

its

k L ; and

upon

juft

Then fliall the K is moved into

the

particles

have

&,

acquired the rangement represented by the adjacent points in which a is nearer to b than b to c, and #, #, c, d) e, f> g :

b nearer

and

to c than c to d,

^nearer to e than e tof, and

BUT now the chord

9.

tuation

1

point K,

more

to

move

having recovered

though by the force

the fame

as far forwards, as

the motion of effect of

d than d to

nearer laftly e

and

tf,

t<

its

rectilinear

fi-

L, the following motion will be changed, for the which before advanced with a motion more aud

accelerated,

go on near

7c

c nearer to

it

way

it

as before,

was

at firft

will henceforth be

which upon the

it

has acquired it will it has advanced

till

drawn backwards

yet

;

The

gradually leffened.

particles a, #, c, d, e,

f^ g

will be,

that by the time the chord has made its utmoft advance, and thefe particles will be is upon the return, put int o a contrary

rangement ;

fo that

f

fliall

be nearer to g, than e to f,

than d to e \ and the like of the ^ nearer to come to the firft particles a, #, whofe diflance

f

nearly or quite as follows.

what

The

it

was

at

which the

firing refumes

and

till

you

will then be

All which will

prefent diftance between

that the elaftic power, by which maintain that diftance, though -,vith

firft.

reft,

a and b

appear is

fuch,

a repels #, is ftrong enough to a advance with the velocity,

its

rectilinear

figure

;

and the motion

CHAP.

PHILOSOPHY.

6.

motion of the

a

particle

afterwards flower,

being

between a and

elafticity

prefent

to

as

<r,

is

it

ftill

till

diminifli,

from a

at prefent

;

the

more than between them. There I

will

fufficient to preferve the diftance fore while it accelerates I it will

ftance be will

273

I

be

retard

a.

The

di

as

near

come about

for after the

diftances

ab and be are become equal* the particle I will continue c its by its own power of in velocity fuperior to that of till fuch time as the increafe of elafticity between activity, I

and

c

more than

be between a and

{hall

I

fliall

fup-

power of inactivity in b made a on the fide of a than on the fide greater elafticity neceflary of c to pufh b forward, fo what motion b has acquired it will retain by the fame power of inactivity, till it be fuppreiTcd by a greater elafticity on the fide of c, than on the fide of a.

prefs

But

its

as

motion

foon

for as the

:

begins to ftacken

as b

its

pace the diftance of b

widen as the diftance ab has already done. Now as a acts on &, fo will I on c c on d, &c. fo that the diftan ces between all the particles a b ^>/,g will be fucceiTively contracted into the diftance of a from &, and then dilated Now becaufe the time, in which the chord defcritas, again. from

c will

,

y

this

up

prefent

half of

its

in defcribing the

y

",

is about equal to that it took the particles a y b will be as long as before in contracting it, and

vibration,

former

in dilating their diftance,

;

And

will return nearly to their original diftance. farther, b> c, which did not begin to approach fo foon

the particles as a, b y

recede

are ;

now about

as

much

and likewife the

proach after

b,

cy

longer, before they begin to d which began to particles c, y ap

begin to feparate

that the particles-,

later.

Whence

whofe diftance began to be N n

it

appears

leflened,

when that

Sir I

274 that of a, b

was

firft

SAAC NEWTON'S

BOOK

II.

enlarged, viz. the particles fig, fhould

be about their neareft diftance, when a and I have recover ed their prime interval. Thus will the particles a, b y r, dr

nave changed their iituation

*>/>

But

as the

farther,

in

the

manner

afTerted.

g or F, G gradually approach

particles f,

move by degrees the fucceeding par B did by a like a great length, as the particles A, chord has made its So when the that, greateil: ad approach. vance, being arrived into the fituation I * L, the particles mo each other, they will

ticles to as

ved by JS

e,

it

will

have the rangemcnt noted by the points

{, M, 0j AJ AC,

y,

Where

g.

the particles in the line

the diftance

i.

is

a,

AH;

/?

,

a, 5, y,

are at the original diftance of

are the neareft of

equal to that between a and

all,

and

.

IO. By this time the chord I *L begins to return, and thediftance between the particles a and /3 being enlarged to its original magnitude, a has loft all that force it had acqui red by its motion, being now at reft ; and therefore will return with the chord,

making

greater than the natural

becaufe

its

motion forward

;

for is

the diilance between

& will not return

and

fo foon,

not yet quite fupprefTed, the

> not being already enlarged to its prime dimenbut the recefs of a, by diminiming the prefTure up^

diftance lion

on

|8

:

by

its

elafticity,

will

occafion the motion of

to be

time by the adion of y, and then {hall $ begin to return at which time the diikmce between y and /\ (nail by the fuperior aclion of j\ above be en ftopt in a

little

:

y> and therefore larged to the dimension of the diftancc foon after to that of a.@. Thus it appears, that each cl fjiefe

particles goes

on

to

move

forward,

till its

diftance

from the

CHAP.

P

6.

HILOSOPH

the preceding one be equal to whole chain a, 6, 7, f, n,

A

Y.

275

original diftance

its

the

;

having an undulating motion forward, which is ftopt gradually by the excefs of the expaniive power of the preceding parts above that of the

hinder.

they were

Thus are moved

,

thefc parts fucceifively ftopt, when the chord has

fo that

;

as before its

regained

the expansion of the parts of the air will have advanced fo far, that the interval between *, rectilinear fituation,

which to

its

and

at prefent natural fize

and

is

mofl contracted,

will then

the diftances between

:

and

*

and

be reftored

9,

and

9

A<

A,

being fucceilively contraded into the prefent diftance of ( from and again enlarged ; fo that the fame effect fhall be produced upon the parts ^y ^

v,

y

,

,

beyond

by the enlargement of the diftance between thofe two

K,

as

^

was occaiioned upon the

particles <*, 5, y, fl, ^ by the enlargement of the diftance a /3 to And therefore the motion in the air natural extent.

particles, vi,

its

will

9,

A,

&

T, %<>

be extended half

the diftance between is

prefent between

at

in

motion

taking

much

as v

and

%

and

*,

the

farther as at

which

that,

the particles of the air

all

rangement

exprefled

III. by the points a, $, y> /> i> wherein the particles from a to J have j

and

prefent,

contraded into

i,

fl,

>-.

to

yj

in

J> *>

p>

figure ^> T,

each other gradually diminished, the diftances between particles

,

being contraded the mofl: from the natural

ance between

tl-ofe

particles,

much augmented, and ticles T, $>

and the diftance between

$

\

from

their diilances

t;

dift

a, &

the diftance K-twcen the middle par

M becoming equal to the natural. The partit which follow %, have their diftances gradually

s,

,

Nn

x

g

and

Sir Is A

276 and

greater,

NEWTON'S

AC

the particles

v,

,

the particles <7, /;, c, d, <?,/*, , tne former figure. Here v, J

m

Hi

TT, p, <r,

T,

<p

BOOK II.

being ranged

or like the particles it

(, *,

will be underftood, by

like 9,

Aj

what

has been before explained, that the particles (, * being at is at their natural diftance from each other, the particle the and them between A the </\, /3, e, y, firing reft,

particles

and the

being in motion backward,

^

a, 9, A,

v,

J, w, /,

between

ticles

*

er,

T

in

and

reft

motion forward

moving

fafter

:

of the

particles

each of the par

than that, which im

but of the particles from 5 to <p, on mediately follows it ; behind thole the contrary, moving on fafter than thofe,

which precede.

BUT now the

ii.

though

figure, firft

iituation

that whereas

I

it

fhall

having recovered

ftring

go on

till it

its

rectilinear

return near to

its recoiling, a be its motion there will in fa ; yet change returned from the fitliation 1 * L with an ac

K L,

it

celerated motion,

its

motion

fhall

from hence be retarded

The ef again by the fame degrees, as accelerated before. fect of which change upon the particles of the air will be As by

this.

tiguous to terval a

/2

it

the accelerated motion of

moved

fafter

than

,3,

Ib

greater than the interval

was made likewife to move

fafter

y,

than

y,

the chord

as to

make

,

con

the in

and from thence and the diftance be

and y rendered greater than the diftance between y fo of the reft ; now the- motion of a being diand the diftance between A. fhall overtake it, minifhed, tween

and

and y,

/3

n,

18

and

be reduced into that, which

the interval between

is

at prefent

between

and

and y being inlarged into the pre fent

CHAP.

PHILOSOPHY.

6.

between * and

fent diftance is

when

but

;

277

the interval

/2

y

which is at prefent between * and #> diftance between y and <A mall be enlarged to the preand the diftance between A diftance between y and

increafed to that,

the fent

,

inlarged into the prefent diftance between y and j\ ; and the lame of the reft. But the chord more and more

and

g

its

fiackening

the diftance between

pace,

tt

and

/3

fliall

more and more diminifhed and in confequence of diftance between and y {hall be again contracted, ;

to

its

fpace

;

prefent dimension, while the interval y

be

that the firft

in

and afterwards into a narrower j\

fhall dilate into that at prefent

it is fo much enlarged, it mall Thus by the reciprocal expansion and con contract again. and , by that time the chord traction of the air between

between

a.

and

,

and

as

foon as

fhall be ex got into the fituation I K L, the interval into the prefent diftance between a and and by ; panded is

that time likewife the prefent diftance of a from Q will be contracted into their natural interval for this diftance will :

be about the fame time in contracting it felf, as has been taken up in its dilatation ; feeing the ftring will be as long as it has been in re in returning from its rectilinear figure, covering

which

it

from

will be

its

made

between

fituation in the

I

x.

This

I,.

particles

is

the

between a and

change .

As

and

becaufe each preceding parti , cle advances fafter than that, which immediately follows it 5 for thofe

their diftances will be dilated into that, which fucceilively at prefent between and as foon as any two

is

particles

.

And

are arrived at their natural diftance, the hinder

moft of them

fhall

be ftopt, and immediately after return^ chc

Sir

278

ISAAC NEWTON'S

between the returning

diftanccs

And

than the natural.

extend fo

this dilatation

by that time the chord

for,

K L,

being greater of thefe diftances fhall

particles

is

returned into

that the particles % iliall be natural diftance. But the dilatation of i

iituation

I

the interval

\

T<P into that at prefent

between

removed fhall i

will agitate a part

the chord

an

of the

air

intire vibration,

the rangement

the

moved

contract

and the

particles T

fo that

;

of the

particles

air will take

xprefted by the points,, l^n^i^o^p^q^r^s^

in which t, to, w> Xyjy, z> J j ij 3 > 4o T:> 6j> 7> 8 the natural diftance of the particles, the diftance

no

greater than

mn, and

fo on,

are at

/m, mn

:

than Im, and

,

its firft

to their

when IKL, having made

beyond

returned into the iituation

is

and

two

contraction of the diftance between thofe

and p

BooKlI.

greater

you come

till

to qr, the widcft of all: and then the diftances gradually diminifh not only to the natural diftance, as 7//A'., but till

they are contracted as much as J T was before j which falls out in the points 2,3, from whence the diftances augment till .again, you come to the part of the air untouched. 12.

T

ii

i

s

is

the motion, into which the air

the chord makes one vibration, and the whole

is

put,

while

kncth o of

r

thus agitated in the time of one vibration of the chord our author calls the length of one pulfe. When the >es on to make another vibration, it will not only contiri'c to <

agitate

the air at prefent in motion, but fpread the puifation much farther, and by the fame as be

of the

air as

fore.

For when the chord returns into )

dej

I in fliall be

brought into

it

its

,

iilinear

ntu-

moft contracted ftate

CHAP.

PHILOSOPHY.

6.

279

qr now

in the ftate of greateft diktation iLail be re natural diftance, the points 7^, x now at their natural difhnce fhall be at their greateft diftance, tlie points i, g now moft contracted enlarged to their natural diftancc, ftate,

duced to

its

and the points 7, 8 reduced

to their

and the contradion oi them

will carry the agitation of the

air as hir

chord, its

beyond them,

when

it

When

rectilinear figure.

ation I&L,

Im

as that

the fituation

the chord

mall recover

ftate:

motion was carried from the

moved out of

firft

moft contracted

IKL

natural dimenfions,

its

into

got into the fitu

is

w

qr be

of greateft contraction, x brought to its natural dimenfion, the diftanee i 3 enlarged to the utmoft, and the points 7, 8 fhall have recovered their na

reduced to

its

ftate

and by thus recovering themfelves they fhall ; the air to as great a length beyond them, as it was agitate moved beyond the chord, when it firft came into the fitu tural diftanee

ation I?cL. its

When

the chord

rectilinear fituation,

Im

is

fhall

returned back again into

be in

utmoft

its

dilatation,.

w

X reduced into q r reftored again to its natural diftanee, fhall recover its natu its ftate of i contraction, 3 greateft ral

dimenfion, and

78

be in

its

ftate

of greateft dilatation.

moved as far beyond the points was moved beyond the chord, when it before made

By which means the 7, 8, as it return back to

its

air fhall

its

be

rectilinear fituation

;

for the particles.

have been changed from their ftate of reft ami their natural diftanee into a ftate of contraction, and then have 7^ 8

proceeded to the recovery of their natural diftanee, and af of it, in the fame manner at, the

ter that to a dilatation

to the particles contiguous

chord were agitated

before.

In

280 the

Sir I

la ft

place,

s

A A c

when

N E w T o N'S

the chord

is

BOOK II.

returned into the fituation

the particles of air from / to J\ fhall acquire their prefent rangement, and the motion of the air be extended as

t

KL,

much

farther.

And

the like will

happen

after every

com-

of the firing. plcat vibration 13.

(hews it

will

body.

CONCERNING

our author this motion of found, compute the velocity thereof, or in what time reach to any propofed diftance from the fonorous For this he requires to know the height of air, hav

how

to

ing the fame denfity with the parts here at the furface of the earth, which we breath, that would be equivalent in

This is to weight to the whole incumbent atmofphere. In be found by the barometer, or common weatherglass. that inftrumcnt quicklilver is included in a hollow glafs at the The bottom is open, but top. into quickfilver contained in a veflel open to the

cane firmly clofed

immerged air.

Care

is

taken

when

the lower end of the cane

is

immer

cane be full of quickfilver, and that no air ged, that the whole infimiate itfelf. When the instrument is thus fixed, the quick in the cane being higher than that in the veflel, if the top of the cane were open, the fluid would foon link out of the glafs cane, till it came to a level with that in filver

the

veflel.

that the air,

But the top of the cane being doled up, fo which has free liberty to prefs on the quick

filver in the veflel,

cannot bear

at all

on

that,

which

is

with

the quickfilver in the cane will be fufpended to fuch a height, as to balance the preflure of the air on in the cane,

the quickfilver in the

x

I

veflel.

Here

it

is

evident,

that the

weight

CHAP.

P

6.

HILOSOPH

V.

weight of the quickfllver in the glafc cane the preflure of fo much of the air, as is

281

equivalent to perpendicularly over

the hollow of the cane air

may

enter,

;

for if the

there will be

no

is

cane be opened that the

farther ufe of the quick fil-

ver to fuftain the preflure of the airwithout ; for the quickfilver in the cane, as has already been obferved, will then fu fafide to a level with that without. Hence therefore if the

pro portion between the denfity of quickfllver and of the air we breath be known, we may know what height of fuch air would form a column equal in weight to the column of quickfll ver within the glafs cane. When the quickfllver is fuftained in the barometer at the height of go inches, the height of fuch a column of air will be about 19715- feet; for in this cafe

the air has about ^-Q of the denfity of water, and of quickfllver exceeds that of water about

the denfity I 3

times,

of the ches

air

fo that the

about

denfity of quickfllver exceeds that 11890 times, and fo many times 50 in

make 19715*

feet.

Now

Sir

ISAAC

NEWTON

de

termines, that while a fliould

pendulum of the length of this column make one vibration or fwing, the fpace, which any

found will have moved, fliall bear to this length the lame the circumference of a circle bears to the di proportion, as that is, about the proportion of 55-5* to ; our author here confiders fingly the gradual Only in the air from of found to particle i;i the particle progrefs manner v/c have explained, without taking into confidera-

ameter thereof j 1 1

a

,

tion the

magnitude of thofe

particl

And though

there

for the motion to be requires time propagated from one par*

Princ.

phUof

Li'.i.U. prop. 49.

O

o

ticle

282

Sir Is A

AC

NEWTON'S

BooKlI.

to the whole of yet it is communicated the fame in inftant: therefore whatever propor an particle tion the thicknefs of thefe particles bears to their diftance

tide to another,

from each

in the

other,

of found be

fwifter.

Again

compofed of the

ply

fame proportion

we

the air

motion

will the

breath

is

not fim-

by which found

elaftic part,

con

is

a different na veyed, but partly of vapours, which are of of found we the of motion ture ; and in the computation

ought to find the height of a column of this pure air on whofe weight fhould be equal to the weight of the quickly,

and this pure air being a of this pure air will column the of that we breath, part only On both thefe accounts the be higher than 19715* feet. filver in

the cane of the barometer,

motion of found

is

1 14,1 feet in one Se miles in a minute, whereas by the

found to be about

cond of time, or near

i 3

computation propofed above, in one fecond.

WE tions

obferve here,

may

of our author

it

fliould

it

that

move but 979

from

feet

thefe demonftra-

that all founds whether a-

follows,

cute or grave move equally fvvift, and that found is fwifteft, when the quickfilver ftands higheft in the barometer. I

j-.

THUS much of

thefe fluids

from

alfo gravitate

the appearances,

their gravitation

toward the

moon

;

which

toward the

are caufed in earth.

for in the laft

They

chapter

it

has been proved, that the gravitation between the earth and moon is mutual, and that this gravitation of the whole bo dies arifes

from

that

power acting

in all their

parts;

fo that

every

CHAP.

PHILOSOPHY.

6.

every particle of

and every this

no

moon

the

partiele

gravitates

283

toward

the earth toward the

ot

in the lea,

earth,

moon.

moon

gravitation of thefe fluids toward the feniible effect , except only

the

produces cuufes

it

v,

But

the tidi

16.

THAT

the tides

depend upon the influence of the

moon

has been the receiv'd opinion of all antiquity ; nor is there indeed the leaft fhadow of reafon to fuppoie otherwife,

how fteadily they accompany the moon's how the moon cauied them, and by what Though confldering

ple

it

was enabled

was a

to

produce

fo diftingui/lVd

moon

is

princi

an appearance,

philofophy to unfold which teaches, not here alone concerned , but that the

fecret left for this

that the

courfe.

:

fun likewife has a confiderable mare in their production; though they have been generally afcribed to the other lu becaufe its effect is greateft, and by that means minary, the tides more immediately fuit themfelves to its motion;

more by enlarging or rethan by any difHnct effects. Our author finds the power of the moon to bear to the This to I of the fun about the proportion of 4, the fun difcovering

ftraining the

moon's

its

influence

power,

-

.

power

he deduces from the obfervations made

at

the

mouth of

the river Avon, three miles from Briftol, by Captain S T u RMr. COLEPRESSE, of the height M E Y, and at

Plymouth by

is raifed in the conjunction and oppoof the luminaries, compared with the elevation of it, the lirft being cauied the moon is in either ;

to which the water fition

when

quarter

Oo

2.

by

Sir I

284

s

AAc

N E w T o N'S

BOOK II. and the o-

bv the united actions of the fun and moon,

ther by the difference of them, as mall hereafter be fhewn.

THAT

17.

the fun fhould have a like effect on the

fea,

the fun likewife attracts very manifeft; fince And this earth is compofed. of which every lingle particle, in both luminaries fince the power of gravity is reciprocally

as the

moon,

is

in the duplicate proportion of the diftance, they will not draw all the parts of the waters in the lame manner ; but

mufl

act

upon the

nearcft parts ftronger, than

moteit,

producing by

We

now

fhall

attempt to fhew

and moon on the duce

all

1 8. lias

how

waters, by being

combined

the appearances oblerved in the

To

been

upon the

re-

an irregular motion. the actions of the fun

this inequality

together, pro

tides.

begin therefore, the reader will remember what that if the moon without the fun would

faid above,

have defcribed an orbit concentrical to the earth, the action of the fun would make the orbit oval, and bring the moon nearer to the earth at the new and full, than at the quarters*.

Now our excellent author obferves, that if inftead of one moon', we

of moons, contiguous and occupying the fuppofe a ring orbit of the moon, his demonftration would (till take

whole place,

and prove that the

parts

of this ring in palling from the would be accelerated,

or oppofition quarter to the conjunction

and be retarded again

in

palling from the conjunction or op

to the next quarter. pofition -

Chap.

And 3.

as this effect

does not de-

t3

pend

CHAP.

PHILOSOPHY.

6.

285

pend on the magnitude of the bodies, whereof the ring is compofed, the fame would hold, though the magnitude of thefe moons were fo far to be diminiihed, and their num ber inereafed, till they fhould form a fluid Now the earth turns round continually upon its own center, cauf<l

.

ing thereby the alternate change of day and night, while by this revolution each part of the earth is fucceflively

brought toward the fun, and carried off again in the fpacc of 14, hours. And as the fea revolves round along with the earth fort

itfelt

in this diurnal motion,

fuch a fluid

it

will

reprefent in fome.

rino;. D

19. BUT as the water of the fca does not move round with fo much fwiftnefs, as would carry it about the center

of the earth in the circle it now delcribes, without being fupported by the body of the earth ; it will be necefTary ta confider the water under three diflinct cafes. The firft cafe fhall

fuppofe the water to

move with

the degree of fwiftnefs^

required to carry a body round the center of the earth difingaged from it in a circle at the diftance of the earth's

femidiameter, like another moon. the waters

make but one

The

fecond cafe

is,

that

turn about the axis of the earth

with the moon ; fpace of a month, keeping pace the water fhould preferve parts of continually The third the fame fituation in refpect of the moon,.

in the

fo that all

cafe fhall be the real locity

one of the waters moving with a ve

between thefc two,

requires, nor

fo

Newt.

neither fo fwift as the

firfl

cafu

flow as the fecond. Price, philof. Lib.

I.

prop. 66. coroll.

18.

IN.

286

Sir Is A

NEWTON'S

AC

In the hrit cafe the waters,

>.

BOOK

the body

like

II.

which

they equalled in velocity, by the action of the moon would be brought nearer the center under and oppofite to the moon, than in the- parts in the middle between thefe eaftward or

That fuch

weftward.

the moon's action

mentioned of the

a

body would

upon

it,

clear

is

fo alter

its

diftance by

from what has been

changes o in the moon's motion caufed

like

And computation fhews, that the differ by the fun ence between the greateit and leaft diftance of fuch a body But in the fecond feet. would not be much above 4 '.

cafe, where all the parts of the water preferve the fame fituation continually in refpect of the moon, the weight of thofe under and oppofite to the moon will be diminished

parts

by the moon's

and the

action,

parts

in the

middle between

this thefe will have their weight increafed being effected as the fun diminimes the attracti fame the in manner, jult on of the moon towards the earth in the conjunction and :

but increafes that attraction in the quarters. oppofition, For as the nrlt of thefe confequences from the fun's acttion

on the moon

is

occafioned by the moon's being

at

tracted by the fun in the conjunction more than the earth, and in the oppofition lefs than it, and therefore in the

common made

to

in the

other

not have ly

motion

of

its

is

left

middle

:

earth

as

it

and moon, the moon is in one cafe too fait, and

were behind

;

fo the

earth will

drawn towards the moon fo ftrongand yet more forcibly than the re-

parts

as the nearer parts,

moteft

the

advance toward the fun

and therefore fmce the earth and moon move each '8.

month

CHAP.

PHILOSOPHY.

6.

month round the earth

on the

produced,

the

ter or to

common

their

moves round

of

while gravity , the fame effect will be

this center,

parts

of the water neareft to that cen

as the

moon,

center

287 3

moon

feels

from the fun when of the

in conjunction, and the water on the contrary fide earth will be aftected by the moon, as the moon is fun,

when

in oppofition

b

that

by the

in both cafes the

weight of the water, or its propenfity towards the center of the earth, will be diminimed. The parts in the middle between ;

is,

thele will have their weight incrcafed, by being prefled towards the center of the earth through the obliquity of

upon them

the moon's action

to

action

its

upon

the earth's

center, juft as the fun increafes the gravitation of the

from the fame caufe

in the quarters feft,

c

now

But

it is

that

is leaft,

;

have the greatefl weight, will fubfide. Therefore cafe there would be no tide or alternate riling and of the water,

but the water would form

oblong figure,

whofe

moon.

Sir

the

moon

maniwhere the weight of the fame quantity of water there it will be accumulated while the parts, which .

of

By

in

this

falling

an would prolonged pafs through AC NEWTON'S computation the it

felf into

axis

Is A

above the diameters perpt ular to it, that is, the height of the waters under and opf>ofite to the moon above their height in the middle between chefe ph excefs

ces ~

this axis

eaftward or

wcftward cauied by the moon,

is

about

feet. -

Ch.

3.

f

.

*Ch.

3

f)

i'.

I

ZI.

