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 :
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.
/.
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J.
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ulr.
p.
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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
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,
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Mr Thomas Fellows Mr Francis Fennell Mr Michael Fenwick John Ferdinand, Tern pie,
of
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Fry, Merchant Francis Fu'jim, Efq;
Rev.
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n-jcl
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Fuller,
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Henry Gatham John Gay
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Mr Mr
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Thomas
Dennis Farrer,
of
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His
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/vir
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Fiercher
John Efq;
Fyme Francis Fayram, Bogkftlltrm
London
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College,
Jofeph Eyles Right Hon. Sir Robert Eyre, Lord Chief Juftice of the Cvnimon
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F.fq;
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Rev. James Fynney, D. D. Pre bendary of Durham Capt.
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Philip Finchtr
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Mr
York Edward Finch,
of
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Hun
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Gee
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Clandifh Gilbert,
ef
Trinity College, Dublin
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John Gilbert John Girardcx, Efq; Mr John Girl, Surgeon Rfv. Dr. Gilbert, Dean of Exe ter, 4 Books
tingdon
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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
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unfdon Right Hon. Lord John iladdon, M. B. of Chrift !
Church, Oxon Mr Hames
Jeilis
Arthur Greenhi.l
Grtenway,
of
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Hare,
Efq;
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of
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Hon.
Harley,
n;r
jor.arhan
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of BarbadoeJ,
Jciemiah Harmin
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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
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Samuel Handly Gabriel Hanger, Efq; James Ilannott, of Spittle-Field;,
Grange Samuel Grey,
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Book-
York
in
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Thomas Grainger
S'
feller
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U/tivtr/ity
of Edinburgh
Mr
Mr
George Graham
Moifunr
for cf Divinity in the
Mr John Hamilton Mr Thomas Hammond,
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Hu]]fey,E/^;
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Richard Grimes
M.D. an</Poliater Leidcniis Rev. Mr Grofvcnor Mr Richard Grofvcnor
Thomas
Savilian.
John Ilamerfe
r
Sir
Sir
Francis
\
Modern
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Ox.
in
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chant Bart.
Thomas Goodwin
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in
M.D.
Griffiths,
&
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Edmund
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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\
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Peter Hinde,
Rev.
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Edmund Thomas
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Mr
Mr
Benjamin Heath
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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
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
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Timothy Lane
Rev. Dr. Lsney, Mufltr of
Pem
broke Hall, Camtr. z Books Peter de Langley Rev. Mr Nathaniel Lardner Mr Larnoul
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Henry
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<j/Bimop's
Laurence, Refltr
Waremouth
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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
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Hugh
M. A. Vicar York (hire
Rev.
hfq;
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Rev.
Mr
Mr Kidbey Mr Robert Kidd
Bookfelleri
Jobber, Efq;
George Johnfon,
of
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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
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Nathaniel Lloyd, Merchant
Samuel Lobb, Bookfeller at Chelmsrord William Lock, Efq, Mr James Lock, 2 Books Mr Jofhua Locke Charles Lockier, Efq;
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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
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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-
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Luderj, Merchant
the-
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M. A.
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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;
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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
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Mrs
Mr
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Richard Lockwood, Efq; Mr Bartholom. Lottus, 9 Books William Logan, M. D.
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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,
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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
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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
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
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Robert Myddleton, Efq; Robert Myhil, Efq;
David Mitchell, Efq; Mr John Mitton
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Mr
Richard Nutley, Efq; John Nutt, Merchant
William Mingay D. John Mifaubin, A/. Mrs Frances Mitchel
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Mr
Murden
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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
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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
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Efq;
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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;
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Jan.
Oudam, Merchant
tu
Rotterdam
Mr
Overall
John Overbury, Efq; Charles Overing
Mr Mr
Thomas Owen
.;
Charles Owfley, Efq;
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John
Owen
Thomas Oyles
Newnham
Newton, iz Books
P.