THI

Sir

NE

ISAAC

\v

To

BOOK II.

x*s

THUS

the difference of height in this latter fupfhort of twice that difference in the pre pofition But the cafe of the fea is a middle between thefe ceding. o

II.

is

little

for a body, which ihonld revolve round the center of the earth at the diftancc of a femidiameter without prefling

two

:

on the

muft perform its period in lefs than whereas the earth turns round but once

earth's furface,

an hour and

half,

and

in a

day

the

moon

;

it

that the real

of the waters keeping pace with

in the cafe

mould

motion

quired in thcfe two

turn round but once in a

cafes.

month

:

water

is

between the motions

Again,

if

the waters

ot the

as fwiftly as the rirft cafe required,

their

fo

re

moved round

weight would be

their motion ; for this cafe fuppofes the body to move fo, as to be kept revolving in a circle round the earth by the power of gravity without prefling on the earth at all, fo that its motion jufl fupports its weight. But if the power of gravity had been only part of

wholly taken oft by

^

the body could have moved thus without prefthe on earth, and have been as long in moving round, fing as the earth it felf is. Confequently the motion of the

what

it is,

earth takes off from the weight of the water in the dle between the poles, where its motion is fwiftefr,,

mid

-^ part

of

its

and no more. weight d>

Since therefore in the

firft

weight ot the waters mud: be intirely taken off by their motion, and by the real motion of the earth they Icfe the motion of the water will fo little only part thereof,

tale the

~

diminifh their weight, that their figure will much nearer refemble the cafe of their keeping pace with the moon than the other.

Upon

the whole, I

if

the waters

moved with

the

velo-

CHAP.

PHILOSOPHY.

6.

289

to carry a body round the center of the velocity neccftary earth at the diftance ot the earth's femidiameter without

bearing on the

moon

to the

at

the water

furfacc,

would be loweft under

gradually as it moved on with the earth came half way toward the place oppolitc

rife

it

till

eaftward,

came

its

and

moon,

from thence it would fubftde again, till it where it would become as low as afterwards it would rife again, till it came half ;

to the oppoiition,

firft

;

place under

to the

way would

till

fubiide,

it

moon

the

came

;

and from hence

a fecond time under the

it

moon.

But in cafe the water kept pace with the moon, it would be higheft where in the other cafe it is loweft, and loweft where

in the other it is higheft ; therefore the diurnal motion of the earth being between the motions of thefe two cafes, it will caufe the higheft place of the water to of the greateft height in thefe two fall between the places

The

cafes.

for

water

fome time

way

as

rife,

it

to the oppofite

height before

it

from under the

pafTes

but defcend again before place,

and

(hall

it

come

moon

fhall

arrives half

to

leaft

its

becomes oppoftte to the moon; then

it

fhall

till it has pafTed the place again, continuing fo to do fubfide before but it comes to the to the moon, oppofite

rife

middle between the places oppofite to and under the

and

it

laftly

fliall

come

to

cond time under the moon.

its

loweft, before If

A

(in fig.

it

in,

moon;

comes a

fe

1 1 3, 1 14.)

D

EF reprefent the moon, B the center of the earth, the oval C in fig. in. will reprefent the fituation ot the water in the firft

cafe

the line

but

if

CDEF

in

;

the water kept pace with the moon, ng. would reprefent the fitua-

fig.

P p

tion

AC

Sir Is A

290

tion of the water

;

NEWTON'S

but the line

CDEF

BOOK

in fig. 1 14,.

II.

will re-

motion of the water, as it prefent the feme in the real in all thefe in its diurnal rotation the earth accompanies :

C

and E being the places where the water is lowfigures and D and F the places where it is higheft. Purfueft, ant to this determination it is found, that on the fhores, lie expofed to the open fea, the high water ufually out about three hours after the moon has pafled the

which falls

meridian of each place.

LET

xx. ner,

in

this fuffice in

which the moon

to be noted,

general for explaining the man upon the feas. It is farther

acts

that thefe effects are greateft,

when

the

moon

a

over the earth's equator , that is, when it fhines perpen dicularly upon the parts of the earth in the middle between is

For if the moon were placed over either of the the poles. it could have no effect upon the water to make it afcend

poles,

So that when the moon declines from the etoward either pole, it's action muft be quator fomething and that the more, the farther it declines. diminished,

and defcend.

The

tides

jaeareft to

likewife will be greateft, when the moon it's action the ftrongeft. then being

THUS much

xg.

is

the earth,

of the action of the moon.

That

the fun fhould produce the very fame effects, though in a lefs degree, is too obvious to require a particular expla but as was remarked before, this action of the nation :

*

See below

44.

fun

CHAP.

P

6.

HILOSOPH

Y.

fun being weaker than that of the moon, will caufe the more nearly the moon's conrfe, and

tides to follow

pally

fhew

fecls ot

princi

fell

it

by heightening or diminifhing the

Which

the other luminary.

is

the occafion,

ef-

that-

the higheft tides are found about the conjunction and oppofition of the luminaries, being then produced by their uni

and the weaken1

ted action, the

moon

;

about the quarters of water

tides

moon

becaufe the

in this cafe railing the

and depreiTing it where the it, the ftronger action of the moon is in part retunded and weakened by that of the fun. Our author

where the fun depreffes fun

raifes

it,

computes that the fun of the water in the it

as

will

firft

However

much.

add near two feet to the height and in the other take from

cafe,

the tides in both

fame hour of the moon.

But

comply with the

at other times

,

between

the conjunction or opposition and quarters, the time de viates from that forementioned, towards the hour in which

make high water, though ftill it keeps nearer to the moon's hour than to the fun's.

the fun would

2.4.

AGAIN

the tides have fome farther varieties from

where they happen northward II?.) reprefent the axis, on

the fituation of the places

orfouthward.

which the

much

Let

pP

(in

fig.

earth daily revolves,

and

figure of the water, bed within this figure.

let

nB

hp

H

P reprefent the

ND

be a globe infcrito be advanced the moon Suppofe from the equator toward the north pole, fo that h H the axis of the figure of the water j5AHPE# fhall decline

towards the north pole

N

let

;

take any place

P

p i

G

nearer to the

Sir Is A

292

NEWTON'S

AC

BOOK II.

the north pole than to the fouth, and from the center of the earth C draw C G F ; then will G F denote the altitude to

which the water

above the horizon

is

raifed

by the

in the fpace

:

tide,

when

the

moon

is

of twelve hours, the earth the place G will be removed

having turned half round its axis, to g y but the axis h H will have kept its place preferring its fituation in refpect of the moon, at leafl will have moved no

more than

the

moon

has

done

which

in that time,

is

it

not

Now in this cafe neceflary here to take into confederation. the height of the water will be equal to gf^ which is But whereas G F is the altitude at not fo great as G F.

f

will high water, when the moon is above the horizon, g be the altitude of the fame, when the moon is under the The contrary happens toward the fouth pole, for horizon.

KL

is lefs

than k L

Hence

is

proved,

that

when

the

moon

from the equator, in thofe places, which are on the fame fide of the equator as the moon the tides are declines

,

when

greater,

under

it \

moon

above the horizon, than when and the contrary happens on the other fide of the

is

the equator.

Now the

ance of on,

from

thefe principles may be explained all in the tides the afTift~ ; appearances only

known

by

additional remark, that the fluctuating moti the water has in flowing and ebbing, is of a

this

which

durable nature, and would continue for fome time, though the action of the luminaries fhould ceafe ; for this prevents the difference between the tide when the moon is above the

CHAP.

PHILOSOPHY.

6.

and the

the horizon, fo great,

being

makes the

tide

greatell

10!

\\.

moon, but to be a tide

mouth they ,

are

THIS

when

as the rule laid

or

the

down

el

two

moon

below '!

rcqniu

it

from

his likcu ife

:KU and

ilu-

UJMM

-nilol

ai

full

and Ply

found the third atu

doctrine farther fhews us,

fpring tides fall

is

293

out about the

new and

why

not only the

moon, and the but likewife how it comes full

neap tides about the quarters ; to pafs, that the greateft fpring tides happen about the equi noxes ; becaufe the luminaries are then one of them over the It equator, and the other not far from it. appears too, why the neap tides, which accompany thefe, are the leaft of all j

for the fun

continuing over the equator continues to have power of lefTening the moon's action, and the

ftill

the greater!:

moon

in the quarters being far

poles,

has

17.

its

removed toward one of the

power thereby weakned.

MOREOVER

the action of the

moon

being ftronger,

when near the earth, than when more remote if the moon, when new fuppofe, be at its neareft diftance from the earth, whence it is, that it (hall when at the full be fartheft off; ;

two of the very

largeft fpring

tides

do never immediately

fucceed each other.

BECAUSE folftice to

from the is

the fun in

its

pafiage

from the winter

fummer recedes from the earth, and fummer folftice to the winter approaches the

palling it,

and

therefore nearer the earth before the vernal equinox than after,

Is A AC

Sir

NEWTON'S

BOOK

II.

but nearer after the autumnal equinox than before

after,

;

the grcateft tides oftncr precede the vernal equinox than follow it, and in the autumnal equinox on the contrary

they oftncr follow

THE

19.

come

than

it

altitude,

before

it.

which the water

to

is

raifed in the

open ocean, correfponds very well to the forementioned calcu lations j for as it was fhewn, that the water in fnring tides fhould

6

is

or

7

oceans

Ethiopic

water

the height of

rife to

tides to

;

I

o or

1 1

and the neap Atlantic and

feet,

accordingly in the Pacific, in the parts without the

obferved to

rife

about 6, 9,

1

1 or

i

the

tropics, j*

feet.

In the

that fea.

faid to be greater than in the is reafon of the wide extent of to be by ought For the fame reafon in the Ethiopic ocean be

tween the

afcent of the water tropics the

Pacific ocean this elevation

other,

as

it

lefs

is

than with

by reafon of the narrownefs of the fea between the coafts of Africa and the fouthern parts of America. out,

And

iflands in fuch

narrow

feas,

But

if far

now

from fhore,

have

ports where the water flows in with great violence upon fords and fhoals, the force it acquires by that means will carry it to a much

lefs

tides

than the

coafts.

in thofe

and defcend to 30, greater height, fo as to make it afcend or even jo feet and more ; inftances of which we have

40 at

Plymouth

St. Michael's

Pegu

,

and

in

the Severn

and Auranches

in

near

Normandy

Chepftow at

;

;

at

Cambay and

in the Eaft Indies.

AGAIN

the tides take a confiderable time in palling Thus the tide, through long ilraits, and fliallow places.

30.

3

which

CHAP. which

PHILOSOPHY.

6.

made on

29$

the weft coaft of

Ireland and on the coaft of Spain at the third hour after the moon's coming to the meridian, in the ports eaftvvard toward the Britiili channel falls out later, and as the flood that chan nel

is

ftill

later

and

later,

hours in coming up to

31. IN the

from

different

laft

paries fo that the tide takes

London

place tides

feas,

and

as

up up full twelve

bridge.

may come to the fame port they may interfere with each

they will produce particular effects. Suppofe the fea come to a port at the third hour after

other,

from one

tide

the moon's paffing the meridian

of the place,

but from

another fea to take up iix hours more in its paflage. Here one tide will make high water , when by the other it fhould be loweft ; fo that when the moon is over the equator, and the

two

tides are equal,

of the water

by one

moon is

tide,

at all

fituated

other.

there will be

for as

much

no

as the

riling

water

is

and

falling

carried off

will be fupplied by the other. But when the from the equator, the fame way as the poit we have fhewn that of the two tides of the

it

declines ,

made each

ocean, which are

when

;

the

moon

is

day, that tide, which is made is greater than the

above the horizon,

Therefore in

this cafe,

as four tides

come

to this

two greateft will come on the third, an J port each day the on the ninth hour after the moon's pail ing the meridian, and the two hour.

leaft

Thus from

at the fifteenth

and

at the

the third to the ninth hour

twenty

hril

more water

will be in this port by the two greateft tides than from the ninth to the fifteenth, or from the twenty iirft to the followii

Sir Is A

296

tide

water brought by thefe

tween the two firft

NE w TON'S

BOOK II.

where the water

following third hour, great and one fmall

AC

;

tides,

Icaft tides,

that

is brought by one but yet there will be more than what will be found be

is,

between the

fifteenth

and

Therefore in the middle between the

hour.

twenty third and ninth hour, or about the moon's letting, the wa ter will be at its greateft height ; in the middle between the ninth and fifteenth,

as alfo

between the twenty have its mean height

firft

and

and be ; following third hour it will loweft in the middle between the fifteenth and twenty firft Thus here the water hour, that is, at the moon's riling. will

have but one flood and one ebb each day. When the the is on the other fide of the flood will be equator,

moon

turned into ebb, and the ebb into flood ; the high water fail ing out at the rifing of the moon, and the low water at

Now this is the cafe of the port of Batfham the fetting. in the kingdom of Tunquin in the Eaft Indies ; to which port there are iflands

two

which are

inlets,

one between the continent and die

called die Manillas.,

and the other between

the continent and Borneo,

3 1.

THE next thing to be confidered

is

the effed,

which

thefe fluids of the planets have bodies to which they belong.

upon the folid part of the And in the firft place I fhall fliew, that it was neceflary upon account of thefe fluid parts to form the bodies of the planets into a figure femeBecaufe the thing different from that of a perfect globe. diurnal rotation,

and the

like

which

motion we

o>

fee in

rth

performs about

fome of the other

its

axis,

plane.

which

CHAP. ''which

PHILOSOPHY.

6.

297

an ample conviction that they all do the like) will with which bodies are attracted upon

is

diminish the force, all

the parts of their furfaces,

upon which they fubftance refting force it

which

it

except at the very poles, a (lone or other weighty

furface of the earth, by the from the motion communicated to

upon the

receives

by die earth,

Thus

turn.

it

its

weight prevented not,

would con

tinue that motion in a ftraight line from the point where it received it, and according to the direction, in which it

was given, that is, in a line which touches the furface at that point ; infomuch that it would move off from the earth in the fame manner, as a weight faften'd to a ftring and whirled about endeavours continually to recede from and would forthwith remove it felf

the center of motion to a greater diftance retains

And

it.

,

from

farther,

it,

if

loofed from the ftring

as the centrifugal force,

fuch a weight prefles from the center of

by how much

greater, it

moves

on the

;

fo

earth,

greater the velocity

it is

motion, is with which

fuch a body, as I have been fuppofing to lie would recede from it with the greater force,

the greater the velocity is, earth's furface it refts upon diftant

its is,

which

with which

from the

poles.

with which the part of the

moved, that is, the farther But now the power o( gravity

is

to prevent bodies in any part of the earth from being carried off from it by this means ; however it is an cflort contrary to that of gravity, plain that bodies having though much weaker than it, their weight, that is, the de is

great

enough

gree of force,

with which they are preflcd to the earth, and be the more diminiilted,

will be diminifhed thereby,

die

Sir

298

N E w T o N'S

ISAAC

BOOK II.

the greater this contrary effort is ; or in other words, the will weigh heavier at either of the poles, than

fame body

upon any other part of the earth ; and if any body be removed from the pole towards the equator, it will lofe of its weight more and more and be lighteft of all at ,

the equator,

that

is,

THIS now

33.

is

middle between the

poles.

eafily applied to the waters

of the

in the

and mews that the water under the

poles will prefs

bly to the earth, than at or near the equator ly that

ing

it

which

makes room

Jn which

let

:

feas,

forci

and confequent-

place, till for receiving a greater quantity,

additional weight Toilluftrate this more

its

the diameter

muft give

preffes leaft,

more

by afcend-

which by

whole upon a ballance. particularly I mail make ufeof fig. 116"

may

place the

A C B D be a circle, by whofe revolution about A B a globe mould be formed, reprefenting a

globe of folid earth. Suppole this globe covered on all fides with water to the fame height, fuppofe that of EAorBF> at

which

ACBD

;

diftance the

then

the water

But

it is

EGFH

circle

furrounds the circle

evident, if the globe of earth be at reft,

which furrounds

it

will

reft

in that iituation.

the globe be turned inceftantly about its axis AB, and the water have likewife the fame motion, it is allo if

from what has been explained, that the water be circles E H F G and A D B C will remain no longer o in the prefent fituation, the parts of it between H and D, and between G and C being by this rotation become lighter, than evident,

tween the

the parts between E and A and between B and F ; fo that the water over the poles A and B muft of neceffity fubhde, and the

water

CHAP.

PHILOSOPHY.

6.

water be accumulated over

D

299

and C,

till the greater quan the defect of its weight. fupply be the cafe, were the globe all covered with

in thefe latter places tity

This would

And

water.

the fame figure of the furface

would

alfo

be

if fome part of the water adjoining to the globe preferved, in any part of it were turned into folid earth, as is too

evident to need any proof; becaufe the parts of the water remaining at reft, it is the fame thing, whether they con tinue in the ftate of being eafily feparable, which denomi

them

nates

fluid,

or were to be confolidated together,

Co

make

a hard body : and this, though the water fhould in fbme places be thus confolidated, even to the furface of it. as to

Which fhews no

that the

form of the

folid part

of the earth makes

alteration in the figure the water will take

confequence earth

from being

quite deferted,

ven them

much

covered on

fome

in order to the preventing entirely

overflowed

,

and by

:

parts

of the

and other

parts

the folid parts of the earth muft have gi the fame figure, as if the whole earth were

all fides

with water.

34. FARTHER, I fay, this figure of the earth is the fame, as it would receive, were it entirely a globe of wa ter, provided that water were of the fame denfity as the fubftance of the globe. For fuppofe the globe and that the now liquified, globe

EHFG,

by as

its

rotation about

we have been

fhould be

would

its

axis fhould

defcribing,

the

ACBD

figure of the water

by fuch a ^

to be

receive fuch a figure

and then the globe

confolidated again,

plainly not be altered,

ACBD

entirely water,

confolidation. 35*.

BUT

ISAAC

Sir

300

N E w T o N'S

BOOK II.

57. BUT from this Lift obfervation our author is ena bled to determine the proportion between the axis of the earth drawn from pole to pole, and the diameter of the c-

upon the fuppofition that all the parts of the earth are which he does by computing in the firft the proportion of the centrifugal force of the parts un

quator,

of equal denfity

;

place der the equator to the as iidering the earth

power a

of gravity

fpheroid

,

;

and then by con-

made by

the

revo

lution of an ellipfis about its lelTer axis, that is, fuppofing the to be an exact ellipfis, from which it can dif line

MILK

fer

but

by reafon that the difference between the

little,

lefler axis

M L and the

this fuppoiition,

particles

greater

I

K

is

but very

fniall.

and what was proved before,

which compofe

that

the earth have the attracting

From all

the

power

in the preceding chapter, he finds at what diexplained ftance die parts under the equator ought- to be removed from the center, that the force, with which they fball be attracted

diminifhed by their centrifugal force, mall in a ballance with thofe which parts

to the center,

be

fufficient to

keep thofe

lie

under the

poles.

And upon

the fuppofition of

all

the

the parts of the earth having the fame degree of denfity, earth's furface at the equator muft be above 17 miles more diftant

from the center, than

at the

a

poles

.

AFTER

this it is fhewn, from the proportion of the of the earth to its axis, how the lame diameter equatorial be determined of any other planet, whofe deniity in 36".

may

Newton

Frinc. Lib. Ill prop. 19.

comparifon

PHILOSOi'H Y.

CiAp.6.

301

companion of the dcnfity of the earth, and the time of its revolution about its axis, are known. And by the rule de livered for this,

it

of lo to

found, that the diameter of the equa its axis about the proportion

9% and

form to the Lvts of

this

accordingly this planet appears of an oval The mo ft confiderable efaftronomers.

fpheroidical

into confideration ly

is

Jupiter fhould bear to

tor in

;

figure our author takes likewife is that bodies are not equ.

one of which

all distances from the poles; but near the equa where the diftance from the center is great/eft, they arc-

heavy in

tor,

lighter than towards the poles

:

and nearly

in this

proportion,

that the actual power, by which they are drawn to the center, their abfolute rcfulting from the difference between gravity and centrifugal force, is reciprocally as the diftance from

the center.

That

this

may

not appear to contradict what power of gravi

has before been faid of the alteration of the ty,

in proportion to the

change of the diftance from the cen

proper carefully to remark, that our author has demonftrated three things relating hereto the firft is, that ter,

it

is

:

power of gravity as we recede from the been fully explained in the kft chapter, which has center, decreafe of the

upon fuppofition that the earth and planets are perfect from which their difference is by many degrees too fpheres, little

next

to require notice for the purpofes there intended is,

:

the

that whether they be perfect fpheres, or exactly fiich

have now been mentioned, the power of gra defcend in the fame line to the center, is at all diftances as the diftance from the center, the parts of the fpheroids vity,

as

as

we

Lib

III prop. 19.

earth

Sir Is A

302

NEWTON'S

AC

BOOK

II,

body by drawing the body towards them and both center gravitation towards the

earth above the

*

IciTening

thele

we

its

;

relate to gravity

allertions

mentioned

in this place,

the third

alone:

that the

adual force on

which bodies are parts of the furface, with is in the proportion here aiiigned \

what

is

different

drawn

to the

[

center,

.

THE

next effect of this figure of the earth

is

an

that pendulums of obvious confequence of the former: the fame length do not in different diftances from the pole

mike

their vibrations in the

fame time

;

but towards the poles,

where the gravity is ftrongeft, they move quicker than near the equator, where they are lefs impelled to the center ; and accordingly pendulums, thatmeafure the fame time by their vibrations,

muft be

diftance.

Both which deductions are found true

fhorter near the poles than at a greater in fact ; of

which our author has recounted particularly feveral experi ments, in which it was found, that clocks exactly adjufted to the true meafure of time at Paris,

when

tranfported nearer to

became erroneous and moved too flow, but were

the equator,

reduced to their true motion by contracting their pendulums. Our author is particular in remarking, how much they loft of while the pendulums remained unaltered ; and what length the obfervers are faid to have fhortened them, to And the experiments, which appear bring them to time. their motion,

to be

mod

carefully

made, fhew the earth

die middle between the poles, as it

by

his

much

as

to be raifed in

our author found

c

computation 3

Lib.

I.

.

b

prop. 73.

Lib; III. prop. :o.

c

Ibid.

THESE

CHAP.

PHILOSOPHY.

6.

303

THESE

39. experiments on the pendulum our author has been very exat in examining, inquiring particularly

how much

the extenfion of the rod of the

pendulum by

the great heats in the torrid zone might make it necefTary to fhorten it. For by an experiment made Pic ART, and

by

another made by

DE

LA HIRE, heat, though not very intenfc, was found to increafe the length of rods of iron. The ex

periment of Pic ART was made with a rod one foot long* in winter, at the time of frofl, was found to increafe

which

in length

by being heated

at the

fire.

In the experiment

DE

LA HIRE a rod of fix foot in length was found v when heated by the dimmer fun only, to grow to a greater of

length, than

it

had in the

aforefaid cold feafon.

From which

obfervations a doubt has been raifed, whether the rod of the

pendulums in the aforementioned experiments was not extended by the heat of thofe warm climates to all that the obfcrvers found thcmfclves obliged But the experiments now mentioned by. For in the firfl of them the rod of a fliew the contrary. excefs of

to lefTen

length,

them

was lengthened no more than ~ part of what the pendulum under the equator mu ft be diminimed ; and there foot long

fore a rod of the length of the

pendulum would not

have-

of that length. In the experiment of DE LA HIRE, where the heat was lefs, the rod of fix foot - of what the long was extended 110 more than pendulum

been extended above

muft be fhortened

;

fo that a

rod of the length of the pen or of that length.

dulum would not have gained above ^

\-

And

the heat in this latter experiment, though lefs than in the. former, was yet greater than the rod of a pendulum can ordinarifo

ISAAC NEWTON'S

Sir

304.

BOOK II.

in the hotted country ; for metals receive a dinarily contrail heat when expofed to the open fun, certainly much great

human

greater than that of a ufually fo expofed,

But pendulums are not

body.

and without doubt

thefe experiments

in

were kept cool enough to appear fo to the touch which they would do in the hotted: place, if lodged in the fhade. Our ;

author therefore thinks difference obferved

it

to allow about p of the

enough

upon account of the greater warmth of

the pendulum.

THERE

40.

is

a third effect, which the water has on the

earth by changing its figure, that is taken notice of by our author; for the explaining of which we (hall fir/1 prove, that bodies defcend perpendicularly to the furface of the

earth in

all

places. is

fervation,

The manner of collecting this from obThe furfaces of all fluids reft paral

as follows.

to that part of the furface of the fea, which is in the fame place with them, to the figure of which, as has been parti For cularly fhewn, the figure of the whole earth is formed. lel

it

any hollow

the fea

it is

;

vefTel,

open

at the

bottom, be immerfed into

evident, that the furface of the fea within the

veflel will retain the

fame figure

it

had

,

before the veiTel

communication with the external water is not cut off But all the parts of the water by the veile!. being at reft, it is as clear, that if the bottom of the veflel were cloied, the forure of the water could receive no change O D inclofed

it

thereby, fea

;

;

fince

its

even though the

any more than from

power

of

gravity,

veflel

were

railed out

of the

the infenfible alteration of the

confequent upon the augmentation of the

CHAP.

PHILOSOPHY.

6.

305

the diftance from the center.

defcend in

for if

ids;

But now it is clear, that bodies perpendicular to the furfaces of quiefcent flu the power of gravity did not act perpendicular

lines

to the furface ly

could not

of

bodies which

fluids,

fwim on them

they arc feen to do ; becaufe, if the power fuch bodies in a direction oblique to the

reft, as

of gravity drew

furface whereon they lay, they would certainly be put in motion, and be carried to the iicle of the veflel, in which

the fluid was contained, that

way

the action of gravity in

clined.

HENCE

4,1;

it

follows, that as

we

(land,

our bodies are

to the furface of the earth.

Therefore in perpendicular going from north to fouth our bodies do not keep in a Now in all diftances from the pole the direction. parallel

fame length gone on the earth

change

will not

our bodies,

in the pofltion of

make

the fame

We

but the nearer

are to the poles, we muft go a greater length to caufe the I L K fame variation herein. Let (in fig. 1 1 7) reprefent the figure of the earth, M, L the poles, I, K two

M

op-

pofite points

and

PO

L

draw

;

in the

middle between thefe

be two arches,

T \V, V

OR

in S.

Let

TV

being moft remote from the pole

O R, each perpendicular to the and let T \V, V X meet in Y, and

X, P Q.,

furface of the earth,

P Q,

TV

poles.

Here

it is

evident, that in paiTing

from

V

to

T the

pofltion of a man's body would be changed by the under T Y V, for at V he would ftand in the line YV angle continued upward, and at T in the line Y T ; but in palling

from O

to

P the pofltion of

his

body would be changed by

R

r

the

Sir I

306

s

AAc

N E w T o N'S

BOOK II.

Now I fay, if thefe two angles are the angle under OS P. is the arch P O longer than T V : for the figure equal

MILK

the figure will be being oblong, and IK longer than ML, more incurvated toward I than toward L ; fo that the lines

TW

and V

X

will

meet

in

Y before they are drawn out to and O R muft be continued

fo great a length as the lines P Q_ before they will meet in S. to,

YV

are Shorter than P S

and

S V,

Sinee therefore

TV

muft be

lefs

YT

and

than OP.

TYV

and OSP are each ~ part of If thefe angles under the angle made by a perpendicular line, they are faid each And the unequal length of thefe to contain one degree. arches

OP

and

VT

from north pafling

gives occafion to the after tion, that in to fouth the degrees on the earth's fur-

face are not of an equal length, but thofe near the pole For the length of longer than thofe toward the equator. the arch on the earth lying between the two perpendiculars, which make an angle of a degree with each other y is called the length of a degree

4,1. It

THIS

on the

figure of the earth has

earth's furface.

fome

effec~l

on

eclipfes-

has been obferved above, that fometimes the nodes of the

moon's

orbit lie in a ftraight line

drawn from the fun

to

the earth; in which cafe the moon will crofs the plane of But whenever the the earth's motion at the new and full.

moon

near the plane at the full, fome part of the pafTes earth will intercept the fun's light, and the moon mining only with light borrow'd from the fun, when that light is

prevented from falling on any part of the moon, fa much of her body will be darkened. Alfo when the moon at the

new

CHAP. new

PHILOSOPHY.

6.

307

near the plane of the earth's motion, the inhabitants on fome part of the earth will fee the moon come under is

the fun, and the fun thereby be covered from them either Now the figure, which we have (hewn wholly or in part. to belong to the earth, earth

will occaiion

the

diadow of the

on the moon not to be

diameter from

perfectly round, but caufe the eaft to weft to be fome what longer than the

diameter from north to fouth.

In eclipfes of the fun this

figure of the earth will make fome little difference in the where the fun (hall appear wholly or in any given place,

the earth, part covered. Let A B C D (in fig. 1 1 8.) reprefent A C the axis whereon it turns daily, E the center. Let F A G C

a perfect globe infcribed within the earth. Let H I reprefent be a line drawn through the centers of the fun and moon, crofthe earth in K, and the furface of the fing the furface of in L. Draw E L, which will be perpendicular infcribed globe to the furface of the globe in

1,

:

and draw likewife K M,

be perpendicular to the furface of the earth Now whereas the eclipfe would appear central at L, in K. if the earth were the globe A G C F, and does really appear fo that

fo at is

K

fhall

it

;

I

different

fay,

the latitude of the place K latitude of the place

from the

on the

L on

real earth

the globe

FAGC. What

is called the latitude of any place is determined which the line the perpendicular to the furface of angle by the earth at that place makes with the axis ; the difference

a perpendicular line or this angle, and that made by fquare being called the latitude of each place. But it might makes with C here be proved, that the angle which K

between

M

M

is lefs,

than the angle

made between

R

r

z

LE

and EC:

confe-

quently

Sir

308

N E w T o N'S

ISAAC

qucntly the latitude of the place

greater, than the la

is

which the place L would have.

titude,

THE

43.

the earth,

id

K

BOOK II.

is

next effed, which follows from that gradual

change

this

in the diftance

figure of

of the

fix-

from the equinoctial points, which aftronomers obBut before this can be explained, it is neceflary to

liars

Icrvc.

fomething more particular, than has yet been done, concerning the manner of the earth's motion round the iun.

lay

I

44..

T has already been

faid,

that the earth turns round

each day on its own axis, while its whole body is carried How thefe two motions round the fun once in a year. are joined together may be conceived in fome degree by the motion of a bowl on the ground,

where the bowl

in

rouling on continually turns upon its axis, and at the fame But time the whole body thereof is carried ftraight on. to be

exprefs let A (in fig. lip) reprefent the fun four different fituations of the earth in its orbit

more

BCDE

moving about trfe fun, Tn axis, about which the earth

all thefe

let

FG

reprefent the

The points F, G daily turns. are called the poles of the earth ; and this axis is fuppoled to keep always parallel to it felf in every fituation of the earth

;

at leaft that

it

would do

fo,

were

it

not for a

the caufe whereof will be explained in When the earth is in B, the half HI K will

minute deviation,

what

follows.

HLK

be illuminated by the fun, and the other half will Now if on the globe any point be taken be in darknefs. in

CHAP.

PHILOSOPHY.

6.

30?

middle between the poles, this point fhall defcribe' the motion of the globe the circle MN, half of which by is in the enlightened part of the globe, and half in the dark part. But the earth is fuppofcd to move round its axis in the

with an equable motion ; therefore on this point of the globe the fun will be feen juft half the day, and be invifi-

And the fame will happen to every point of this circle, in all fituations of the earth during h whole revolution round the fun. is called This circle ble the other half.

MN

the equator, of which

we have

before

made mention.

Now

45-. fuppofe any other point taken on the furface of the globe toward the pole F, which in the diurnal re volution of the globe fhall defcribe the circle OP. Here half it this circle is more than that enlightned by appears

and confequently

that in any particular point of the fun will be longer feen than lie hid, that is the day will be longer than the night. Again if we confider the fame circle O P on the globe fituated in D the op-

the fun,

this circle

we

pofite part of the orbit

from

any place of

the night will be as

this circle

B,

fhall fee,

that here in

much

longer

than the day.

46. I N thefe fituations of the globe of earth a line drawn from the fun to the center of the earth will be obliquely inclined toward the axis F G.

Now

fuppofe, that

fuch a line drawn from the fun to the center of the earth,

when

in

C

or E,

would be perpendicular

to the axis

F

(.

m

1

o

Sir I

s \

AC

N E w T o N'S

BOOK II.

in (which cafes the iun will fhine

perpendicularly upon the equator, and confequcntly the line drawn from the center ot the earth to the fun will crofs the equator, as it paries through the furface of the earth ; whereas in all other fituations of the globe this line will pafs through the furface of the globe at a diftance from the equator either north

ward cle

or fouthward.

OP

Now

will be in the light,

in both thefe cafes half the cir

and half

in the

dark

;

and there

place in this circle the day will be equal Thus it appears, that in thefe two oppofite

fore to every

to the night.

fituations of the earth the

but in

of the

day all

is equal to the night in other fituations this

all

globe ; parts equality will only be found in places fituated in the very middle between the poles, that is, on the equator.

THE

times, wherein this univerfal equality between 4/7. the day and night happens, are called the equinoxes. Now it has been long obferved by aftronomers, that after the earth hath fet out from either equinox, fuppofe from E

(which will be the fpring equinox, if F be the north pole) die fame equinox fliall again return a little before the earth has

made

a compleat revolution round the fun.

This

re

turn of the equinox preceding the intire revolution of the earth is called the preceiuon of the equinox, and is caufed

by the protuberant figure of the

SINCE quator, when 4,8.

the earth

is

earth,

the fun fhines perpendicularly upon the ethe line drawn from the fun to the center

perpendicular to the earth's

axis,

in this cafe

the

CHAP.

PHILOSOPHY.

6.

the plane,

may

quator, will not

do

311

which fhould cut through the earth

the e-

at

be extended to pafs through the fun; any other pofition of the earth.

but

it

Now

fo in

us confider the prominent part of the earth about the equator, as a folid ring moving with the earth round the let

At the time of the equinoxes, this ring will have the fame kind of fituation in refpect of the fun, as the when the line of the nodes is di orbit of the moon has,

fun.

rected to the fun

moon's

;

and

at all other times will refemble the

orbit in other fituations.

Confequently

this

ring,

which otherwife would keep throughout its motion paral lel to it felf, will receive fome change in its pofition from the action of the fun

The the equinox. ftood as follows. Let E

upon manner

except only at the time of change may be under-

it,

of this

ABCD

(in fig.

no)

the center of the earth, S the fun

,

reprefent this ring,

AFCG

a circle de-

fcribed in the plane of the earth's motiorv to the center E.

Here A and C

are the

crofTes the

tjuator of the equinox

two

tails

earth's

when

out,

in

points,

plane of the

which the

motion

the ftraight line

Now tinued would pafs through the fun. what was faid above concerning the moon, bit it

was in the fame

;

earth's e-

and the time

let

AC

when

thence

body were fuppofed to be cirde A B C D, what effect the

will be underftood, if a

ving in any part of this on of the fun on the body

the pofition of die line AC. perpendicular to SE, if the circle

her or

From

fituation with this ring.

between

A and H,

w ould T

mo acti

have toward changing

In particular HI being drawn body be in any part of this

or between 3

con

us recollect

C

and

I,

the

hV AC

Sir I

312

NEwTo

AAc

s

"^

would be of the

it

C toward D

AC

follows,

;

C and

I,

are

to

move toward D C,

tendency,

move toward

B,

in

the contrary way. Hence round the center

A

ring between A and H, and by the fun, that they

;

and

fituation

move toward

to

of the

B,

line

AC

and the point

the parts of the ring between will have the oppofite to move the contrary the line

but

and between

And

this

fo influenced

change the

fo to

will endeavour,

H and

fhall

were

any other part and C, or between I and A,

if it

that as this folid ring turns

as to caufe the point

C

H

would be turned

of the earth, the parts of

between

but

between

circle, either

the line

A

that the point

fo turned,

;:nd the point

BOOK II.

N'S

all

I

and A,

AC

difpofe fince thefe laft

named

parts are larger than the other, they will prevail over the other, fo that by the will be fo action of the fun upon this ring, the line

way.

AC

that

turned,

toward D, fun in

its

A

and vifible

tion of the line

continually be more and more moving Thus no fooner mail the toward B.

fliall

C

motion have departed from A, but the

mo

AC

and

fhall haften

from thence the motion of fun's fecond conjunction

A

its

meeting with C,

this line fhall

with

A;

again haften the

for as this line fo turns,

continually moving toward D, fo the motion is the fame way as from S toward T. that

49.

is

THE moon

will have

the fun, and operate on portion as .fame.

its

force

But the

on the

effect

it

on

more

fea

fun's viilble

this ring the like effect as ftrongly, in the fame pro

exceeded that of the fun on the

of the action of both luminaries will

be greatly diminiflied by reafon of

this ring's

being connect ed

CHAP.

ed to the

moon

PHILOSOPHY.

6. reft

of the earth

have not only

this

for

;

by

this

313

means the fun and

ring to move,

but likewife the

whole globe ot the earth, upon whofe fpherical part they have Befide the erTect is alfo rendred no immediate influence. by reafon that the prominent part of the earth is not all under the equator, but fpreads gradually from

lefs,

collected

thence toward both poles.

Upon

fun alone carries the nodes of the revolution in about

19

years,

die whole,

though the

moon through an

intire

the united force ot both lu

minaries on the prominent parts of the earth will hardly carry round the equinox in a lefs fpace of time than 16000 years.

To

this

motion of the equinox we muft add ano and moon up

ther confequence of this action of the fun

on the elevated

parts of the earth, that this annular part of the earth about the equator, and confequently the earth's axis, .will twice a its inclination year and twice a month

to the plane of the earth's motion, juft

as the inclination

the fun

is

5-1.1 mall

ticularly

now

But

this

change

is

its

very infeniible.

the prefent chapter with our great into the inquiry figure of the fecondary planets, par finifh

of our moon, upon the figure of which

parts will have

fame

reftored,

of the moon's orbit by the action of

annually twice diminished, and as often recovers

original magnitude.

author's

change and be again

fide

an influence.

towards the earth,

but once round

its

axis in the

its

fluid

The moon and

turns always tl confequently revolves

fpace of an entire S f

month

;

for

AC

Sir Is A

N EW TON'S

BOOK

for a fpectator placed without the circle, in which the moves, would in that time obferve all the parts of the fuccefiivcly to pafs is,

once before

his

II.

moon moon

view and no more, that

whole globe of the moon has turned once round. the great flownefs of this motion will render the cen

that the

Now

of the waters very weak, fo that the figure of the moon cannot, as in the earth, be much af fected by this revolution upon its axis but the figure of thofe waters are made different from fpherical by another caufe, trifugal force of the parts

:

viz. the action of the earth upon them ; by which they will be reduced to an oblong oval form, whofe axis prolonged would pafs through the earth; for the fame reafon, as we

have above obferved,

that the waters of the earth

would

the like figure, if they had moved fo flowly, as to keep And the folid part of the moon muft pace with the moon. but this ele correfpond with this figure of the fluid part takes,

:

vation of the parts of the moon is nothing near fb great as is the protuberance of the earth at the equator, for it will not

exceed 93 englifh

THE what earth.

feet.

waters of the

moon

will

have no

tide,

except

from the motion of the moon round the For the conversion of the moon about her axis is e-

will arife

quable, whereby the inequality in the motion round the earth difcovers to us at fome times fmall parts of the moon's furface towards the eaft

hid

and

as the axis,

or weft,

which

whereon the moon

at

other times

lie

oblique to her motion round the earth, fometimes fmall parts of her ;

turns,

is

furface

CHAP. furface

6.

PHILOSOPHY and fometimes the like toward which at other times are out of fight'

toward the north,

the fouth are vifible,

Thefe appearances make what

is

called the libration of the

moon, difcovered by HEVELIUS.

But

now

as

the axis of

the oval figure of the waters will be pointed towards the earth, there muft arife from hence fome fluctuation in them;

and

beiide, ,

by the change of the moon's diftance from the

they will not always have the very fame height.

Sf

2

BOOK

III.

6

Sir I

s

A

AC

N E w T o N'S

BOOK CHAP Concerning the caufe of rent in the

BOOK

III.

IIL I.

COLOURS inhe

LIGHT.

FTER this view which has been taken A A c N E w T o N'S mathema of Sir I s

tical

principles

of philofophy, and the

he has made of them, in explain ing the fyftem of the world, &c. the courfe of my defign directs us to turn tife

work,

his treatife

our eyes to that other philofophical we mall find our great

of Optics, in which

author's inimitable genius difcovering

it

felf

no

lefs,

than in the

CIA?,

i.

PHILOSOPHY.

317

the former; nay perhaps even more, fince this work gr many inftanccs of his iinguhr force of reasoning, and of his unbounded invention, though unaflifted in gn as

meaiure by thofe rules and genera] precepts, which facili of mathematical theorems. Nor yet

tate the invention this

has

work inferior made known

to the other in ufefulnefs to us

one great principle

;

lor

as that

in nature,

by

motions are continued, and by which the frame of each globe is preferved ; fo does this point out

which the

celeftial

to us another principle no lefs univer/al, upon which de pends all thofc operations in the fmaller parts of matter, for all

whofe fake the greater frame of the univerlc is creeled ; immenfe globes, with which the whole heavens are

thofe

filled, being without doubt only defign'd as fo many con venient apartments for carrying on the more noble opera Which {in tions of nature in vegetation and animal life.

abundant proof of the excellency of gle coniideration gives our author's choice, in applying himfelf carefully to ex

amine the action between

light

and

bodies,

fo

neceflary

of thefe productions, that none of them can be fuccefsfully promoted without the concurrence of in all the varieties

heat in a greater or

1.

'Tis

true,

lefs

degree.

our author has not

made

fo full a

dilcovery

of the principle, by which this mutual action between light and bodies is caufed ; as he has in relation to the power, by

which the planets are kept in their courfes : yet he has led us to the very entrance upon it, and pointed out the path fo plainly which muft be followed to reach it ; that one may be

Sir I s A

318 be bold to

fay,

Ac

N E w r o N'S

whenever mankind mail be

BOOK

III.

blefied with this

improvement of their knowledge, it will be derived fo di our author in this rectly from the principles laid down by book, that the greateft fhare of the praifc due to the dif covery will belong to him. 5. I

fhall

IN fpeaking of the progrefs our author has made, three things, the two firft relating diftinctly purfue

to the colours of natural bodies

for in the firft

:

head

{hall

be fhewn, how thofe colours are derived from the proper ties of the and in the fecond upon what light itfelf ; but the third head properties of the bodies they depend difcourfe fhall treat of the action of bodies :

of

my

upon

light in refracting, reflecting,

and

inflecting

it.

THE

firft of thefe, which mall be the bufinefs of 4. the prefent chapter, is contained in this one proposition that the fun's direct light is not uniform in refpect of colour, not :

being difpofed in every part of nefs,

which the whole

raifes

;

it

to excite the idea

but on the contrary

of whiteis

com-

a

of rays, one fort of which if apofition of different kinds lone would give the fenfe of red, another of orange, a third of yellow, a fourth of green, a fifth of light bh a fixth of indigo, and a feventh of a violet purpkd all thefe rays together by the mixture of their fenlations ;

upon the organ of fight the fenfe ot whiten efs, 'ts own cdoi each >\d though ray always imprints t ail the difference between the colours of bodies when imprefs

!

\

I

in

open day

light

arifcs

from

t!iis 3

that colouixd

!

CHAP. do not

PHILOSOPHY.

i.

of rays falling upon them in emuch more copioufly than o-

reflect all the forts

but fome

forts

qual plenty, thers ; the body appearing of that colour,

coming from

light

5-.

it

is

319

of which the

moft compofed.

THAT the light of the fun

is

as has

compounded,

been

with a priim. By a prifm I here proved by refracting mean a glais or other body of a triangular form, fuch as is reprefented in fig. ill. But before we proceed to the illustration it

is

faid,

of the propofition

we

cefiary to fpend a

few words

have jufl in

now

laid

down,

explaining what

it is

will

be ne-

meant by

the refraction of light ; as the defign of our prefent labour is fome notion of the fubject, we are engaged in, to

to give

fuch

as are

6.

IT

is

not verfed in the mathematics. well

through the air

known,

that

when

falls

a ray of light palling the furface of tranf-

obliquely upon any parent body, fuppofe water or glafs, and enters it, the ray will not pafs on in that body in the fame line it defcribed

through the air, but be turned off from the furface, fo be lefs inclined to it after palling it, than before, Let

as to

ABCD AB

(in fig.

ixi.) reprefent a portion of water, or glals, it, upon which the ray of light E F falls

the furface of

obliquely ; this ray fhall not go right on in the courfe de lineated by the line FG, but be turned off from the furface

AB

into the line

than the line E F

is,

in

FH,

lefs

inclined to the furface

which the ray

is

incident

upon

AB that

furface.

4 7

c

Sir I

V2O

ON

7.

S

the other hand,

luch body into the

t\y

N E W T O N'S

AAC

when it is

after

hice

pafies through, than before.

it

its

emergence

goes out of the furface

the light pailes out of a-

inflected the contrary way, rendred more oblique to the fur-

air,

being it

BOOK III.

C D,

Thus

FH, when up towards

the ray

will be turned

that furface, going out into the air in the line HI. 8. THIS turning of the light out of its way, as it pafles from one tranfparent body into another is called its refraction, Both thefe cafes may be tried by an eafy experiment with a bafon and water. For the firft cafe fet an empty bafon

in the funfliine or near a candle,

making a mark upon

the bottom at the extremity of the fhadow call: by the brim of the bafon , then by pouring water into the bafon will obferve the

fhadow

you and leave the bottom a good diftance from the mark.

to fhrink,

of the bafon enlightned to ABC (in fig. 1 13.) denote the empty bafon, EAD the light fhining over the brim of it, fo that all the part ABD be fhaded. Then a mark being made at D, if water be Let

poured into the bafon (as in fig. 1 14.) to F G, you fhall obierve the light, which before went on to D, now to come

much

fhort of the

mark D,

falling

on the bottom

in the

and leaving the mark D a good way within the which fhews that the ray E A, when it enlightened part point H,

;

enters the water at

I,

goes no longer ftraight forwards, but and made to go nearer the

at that place incurvated,

,

The

other cafe may be tryed by putting an body empty bafon, placed lower than your and then receding from the bafon, till you can but juft

endicular.

any fmall

into

fee

CHAP.

PHILOSOPHY.

i.

body over the brim. with water, you fhall

fee the filled

ABC

(in fig.

1

15-.)

if

the bafon be

the body to he prefently obferve Let farther off from the bafon.

though you go

vifible,

After which,

321

denote the bafon

as before,

D

the

body

the place of your eye, when the body is feen juft it, If it be then over the edge A, while the bafon is empty.

E

in

filled

with water, you will obferve the body

ftill

to be vifible,

farther off Suppofe you fee though you take your eye the body in this cafe juft over the brim A, when your eye is at F, it is plain that the rays of light, which come from

your eye have not come ftraight on, but are bent at A, being turned downwards, and more inclined to the furface of the water, between A and your eye at F,

the

to

body

than they are between

9*

THIS we hope

A and is

the

body D.

fufficient to

make

all

our readers

writers of optics mean, when they the refraction of the light, or fpeak of the rays of fhall therefore now refraded. goon to

what the apprehend, mention

We

light being

prove

the afTertion advanced in the forementioned propofition, in. relation to the different kinds of colours, that the dired: light

of the fun exhibits to our fenfe

which may be done

:

in

the following manner. 10. IF a ftine into

be

it

room be darkened, and through a fmall hole in the

made immediately

to fall

upon

the fun permitted to

window

a glafs prifm

,

iliutter,

the

and

beam of

through fuch a prifm be parted into rays, the forementioned colours. In this man-

light fhall in paffing

which exhibit

all

T

t

ncr

AC

Sir Is A

322 nerif AB(in hole in

from the

116) reprefent the window

fig.

DEF

it ;

fun,

the prifm

which

on the prifm at go on to X, but

NEWTON'S

paiTes

and

Y,

it

ZY

a

BOOK III. fhutter

beam of

;

C

the

coming through the hole, and falls up the prifm were removed would

;

in entring the

furface

BF

light

of the

glafs

it

W

been explained, into the courfe Y the fecond furface of the prifm DF in W, falling upon going out of which into the air it fhall be again farther in Let the light now, after it has paiTed the prifm, be flected. be turned

(hall

received

and

upon

off,

as has

a fheet of paper held at a proper diftance, upon the paper the picture, image, or fpect-

fhall paint

it

rum L M

of an oblong figure, whofe length fhall much ex ; though the figure fball not be oval, the

ceed

its

ends

L and

breadth

But now

M

being O femicircular and the fides

ftraio-ht. 5

figure will be variegated with colours in this From the extremity to fome manner. length, fuppofe to the line n 0, it fhall be of an intenfe red ; from n o to this

M

it fhall be an orange ; from f q to r s it fhall be yel low ; from thence to / u it fhall be green ; from thence to iv X blue ; from thence to / & indigo ; and from thence

pq

to the

II.

end

violet.

THUS

it

appears that the fun's white light by

fage

through the prifm,

ded

into rays,

which

is

fo

changed

as

now

its

pa-

to be divi

exhibit all thefe feveral colours.

The

queftion is, whether the rays while in the fun's beam be fore this refradtion poffefled thefe properties diftinclly ; fo that

fome

beam would without the reft have and another part alone have given an

part of that

given a red colour,

orange,

CHAP.

PHILOSOPHY.

i.

323

is polTiblc to be the cafe, appears- from orange, &c. That this convex if a that hence; glafs be placed between the paper

which may

and the prifm,

out of the prifm into fun's direct rays

fpot

;

and

collect all the

focus

if that

formed by fuch a

rays proceeding

focus, as a burning glafs doe, the

its

upon the

fill

the

upon

glafs

pap

r

;

j<

The white, juft like the fun's direct light. let PQ^ (in fig. 117.) be the convex gials, meet upon the paper in the point fing the rays to or rather (hall that I of N, light fpot appear white, point fay But it is evident without the lealt tincture of any colour. as before,

v.