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Newton
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John Niccol,
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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;
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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,
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of
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Mr
Prior, Efq;
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Thomas Purcas Robert Purfe
John Putland George Pye, M. D. Samuel Pye, M. D. Mr Samuel Pye, Surgeon
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Cambridge
The Phyfiological Library
Port
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Sir
John Phillipfon, Efq; William Phipps, L. L. D.
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Thomas
John Porter Jofeph Porter
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Pool, Apothecary
Dr. John Pringle
Efq;
College,
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Thomas
Phillips, Efq;
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Paulin
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Mr Mr Mr
Peyton, of St. John's
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Robert
Mr Mr
Mr Henry
College, Cambridge Daniel Phillips, M. D.
Thomas Phillips, Efq; Mr Gravet Phillips
M. D.
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Mr
Kent
in
John
Parratt,
Thames-
of
Street
Parne, Fdlow
Reclor of Holywell
Petitt,
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John Prat,
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Penton
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Philip Pennington
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in the
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Pyle, of Lynn John Pine, Engravtr
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Hit Grace the
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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
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Thomas Robirfon,
John Ranby, Surgeon
Rev.
Mr
lUwthew Robinfon.
Rand
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Richard Randall
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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
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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
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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
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-
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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.
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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
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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
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George Virgoe
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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
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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
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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;
Samuel Wellcy, jun. Gilbert Weft, Efq, Rt. Hon. Richard Weft, Eft;
Lite
Weil
Weftern,
Prebendary of
//;
Amfterdam Dover- Street
Mr Matthew Weftly MrTho. Wefton, 0/"Greenwich Matthew Wcymondefold,
Efq;
Woodward
W
Charltoo W.oollnfton, Efq; Tslr William Wool:afton
Wight Woolly, Jcfias
Efq;
of : he Jf.nntl of
j;
Chriftophcrs iliian-,s,
Mr
Efq;
B. D. Phil.p Williams, E. A. of Jefus
Williams,
College, Oxon Francis Wiiliams
Mr
Coll. Adam William/on R( bcit Willimott |ohn Willis, Efq; Edward Wilmor, A/. D. Mr Robert Willmott
Hon.
Mr
Willoughby
Jofepli
Mr
illys,
Eft;
John Wilmer, Merchant
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John Wilmer, Apothecary Wiimott, Bookfeller in Oxford Richard Wilibn, of Leeds, Efq; Rev. Mr Daniel Wilibn, Preben dary cf the Church of Hereford William Windc, Efq; Mr Samuel Winder, jun. Sir William Windham L\ir.
Mr
John Windfor
Library of
Wind for College
Mr Winnington Mr Winnock
Efq;
Library of the Cached.
T
r/W
Wordfworth,
orcefter
jtm. Eft;
Mr
John \Voi fter, Merchant Rev. Dr. William Wotton
John
Wowen of the Middlein
Henry* Wright, cf Molberly,
Che (hi: e, Efq; Samuel Wright, Efq; William Wright, cf Offerton, in
Mr Mr
Cheihire, Efq;
Wright William Wright, of Baldock,
Hertfordfliire
Rev.
Mr
Wrigley, Fellow cf
John's College, Rt. Hon.
St.
Cambridge
Thomas Wyndham,
LJ.
Ccmmon
Chief Jujiice of the Pleas, of Ireland
Mr
Wyeth Thomas Wyndham,
Rev.
Jofeph
Mr
Mr
Herbert Weftfaling, Efq; Wefftein and Smith, AlcJJieiirs 'in
Ikes,
n
Lord high Chancellor cf Ireland
in
i
Jofeph
Jofiah Woolafton, Efq; Mr Woolball, Merchant 7 Francis ool!afton, Efq;
Edward Wright, Temple, Efq;
VVi.^ism V.
Thomas Weft, Efq; Jv. Thomas Welt
Led feller i
W
Prebendary of Worceftcr
Mr
Mr
Mr
Mr
D. D.
Mr ]. Woods, 0/Bramflior,A/rr^. Mr Benjamin Woodroof,
John W:l:e?, John V
W
Efq; Efq;
M
John Woodhoufc,
Mr Wilkins Boatyller Mr Abd Wilknilon Mr William Wilks
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