HGIK

that into this fpot are

when mews that

fore

now

feparate gave

whitenefs

we

gathered

all

may

all

thofe rays,

which be

thole different colours

be

made by mixing

;

which

thofe colours

:

can be proved that the glafs PQ^ does not alter the colour of the rays which pafs Which is done thus* if the paper be made through it. efpecially

if

coniider,

it

:

to

approach the

felves

PQ^, the colours will manifeft themas far as the magnitude of the fpectrum, which the glafs

paper receives, will permit. Suppofe it in the iituation hgik, it then receive the fpectrum /;#, this fpectrum fhall be much fmaller, than if the were removed, glafs

and that

PQ

and therefore the colours cannot be

fo

much

feparated ; but fhall yet the extremity manifestly appear red, and the other extremity / fhall be blue ; and thefe colours as

m

well as the intermediate ones fhall difcover thtmfelves

the farther the paper is removed from the larger the fpectrum is the fame thing

perfectly,

N,

more that

happens, if die paper be removed farther off from P Q^ than N. Sup-

is,

:

T

t

^

pole

NEWTON'S

AC

Sir Is A

324-

BOOK III.

pofe into the pofition 9y*, the fpe&rum A^ painted upon it fhall again difcover its colours, and that more diftinc~tly, the farther the paper is removed, but only in an inverted or der: for as before, when the paper was nearer the con

vex

glafs,

than at

N,

and the under red

blue,

and the under blue II.

:

the upper part oi: the image was now the upper part fhall be red,

;

becaufe the rays crofs at N.

NAY farther that the

whitenefs at the focus

N

3

is

made

union of the colours may be proved without re moving the paper out of the focus, by intercepting with

by the

any opake body pait of the light near the glafs; for if the under part, that is the red, or more properly the red-making rays, as they are ftyled by our author, are intercepted, the the inferior fpot (Kail take a bluifh hue ; and if more of nor cut t hat neither the fo are off, red-making orangerays

and

if you pleafe the yellow-making rays likeupon the fpot then fhall the fpot incline more In like manner if you and more to the remaining colours.

making

rays, wife, mall fall

;

cut off the upper part of the rays, that is the violet coloured or indigo-making rays, the fpot fhall turn reddifh, and become.

more

fo,

the

more of

thofe oppofite colours are intercepted

THIS! think abundantly proves that whitenefs may be produced by a mixture of all the colours of the fpecAt leaft there is but one way of evading the pretrum. fent arguments,

which

is,

by afferting that the rays of

light

prifm have no different properties to ex or the other colour, but are in that refpecl per

after pailing the

hibit this

.

fectly

CHAP.

PHILOSOPHY.

i.

325

which pafs to the un fedly homogcneal, To that the rays der and red part of the image do not differ in any pro perties violet

whatever from thofe, which go to the upper and but that the colours of the fpedrum are part of it ;

of the rays, made produced only by fbme new modifications different termi the the paper by upon if indeed this affertion can nations of light and fhadow

at their incidence

:

be allowed any place, after what has been faid ; for it fecms to be fufficiently obviated by the latter part of the pre

ceding experiment, that by intercepting the inferior part of the light, which comes from the prifm, the white fpot

and by flopping the upper part the

fhall receive a bluiih cad:,

fpot

fliall

turn red, and

in both cafes recover

its

colour,

when

the intercepted light is permitted to pafs again ; though in all thefe trials there is the like termination of light and fliadow. However our author has contrived fome experi

ments expreily to fhew the abfurdity of this fuppofition ; all which he has explained and enlarged upon in fb diftincl and expreffive a manner, that it would be wholly unneceffary to repeat tion that of them, before us.

If you

them in this place a which may be tried .

(

draw upon the paper

the fpot N,

the

and then

the paper be

rsvt

if

A* ftill

HG

I

only

men

the experiment

K, and through

w A*

ftraight line

the line 7^

I fhall

in

much

parallel to the horizon, inclined into the (ituation

remaining

parallel to the hori/on,

the fpot N fhall lofe its whitenefs and receive a blue tin cture j but if it be inclined as much the the contrary way,

lame fpot

(hall

exchange

its

Opt. B.

I.

white colour for a reddifh dye. part i. prop

i.

Ml

3

i6

Sir

NE

ISAAC

\v

To

BOOK III.

N'S

All which can never be accounted for by any difference in

the termination of the light and fhadow, which here is "one at all ; but are eafily explained by fuppofing the upper part of the to give th

whenever they enter the eye, difpofed of the dark colours blue, indigo and

ays,

ifation

violet; and that the under part is fitted to produce the for when the bright colours yellow, orange and red paper that the is in the fituation rstu^ it is plain upper part of :

the light falls more directly upon it, than the under part, and therefore thofe rays will be mod: plentifully reflected from it ; and by their abounding in the reflected light will it to incline to their colour. Juft fo when the paper inclined the contrary way, it will receive the inferior rays moft directly, and therefore ting the light it reflects with their

caufe is

colour.

14. IT rays of

is

now

light to

to be proved that thefe diipofi tions of the produce fomc one colour and fome another,

which manifeft themfelves wrought by any action

after their

ot

originally inherent in thofe rays

affords each fpecies

being refracted, are not upon them, but are

the prifm

an occafion

;

of

and

that the prifm only

fhewing

them one from another,

by feparating while they were blended together in the But that this fun's light, lay conceaFd. lity

ved, if

it

the rays,

its

direct is

diftinct

which

fo,

qua

before,

beam of

the

will be

pro can be fhewn that no prifm has any power upon which after their paflage through one prifm are

rendered uncompounded and contain in them but one co lour, either to divide that colour into feveral, as the fun's light

CHAP. light

is

PHILOSOPHY.

i.

divided,

much

or fb

as to

change

into-

it

any other

This will be proved by the following experiment

colour.

The fame

thing remaining, as in the

firft

experiment,

''.

let

NO

another prifm (in fig. 118.) be placed either immedi after the firft, in a or at fome diftance ately, perpendicular pofture, firft

the rays ifluing from the prifm could divide the light into coloured rays, as the firft has done, it

fo that

fideways.

it

fhall

Now

refract

if this

upon it would divide the fpectrum breadthwife into colours, as before it was divided lengthwife but no fuch thing is obferved. If LM were the fpectrum, which the firft prifm D E F would paint upon the paper H G I K P Q. lying in falling

;

;

an oblique pofture fliall be the fpectrum projected by the fecond , and fliall be divided lengthwife into colours correfponding to the colours of the fpectrum fioned like them by the refraction of the its

breadth fhall receive no fuch divifion

each colour

fhall

Ij-.

THE

fame

experiment.

the fpectrum

LM

LM, which is

yet

prifm,

but

as

much

proves die whole aiTertion.

much

Our author

occa-

on the contrarv j

be uniform from fide to fide,

as in the fpectrum

ther

:

'

LM, and firft

confirmed by ano

farther

teaches that the colours of

the firft experiment arc yet compound fo not much as in the fun's direct ed, though He light. fhews therefore how, by placing the prifm at a diftance fiom the hole, and the by the ufe of a convex glcifs, to in

feparate

colours of the fpectrum, and to any degree of exactnefs b .

Newt. Opt. B.

i.

part

i.

make them uncampoundcd And he fhews when thi>

cxperim. f.

b

Ilkl p;

3 28

Sir I

s

AAc

N E w T o N'S

BOOK

III.

done fufficiently, if you make a fmall hole in the paper whereon the fpectrum is received, through which any one iort of rays may pafs, and then let that coloured ray fall io upon a as to be refracted by it, it fhall in no cafe whatever priiin

is

,

change its colour but fhall always a firft, however it be refracted ;

retain

it

perfectly as at

.

NOR

1 6.

yet will thefe colours after this full feparation

of them fuffer any change by reflection from bodies of dif

on the other hand they make all bodies pla ced in thefe colours appear of the colour which falls upon ferent colours

them light is

b

;

for minium in red light will appear as in open day but in yellow light will appear yellow ; and which

:

;

more extraordinary,

in green light will appear green, in blue,

and

in the violet-purple coloured light will appear of a purple colour; in like manner verdigreafe, or blue bife, will on the appearance of that colour, in which it is :

blue

;

placed

put

fo that neither bife placed in the red light fhall be able to give that light the leaft blue tincture, or any other diffe

rent

from red

;

nor fhall

minium

exhibit the leaft appearance lour diftinct from that it is placed

light

in the indigo or violet

of red, or any other co

The

in.

only difference

is, that each of thefe bodies appears moft luminous and bright in the colour, which correfponds with that it exhibits in

the day light, and dimmeft in the colours moft remote from that is, though minium and bife placed in blue light ;

that

ihall

blue,

both appear blue, yet the

and the minium Newt. Opt.

3

B.

of a i.

bife fhall

appear of a bright but

dusky and obfcure blue:

part 2. expcr.

b j-.

Ibidexpcr. 6,

if

CHAP.

PHILOSOPHY.

i.

329

minium and bife be compared together in red light, the minium fliall afford a brisk red, die bife a duller colour, if

though of the fame

AND

17.

this

fpecies.

not only proves the immutability of

all

and uncompounded colours ; but likewife un the whole myftery, why bodies appear in open day

thefe fimple folds light

than

of fuch different colours, it confifting in nothing more this, that whereas the white light of the day is com-

pofed of all forts of colours, fome bodies reflecl: the rays of one fort in greater abundance than the rays of any other a .

Though all

it

appears by the forecited experiment, that almofl fome portion of the rays of every

thefe bodies reflecl:

and give the fenfe of particular colours only by the predominancy of fome forts of rays above the reft. And what

colour,

has before been explained of composing white all the colours of the fpedtrum together fhews

nothing more

is

required to

make

by mingling clearly,

that

bodies look white, than

a power to reflecl indifferently rays of every colour. But more fully appear by the following method: if

this will

near the coloured fpeclrum in our firft experiment a piece of white paper be fo held, as to be illuminated equally by all the parts of that fpedtrum, it fhall appear white ; where as if

it

other,

feem

be held nearer to the red end of the image, than to the it fhall turn reddifh; if nearer the blue end, it fliall

bluifh

b .

f

Newton Opt,

B.

I.

fc

prop. 10.

U

u

Ibid cxp. 9.

1 8,

OUR

Sir

330

OUR

ISAAC NEWTON'S

BooxIIL

and circumfpect author farther by mixing the powders which paint to produce ers ufe of feveral colours, in order if polllble a But in this he a white powder by fuch a compofition 1 8.

examined

indefatigable

his theory

.

found fome

difficulties

Each

for the following reafons.

of thefc coloured powders reflects but part of the light, which is caft upon them; the red powders reflecting little green or blue, and the blue powders reflecting very little red or nor the green powders reflecting near fo much of yellow,, the red or indigo and purple, as of the other colours : and

when any of thefe

befides, as

our author

calls

are

examined

in

homogeneal

the colours of the prifm,

when

light,

well fe-

though each appears more bright and luminous in day-light colour,, than in any other ; yet white bo dies, fuppofe white paper for inftance, in thofe very colours parated,

its

own

exceed thefe coloured bodies themfelves in brightnefs ; fo that white bodies reflect not only more of the whole light than coloured bodies do in the day-light, but even more

of that very colour which they

which considerations make

it

reflect moil All copioufly. manifert that a mixture of thefe

will not reflect fo great a quantity of light, as a white body of the fame flze ; and therefore will compofe fuch a colour as

would are

refult

from a mixture of white and black,

fuch as

grey and dun colours, rather than a Itrong white. fuch a colour he compounded of certain ingredients

all

Now

which he

particularly fets

down,

in fo

much

that

compohtion was ftrongly illuminated by the beams,

it

when

fun's

the

direct

would appear much whiter than even white paNewt. Opt.

B,

T.

part

i,

cxp

15-.

per,

CHAP.

331

Nay he found by

considerably fhaded.

if

per,

PHILOSOPHY.

i.

trials

how

to proportion the degree of illumination of the mixture fo that to a fpettator at a proper difbnce it and

paper,

could not well be determined which was the more perfect colour ; as he experienced not only by himfelf, but by the concurrent opinion of a triend, who chanced to vifit him I muit not here owhile he was trying this experiment. the of fuch a mix of method whitenefs mit another trying

propofed in one of our author's

ture, a

ject

:

which

the fun

letters

on

this

fub-

by a beam of then to receive the

to enlighten the compoiition

is

let into

a darkened

room

and

,

upon a piece of white paper, obferthe paper appears white by that reflection ; whether ving for if it does, it gives proof of the compolition's being white ;

reflected light

becaufe

when

coloured body, is

the

trial

from

it

the paper receives the reflection from any it looks of that colour. Agreeable to this

he made upon water impregnated with foap,

and agitated into a froth fhort time exhibited

b :

for

upon the

when

little

this froth after

bubbles,

fome

which compo-

a great variety of colours, though thefe colours to a at a fmall diltance difcover'd themfelves fpectator ;

fed

it,

diltinctly

when

the eye was fo far removed, that each little bub ble could no longer be diftinguimecl, the whole froth

yet

by

the mixture of

all

thefe colours

appeared intenfly white,

19. OUR author having fully fatisfied himfelf by thefe and many other experiments, what the refult is of mixing f Phflof.

Tran&ft. N. 88, p. 7099.

Uu

>>

i

Opt. B.

I.

par. 2. exp. 14.

together

ISAAC NEWTON'S

Sir

332

BOOK III.

colours ; he proceeds in the next all die prifmatic whether this appearance of whitenefs be place to examine, raifed by the rays of thefe different kinds acting fo, when

together

as to caufe each of them to they meet, upon one another, fcnfe of whitenefs upon the optic nerve ; or whe the imprefs ther each ray does not make upon the organ of fight the

fame impreiTion,

as

when

feparate

and alone

;

fo that the

not excited by the impreiTion from any one part of the rays, but refults from the mixture of all thole And that the latter fentiment is the different fenfations. idea of whitenefs

true one,

is

he evinces by undeniable experiments.

a ao. IN particular the foregoing experiment , wherein furnifhes of convex was in that this the ufed, glafs proofs :

when

N

brought into the fituation the colours, that at difappeared, begin to the paper

is

N

which (hews

that

colorific qualities,

ed.

when dined

y *, beyond emerge again ; 6

by mingling at N they did not lofe their though for fome reafon they lay conceal

This farther appears by that part of the experiment, the paper, while in the focus, was directed to be en-

ways ; for when the paper was in fiich a muft of necefTity reflect the rays, which arrival at the point N would have given a blue,

different

fituation,

that

before their

it

colour, thofe rays in this very point itfelf by abounding in, the reflected light tinged it with the fame colour ; fo when the

moft eopioufly the

paper

reflects

come

to the point

N

rays,

exhibit redaefs,

which before they thofe fame rays tin-

e

I

Ibid.exp. 10.

durs

PHILOSOPHY.

CHAP.I.

333

the light reflected by the paper from that very point

own

with their

THERE

11.

proper colour. is

a certain condition relating to fight, which

an opportunity of examining this ftill more fully: that the impreilions of light remain fome fliort this,

affords it is

ipace

upon

in a circle,

the eye; as when a burning coal is whirl'd about if the motion be very quick, the eye fhall not

be able to diftinguim the coal, but fliall fee an entire circle The reafon of which appearance is, that the imfire.

of

made by the coal upon the eye in any one fituation worn out, before the coal returns again to the fame

preflion is

not

place,

and renews the

hint to try, fucceflively

fhould be

feniation.

This gives our author the

whether thefe colours might not be tranfmitted to the eye fo quick, that no one of the colours

diftincl:ly

perceived, but the mixture of the fen-

mould produce a uniform whitenefs ; when the rays could not aft upon each other, becaufe they never fliould meet, but come to the eye one after another. And this thought fations

he executed by the following expedient

a .

He made

an in-

ftrument in friape like a comb, which he applied near the convex glafs, fo that by moving it up and down flowly the teeth of it

might intercept fometimes one and fometimes

another colour; and accordingly the light reflected '.from the paper, placed at N, mould change colour continually. But

now when the comb-like inftrument was moved very quick.,, the eye loft all preception of the diftindl: colours, which came to it from time to time, a perfecl whiteneli refulting from die -Opt. pag.

Hi.

mixture

mixture of

Now

NEWTON'S

AC

Sir Is A

BOOK III.

thofe diftinct impreflions in the fenforium. can be no fufpicion of the feveral

all

in tins cafe there

coloured rays acting upon one another, and making any the eye, feeing change in each other's manner of affecting

much

fo they do not

OUR

11.

as

meet together

author farther teaches us

there.

how

to view the fpec-

experiment with another prifm, fo that it {hall appear to the eye under the a And in this fhape of a round fpot and perfectly white

trum of colours produced

in the firft

.

cafe if the

comb be

ufed to intercept alternately fome of

the colours, which compofe the fpectrum, the round fpot {hall change its colour according to the colours intercepted ; if the comb be moved too fwiftly for thofe changes to be distinctly perceived, the fpot mall feem always white, as

but

b

before

.

BESIDES

ag. verfal

this whiteneis,

compofition of

all forts

ticularly explains the effects

tures;

which

refults

of colours,

of other

lefs

from an uni-

our author par

compounded mix

fome of which compound other colours

like

fome

of the fimple ones, but others produce colours different from For inftance, a mixture of red and yellow any of them.

compound

a colour like in appearance to the orange, which lies between them ; as a competition of yel

in the fpectrum

low and blue But red and like to

is

made

violet

make a green. compounded make purples un

ufe of in all dyes to

purple

any of the prifmatic colours, and thefe joined with Opt. B. I part

z.

exp.

u.

*>

Ibid prop. 4, 6.

yellow

CHAP.

PHILOSOPHY.

r.

335

yellow or blue make yet new colours. Befides one rule to be obferved, that

colour which nerates

into

is

here

when many different colours are mixed,

the

from the mixture grows languid and dege So when yellow green and blue whitenefs. arifes

mixed together, the compound will be green; but if this you add red and purple, the colour fliall firftgrow dull

are to

and at length by adding more of thefe colours lefs vivid, mail turn to whitenefs, or fome other colour

and

l

it

.

14.

ONLY

here

is

one thing remarkable of thofe

com

pounded colours, which

are like in appearance to the fimple ones ; that the fimple ones when viewed through a prifm fliall retain their colour, but the compounded colours fecn flill

through fuch a glafs mall be parted into the fimple ones of

which they are the aggregate.

And

for this reafon

any body

illuminated by the fimple light fhall appear through a prifm and have its minuteft parts obfervable, as may cadiftinctly, fily

be tried with

very fmall parts

or other fuch

flies, ;

little

bodies,

which have

but the lame viewed in this manner

when

enlighten'd with compounded colours fliall appear confuied, their fmalleft the parts not being difKnguifhable. thefe as like wife how prifm feparates compounded colours,

How

it

divides the light of the fun into

been explained; but

ij".

IN

the

fuffice to give

is

its

.olours,

referved for our in!

mean time what

has been faid,

a tafte of our author's a

A

Opt. pag. f\.

way of

has not yet chapter. I hope, will arguing, and

S3 6 in

ISAAC NEWTON'S

Sir

fome meafure to

this

illuflrate

BOOK III.

the propofition laid

down

in

chapter.

1 6. THERE are methods of feparating the heterogene ous rays of the fun's light by reflection, which perfectly confirm this reafoning. One of which confpire with and ways may be this. Let AB (in fig. 119) reprefent the win

dow rays

room; C

fhutter of a darkened

D E F, G H I two prifms

;

fides

EF and GI

parallel

by

;

be contiguous, and the

means the

this

a hole to let in the fun's

fo applied together,

light will pafs

out any feparation into colours ceived by a third prifm

:

IKL,

it

but

if

fhall

fides

that the

DF,

GH

through them with it be afterwards re be divided fo as to

form upon any white body P Q. the ufual colours violet at m^ blue at n green at <?, yellow at r, and red at s. But .becaufe it never happens that the two adjacent furfaces EF and G I perfectly touch, part only of the light incident up ,

y

on

EF

and part fhall be tranfmitted, the reflected part be received by a fourth and it a white A3/\, palling through prifm paint upon body Z r the colours of the prifm, red at /, yellow at //, the furface

reflected.

Let

flball

be

now

green If the at/. prifms DEF, GHI be flowly turned about while they remain contiguous, the

at

W)

colours

blue at

,r,

violet

the body PQ^ fhall not fenfibly change their fuch time as the rays become pretty oblique to the furface EF; but then the light incident upon the

upon

fi tuition,

furface

of

all

upon

EF

till

fhall

begin to be wholly reflected.

Arid

firft

the violet light fhall be wholly reflected, and there will

difappear

at

m

,

appearing

inftead

thereof at

CHAP. at

PHILOSOPHY.

i.

and increafmg the

/,

violet

light

falling

337 there

,

the

If the prifms D l< , G H I other colours remaining as before. be turned a little farther about, that the incident rays be come yet more inclined to the furfacc E F, the blue fhalj ;

l

be totally reflected, and fhall dilappear in ;/, but appear at And the fame A' by making the colour there more intcnfc. till all the colours are be continued, fucceffively remov may

But in any cafe, fuppofe and the^blue have forfaken the furface P Q^ and the furface zr, the green, yellow, and red only appear upon ed from the furface PQ^to zr.

when

the violet

remaining upon the furface PQ.; if the light be received upon a paper held any where in its whole paflage between the coming out of the prifms D E F, G I H and its inci light's

dence upon the prifm IKL, it fhall appear of the colour compounded of all the colours feen upon PQ^; and the re flected ray, received upon a piece of white paper held any where between the prifms DBF and A 02, fhall exhibit the co lour compounded of thofe the furface P Q is deprived of mixed with the fun's light whereas before any of the light was reflect ed from the furface E F, the rays between die prifms G H I and :

IKL would appear white ; as will like wife the reflected ray both before and after the total reflection , provided the differ ence of refraction by the furfaces

D F and D E

I call here the fun's light white, as I is

more exact to

afcribe to

it

have

all

be inconfiderable.

along done

;

but

it

fomething of a yellowifh tincture,

occafloned by the brighter colours abounding in it ; which the colours of the reflect is neceflary in examining

caution

ed beam,

when

all

the violet and blue are in

X

x

it:

for this

yellowifh

Sir

338

BOOK III.

turn of the fun's light caufes the blue not to be it, as it fhould be, were the light perfe&-

yellowifli

fo vifible in

quite ly

N E w T o N'S

ISAAC

white

;

but makes the

beam of

light incline

rather to

wards a pale white.

CHAP. Of

the properties of their

AFTER

II.

BODIES,

COLOURS

having fhewn in the

upon which

depend.

laft

chapter ,

that the

difference between the colours of bodies viewed in ois only this, that fome bodies are difpofed to of one colour in the greateft plenty, and other

pen day-light reflect rays

bodies rays of fome other colour; order now requires us to examine more particularly into the property of bodies?

But this our author (hews gives them this difference. to be nothing more, than the different magnitude of the

which

particles,

which compofe each body this I queftion not no fmali paradox. And indeed this whole chap:

will appear

er

any affertions, but what will be although the arguments for them are Co ftrong

will contain fcarce

mofi: incredible,

and convincing,

that they force our affent.

In the former

chapter have been explained properties of light, not in the leaft thought of before our author's difcoyery of them j

yet are they not difficult to admit, as foon as experiments arc known to give proof of their reality ; buc fome of the proto be ftated here will, I fear,, be accounted almoft pofitions which belief, notwithftanding that the arguments,

pad

by

th

CHAP.

PHILOSOPHY.

2.

339

For it is proved by they are eftablifhed are unanfwerable. our author, that bodies are rendered tranfparcnt by the minute-

and become opakeby having them

nefs of their pores,

large

;

and more, that the mod tranfparent body by being reduc ed to a great thinnefs will become lefs pervious to the light. a.

BUT

whereas

fo yet remains

it

among

had been the received opinion, and all

who

have not ftudied

that light is reflected from bodies fophy, their folid parts, rebounding from againft ball or other elaftic fubftance would do,

this

philo-

its

by impinging them, as a tennis

when

{truck a-

hard and refifting furface ; it will be proper to gainft any with declaring our author's fentiment concerning this, begin

who mews by many arguments caufed by any fuch fet

the

down,

means

a

that reflection cannot be

fome few of

:

referring the reader to

his

proofs

I fhall

our author himfelf for

reft.

.

IT

is

well

that

known,

when

light falls

upon any

part of it is reflected and for is which it tranfmitted ; ready to account, by fay part the of enters the that light pores of the glafs, and ing part

tranfparent body,

part impinges

for inftance, glafs

upon

its

folid

parts.

But when the tranfmit

ted light arrives at the farther furface of the glafs, in paffing out of glafs into air there is as ftrong a reflection caufed,

Now

or rather fomething ftronger. ed , how the light fhould find as air to ftrike againft as in

the

Opt. Book

it

glafs, II.

X

is

not to be conceiv

many

folid

parts in the

or even a greater

num-

prop. 8.

x x

ber

Sir I

34

ber of them.

s

A Ac

And

to

N E w T o N'S

augment the

BOOK if

difficulty,

III.

water

be placed behind the glafs, the reflection becomes much weaker. Can we therefore fay, that water has fewer folid parts

we

for the

light to ftrike againft,

than the

air

?

And

if

what reafon can be given for the reflection's be ing ftronger, when the air by the air-pump is removed from behind the glafs, than when the air receives the rays of

fhould,

light.

Beftdes the light

may

be fo inclined to the hin

der furface of the glafs, that it fhall wholly be reflected* which happens when the angle which the ray makes with the Rirface does not exceed about 4.9 ~ degrees ; but if the inclination be a very will be tranfmitted

;

little

increafed, great part of the li^ht light in one cafe fhould

and how the

meet with nothing but the

folid and by parts of the air, inclination find in pores great plenty, It cannot be faid, that the wholly inconceivable. light reflected by ftriking againft the folid parts of the furface

fo fmall a is

is

change of

its

becaufe without making any change in that by placing water contiguous to it inftead of air, great part of that light fhall be tranfmitted, which could find no pafiage through the air. Moreover in the laft ex

of the

glafs

;

furface, only

in the preceding chapter, when by turn the blue light became the DEF, GHI, ing prifms wholly reflected, while the reft was moftly tranfrnitted, no pofCble reafon can be afligned, why the fliould

periment recited

blue-making rays

meet with nothing but the folid parts of the air between tlie prifms, and the reft of the light in the very fame obli in abundance. quity find pores es

Nay

touch each other, no reflection

farther, at all

is

when two glafTmade though ;

it

CHAP. it

PHILOSOPHY.

2.

341

how the rays fhould avoid when contiguous to other glafs, any

does not in the leaft appear,

the folid parts of glafs,

more than when contiguous

to

air.

Hut in the

laft

place

not to be comprehended, how fuppofition upon the moft poliftied fubftances could reflect the light n that it

this

regular

is

manner we

ing glafs

is

find they do; for when a polifhed look covered over with quick filver, we cannot fuppofe

the pardcles of light fo much larger than thole of the quickfilver, that they fhould not be fcattered as much in reflection) as a parcel

of marbles thrown

down upon

a

rugged pavement,

The only caufe of fo uniform and regular a reflection muft be fome more fecret caufe, uniformly ipread over die whole furface of the glafs.

B u T now,

4.

ft nee

the reflection of light from bodies

does not depend upon its impinging againft their folid parts, And firft it isfome other reafon muft be fought for. that the leaft parts of almoft all bodies are doubt tranfpapaft a befides that rent, even the microfcope fhewing as much this

Take

method.

it any thin plate may be experienced by of the opakeft body, and apply it to a fmall hole defigned for the admiiTion of light into a darkened room ; however that may feem in open day-light., it fhall un

opake

body

der thefe circumftances Efficiently difcover

provided only the

do not

eafily

fuperficies

;

its

tianfparency,

White metals indeed

fhew themfelves tranfparent

almoft reflecting firft

body be very thin.

in thefe trials,

tru

the light incident upon them at their the caufe of which will appear in wl. all

1

Opt. Book

II. par. 3. prop, i*

lows

Sir I S'A A c

N E w T o N'S

BOOK IIL

But yet thefe fubitances, when reduced into

parts

of extraordinary minutenefs by being difTolved in aqua

fortis

follows

'.

or the like corroding liquors

5-.

SINCE

do

alfo

become

traniparent.

therefore the light finds free paflage through let us confider the largenefs of

the leaft parts of bodies, their pores,

and we

fhall find, that

whenever a ray of

light

through any particle of a body, and is come to its farther furface, if it finds there another particle con will without interruption pafs into that particle; tiguous, it has pafled

as light will pafs through one piece of glafs into ano ther piece in contact with it without any impediment, or any part being reflected : but as the light in paiTing out of or any other tranfparent body, (hall part of it be re

juft

glafs,

flected back,

other tranfparent body paffes out of ; the fame

if it enter into air or

of a different denfity from that

it

thing will happen in the light's paflage through any parti. cle of a body, whenever at its exit out of that particle it

meets no other particle contiguous, but muft enter into a in this cafe it fhall not all pafs through, but pore, for part Thus will the light, every time it of it be reflected back. enters a pore, be in part reflected , fo that nothing more leems necelTary to opacity, than that the particles, which compofe any body, touch but in very few places, and that the of it are numerous and large, fo that the light may pores in part

be reflected from

it,

and the other

part,

which en

too deep to be returned out of the body, by numerous 3 which in all probabireflections may be itifled and loft ; ters

b

17.

Opt. Book

II.

p*r. j. prop. 4.

lity

CHAP.

PHILOSOPHY.

2.

as often as

lity happens, of the body, J

all

*

ed back, but

THIS

6.

fity

oyl

ftopt,

and deprived of any

farther

motion

'.

up the pores with any fubftance of near the lame denwith their parts. As when paper is wet with water

when

;

varnifhed All

;

linnen cloth

either

is

or the oculus

mundi

dipt in water, oyled, or ft

one fteeped

which experiments confirm both the is

light

bodies

;

alfo the fecond, it

that

its

in

water

firft aflertion,

not reflected by ftriking upon the

and

by the reflections it

the fcht which does fo not beinir O O rcflcdt-

notion of opacity is greatly confirmed by the that opake bodies become cr;-n> parent by fill

oblervation,

ing

343

impinges againft the (olid part

it

folid is

pailage

undergoes in the pores

;

b .

thai

parts

of

obftrucl-

iincc

\\\

find

abundance through bo folid parts is increafed, on

in thefe trials to pafs in greater

dies,

when

the

number of

their

by taking away in great meafure thofe reflections ; which the pores with a fubftance of near the fame dcnfifilling

ly

ty with the parts

of the body will do.

Befides as filling

the pores of a dark body makes it tranfparent ; fo on the other hand evacuating the pores of a body transparent, or As feparating the parts of fuch a body, renders it opake.

or wet paper by being dried, glafs by being reduced to powder or the furface made rough; and it is well known tl> falts

cracks in them by their opacity, Juft water itfeU becomes impervious to the light by Leii formed into many fmall bubbles, whether in froth, or by glafs veffels difcover

fo

being mixed and agitated with any quantity Opt. Book Il.pag-

b

!<

4

Ibid,

of a liquor

png -

Sir Is A

344with which

it

NEWTON'S

AC

will not incorporate,

BOOK

III.

fuch as oyl of turpentine,

or oyl olive.

A CERTAIN electrical experiment made by Mr. HAUKS-

7.

BEE

not perhaps be ufelefs to clear up the prefent fpe-

may

by fhewing that fomething more is necefTary bemere porofity for tranfmitting freely other fine fub-

culation, fides

The experiment is this ; that a glafs cane rubbed put forth its electric quality would agitate leaf brafs inclofed under a glafs vefTel, though not at fo great a diftffonces. till

it

no body had intervened yet the fame cane its influence on the leaf brafs by the inter1 of a of the finch whofe muflin, pofition piece pores are immenfely larger and more patent than thofe of glafs. jince,

as if

would

lofe all

8.

THUS!

have endeavoured to fmooth

to the unfolding

as I could,

now

for I fhall

pear of

;

proceed to (hew the reafon

this

My

different colours,

is

when

which children

render

hey br

divert themfelves in

will

be

blowing bubbles of water

And

as all natural bodies

pn

that thele

and thinner

igc fucceffively their colours

principle,

9.

from

till

t!

theirs.

OUR it

;

bodies ap

no doubt

tenacious by the folurion of foap. bubbles, as they gradually grow thinner

,ider

why

much

nature

I

made i

as

inform him that the knowledge deduced from that ludicrous experiment, with

fufficiently (urprized,

of

my way,

yet greater fecrets in

author after preparing water with foap, fo as to very tenacious, blew it up into a bubble, and plac3

in]

CHAP.

PHILOSOPHY.

2.

345

that it might not be irregularly agitated it under a glafs, as the water by fubiiding changed the ed obferv the air, by thicknefs or the bubble, making it gradually Icfs and lefs till <1 colours at the the bubble broke ; there fuccellively appe

ing

m

which fpread themfelvcs into rings furroundtop of the bubble, the top and defcending more and more, till they vanished ing

at the

bottom

in the

a

fame order

The colours emerged in this order:

in whicli they appeared red, then blue ; to which .

firft

fucceeded red a fecond time, and blue immediately follow ed ; after that red a third time, fucceeded by blue ; to which followed a fourth red, but fucceeded by green

more numerous order

;

after this

a

then yellow, and at lad purple ; then

ot colours,

next green, and after that blue,

firft

red,

violet followed each other again red, yellow, green, blue, in order ; and in the laft place red, yellow, white, blue ; to which fucceeded a dark fpot, which reflected fcarcc

any though our author found it did make fome very obfcure reflection, for the image of the fun or a candle might be faintly difcerned upon it ; and this laft fpot fpread itfelf light,

more and more, till the bubble at laft broke. Thefe co lours were not fimple and uncompounded colours, like thofe which are exhibited by the prifm, when due care is taken but were made by a various mixture of feparate them ;

to

thofe

fimple colours, as will be fliewn in the next chapter: thefe colours, to which I have given the name of

whence blue, lov

green, or red, were not

The

blue,

all alike,

but differed

which appeared next the dark

a* fol-

fpot,

pure colour, but very faint, refembling the sky-colour *

Ibid.

was a ;

the

Obf. 17. &c.

V

y

white

Sir I white next to IT

much

ed

this

s

AAc

N E w T o N'S

a very ftrong

it

and intcnfe white,

which the bubble

tlian the white,

was

at firft pretty

III.

bright-

reflected, before

The

yellow which preced but foon grew dilute; and good,

the colours appeared.

oi

BOOK

the red which went before the yellow at

firft

gave a

tin

cture of fcarlet inclining to violet, but foon changed into the violet of the next feries was deep a brighter colour ;

or.no rednefs in it; the blue a brisk colour, but came much fhort of the blue in the next order ; the green with

little

was but dilute and pale the yellow and red were very and the beft of all the full, bright yellows which appeared ;

of the colours: in the preceding orders the pur but the blue, as was juft nowfaid, the brightwasreddifh, ple eft of all ; the green pretty lively better than in the order

among any

which appeared before

it,

though that was a good willow

the yellow but fmall in quantity, though bright ; the red of this order not very pure : thofe which appeared be

green

;

more

fore yet

obfcure, being very dilute and dirty

likewife the three

Now

IO.

it

is

firft

;

as

were

blues.

evident, that thefe colours arofe at the

as it grew by degrees thinner and thin rop of the bubble, ner: but what the exprefs thicknefs of the bubble was, where

thefe colours appeared upon it, thefe experiments; but was

:h of

mined by aris,

uch

viz. is

by taking the object

glafs

could not be de-

found by another

of a long telcfcope,

and placing it upon a one point, and then water be

in a fmall degree convex,

Eat glafs, fb as to touch it in ing put between them, the fame colours appeared as in the bubble.

CHAP.

PHILOSOPHY.

2.

347

in the form of circles or rinirs O furroundino: O the where the glafTes touched, which appeared black for point want of any reflection from it, like the top of the bubble next to this fpot lay a blue circle, and when thinneft'

bubble,

1

:

next without that a white one; and

l<>

on

in the

lame or

der as before, reckoning from the dark fpot. And hencefor ward I mall (peak of each colour, as being of the lirft, '

cond, or any following order, as

it

is

the

firft,

fecond, or a-

ny following one, counting from the black fpot

in the

ecu

of thefe rings ; which is contrary to the order in which muft have mentioned them, if I fhould have reputed

ter I

them the after

firfl,

fecond, or third, &c.

in order,

as

they ar

one another upon the top of the bubble.

BUT now by measuring the diameters of each of theft and rings, knowing the convexity of the teleicope glafs, the thicknefs of the water at each of thofe rings may be determi il.

ned with great exactnefs

for inftance the thicknefs

:

of

it,

where the white light of the firft order is reflected, is about 3 | fuch parts, of which an inch contains ioooooo b '

And it

meafure gives the thicknefs of the bubble, where appeared of this white colour, as well as of the water this

between the glades ; furrounds the water

though the tranfparent body which

two cafes be very different our author found, that the condition of the ambient body would not alter thefpecies of the colour at all, though in thefe

:

for

it

might

glafs,

its

ftrcngth and bright ncfs; lor pieces of Mufco, fo thin as to appear coloured by

which were

'

being

IbiJ. Obf.

10.

Y

b

y

II

-L

106.

wet

Sir I

34.8

s

N E w T o N'S

AAc

BOOK III.

wet with water, would have their colours faded and made Ids bright thereby but he could not obferve their fpecies ;

be changed. So that the thicknefs of any tranfparcnt body determines its colour, whatever body the light

at all to

pa lies through in

ii.

BUT

it

:

to

it

\

was found that

would not under lours

coming

different tranfparent bodies the fame thicknefles exhibit the fame co

forementioned

for if the

glafTes

were

laid

upon each

other without any water between their furfaces, the air itfelf would afford the fame colours as the water, but more

expanded, infomuch that each ring had a larger diameter, So that the thicknefs of the all in the fame proportion.

and

proper to each colour was in the fame proportion larger, than the thicknefs of the water appropriated to the fame b

air

.

1 3. I F

we examine with which

be

care all the circumftances of thefe

enumerated

the next chap be furprized, that our author takes them to c bear a great analogy to the colours of natural bodies For the regularity of thofe various and fbange appearances colours,

ter,

will

in

we fhall not

.

relating

which makes the moft myfterious part of the acti on between light and bodies, as the next chapter will fhew,

to them,

is

to convince us that the principle,

fufficient

from which

they flow, is of the greateft importance in the frame of nature ; and therefore without queftion is defigned for no lefs a purpofe than to give bodies their various colours, to

which end L'fcr.

it

feems very

ii.

l

fitly

fuited.

Obfcrv. /. compared with Obitiv

For

if

any fuch

tranf-

IbiJ. prop. j.

parent

PHILOSOPHY.

CHAP.

2.

parent

fubftancc

one

any

colour

broken

or

into

of

thicknef;

the

be

fliould

fragments

cut

to

proper

/lender

into

not

does

it

,

349 produce threads

,

but

appear

fame colour- and a heap ol Inch So that tl frame a body of that colour. without difpute the caufe why bodies are of this or the

thefe fliould

retain the

fragments fliould is

other colour, that the particles of

which they

Which

are

compe

confirmed by the analogy between die colours of thin plates, and the co For example, thele plates do not lours of many bodies. ted are of different

ii/

look of the fame colour feen direct

;

is

farther

when viewed

tor if the rings

obliquely, as when a com

and colours between

glafs are viewed firft in a direct manner, and then at different degrees of obliquity, the rings will be obferved to di

and plane late

themfelves

which

more and more

as the

obliquity

fliews that the tranfparent fubftance

is

incrcafed

between the

-1

;

glafies

does not exhibit the fame colour at the fame thicknds in all

of the eye fo the colours in the juft very (aim a of tail as the tail peacock's part change, changes pofturc of the fight. in Alfo the colours of filks, cloths, refpecl fituations

:

which w atcr or oyl can intimately penetrate, become faint and dull by the bodies being wet with fuch fluids, and recover their brightness again when and other fubftances,

dry; juft as

grew

faint

the colours

it

was before

7

laid that

and dim by wetting.

which

painters ufe will

To 1>.

of Mufcovy may be added,

plates this

a little

gl. tl,

beii

changed by ground very elaborately, without queftion by the diminuti* ot their All which particulars, and parts. many more th "

Obfcrv i

Sir I

s

NE

A Ac

\v

To

BOOK

N'S

III.

might be extracted from our author, give abundant proof of the I mall prefent point. only fubjoin one more: thefe tranfpareut plates tranfmit through them all the light they do not re-

when looked through

fled; fo that

which

they exhibit thofe colours,

from the depriving white light of the colour re This may commodioufly be tryed by the glades fo

rcfult

flected.

often mentioned

which

;

if

looked through exhibit coloured

order ; for the mid rings as by reflected light, but in a contrary dle fpot, which in the other view appears black for want

of reflected

now

light,

the blue circle;

looks perfectly white, oppofite to the light appears this fpot

next without

tinged with a yellowifh red ; where the white circle ap a peared before, it now feems dark ; and fo of the reft

Now liated lofs

.

lame manner, the light tranfmitted through fo a darkened room appears greenifh by the into gold

in the

of the yellow

14.

HENCE

which gold

light,

it

follows,

that

reflects.

the colours of bodies

give a very probable ground for making conjecture concerning b reafon for the magnitude of their conftituent particles .

a conjecture is, calling order of any colour. it

its

being

My

difficult to fix

certainly the

The

green of vegetables our au thor judges to be of the third order, partly bccauie of the inand partly from the changes they tenfencfs of their colour ;

fufFer

when

more

perfect

ringe or red

they wither, turning at flrft into a greenifh or fome ot them to an o-yellow, and afterwards

;

which changes fcem

to be effected

from

their

dcnfer by the exhalation of their ringing particles growing 1

Obferr. 9.

b Ibid

-

prop.

nxoifture

CHAP.

PHILOSOPHY.

2.

35

r

moifture, and perhaps augmented Jikewile by the accrel How the nr of the earthy and oily parts of that tnoifture. tioned colours fliouU arife from increaimg the bulk ol th particles,

is

evident; feeing thole colours lie without the rin[:; and are therefore formed wli glafles,

green between the the

And

reflccls them is thickevtranfparent fubftance which that the augmentation of the denfity of the colorific

of the fame efrecl:, will confpire to die production be evident ; if we remember what was laid of the dif

particles will

ferent fize

of the

rings,

glafTes, from their o

fize

when air was included between tKe when water was between them ;

which fhewed that a fubftance of a greater denfity than another gives the fame colour at a lels thicknefs. Now the changes likely to be

wrought in the denfity or magni the parts of vegetables by withering feem not than are diffident to change their colour into tliofe of greater, the fame order; but the yellow and red of the fourth order tude of

are not full

enough

to agree with thofe, into

nor

which

thefe fub-

the green of the fecond fufficientl) good to be the colour of vegetables ; fo that their colour muft of necefiity be of die third order, fiances

77.

change,

THE

is

blue colour of iyrup

of

violet >

our auth

fuppofes to be of the third order; lor acids, as vinegar, with this fyrup change it red, and fait of tartar or other uK lies

mixed therewith turn

it

green.

But

if

of the fyrup were of the fecond order,

the blue colour

the

red colour,

which acids by attenuating its parts give it, mull be of the firft order, and the green given it by alcalies by incraflkting

Sir Is A its

particles

NEWTON'S

AC

BOOK III.

fhould be of the fecond ; whereas neither of thofe

enough, efpecially the green, to anfwer thofe produced by thefe changes-, but the red may well enough be allowed to be of the fecond order, and the green colours

is

perfect

of the third

which

in

;

cafe the blue

muft be

like wife of

the third order.

1 6.

THE

be of the

azure colour of the skies our author takes to

firft

order,

which

requires the fmalleft particles like to be exhibited

and therefore moft

of any colour,

by

vapours, before they have fufficiently coalefced to produce clouds of other colours.

17.

THE

moft

order, if

firft

the orders.

all

nen, tals

intenfe

and luminous white

paper, and to be of the former

fuch like fubftances to be

The

thefe.

of the

is

ftrong it is a mixture of the colours of Of the latter fort he takes the colour of lin-

lefs

opacity of

all

fort.

;

but white

The arguments

for

it

bodies has been (hewn to

me are arife

from the number and ftrength of the reflections made with them ; but all experiments mew, that the ftrongeft re flection is made at thofe furfaces, which intercede tranfpain

rent bodies differing moft in denfity. Among other inftances of this, the experiments before us afford one ; for

when

air

only

is

included between the glades, the coloured more dilated, as has before been faid,

rings

are not only

than

when water

>re

r

is

luminous and

medium

between them bright.

It

;

but are likewifc

much

follows therefore, that what-

pervades the pores of bodies,

if

fo

be there is

CHAP. is

PHILOSOPHY.

2.

35 3

any, thofe fubftances mufl be mod opake, the denfity of molt from the deniity of the medium, parts differs

whofe

which fills their pores. But it has been kifliciently proved in the former part of this tract, that there is no very denfc medium lodging in, at leaft pervading at liberty the pores of bodies.

And

is

it

For when

riments.

farther

air

is

proved by the preicnt expe

inclofed

by the denfer fubftance

the rings dilate themfelves, as has been faid, by be ing viewed obliquely; this they do fo very much, that at different obliquities the fame thicknefs of air will exhibit all

of

glafs,

forts

of colours.

The

bubble of water, though furrounded air, does likewife change its

with the thinner fubftance of

colour by being viewed obliquely; but not any thing near much, as in the other cafe; for in that the fame colour

fo

might be at

feen,

when

the rings were viewed moit obliquely, thicknefs it appeared at un

more than twelve times the

der a direct view; whereas in this other cafe the

thicknefs

was never found confiderably above half as much again. Now the colours of bodies not depending only on the li^ht,

upon them perpendicularly, but likewife falls on them in all which upon that, degrees of obliquity; if the medium their furrounding particles were denfer than that

is

incident

thofe particles, all forts

from them

of colours muft of neceffity be reflected make the colours of all bodies

fo copioufly, as would

But on the white, or grey, or at beft very dilute and imperfect. other hand, if the medium in the pores of bodies be much rarer than their particles,

the colour reflected will be fo

little

changed by the obliquity of the rays, that the colour pro duced by die rays, which fall near the perpendicular,

Z

may'

z

fo

Sir Is

354fo

much abound

in the refle&ed light, as to give the

with

their colour

NEWTON'S BOOK III.

A AC

little

To

allay.

this

may

body

be added, that

when is

the difference of the contiguous tranfparent fubftances the fame, a colour reflected from the denfer fubftance

reduced into a thin plate and furrounded by the rarer will be more brisk, than the fame colour will be, when reflected

from a thin

plate

blowing

glafs very

and

fur-

our author experienced

by

formed of the

rounded by the denfer

as

;

thin at a

rarer fubftance,

lamp

furnace,

which exhibited

open air more vivid colours, than the tween two glafles. From thefe confiderations in the

does be

air it is

manifefl, that if all other circumftances are alike, the denfeft bodies

moft opakj.

will be

But

it

white metals can hardly be

was obferved

made

before,

fo thin, except

that thefe

by being

diflblved in corroding liquors, as to be rendred tranfparent ; though none of them are fo denfe as gold, which proves their great opacity to have fome other caufe befides their more fit to produce this, than fuch a denfity ; and none is fize of their particles, as qualifies them to reflect the white

of the

firft

1 8.

order.

FOR

producing

black

the particles

to

ought

be

fmaller than for exhibiting any of the colours, viz. of a fize anfwering to the thicknefs of the bubble, whereby re flecting

little

or

no

light

it

yet they mult not be too fmall,

appears

colourlefs

for that will

;

but

make them

of reflections in the inward tranfparent through deficiency fufficient to flop the light from going the of body, parts

through

it j

but they muit be of a fize bordering upon that difpofed

CHAP.

PHILOSOPHY.

2.

355

difpofed to reflect the knit blue of the firft order, which why blacks ufually partake a little fee too, why bodies diflblved of that colour. by fire affords an evident reafbn

We

and why in grinding glalTcs up or putrefaction turn black : on copper plates the duft of the giafs, copper, and /and it is ground with, become very black : and ia the laft place

why their

communicate

thefe black fubftances

which

hue;

is,

great minutenefs of

that their particles

them

fo eafily to others

by reafon of the

eafily overfpread the grofler par-

deles of others.

19. I SHALL now finifh this chapter with one remark of the exceeding great porofity in bodies neceflarily requi red in all that has here been faid ; which, when duly confidered, muft appear very far-prizing ; but perhaps it will be matter

of greater furprize, when I affirm that the fagacity of our author has difcovered a method, which bodies

may

by

become

fo

eafily

how any

the Icaft portion of matter may be wrought into a body of any afligned dimen ons how and yet the pores of that none of great fo ever , ;

nay

;

body

them

greater, than

any the (mailed: magnitude propofed at pleafure; notwithftanding which the parts of the body fhall fo touch, that the body itfelf fhall be hard and (olid \ The manner is this: fuppofc the be of of

body

fuch figures,

that

when

compounded

particles

together the pores found brtween them may be equal in bignefs to the particles ; how this be and effeded, may yet the body be hard and laid

iolid,

is

not difficult to imderftand

and the pores o/ fuch

;

a bo-

Opt. pag 143.

^

L l

dy

Sir

ISAAC NEWTON'S

BOOK III.

dy may be made of any proposed degree of

fmallnefs.

But

the folid matter of a body fo framed will take up only half the fpace occupied by the body; and if each conftituent of other lefs particles according to be

compofed

particle

the fame rule, the folid parts of fuch a body will be but a fourth part of its bulk ; if every one of thefe lefler parti

be compounded in the fome manner, the folid whole body fhall be but one eighth of its bulk ; the of parts and thus by continuing the compofition the folid parts of die body may be made to bear as fmall a proportion to the whole magnitude of the body, as fhall be defired, notwith-

cles again

will be by the contiguity of its parts ca ftanding the body Which in any degree hard. fhews that this of being pable whole globe of earth, nay all the known bodies in the u-

niverfe together,

as far as

we know, may

be compounded,

of no greater a portion of folid matter, than might be re duced into a globe of one inch only in diameter, or even

We

fee therefore how by this means bodies may earare enough to tranfmit light, with all that made fily aeedom pellucid bodies are found to do. Though what is the real ftruclure of bodies we yet know not.

lefs.

be

CHAP. Of

the

III.

REFRACTION, REFLECTION^ INFLECTION of LIGHT.

and

T

HUS

much of

method now

the colours of natural bodies; our

leads us to fpeculations yet greater,

no lefs

CHAP. lefs

PHILOSOPHY.

3".

than to lay open the caufcs of

For

all

557

that has hitherto

been

muft

in this chapter be explained, how the: prifm feparates the colours of the fun's light, as we found related.

in the

firft

it

chapter

;

difcourfed of in the

and why the thin tranfparcnt plates chapter, and consequently the par

laft

of coloured bodies, reflect that diverfity of colours only by being of different thickneflcs.

ticles

F o R the firft it is proved by our author, that the colours fun's light are manifefted the of by the prifm, from the rays different of refraction that the violet; degrees undergoing i.

making

which go

rays,

in the firft

image moft refracted

upper part of the coloured of the firft chapter, are ther experiment to the

that the indigo-making ; rays are refracted, or turned out of their courfe by pafling through the prifm 5 but more than fomething lefs than the violet-making rays,

the blue-making rays; and the blue-making rays more than the green; the green-making rays more than the yellow; more than the orange; and the the

yellow

rays

orange-making

more than the red-making, which

fracted.

The

firft

proof of

are leaft

of

all

re

that rays of different co If you take this. bodv,

this,

lours are refracted unequally is any and paint one half of it red and the other half blue,

the;'

through a prifm thofe two parts fhall ap which can be can fed no pear feparated from each other otherwife than by the prifm's refracting the lio;ht of on

upon viewing

it

;

half

more than

half will be

fche

light

moft refracted

of the other ;

for if the

the prifm in fuch a fituation, that

half.

But the

blue-

body be fcen througK the body {hall appear lifted

Sir Is

A AC

NEWTON'S

BOOK III.

upwards by the refraction, as a body within a bafon of water, in the experiment mentioned in the firft chapter, the water, fo appeared to be lifted up by the refraction of

lifted

as to be feen at a greater diftance than

when

the bafon

is

the red ; empty, then fhall the blue part appear higher than but if the refraction of the prifm be the contrary way, the blue part fhall be deprelTed more than the other. Again, after laying fine threads

of black

filk acrofs

each of the co

and the body well inlightened, if the ing from it be received upon a convex glafs, may by refracting the rays caft the image of lours,

upon a

piece of white paper held

beyond the

will be feen that the black threads

com

rays fo

that

the glafs

it

body ;

then

red part of upon the image, and thofe upon the blue part, do not at the fame time appear diftinctly in the image of the body projected

it

by the

glais

on the blue not be

but

;

part

the paper be held

if

may

feen diftinct

muft be drawn

the

upon the

farther ofT

red

that the threads

fo,

diftinctly appear,

part

from the convex

the threads can ;

but the paper

glafs to

make

the

threads on this part vifible ; and when the diftance is great enongh for the threads to be feen in this red part, they become Whence it appears that the rays pro indiftinct in the other.

ceeding from each point of the blue part of the body are iooner united again by the convex glafs than the rays which come Irom each point of the red parts*. But both thefe i .

that the blue-making rays, as well in the fmall periments prove refraction of the convex glafs, as in the greater refraction cf the prifiw, are more Lent, than the red- making rays. Newt. Opt.

B.

I.

part,

i,

prop.

I.

3.

THI

s

CHAP. 3

.

PHILOSOPHY.

2.

THIS

559

fcems already to explain the reafon of the co -

made by refracting the fun's light witha prifrn; though our author proceeds to examine that in particular, and proves that the different coloured rays in that fpectrum

loured fpectrum

are in different degrees refracted ; by fhewing how to place the prifm in fuch a poflure, that if all the rays were re fracted in the fame manner, the fpectrum fhould of necefli-

whereas in that cafe if the angle made by round two furfaces of the prifm, through which the light that is the angle DFE in fig. 116, be about 63 or 64* paffes, degrees, the image inftead of being round fhall be near

ty be

:

the

five

times as long as broad

a difference enough to fhew

;

a great inequality in the refractions of the rays, which go to To kave no fcruple the oppofite extremities of the image.

unremoved, our author is very particular in fhewing by a great number of experiments, that this inequality of refra

and that it does not depend upon any ir of the glafs; no nor that the rays are in their paffage through the prifm each fplit and divided ; but on ction

is

notcafual,

regularities

the contrary that every ray ot the fun has its own peculiar degree of refraction proper to it, according to which it is more or lefs refracted in paiTing through pellucid (ubftances a always in the fame manner

.

That the

rays are not fplit

and multiplied by the refraction of the prifm, the third oi the experiments related in our firft chapter (hews very clear ly

;

the

for if firfl

they were,

refraction

fhould be no

lefs

and the length of the

were thereby occafioned

dilated

by the

O;t. B,

I.

,

(peel

rum

it*

the breadth

crofs refraction

cf the

part. I. plop, :.

CO

fe

Sir

ISAAC NEWTON'S

BOOK III.

.cond prifm ; whereas the breadth is not at all increafed , but the image is only thrown into an oblique pofture by the upper part ot the rays which were at firft more refracted

than the under

part, .being again

turned fartheft out of their

But the experiment mod exprefsly adapted to prove of refraction is this, which follows*. regular diverfity

courfe. this

Two

boards

A B, CD

(in fig. I go.) being erected in a dar proper diftance, one of them A B being near the window-fhutter E F, a fpace only being left for die prifm G H I to be placed between them ; fo that the

kened room

at a

M

of the window-fhutter at the hole rays entring may af ter palling through the prifm be trajected through a fmaller hole K made in the board A B, and pafTmg on from thence

go out

at

another

L made

hole

in the

board

C D

of

the fame fize as the hole K, and fmall enough to tranfmit the rays of one colour only at a time ; let another prifm

NOP

be placed

board

after the

the holes fing through

CD

K and L, and

to receive the rays pafafter refraction by that

let thofe rays fall upon the white furface QJR. Supthe violet light to pafs through the holes, and to pofe firft to J, which if the be refracted by the prifm prifm were removed fhould have paiTed right on to \V. If the be turned {lowly about, while the boards and prifm G H I remain fixed, in a little time another colour prifm were will fall upon the hole L, which, if the prifm

prifm

NOP

MOP

NOP

NOP

taken away, would proceed like the former rays to the fame but the refraction of the prifm NOP fhall not car j point

W

ry thefe rays to

S>

but to fome place Opt. B.

I.

part

i.

Expcc.

lefs

diftant

from

W as

6.

to

CHAP. to/.

PHILOSOPHY.

3.

Suppofe

making prifin

now

the rays which go to / to be the indigo-

It

manifeft that the boards

rays.

NOP

361

is

AB, CD, and

remaining immoveable, both the violet-making

and indigo-making

rays are incident alike

upon

the prifm

NOP,

for they are equally inclined to its

in the

fame part of that furface ; which mews that the indigo-

furfaceOP,and enter it

their courfe by the re rays are lefs diverted out of fraction of the prifm, than the violet-making rays under an

making

exact parity of

H

all

circumftances.

be more turned about,

Farther, if the prifm

G

the blue-making rays pate I fall thefe fhall hole the L, upon the furface Q^R through are and therefore at as below I, i>, fubjedted to a lefs re fraction than the

ceeding lefs

it

'till

And thus by pro indigo-making rays. found that the green-making rays are

will be

refracted than the

blue-making

according to the order in

and

rays,

which they

lie

fo

of the

reft,

in the coloured

Ipectrum.

be

of the different coloured rays to 4. THIS difpofition refracted fome more than others our author calls their

refpective degrees

of

refrangibility.

And

felf to

ence of refrangibility difcovers next ftep is to find the rule it obferves. it

fince this differ

be

fo regular,

the

fine of is a common principle in optics, that the 5-. I T of the refracted an the angle of incidence bears to the fine

If

AB

re-

(in fig. 131, 151) given proportion. the furface of any refracting fubitance, fuppofe of prefent that furwater or glafs, and C D a ray of light incident upon aa

gle

a

A

Sir 1

s

N E w T o N'S

AAc

BOOK

III.

point D, let D E be the ray, after it has parted the if the into the fubftance ; ray pafs out of the air whofe furface is A B (as in fig. 131) it fhall be turned

face in the

AB

furface

from the

furface,

be

air it fhall

and

bent

if

it

pafs

towards

G

out of that fubftance into

it

be drawn through the point furface A B, the angle under F

(as

D

CDF

in

fig.

151)

But

if

perpendicular to the

made by

the incident

ray and this perpendicular is called the angle of incidence; and the angle under B D G, made by this perpendicular and the And if ray after refraction, is called the refracted angle.

the circle

D

H

in

ing

let

under

HFIG

and fall

CDF

be defcribed with any interval cutting C I, then the perpendiculars H K, I L be upon F G, H K is called the fine of the angle the angle of incidence, and I L the fine of

DE

in

EDG

the refracted angle. The firft of called the fine of the angle of incidence, or more briefly the fine of incidence, the latter is the fine of the refracted angle, or the fine of refraction. And it

the angle under

thefe fines

is

by numerous experiments that whatever the of incidence H K bears to the fine of fine proportion refraction I L in any one cafe, the fame proportion fhall has been found

hold in

all cafes

;

that

is,

the proportion between thefe fines

remain unalterably the fame in the fame refracting fub ftance, whatever be the magnitude of the angle under CDF. will

6.

every

BUT now

becaufe optical writers did not obfervc that: as has light was divided by refraction,

beam of white

been here

explained,

this rule collected

by them can on

underftood in the grofs of the whole beam ly be

after refracti'

CHAP.

PHILOSOPHY.

3.

and not

363

much

of any particular part of it, or at moft only of the middle It therefore part of the beam. was incumbent upon our author to find by what law the fraction,

fo

rays were parted from each other; whether each ray apart obtained this property, and that the feparation was made by the proportion between the fines of incidence and refracti

on being the

in

each fpecies of

was

light

divided

rays

different

fome other

by

or

;

rule.

whether he

But

proves by a certain experiment that each ray has its fine of incidence proportional to its fine of refraction; and farther

(hews by mathematical reafoning, that

it

muft be

fo

upon

only that bodies refract the light by acting upon it, in a direction perpendicular to the furface of the and upon the lame fort of rays always in refracting body, condition

an equal degree

at the

fame

diftances*.

O

u R great author teaches in the next place how from 7. the refraction of the moft refrangible and leaft refrangible rays to find the refraction of

method

this:

is

if

all

the intermediate ones

b .

The

the fine of incidence be to the fine of re

fraction in the leaft refrangible rays as

A

to

B C, (in fig. 133) and

of refraction in the rnoft refrangible as A to B D; E be taken equal to C D, and then E D be fo divided

to the fine if

C

in F, G,

E C,

I, K, L, that ED, E F, EG, EH, El, EK, EL, be proportional to the eight lengths of mufical which found the notes in an F, D beim;

H,

(hall

chords,

c

the length of the key, a

E F

the length b

Opt. pag. 67, 68, &c.

Aaa

i

of

%

e tone above

'

Ibid.

I'

tli

ISAAC NEWTON'S

Sir

364

EG

that key,

E

fourth,

BOOK III,

the length of the lefler third, E H of the E K of the greater fixth, E L of fifth,

of the

I

the feventh, and E C of the octave above that key ; that is if the lines E D, E F, E G, E H, E I, E K, E L, and E C bear the fame l

-, J-, g, -, refpeftively proportion as the numbers, j, ~, v, then (hall B D, BF, be the two limits ot the lines of refraction of the violet-making rays, that is the violet-making rays fhall ,

not

of them have precifely the fame fine of refraction

all

,

but none of them fhall have a greater fine than B D, nor a lefs than B F, though there are violet-making rays which

anfwer to any fine

of

refraction that

tween

In

the

thefe

two.

fame

can be

taken be

manner B F and B G

are the limits of the fines of refraction of the indigo-ma are the limits belonging to the blueking rays ; B G, B

H

making king

B H, B I the limits pertaining to the green-ma B I, B K the limits for the yellow-making rays;

rays;

rays,

B K, B L the B L and B C

limits for the

orange-making rays ; and

belonging to the red- making tions

from each other

WHEN

found to 78.

A

Thefe are the propor

rays of light are feparated

in refraction.

light pafTes out

of

glafs

into air,

our author

B C as yo to 77, and the fame A to B D as yo And when it goes out of any other refracting fubto

(tance into air,

one

rays.

by which the heterogeneous

8.

tartly,

the extreme limits of the fines of refradtion

the excefs of the fine of refraction of any its fine of incidence bears a con-

of rays above fpecies

ftant proportion, which holds the fame in each fpecies, to the excels of the fine of refraction of the fame fort of rays

above

PHILOSOPHY.

C UP. 3.

above the line of incidence into the air out of

365 glafs

;

provided

the fines ot incidence both in glals and the other fubflance This our author verified by tranfmitting the are equal. light

through prifms of glafs included within a prifmatic and draws from thofe experiments the fol ;

vdlcl of water

lowing obfervations fo

through ftances

many

:

that

furfaces

whenever the

light in

palling

parting diverfe tranfparent fub-

by contrary refractions made to emerge into the direction parallel to that of its incidence, it will

is

air in a

afterwards white at any diflance from the prifms,. if the direction fhall pleafe to examine it ; but

appear

where you

emergence be oblique to its incidence, in receding its the from edges fhall appear tinged place of emergence with colours: which proves that in the firfl caie there is

of

its

of each fpecies of rays, but inequality in the refractions that when any one fpecies is fo refracted as to emerge pa rallel to the incident rays, every fort of rays after refracti

no

on

fhall likewife

be parallel to the fame incident rays,

to each other;

whereas on the contrary,

any one

incident light, oblique to the

fpecies

fort are

(hall

be oblique to each other,

From

if

and

the rays of the feveral

and be gradually hence he de

by that obliquity. feparated duces both the forementioned theorem, and alfo this other ; the proportion of the fine of in that in each fort of rays

of the ray cidence to the fine of refraction, in the paflage is compounded, out of any refracting fubflance into another, would have to of incidence of the proportion to which the fine of that ray out of the the fine of refraction in the

paflage

firft

fubftance into any third,

and of the proportion which the

'Sir

366

the fine of incidence in the

NEwTo

ISAAC

would have

N'S

BOOK

III.

to the fine of refraction

pafTage of the ray out of that third Jubilance into

From fo fimple and plain an experiment has our moit judicious author deduced thefe important theo rems, by which we may learn how very exact and circum-

the fecond.

fpedt

he has been in

notwithstanding

his

this

whole work of

great

in

particularity

his optics

;

explaining

that his

and the numerous collection of experiments he has made to clear up every doubt which could ariie, yet at the lame time he has ufed the greateft caution to make doctrine,

out every thing by the fimpleft and 9.

ction,

OUR

eafieft

means

poflible.

author adds but one remark more upon refra that if refraction be is, performed in the man

which

ner he has luppofed from the refracting

being prefTed by the

light's

power perpendicularly toward the furface of the body, and confequently be made to move fwifter

refracting in the body than before act equally at

all

its

incidence

diftances or

;

whether

this

power

otherwife,

provided only its power in the fame body at the fame diftances remain with out variation the fame in one inclination of the incident rays as well as another ; he obierves that the refractinowers in different bodies will be in the duplicate

po

proportion

of the tangents of the leaft angles, which the refracted light can make with the furfaces of the refracting bodies \ This obfervation

may

When

be explained thus.

into any refracting fubftance,

has been

it

the light paries

fhewn above

that

the fine of incidence bears a conftant proportion to the fine a

Opt. B.

II. par.

5.

prop,

i

of

CHAP. of

PHILOSOPHY.

3.

refradtion.

Suppofe the light to pafs to the

body A B C D (in fig. 1 3 4) in the line E F, and to fall

refra&ing

upon it at the point F, and then to proceed within the body in the line FG. Let HI be drawn through F perpendicular to the furface A B, and any circle K L N be defcribed to the cen

M

Then from

ter F.

the incident

O and P where

this circle cuts

PR

and

refradted ray, the perpendiculars OCb the proportion of OCt to will remain

PR

being drawn, the fame in

the points

the different obliquities, in which the fame ray of light can fall on the furface AB. Now OQ. is lefs than FL the femidiameter of the circle KLMN, but the more all

EF

the ray

greater will

is

down toward

inclined

OQ.

gnitude of F L.

be,

and

will

the furface

A B,

approach nearer to

the

the

ma

But the proportion of O Q. to P R remain when O Q, is largeft, P R will alfo be

ing always the fame, greateft ; fo that the

toward die furface

more the incident ray EF is the more the ray F G after

A B,

on will be inclined toward the fame.

Now

if

inclined refracti

the line

FST be fo drawn, that SV being perpendicular to FI fhall be to F L the femidiameter of the circle in the conftant pro is that portion of PR to OCt; then the angle under

NFT

which

I

meant by the

leaft

of

refracted ray with this furface, would proceed in this line, if

F lying on the very came to the point F

furface in

any

all

that can be

made by

the

for the ray after refraction, it

were to come

AB; line

to the point

for if the incident ray

between A F and F H, the

forward in fome lineray after refraction would proceed be drawn perpendicu between FT and FL Here if

NW

lar

to

FN,

this

line

NW

in die

circle

KLMN

is

called

the

Sir

368

ISAAC NEWTON'S

BOOK III.

the tangent of the angle under NFS. Thus much being premifed, the ienfeof the forementioned proportion is this. Let there

be two refra&ing fubftances (in fig.

Take

a point, as

I,

in the furface

$) A B C D and E F G H. A B, and to the center I

i 3

with any femidiameter defcribe the

,

circle

KLM.

In like

manner on the furface EF take fome point N, as a center, and defcribe with the fame femidiameter the circle OPQ^. Let the angle under B I R be the leaft which the refracted furface A B, and the angle under light can make with the

FNS

the

lead which the refracted light can make with Then if be drawn perpendicular to

LT

the furface EF.

AB, and P V perpendicular to EF; the whole power, where with the fubftance A B C D acts on the light, will bear to the whole power wherewith the fubftance E F G H acts on, the light, a proportion, on, which

LT

bears to

which

is

duplicate of the proporti

PV.

UPON comparing according to this rule the refrapowers of a great many bodies it is found, that unctu ous bodies which abound moft with fulphureous parts IO.

<5tive

refract the light

two

more in proportion to but that thofe bodies, which feem

or three times

their dcnfity than others

:

to receive in their competition like proportions of fulphu reous parts, have their refractive powers proportional to their denfities ; as appears beyond contradiction by

comparing

the refractive power of fo rare a fubftance as the air with that of common glafs or rock cryftal , thefe fub-

though

ftances are

zooo

times denfer than air; nay the fame pro portion

CHAP.

P

3:

found to hold without

is

portion

H I L O S O P H Y:

36$)

fenfible difference in

com

with pfeudo-topar and glafs of antimony, though the pfeudo-topar be groo times denfer than air, and paring

air

glafs

of antimony no

lefs

than

er in other fubftances,

4400

times denfer.

as falts,

common

This

water,

pow

fpirit

of

wine, &c. feems to bear a greater proportion to their denfities than thefe laft named, according as they abound with fulphurs more than thefe ; which makes our author conclude it

that bodies act

probable,

upon

the light chiefly,

if

not

by means of the fulphurs in them ; which kind of fubftances it is likely enters in fome degree the compoOf all the fubftances examined by fition of all bodies. our author, none has fo great a refractive power, in refpect altogether,

of

denfity, as a diamond.

its

OUR

II.

author fmifhes thefe remarks, and all he offers with obferving, that the action be

relating to refraction,

tween

light

and bodies

which are moft collected

readily

is

mutual, fince fulphureous bodies,

fet

on

fire

by the

fun's light,

when

a burning glafs, act more upon than other bodies of the fame denii-

upon them with

light in refracting

it,

And farther, that the denfeft bodies, which have now fhewn to act moft upon light, contract the greater!

ty do.

been

heat by being expofed to the

HAVING

II.

we muft tion

of

oaffes

fummer

fun.

what

relates to

thus difpatched refraction, addrefs ourfelves to difcourfe of the other opera

bodies

upon

through a

light

furface,

in reflecting

it.

When

light

which divides two tranfparent bodies B b b

ISAAC NEWTON'S

Sir

37 dies

differing

in

denfity

part of

,

another part being reflected. the denfer into the rarer,

body

it

And

only

tranfmitted*

the light pafs out of by being much inclined to

Now that

fuffers the greateft retraction,

is

III:

if

the forefaid furface at length no part of

but be totally reflected.

BOOK

(hall

fhall pafs through ? the light, which of part be wholly reflected with it

Ids obliquity of the rays than the parts pf the light which undergo a lefs degree of refraction ; as is evident

a

,

from the

laft experiment recited in the firft chapter ; where* the prifms D E F, G H I, (in fig. 119.) were turned about, the violet light was firft totally reflected, and then the blue, next tothat the green, and fo of the reft. In con-

as

fcquencc-

of

which our author

lays down this propofition

flexible,

which

are

moft

;

that

thofe rays being moft re-

the fun's light differs in reflexibility, refrangible.

And

collects

from

this,

in conjunction with

other arguments, that the refraction and reflection, of light are produced by the fame caufe? compaffmg thofe different effects only by the difference of

circumftances with which

Another proof being taken by our author from what he has difcovered of the paffage of light through thin traniparent that any particular fpecies of viz. light, of

it

is

attended.

this

plates,

fuppofe,,

for inftance, the

of fuch a fes it,

plate,

red-making if that

rays,

plate be

will enter

and

pafs out

of fome certain trneknef-

be of other thickneffes, it will not break through but be reflected back: in which is feen, that die thick-

;

but

if it

nefs of the plate determines

that plate acts

upon the

whether the power, by which

light, ftall reflect

it,

or fuffer

it

to,

pafs.thiough ig.

BUT

CHAP. 15.

PHILOSOPHY.

3.

BUT

this laft

37!

mentioned furpriimg property of the

action between light and bodies affords the reafon of all that has been laid in the preceding chapter concerning the colours of natural bodies ; and muft therefore more parti

cularly be

and explained

being what will unfold the nature of the action of bodies upon principally illuftrated

,

as

light.

14.

To

begin:

The

object glafs of a long telefcope being

upon a plane glafs, as propofed in die foregoing chap ter, in open day-light there will be exhibited rings of va but if in a darkened rious colours, as was there related room the coloured fpectrum be formed by the prifm, as in the firft experiment of the firft chapter, and the glaffes be laid

;

illuminated by a reflection from the fpeclrum, the rings (hall not in this cafe exhibit the diverftty of colours before defcribed,

but

which

upon

falls

Which {Lews at

crlafTes

appear

fome thickneffea

other places does not reflect ces to give the light paflage

pofe at

the

light

the incident light, at is found in thofe , pla for by holding the glaffes in

reflects it

;

but

it

paries

,

any particular of white paper by holding a piece

yond the lines

of the

colour

from the prifm to the fpectrum, fupfuch a diftance from the prifm that the feveral forts muft be fufficiently feparated from each other \vluu fort of light falls on the glaffes, you will find

the light as

of li r'ht

of

all

the glaffes, having dark rings between. air between the that the thin plate of

glaffes,

at a fmall

that at thofe intervals,

appeared upon the

glaffes,

the light

Bbb x

diftance be

where the dark is

fo tranfmitted, as

ISAAC NEWTON'S

Sir

372 as to

paint

BOOK

III.

upon the paper rings of light having that co This experiment there upon the glafies.

lour

which

fore

opens to us

falls

this

very flrange property of reflection, it fhould bear fuch a relation to the

that in thefe thin plates

thicknefs of the plate, as is here fhewn. Farther, by care the diameters of each ring it is found, that fully meafuring whereas the glafles touch where the dark fpot appears in

where the air the center of the rings made by reflection, of twice the thicknefs at which the light of the firfl ring is reflected, there the light by being again tranfmitted ma

is

kes the that

firfl:

dark ring

thicknefs

which

;

where the

exhibits

gain reflects the light forming the thicknefs is four times the

mitted fo as to is

pears,

it

7, 9,

lucid ring,

it

a-

the fecond lucid ring ; when firfl:, the light is again tranf

the fecond dark ring;

where the

firfl:

air

made ;

ring ap

and

the light 5-,

plate has three times firft

thicknefs, the third lucid ring is has fix times the thicknefs, the third dark

five times the

where

make

the

is

fo

on

:

in fo

much

that the thicknefles, at

reflected, are in proportion to the

&c. and the

thicknefles,

where the

numbers

which I, 3,

light is tranf

mitted, are in the proportion of the numbers o, i, 4, 6, 8, And thefe proportions between the thicknefles which

&c.

reflect

and tranfmit the

light

remain the fame in

all fitua-

of the eye, as well when the rings are viewed obliquely, We muft farther here as when looked on perpendicularly. tions

obferve, that thejight, when it is reflected, as well as when it is tranfmitted, enters the thin plate, and is reflected from its far ther furface; becaufe, as was before remarked, the altering the tranfparent body behind the farther furface alters the de

gree

CHAP.

PHILOSOPHY.

3.

gree of reflexion has

its

373

when

a thin piece of Mufcovy glaf wet with water, and the colour of made dimmer by being fo wet ;*J which fhcws that as

farther furface

the glafs the light reaches to the water, utherwife

not be influenced by

its

reflection could

But yet this reflection depend fome from the firft furface to the power propagated upon fecond ; for though made ]at the fecond furface it de pends

alfo

upon the

it.

firft,

becaufe

it

depends upon the di-

ftance between the furfaces; and befides, the

which the flection ce,

:

body through

light paries to the firft furface influences the re

for in a of Mufcovy glafs, wetting the furfa plate firft receives the light, diminishes the reflection?

which

though not quite do. plates

fo

much

as wetting the farther furface will

Since therefore the light in palling through thefe thin at fome thicknefles is reflected, but at others tranfmit-

ted without reflection,

it is

evident,

that this reflection

is

caufed by fome power propagated from the firft furface, Thus is every ray which intermits and returns fucceflively. alternate reflections and tranfmiilions at to apart difpofed the fucceflive returns of which difpofition equal intervals; our author calls the fits of eafy reflection, and of eafy tranfBut thefe fits, which obferve the fame law of mifiion. returning at equal intervals, or obliquely perpendicularly

,

whether the plates are viewed in different fituations of the

For what was obferved befon eye change their magnitude. of thofe rings, which appear in open day-light, holds likewife in thefe rings exhibited by fimplc lights ; name in refpect

ly,

that thefe

ferent angle

two

alter

in

the dif bignefs according to are feen : and our author

under which they

lay

Sir

374lays

down

ISAAC NEWTON'S

BOOK III

a rule whereby to determine the thicknefles of .air, which fhall exhibit the fame colour under

the plate of

And the thicknefs of the aereal different oblique views *. plate, which in different inclinations of the rays will exhi open day-light the fame colour, is alfo va b He contrived farther a method rule the fame by of comparing in the bubble of water the proportion be

bit to the eye in

ried

.

which exhibited any colour it, where the fame colour appeared by an oblique view and he found c But farther, if the the fame rule to obtain here likewife

tween the thicknefs of

when

its

coat,

feen perpendicularly, to the thicknefs of ;

.

*

be enlightened fucceflively by all the feveral fpecies of light, the rings will appear of different magnitudes; in glaffes

the red light they will be larger than in the orange colour, that larger than in the yellow, in the yellow larger than in the green, lefs in the blue, lefs yet in the indigo, and

"in

leaft

of

all

in the violet

:

which fhew

sthat the

of the aereal plate is not fitted to reflect that one colour is reflected where another tranfmitted; fracted

and

form the

as the rays leaft rings,

which

a rule

is

fame thicknef^

all

colours,

are moll; laid

but

would have been ftrongly re

down by our au

thor for determining the relation, which the degree of refra&ion of each fpecies of colour has to the thickneffes of

the plate where 15-.

FROM

it is

reflected.

thefe obfervations our author fhews the reafon

of that great variety of colours, which appears in thefe thin in the open white light of the day. For when this white jpktes '.Op', B. II. par. 3. prop. ij.

b

bd

par.

i,

obfcr-. -.

c

Ibid.

O'oferv. 19.

light

CHAP.

light falls its

own

PHILOSOPHY,

3.

on the

colour

;

plate,

375

each part of the light forms rings of different colours not

and the rings of the

being of the fame bignefs are varioufly intermixed, and form 3 a great variety of tints 1 6. IN certain experiments, which our author made with thick glades, he found, that thefe fits of eafy reflection and tranfmiflion returned for fome thoufands of times, and there

by farther confirmed

his

reafoning concerning

them

b .

17. UPON the whole, our great author concludes from fome of the experiments made by him, that the reafon why all of the light incident upon them, tranfparent bodies refract part and reflect another part, i?, becaufe fome of the light, when it

comes

to the furface of the body,

is

in a

fit

of eary tranfmif-

fion, and fome part of it in a fit of eafy reflection ; and from the durablenefs of thefe fits he thinks it probable, that the is put into thefe fits from their firrt emiflion out of the luminous body y and that thefe fits, continue to return at

light

-

without end, unlefs thofe intervals be qua! intervals changed into fome refracting fubftance c I u by the light's entring .

how

to determine the

change which i* made of the intervals of the fits of eary tranfmiflion and re oflection, when die light pafles out of one tranfparent

likewife

has taught

fpacc

fuh-ftance into another.

His rule

is,

when

that

the

light paf-

to the furface, which parts any two trnniperpendicularly thefe intervals in the fubftance, our fubftances, parent fes

Opt. B.

II.

par. 2. pag. 19$. 8cc..

I.-id.

par.

4

*

Jju}. port. 3. prop. 13.

which

Sir Is

377 which the

A AC

light paries,

NEWTON'S

BOOK

III:

bear to the intervals in the fubflance,

enters, the fame proportion, as the fine of a It is farther to be incidence bears to the fine of refraction

whereinto the light

.

obferved, that though the fits of eafy reflection return at conflant intervals, yet the reflecting power never operates, but at

or near a furface where the light would fuffer refraction ; and if the thicknefs of any tranfparent body fhall be lefs than the

of the

intervals

fits,

thofe intervals fhall fcarce be difturbed

fuch a body, but the light flection

fhall pafs

by through without any re

b .

WHAT

the power in nature is, whereby this adlion 1 8. between Kght and bodies is caufed, our author has not difcoBut the efTedts, which he has difcovered, of this vered. are very furprifing, and altogether wide from any con that had ever been framed concerning it ; and from jectures thefe difcoveries of his no doubt this power is to be dedu

power

ced, if we ever can

NEWTON

come

to the

knowledge of it.

Sir I

s

AAc

has in general hinted at his opinion concerning it ; it is owing to fome very fubtle and elaftic fub

that probably ftance diffufed through the univerfe, in which fuch vibrations may 'be excited by the rays of light, as they pafs through it to it, that fhall occafion operate fo differently upon the different places as to give rife to thefe alternate light in

fits

of reflection and tranuniflion, of which we have now been c He is of opinion, that fuch a fubftance may pro fpeaking duce this, and other effedls alfo in nature, though it be fo .

:

rare as not to give *

Ibid. p-op.

any

fenfible refiftance to bodies in *

17,

Ibid prop,

c

13,

Opt.Qu.

mo-

18, Sec.

tion:

CHAP. tion

a ;

PHILOSOPH Y.

4.

and therefore not inconfiftent

above, that the planets

move

in

witli

fpaces free

377

what has been

from

laid

refiftance

b .

IN order for the more full difcovery of this action between and our author bodies, light began another fet of experi ments, wherein he found the light to be acted on as it paries 1 9.

near the edges of folid bodies ; in particular all fmall bo fuch as the hairs of a man's head or the like, held in a

dies,

very fmall

dows.

beam of the

And

in

fun's light,

one of

1

can extremely broad fha-

thefe experiments the

c times the breadth of the body obferved to be bordered with colours

3

fhadow was

Thefe fhadows are

.

5-

d

alfo

This our author calls

.

the inflection of light ; but as he informs us, that he was interrupt

ed from profecuting thefe experiments to any length, I need not detain my readers with a more particular account of them.

CHAP. Of

IV.

OPTIC GLASSES. *

O

NEWTON

R

ISAAC having deduced from his doctrine of light and colours a furpriiing improvement of teleI intend here to give an account, I (hall fcopes, of which I

premife fomething in general concerning thofe inftruments. firft

ft

Sec Coocl. S, i.

? B.

II.

Ch.

i.

<

I

* 1

C

c c

Opt. B. I

III.

Obf.

i

2.

a.

IT

Sir Is A

378 IT

a.

that

NEWTON'S

AC

will be underftood

when

from what has been

upon the

light foils

BOOK HI* faid above,

furface of glafs obliquely,

more entrance into the glafs drawn through the point of incidence perpendicular it

its

fnrface, than before.

point

A

(in fig.

136)

Suppofe a ray of light ifluihg falls

on a piece of

lar

FGH. pafs

A G falling on Here

AG

is

BCDE, whofe

is

B C in the point G, anddraw entrance into the glafs will

the furface

the ray after

on infomeline, asG

that the line

glafs

to that

from the

of a fpherical or globu Let the ray proceed in

BC, whereon the ray falls, center whereof is F. figure, the

furface

the line

after

inclined to the line

is

its

more inclined toward the line FGH for the line F G H is per B C in the point G. By this means> proceeding from any one point

I,

inclined thereto

;

pendicular to the if a number of rays fall on a convex fpherical furface of furface

glafs,

they

fhall

be

reprefented in fig. 137,) fo as to be gathered clofe together about the line drawn through the center pretty 0f the glafs from the point, whence the rays proceed ; which inflected (as

is

we fhall

the axis of the giafs or the be fo the near rays proceed may glais> that the rays fhall after entring the glafs ftill go on to fpread themfelves, but not fo much as before ; fo that if the rays line

henceforward

call

:

point from whence the

were to be continued backward

(as

in fig. i 3 8,) they

mould

gather together about the axis at a place more remote from the glafs, than the point is, whence they actually proceed. In thefe and the following figures A denotes the point to which the rays are related before refraction, Bthe point to which they are directed afterwards, and C the center of the refracting furface.. Here

we may obferve, that it

fuch a figure, that

all

is

poflible to

form the glafs of

the rays which proceed from one point fhall

PHILOSOPHY.

CnAP.4-

379

reduced again exactly into one point on But in glafles of aipherical form though this

{hall after refraction he

the axis of the

glafs.

does not happen; yet the rays, which

fall

within a moderate di-

/lance from the axis, will unite extremely near together. If the iurface, after refraclion it fliall light fall on a concave (pherical

fprcad quicker than before (as in rig. 139,) unlefs the rays proceed from a point between the center and the iurface of the glais .If

we fuppofe the rays of light, which fall upon the glafs, not to proceed from any point, but to move fb as to tend all to fome the furface ; if the glaf, point in the axis of the glafs beyond have a convex furface,

the rays

fliall

unite about the axis

fooncr, than othcrwife they won Id do (as in fig. 140,) unlefs to which they tended was between the furface and the

point

But

die center of that furface.

they fig.

fliall

:

if

IKIV

the furface be concave,

perhaps converge,

(See

141 and 141.)

F ART n

5.

to the air line

not meet ib footi

i<

R,

bccaufe the light in parting out of glafs in refrac'tion farther oil from the

turned by the

is

the point of incidence perpendicular to furface, than it was before ; the light which

drawn through

the refracting

from

fpreads

face of glafs

before

(as

a point

fliall

a convex furby parting through made either to fprcad lels than

into the air be

in fig.

axis beyond 145,) or to gather about the

But if the rays of light were pro the glafs (as in fig. 144.) in the axis of the glafs, they fliould by a to point ceeding the refraction be

made

to

unite

fooncr

about

that

axis

which

(as

in fig. 1 45-.) If the furface of the glafs be concave, rays in fliall be made to fpread fader (as from a

point

proceed fie

1^6

}

axis of but rays which are tending to a point in the

C

c c

x

the

o

Sir

NEWTO N'S

ISAAC

BOOK

III.

die glafs, ihall be made to gather about the axis farther from the glafs (as in fig. 147) or even to diverge (as in fig. 148,) lies between unlefs' the point, to which the rays are directed,

the furface of the glafs and

4.

THE

rays,

called diverging

converging

which the

;

center.

which fpread themfelves from a point, are and fuch as move toward a point, are called

And

rays.

its

the point in the axis of the glafs, about is called the focus of

rays gather after refraction,

thofe rays.

y. (as

in

I F a fig.

A C B and A D two and

be formed of two convex fpherical furfaces glafs AB is formed of the furfaces

glafs

149,) where the B,

the line

as the line

furfaces,

drawn through the

E F,

is

centers of the

called the axis of the glafs

which diverge from any point of

;

by the refraction of the glafs will be caufed to converge toward fome or at leafl to diverge as from a point more part of the axis, rays,

remote from the

ed

;

for the

two

as this to

concave

converge fooncr.

furfaces,

drawn through formed,

is

axis,

than that from whence they proceed

furfaces both confpire to

But converging rays

upon the rays. glafs

glafs,

this

as the glafs

AB

the centers, to

If

will

produce this effect be caufed by fuch a

a glafs be

(in fig.

formed of two

15-0,)

which the two

called the axis of the glafs.

the line

CD

furfaces are

Such a

glafs fhall

cnufe diverging rays, which proceed from any point in the axis of the glafs, to diverge much more, as if they came from

fomc place

in the axis

of the

to glafs nearer

it

than the point,

whence

ri .

c

i-

CHAP.

PHILOSOPHY.

4.

381

whence

the rays actually proceed. But converging rays will be made either to converge lets, or even to diverge. 6.

I

N thefe glades rays, which proceed from any point axis, will be affected as it were in the fame man

near the

\i they proceeded from the very axis it felf, and fuch as converge toward a point at a fmall diftance from the axis will fuffer much the lame effects from the glafs,as if they converged to

ner, as

fome point

in the very axis.

expofed to a

convex

By

this

means any luminous body

may have an image formed upon beyond the glafs. This may be ca-

glafs

any white body held tried with a common fily

fpectacle-glafs.

For

if

fuch a glafs

be held between a candle and a piece of white paper, if the diftances of the candle, glafs, and paper be properly adjuftedj of the candle will appear very difHnctly upon the the

image

inverted ; paper , but be feen Let AB (in fig. l^i) be the

the reafon whereof glafs,

CD

this

is

.

an object placed

Let the rays of- light, which ilcrofs the axis of the glafs. fue from the point E, where the axis of the glafs croiTes the ob be fo refracted by the glafs, as to meet again abou the

ject,

point F. object,

The

rays,

which diverge from the point

C

of the

meet again almoft at the fame diftance from, for the but on the other fide of the axis, as at G

fhall

the glafs, ; In like manner chc rays, crofs the a.\ rays at the glafs which proceed from the point D, will meet about II on tl.c

other fide of the

axis.

None

of thefe rays, neither thole

which proceed from the point H in the axis, nor thofe which but iffue from C or D, will meet again exactly in one point and at here as is G, U, F, in one they fuppofed -,

yet

place,

.IV.

ill

82

Sir

ISAAC NEWTON'S

BOOK III.

be crouded fo clofc together, as to make a diftinct image of the object upon any body proper to reflect it, which fhall be held there.

7..

IF the object

be too near the glafs for the rays to the rays ihall iiTue out of the

converge after the refraction, glafs,

the in

as if they diverged

from a point more diftant from

than that from whence they really proceed glafs, i ya,) where the rays coming from the point fig.

of the object, which fue out of the glafs

more remote from in^ from the point

lies

on the

axis

of the

A

glafs

B,

(as

E if-

as if , they came from the point F the glafs than E ; and the rays proceedC iilue out of the glafs, as if they pro

ceeded from the point G ; likewife the rays which ifTue from the point D emerge out of the glafs, as if they came

G

is on the fame fide Here the point II. the axis, as the point C ; and the point H on the fame In this cafe to an eye placed beyond fide, as the point D.

from the point e.f

the glafs the object fhoiild appear, as ytion

GF

if

it

were

in the iitu-

II.

8. I F the glafs

A B had been concave

(as in, fig. j 5-5,)

to

the glafs the object C D would appear in the fituation G H, nearer to the glafs than really it is. Here alfo the object will not be inverted; but the point G is on on the the lame fide the axe with the point C, and

an eye beyond

H

fame fide

as D,

.

HENCE

CHAP.

PHILOSOPHY.

4.

HENCE may

9.

with convex in that age fuch as are

when

men,

be

underftood,

why

glaffes help the fight in old

becomes unfit to

fee

objects

3%

fpedtacles

age

:

made

for the

eye

except

diftinclly,

remov'd to a very great diftance ; whence all they firft ftand in need of fpeclacles, are ob-

and to hold the object at a But when an greater diftance, than they tiled to do before. object is removed at too great a diftance from the fight,, fcrved to read at arm's length,

it

cannot be feen

from the

light

clearly,

by reafon that a

will enter the eye, objecl:

lefs

quantity of

and the whole

Now by help of a con be held and yet the rays of near, glafs objecl: may light ifTuing from it will enter the eye, as if the objecl: will alfo appear frnaller.

objecl:

an

vex

were

farther

10. as are

removed.

AFTER

die lame

fhort fighted.

manner concave

For

glafies a/lift

fuch,

thefe require the objecl: to be

brought inconveniently near to the eye,

in

order to their

but by fueh a glafs the object maybe removed to a proper diftance, and yet the rays of light enter the eye, as if they came from a place much nearer, feeing

11.

it

diftinctly;

WHENCE

old age objects diftance,

too near,

and

thefe defects of the fight arife, that in cannot be feen diftinct within a moderate

in fhort-fightednefs

will be eafily

not without being brought

underftood,

when

the

manner of

vifion in general fhall be explain'd ; which I (hall now en deavour to do, in order to be better underftood in what 3

follows*

1

Sir

384

I s

\

N E w T o N'S

A c

BOOK III.

The eye is torm'd, as is rcprefented in fig. 1 5-4. of a globular figure, the fore part whereof fcarce more protuberant than the reft is tranfparent. Underneath

follows. it is

this tranfparent part

is

a fmall collection of an

appearance like water, and power as common water ;

it

this

mour, and fills the fpace A B C D lies

the body

DEFG;

this

is

humour

in

has alfo the fame refractive is

called the aqueous

in the folid

figure.

hu

Next beyond

but tranfparent,

it

is

compofed with two convex furfaces, the hinder furface EFG Between the being more convex, than the anterior E D G. outer

membrane A B C, and

membrane, which

this

body

EDGE

is

placed that

exhibits the colours, that TIC feen

round

the fight of the eye ; and the black fpot, which is called the is a hole in this membrane, through which the fight or pupil, .

whereby we fee. This membrane is fixed on outward circuit, and has a mufcular power, where

light enters,,

ly

by

its

by it dilates the pupil in a weak light, and contracts it in The body DEFG is called the cryflailine a ftrong one. humour, and has a greater refracting power than water. Behind

this

the bulk oi

called the vitreous

the eye is filled up with what is this has much the fame refra

humor,

At the bottom of the eye toward nofe the optic glafs enters, as at H, and fpreads it felf all over the iniide of the eye , till Now any object, as within a fmall diftance from A and C.

ctive

power with water.

the inner fide next

the

IK, being placed before the eye, the rays of light ifluing from each point of this object are fo refracted by the con vex furface of the aqueous humour, verge; after

this

as to

be caufed to con

being received by the convex furface E D G of

CHAP.

PHILOSOPHY.

3.

of the cryftalline humour, which has a greater refractive power than the aqueous, the rays, when they arc entered into this furface,

EFG

than the all

ftill

more converge, and

at

going out of

humour of a lefs refractive power are made to converge yet farther. By cryftalline they

the furface

into a

thefe fucceflive refractions they are brought to converge at fo that a diftindt image of die ob

the bottom of the eye, as

ject

L

M

the object

is

And

imprefs'd on the nerve.

is

by

this

means

feen.

II. IT has been

made a

that the

difficulty,

image of

the object impreffed on the nerve is iiwerted, fo that the is impreffed on the lower part of upper part of the image the

But

eye.

this

difficulty,

I think,

can no longer

re

and lower are terms main, if only confider, that upper relative to the ordinary pofition of our bodies :

we

merely and our bodies,

when view'd by the eye, have their image as much inverted as other objects fo that the image of our own bodies, and of other objects, are imprefTed on the eye ;

in the

II.

fame

THE

different

relation to

one another,

as

they really have.

diftinct at very eye can fee objects equally but in one diftance only at the fame

diftances,

That the eye may accomcdate itfclf to different is It is required. diftances, fome change in its humours

time.

my

this change opinion, that

cryftalline

humour,

as I

is

made

in the figure

of the

have indeavoured to prove in ano

ther place. 3

Ddd

1.

IF

Sir I

386 Tg. IF

s

AAc

N E w T o N'S

any of the humours of the eye are too flat, which is the cafe in the light too little

they will refract old age.

BOOK III.

If

who

as in thofe

;

they are too convex,

they refract too

much

;

are fhort-fighted.

14. THE manner of direct vifion being thus explained, proceed to give fome account of telefcopes, by which we view more diftinctly remote objects ; and alfo of microfcopes, I

In whereby we magnify the appearance of fmall objects. the firit place, the moft fimple fort of telefcope is compofed of two glades, either both convex, or one convex,

and the other concave. ed in

fig. 15-5-,

(The

the latter in

firft fort

fig.

of thefe

is

reprefent-

If 6.)

AB

15-. IN fig. 1^5* let reprefent the convex glafs next the object, C D the other glafs more convex near the eye. Suppofe the object-glafs A B to form the image of the ob ject at E F ; fo that if a fheet of white paper were to be

held in

this

place,

pofe the rays,

bout

F, to

Now

the object would appear. fuppafs the glafs A B, and are united a-

which

proceed to the eye

glafs

C

D,

and be there

re

Three only of thefe rays are drawn in the figure, thofe which pafs by the extremities of the glafs A B, and

fracted.

that

which

p^ced

pafTes

its

at fuch a diftance

middle.

If

the

from the image E

glafs

C D

be

F, that the rays,

which pafs by the point F, after having proceeded through the glafs diverge fo much, as the rays do that come from which is at fuch a diftance from the eye as an object,

to

CHAP.

PHILOSOPHY.

3.

to be fecn

diftinctly,

thefe being received

387

by the

eye will

make on

the bottom of the eye a diftinct reprefentation of the point F. In like manner the rays, which pafs through the object glafs A B to the point E after proceeding through

C D

the cye-glais

on the bottom of the eye make a But if the eye be E.

will

diftinct reprefentation

of the point

placed where thele rays, which proceed from E, crofs thofc, which proceed from F, the eye will receive the diftinct imthefe points at the fame time ; and conpreffion of both will alfo receive a diftinct impreflion from all the

fequently intermediate parts of the image E F, that is, the eye will fee the object, to which the telefcope is directed, diftinclly.

The

place of the eye

H E, H

F

ject-glafs

crofs,

AB

is

which

about the point G, where the rays through the middle of the ob-

pafs

to the points

E and F

;

or at the place

where

the focus would be formed by rays coming from the point

H, and refracted by the this

C

glafs

D.

inftrument magnifies any object,

E H F, image E F,

that the angle under

would

the

fee

To

judge

we muft

how much

iirft

obfervc,

which the eye at the point H nearly the fame as the angle,

in is

under which the object appears by direct vilion; but when is in G, and views the object through the telefcope, the eye

it

fees

the fame under a greater angle; for the rays,

which

make a greater angle than coming from E and F crofs in G, the from which the rays, point II to thefe points H proceed and

F.

The

proportion, is

angle at

G

as the diftance

is

greater than that at 11 in the

between the

than the diftance of greater

CD.

Dd

d x

A B and t G from the glafs I

glafles

the point

16.

)

Tins

Sir I

388 1 6.

THIS

s

N E w T o N'S

AAc

telefcope inverts the object

BOOK III.

for the rays,

which

come from the right-hand fide of the object, go to the and the rays, which point E the left fide of the image come from the left fide of the object, go to F the right ;

iide of the image. Thefe rays crofs again in G, fo that the rays, which come from the right Iide of the object, go to the right fide of the eye; and the rays from the lefr ftde

of the object go to the

tclcfcope the iituation as the object ;

fore in this

left

fide of the eye.

There

image in the eye has the fame and feeing that in direct vifion

the image in the eye has an inverted fituation, here, where the fituation is not inverted, the object muft appear fo. This is no inconvenience to aftronomers in celeftial obfervations; but for objects here

two

other convex glaffes,

on the

earth

it

is

ufual to

add

which may turn the

object again elfe to ufe the other kind of reprefented in fig.i 5-7,) or a concave eye-glafs. telefcope with

(as is

1 7.

I

N

this

other kind of telefcope the effect

is

found

The diftincled on the fame principles, as in the former. nefs of the appearance is procured in the fime manner. But here the eye-glafs C D (in fig. i y<5) is placed between the image E F, and the object glafs A B. By this means the rays, which come from the right-hand fide of the object, and pro ceed toward E the left fide of the image, being intercepted by the eye-glafs are carried to the left fide of the eye ; and the rays, which come from the left fide of the object, go to the right fide of the eye ; fo that the impreilion in the eye being inverted the object appears in the fame fituation, as

CHAP. as

PHILOSOPHY.

3.

3%

when

vicw'd by the naked eye. The eye mult here be The degree of magnifying in placed clofc to the glafs. this

inftrument

pals

through the

is

thus to be found. glafs

AB

at

H,

Let the

rays, which after the refradion of

the eye-glafs C D diverge, as if they came from the point G ; then the rays, which come from the extremities of the objed, enter the eye under the angle at G ; fo that here alfo the object will be magnified in the proportion of the diftance between the glades, the eye-glafs.

THE

G from

to the diihnce of

that can be

taken in at one view in die of the on breadth telefcope, depends pupil of the the for as the which to points E, F of the rays, go eye ; each are diftant from other, when they fomething image, 1 8.

ipace,

this

come out of

the

than the pupil,

it

or F

C

if

D,

evident,

they are wider

afunder

that they cannot both enter

In the other telefcope the eye

the eye at once.

is

placed

rays that come from the points crofs each other,, and therefore muft enter the eye

in the point G,

E

glafs is

together.

On

where the

this

account the telefcope with convex glafles thofe with concave. But in

takes in a larger view, than

thefe alfo the extent of the view glafs

is limited, becaufe the eyedoes not by the refraction towards its edges form fo a reprefentation of the object, as near the middle.

1 8.

One kind is only a ot two forts. Microfcopes arc of which the obje& may means the by glafs,

very convex

be brought very near the eye, and yet be feen

diftincllv.

ISAAC NEWTON'S

Sir

39

BOOK

III.

This microfcope magnifies in proportion, as the object by ng brought neal the eye will forma broader impreflion

on the optic

nerve. its

produces Let the object A B

glailes .

and by

Above

this

The

other kind

effects in the

made with convex

fame manner

as the telefcope-

y S) be placed under the glafs C D, (in hg. an let glafs image be formed of this object. i

GH

be placed. By this glafs image let the glafs and B, be the rays, which proceed from the points In particular, let refracted, as is exprefled in the figure. this

A

let

the rays, which from each of thefe points pafs through the middle of the glafs C D, crofs in I, and there let the eye Here the objecl: will appear larger, when feen be placed.

through the microfcope, than if that instrument were re moved, in proportion as the angle, in which thefe rays crofs the angle, which the lines would make, is greater than that is, in the mould be drawn from I to A and B the made of of thedifcance of the up proportion proportion to the diftance of I from the glafs G H y B from A I, object and of the proportion of the diftance between the glafies, to the diftance of the object A B from the giafs C D.

in

I,

that

;

-

I SHALL now proceed to explain the imperfection in thefe inftruments, occahoned by the different refrangibility of the light which comes from every object. This prevents the

image of the object from being formed glafs

the image and make the to latisfy

in the focus of the

object the eye-glafs magnify overmuch, the imperfections of it mult be viiible,

with perfect diftinctnefs \vliole

himfelf,

j

fo that

appear confufed.

if

Our author more

that the different

refrangibility

fully

of the feveral

CHAP.

PHILOSOPHY.

3.

feveral forts

of rays

is

fufficient to

produce

this

391 irregularity,

underwent the labour of a very nice and difficult experi ment, whofe procefs he has at large fet down, to prove, that the rays of light are refracted as differently in the fmall refraction of telefcope glaifes as in the larger of the prifm ; fo exceeding careful has he been in fearching out the true

And

caufe ot this effect.

he ufed,

I

fuppofe,

the greater

had before been generally

caution, bccaufe another reafon

It was the alTigned tor it. opinion of all mathematici in defect that this ans, tekfcopes arofe from the figure, in which the glafles were formed ; a fpherical refracting fur-

face not collecting into

come from any one faid

a .

But

refractions,

to air

after

an exact point

point of

an

all

the rays

glafs,

to the fine

which

as has before

our author has proved, that

as well as in greater,

out of

object,

been

in thefe fmall

the fine of incidence in

of refraction in the red-

making rays, is as yo to 77, and in the blue-making rayshe proceeds to compare the inequalities of re yo to 78 ;

fraction arifing

from

of this different retrangibility

the rays,

with the inequalities, which would follow from the figure For this purof the glafs, were light uniformly refracted. that pofe he obferves,

if

rays iffuing

from a point

fo

remote

from the object glafs of a telefcope, as to be efteemed which is the cafe ot the rays, which come from the parallel, heavenly bodies ; then the diftance from the glafs of the in which the lea ft refrangible rays arc united, will: point, 1 refrangible rays unite,, be to the diftance, at which the as 18 to Z7 y and therefore that ti.c icafl fpace, into which.

mo

*

ISAAC NEWTON'S

Sir

BOOK III.

die rays can be collected, will not be lefs than the be part of the breadth of the the glafs. For if A B (in rig .15-9

all

CD

the glafs,

its

E

axis,

A,

1-

B two

to that axis entring the glafs near

rays of the light parallel its

edges

;

after refracli-

the leaft refrangible part of thefe rays meet in G, the mod refrangible in then, as has been (aid, G I will ;

on

let

H

be to

18

H, as

I

G

to

17;

and the X7th drawn through G, and

part of

I,

that

GH

is,

part of

H

will be the

whence

I ;

if

aSth

KL

be

MN

through H, perpendicular to the breadth of the be will i8th N CD, part of A B, the glafs, and K L the T7th part of the fame ; fo that OP

M

which the

into

the leaft fpacc,

rays

are gathered, will be that is the j-yth

about half the mean between thefe two,

A

part of

10.

B.

THIS

is

the error

ariiingr o

from the

different re-

the rays of light, which our author finds frangibility the other, confequent upon the figure of exceed to vaftly oi

the

In

glafs.

particular,

if

the telefcope glafs be

flat

on

and convex on the other; when the flat fide is turned towards the object, by a theorem, which he has laid down, the error from the figure comes out above 5*000

one

fide,

times great,

that

do, were fpace

O

This other inequality is fo not could telefcopes perform io well as they not that the light does not equally fill all the

than the

lefs

it

which

P, over

toward the middle

And

be fides,

{jually ftrong,

other.

all

of

it is

(tattered, but

is

much more

denfe

that fpace than at the extremities.

the kinds of rays affect not the fenfe e-

the yellow and orange being the ftrongeft^ the

>/.

/

r

,

.

>

PHILOSOPHY.

CHAP.$,

393

the red and green next to them, the blue indigo and vio let much darker and fainter colours ; and it is fhewn being that

and orange,

the yellow

all

and three

fifths

of the

brighter half of the red next the orange, and as great a fliare of the brighter half of the green next the yellow, will be collected into a fpace whofe breadth is not above

the ^ yoth part of the breadth of the

And

glafs.

the re

maining colours, which fall without this fpacc, as they arc much more dull and obfcure than thefe, fo will they be

much more

likewife fect the

able

fenfe in

to

this

telefcopes

is

and therefore call hardly af of And agree the other. comparifon the obfervation of aftronomers, that diffufed

;

between twenty and

fixty

feet

in

length re-

as being about y or 6, at mofl prefent the fixed ftars, about 8 or 10 feconds in diameter. Whereas other argu

ments fliew fenfible

dilated

us,

that they

refraction.

appear to us of any than as their light is

really

any otherwife

magnitude by

do not

One proof

that the fixed Itars

do

not appear to us under any fenfible angle is, that when the moon pafles over any of them, their light does not, like the planets on the fame occafion, difappear by degrees, but vanishes at once.

II.

OUR

author being thus convinced, that telefcopes

were not capable of being brought to

much

greater perfection

than at prefent by refractions, contrived one by reflection, in which there is no feparation made of the different coloured light;

for in every

kind of light the rays

after refle&ion

have the fame degree of inclination to the furface, from whence they are reflected, as they have at their incidence, fo

E

e e

that

ISAAC NEWTON'S

Sir

394

that thofe rays

which come

BOOK

to the furfacein

one

III.

line, will

go

without any parting from one another. Ac in the cordingly attempt he fucceeded fo well, that a hort not much one, exceeding fix inches in length, equalled an or

offalfo in

one

line

dinary telefcope whofe length

w as r

four

kind to greater lengths, have of a anfwer expectation fully

feet.

late

this

Inftruments of

been made, which

.

Of

the

CHAP. V. R A I N B O W.

now

The manner of its explain the rainbow. in the general, before Sir IsAAcNEWTON had difcovered his theory of colours ; but HALL

IS production was understood,

what caufed the diverfity of colours in it could not then be known, which obliges him to explain this appearance parti cularly fon,

;

who

whom we exprefsly

reflection of

was

the

ANTONIO

more

fully

and

The

fhall imitate as follows.

fhewed the rainbow

to be

firil:

per-

formed by the

fun-beams from drops of falling rain, Do MINIS. But this was afterwards

DE

by

diftinclly explained

DES CARTES.

i. THERE appears moil frequently two rainbows; both of which are caufed by the forefaid reflection of the funbeams from the drops of falling rain, but are not pro

duced by all the light which falls upon and are reflected The inner bow is produced by thofe from the drops. which enter the drop, and at their entrance are rays only fo refracted as to unite into a point, as

ther furface of

the drop,

as

is

where the contiguous rays ab,

c

*

Philof.

it

were,

upon

the far

reprefented in fig.

d

y

Tranf. No. 378.

ef,

160

;

coming from the

CHAP.

PHILOSOPHY.

5.

395

iun, and therefore to fenfe parallel, upon their entrance in to the drop in the points by dy j\ are fo refra&ed as to meet together in the point g, upon the farther furface of the drop

Now

from the fame point the angle of incidence of each ray upon being equal to the angle of reflection, the

thefe rays being reflected nearly

of the furface,

the point g rays will return in the lines

g

A,

g

k>

g

/,

in the

fame man

ner inclined to each other, as they were before their inci dence upon the point g, and will make the fame angles with the furface of the drop at the points b, k, /, as at the points By dy fy after their entrance ; and therefore after their emer

gence out of the drop each ray will be inclined to the furface in the fame angle, as when it n*r(l entered it ; whence the lines bmy kn^lo, in which the rays emerge, muft be parallel

to each other, as well as the lines

a

by

c

d

y

efy

in

But thefe emerging rays being nor will not diverge from each other in fpread parallel their paffage from the drop, and therefore will enter the in fufficient plenty to caufe a eye conveniently fituated

which they were

fenfation.

incident.

Whereas

all

the other rays, whether thofc nearer as r j-, or thofe farther off, ae

the center of the drop,

f ^,

from other points in the hin ; namely, the ray f q from the point from tv Andforthu from rs a, and iw# from 0. z, jX, reafon by their reflection and fuccecding refraction they will be icattered after their emergence from the foremenand therefore cannot en tioned rays and from each other, tUy <w*y

will be reflected

der furface of the drop

ter the

any

receive them copious enough to excite eye placed to

diftinct fenfation.

Ece

-x

5,

THE

.

ISAAC NEWTON'S

Sir

396

THE

external rainbow

made between

the incidence

BOOK

III.

formed by two reflections and emergence of the rays ;

is

is to be noted, that the rays g b, g k, g /, at the points b, k y /, do not wholly pafs out of the drop, but are in part reflected back ; though the fecond reflection of thefe particular rays does not form the outer bow.

for

it

For

this

bow

is

made by

which

thofe rays,

after their

en

trance into the drop are by the refraction of it united, be fore they arrive at the farther furface, at fuch a diftance from

when

that furface, they may be re is reprefented in fig. 161; where the rays a , c d, ef, are collected by the refraction of the drop into the point g, and palling on fcom thence that

it,

they

in parallel

flected

fall

upon

lines,

as

upon the furface of the drop in the points &, k y /, and are thence reflected to m, n, 0,paiTing from b to m, from k to For thefe rays after #, and from / to o in parallel lines. ftrike

reflection at m, n> o will meet again in the point p y at the fame diftance from thefe points of reflection m, n, o, as the point g is from the former points of reflection &, k,

/.

Therefore thefe rays in pafjing from f to the furface

of the drop will fall upon that furface in the points , r, s in the fame angles, as thefe rays made with the furface Confequently, when thefe rays into of out the the air, each ray will make drop emerge with the furface of the drop the fame angle, as it made at in 3, d, f, after refraction.

its firft

incidence

;

fo that the lines

q

t,

r v, s iw, in

which

they come from the drop, will be parallel to each other, as well as the lines a, I, c d, cfy in which they came, to the drop,

PHILOSOPHY:

397

drop. By this means thefe rays to a fpe&ator commodioufly iituated will become vifible. But all the other as well thofe nearer the center of the drop x j, z

remote from

it

to the lines

lel

bm,

rays, as thofe

more

will be reflected in lines not paral k n> /0; namely, the ray xj, in the

j\

/3y,

a.,

,

the ray za. in the line 0*, the ray g y in the line in the line e Whence thefe rays A^, and the ray g.

line

H,

fl

and fubfequent refradlion will be from the forementioned rays, and from one ano

after their next reflection

Icattered

and by

ther,

IT

4.

is

means become

that

farther to

the incident rays a

b>

invifiblc.

be remarked, c d>

cf>,

that if in the

and

their

firft

cafe

correfpondent e-

mergent rays h m, kn y I o y are produced till they meet, they will make with each other a greater angle, than any other incident ray will make with its correfponding emer gent

ray.

And

mergent rays q

in the latter cafe, t,

r

acuter angle, than

vy is

s

on the contrary, the e-

w make

f

made

with the incident rays an by any other of the emergent

rays.

OUR

author delivers a method of finding each of thefe extream angles from the degree of refraction being 5-.

by which method it appears, that the firft of thefe the lefs, and the latter the greater, by how much angles the refractive power of the drop, or the refrangibility of given

;

is

And this laft conlideration fully comthe rays is greater. doctrine of the rainbow, and fhews, why the co pleats the lours of each bow are ranged in the order wherein they are feen. 6.

Sup-

6.

of

ISAAC NEWTON'S

Sir

398

A

SUPPOSE

rain,

M

n,

(in fig. i <Ji.) to

Op, Q/,

S

which entring the drops

be the eye, B,C,D,E,F,drops

V it

parcels of rays of the fun, B, C, D, E, F after one reflection f,

M

Now let n be produced to M meets with the emergent ray likewife produced, let

pafs out to the eye in A. till

it

BooKlIL

produced meet its emergent ray produced in *, let Qj- meet its emergent ray in A, let S t meet its emergent li ray in ^, and let V iv meet its emergent ray produced in

Of

r.

M A

the angle under be that, which is derived from the refraction of the violet-making rays by the method we have here fpoken of, it follows that the violet light will only enter the eye from the drop B,

all the other coloured rays thofe rays which are not Scattered, but go out parallel fo as to caufe a fenfation. For the angle, which thefe parallel emergent rays makes with the incident in the moft refrangible or violet-making rays,

palling

below

it,

that

is,

all

being lefs than this angle in any other fort of rays, none of the rays which emerge parallel, except the violet-making,

M

under the angle * A, but the reft mak with the incident a n ing ray greater angle than this will if the below the In manner like pafs angle under O * eye. will enter the eye

M

A

blue-making rays, the blue rays only fhall en ter the eye from the drop C, and all the other coloured rays will pafs by the eye, the violet-coloured rays pafiing above, agrees to the

A

the angle Q A correthofe mail enter only green-making rays, the eye from the drop D, the violet and blue-making rays palling above, and the other colours, that is the yellow and the other colours below.

Farther,

fponding to the

red,

CHAP.

PHI L O SOPH Y.

5.

red, below.

And

it"

SA

the angle

399

anfwt-rs to the refa

ction of the yellow-making vnvs, they only iliall convj the eye from the And in the lad place, if the an drop E. gle belongs to the red-making and Icaft refrangible rays, they only fhall enter the eye from the F, all the

VyA

drop

other coloured rays palling above.

BUT now

7.

found

in

it

any of the

is

that

evident,

lines

all

the drops of water

A *, A A, A ^, A

,,

whether farther

from the

eye, or nearer than the drops B, C, D, E, F, will give the fame colours as thefe do, all the drops upon each

giving the fame colour

line

vilible

fo that the ; light reflected from thefe drops will become copious enough to be whereas the reflection from one minute alone

that

parallel to the lines

a

number of

; drop could not be perceived. But befides, it is farther manifeft, that if the line A 3 be drawn from the fun through the eye,

is,

M

O p,

w,

Qj*, S

f,

V

IPJ,

and

drops of water are placed all round this line, the fame colour will be exhibited by all the drops at the fame diftance from this line. Hence it follows, that when the fun is if

moderately elevated above the horizon, fite

to

it,

and the fun

fpectator with his

if

it

rains

oppo-

upon the drops as they fall, a back turned to the fun muft obferve a co fhines

loured circular arch reaching to the horizon, being red with out, next to that yellow, then green, blue, and on the in ner edge violet ; only this la ft colour appears faint by being diluted with the white light of the clouds, and from anothrt

caufe to be mentioned hereafter I

a .

!

8.

Tn

Sir

400

ISAAC NEWTON'S

BOOK III

THUS

is caufed the interior or The primary bow. of rain fome diftance without this bow will caufe at drops the exterior or fecondary bow by two reflections of the fun's

8.

Let thefe drops be G, H, I, K, L; X^, Z <*, denoting parcels of rays which enter each

light.

A

,

Now

r,

drop. with the

has been remarked, that thefe rays make angle in thofe rays, which

it

vifible refracted rays the greateft

are moft refrangible.

Suppofe therefore the

viiible refracted

each drop after two reflections, pafs out from enter the eye in A, to interfect the incident rays in TT, p, rays,

which

9 refpe&ively. the greateft of

It

is

all,

manifeft, that the angle under next to that the angle under

<p

and <r,

T,

A

is

AT A,

the next in bignefs will be the angle under p* A, the next to this the angle under ZpA, and the leaft of all the an

From the drop L therefore v.hl come to gle under X?rA. the eye the violet-making, or moft refrangib e rays, from the yeliov the blue, from I the green, from and 1

H

K

from

G

the red-making rays

A

and the

;

A

like will

A

and the drops in the lines <p y ?r, p, AT, the drops at the fame diftances from the line all

As

that line.

Whence

bow, which

is

happen to all c

all

11

louiid

appears the reafon of the fecondary the other, having its co

feen without

lours in a contrary order, violet without and red within ; though the colours are fainter than in the other bow, as be ing made by two reflections, and two refractions ; whereas the other bow is made by two retractions, and one reflecti

on

only.

.

THERE

CHAP.

PHILOSOPHY.

5.

40!

THERE is a farther appearance in the rainbow particu larly defcribed

about

five years ago",

which

is,

that under the

upper part of the inner bow there appears often two or three orders of very faint colours, making alternate arches of green, and a reddifh purple. At the time

was taken notice of, b which caufe of it

I

I fhall

,

TON

gave

this appearance thoughts concerning the

my

here repeat.

which

Sir

NEW

ISAAC

polimed and quickrefraction an there is made, whereby fome filvered, irregular fmall quantity of light is fcattered from the principal reflect has obferved, that in

beam

ed,

reflection

.

If

we

glafs,

allow the fame thing to happen in the is caufed, it feems fuffici-

whereby the rainbow the appearance

ent to produce IO.

LET AB (in

is

fig.

now

mentioned.

l6^.) reprefent a globule of water,

B the point from whence the rays of any determinate fpecies being reflected to C, and afterwards emerging in the line CD, would proceed to the eye, and caufe the appear ance of that colour in the rainbow, which appertains to

Here fuppofe, that befides what is reflected re fmall part of the light is irregularly fcatter fome gularly, ed every way ; fo that from the point B, befides the rays that are regularly reflected from B to C, fome fcattered rays

this

fpecies.

will return in other

as

lines,

in

BE, BF, BG, BH, on

Now it lias been obferved above ^ each fide the line BC. that the rays of light in their parTage from one fuperficies of a refracting body to the other undergo alternate fits of Philof.

Tranfaa No. 37^.

b Ibid.

F

c

f f

Opt. B.

II.

part 4.

d

Ch.

3.

14.

/j.o

Sir I

2

eafy tranfmifiion

equal intervals

s

and

AAc

NK

reflection,

infomuch that

;

if

vv

BOOK III.

T o N*S

fucceeding each other at they reach the farther fu-

one iort of thofe fits, they fhall be tranfmitted ; the other kind of them, they fhall rather be reflected back. Whence the rays that proceed from B to C, and perficies in

if in

emerge

in the line

C D,

the fcattercd rays, that

fit of cafy tranfmiflion, a fmall diftance without thefe

being in a

fall at

on

either fide (fuppofc the rays that pafs in the lines BE, BG) fhall fall on the furface in a fit of eafy reflection, and fhall not emerge ; but the fcattered rays, that pafs at fome

diftance without thefe

globule in a furface.

fit

laft,

fhall arrive at the furface

of the

of eafy tranfmiilion, and break through that

Suppofe thefe rays to pafs in the

lines

BF,

BH

;

the former of which rays fhall have had one fit more of eafy tranfmiflion, and the latter one fit lefs, than the rays that pafs

from B to C.

Now

both thefe rays,

when

they go out

of the globule, will proceed by the refraction of the water in trie lines FI, HK, that will be inclined almoft equally to the rays incident on the globule, which come from the fun but ;

the angles of their inclination will be lefs than the angle, in are inclined to which the rays emerging in the line

CD

thofe incident rays. ed from the point

And B

at

fame manner rays fcatter a certain diflance without thefe

after the

emerge out of the globule, while the intermediate rays and thefe emergent rays will be inclined are intercepted to the rays incident on the globule in angles ftill lefs than will

;

the angles, in which the rays

them

F I and

HK

are inclined to

and without

thefe rays will emerge other rays, that ; (hall be inclined to the incident rays in angles yet lefs.

Now

by

CHAP. this

PHILOSOPHY.

5.

403

means

by may be formed of every kind of rays, befid'es the principal arch, which goes to the formation of the rain bow, other arches within every one of the principal of the fame colour, though much more faint ; and this for divers (ucceffions, as long as thefe weak lights, which in every arch grow more and more obfcure, fhall continue vifible. Now as the arches produced by each colour will be vari-

on fly mixed together, the

diversity of colours obferv'd in

thefe

very poilibly arife from them.

fecondary arches

may

II. IN the darker colours thefe arches

may

reach below

the bow, and be feen diftincl:. In the brighter colours thefe arches are loft in the inferior part of the principal light of the

rainbow ; but in all probability they contribute to the red tin which the purple of the rainbow ufually has, and is mod remarkable when thefe fecondary colours appear ftrongeft.

cture,

However thefe fecondary

arches in the brighteft colours

may

extend with a very faint light below the bow, and poilibly the tinge purple of thefe fecondary arches with a reddifh hue. 11. THE precife diftances between the principal arch and thefe fainter arches depend on the magnitude of the are formed. To make them any degree drops, wherein they It is neceffary the drop be exceeding final 1. that they are formed in the vapour of the cloud, the air being put in motion by the kill of the rain

feparate

moft

which

may

it

is

likely,

carry

down

be the reafon,

along with the larger drops

why

thefe colours appear F ff i

;

and

this

may

under djc upper part

Sir

ISAAC NEWTON'S, &c.

Book III.

part of the bow only, this vapour not dcfcending very low. As a farther confirmation of this, thefe colours are feen ftrongeft,

when

the rain

falls

from very black clouds, which fall whereof the air will be

caufe the fierceft rains, by the

moft agitated.

To

the like alternate return of the fits of eafy tranfI 3. million and reflection in the paflage of light through the globules of water, which compofe the clouds, Sir ISAAC

NEWTON at times

afcribes

fome of thofe coloured

appear about the fun and *

Opt. B.

II.

part 4.

circles,

which

moon \ obf.

13

C O N-

CONCLUSION.

405

CONCLUSION, I

R

ISAAC

each of

NEWTON having concluded

his philofophical treatifes

fome general take leave of

given us his firft

reflections,

my

I

fliall

with

now

readers with a fliort

account of what he has there delivered. At the end of his mathematical prin of natural philofophy he has ciples Wherein he the Deity. thoughts concerning of the all in found parts that the fimilitude

obferves,

univerfe

makes

it

undoubted, that the whole

is

governed by

the original is owing of the one fupreme being, the effect of choice which evidently is frame of nature, to ftate the beft methen He briefly and defign. proceeds In fhort, we cannot notions concerning God. taphyfical than as necefconceive either of fpace or time otherwife to

whom

farily

CONCLUSION. farily exifting

;

this

Being therefore, on

whom

all

others de

mud certainly exift by

the fame neceflity of nature. Confequently wherever fpace and time is found, there God

pend,

muft

And as it appears

alfo be.

impoflible to us, that fpace

fhould be limited, or that time fhould have had a beginning, the Deity muft be both immenfe and eternal. i. A T the end of his treatife of optics he has propofed fome thoughts concerning other parts of nature, which he had not diftinctly fearched into. He begins with fome

farther reflections concerning light, which he had not fully In particular he declares his fentiments at large

examined.

concerning the power, whereby bodies and light act on each In fome parts of his book he had given fhort hints <it his opinion concerning this % but here he exprefsly de b clares his conjecture, which we have already mentioned ,

other.

that this power is lodged in a very fubtle fpirit of a great elaftic force diffufed thro' the univerfe, producing not only this, but He thinks it not impollible, many other natural operations. A

that the

power of

this occafion

gravity itfelf fhould be owing to it. On many natural appearances, the

he enumerates

chief of which are produced by chymical experiments. From -numerous obfervations of this kind he makes no doubt, that

the fmalleft parts of matter, when near contact, act ftrongly on each other, fometimes being mutually attracted, at other times repelled.

5.

THE

attractive

Jbr the parts

power

is

more manifefi than

of all bodies adhere

by

this

principle.

the other,

And

the

CONCLUSIO N. name of

attraction,

been very

freely

407

which our author has given to it, has ufe of by many writers, and as much

made

lie has often complained to to by others. What of having been niifunderftood in this matter. he fays upon this head was not intended by him as a phi-

objected

me

b;:t of any appe~s, only to point lofophical explanation out a power in nature not hitherto diilincrly ubicrved, t

manner of its acting, he thought To acquiefee in the a of diligent enquiry. worthy of any appearance by afferting it to be a gene explanation of attraction, is not to improve our knowledge in ral

caufe of which, and the \vas

power

philofophy,

but rather to put a ftop to our farther fearcru

FINIS.

V

39003 00956^59

1

b