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■s^ V 



<* .9 



• I 

Compendious System 

o p 

Natural Philofophy. 

With NOTES, 

• • "•• 



A « » 

Some Occafional R e m a A k is. 


«- -•■» 


VOL. I. 

- » * • m 


1 t -« 

I By y: RO fTNING, M. A. 

Redor of Andbrby in Lincolnshire, ahd late 
! Fellow of MAcbAtEN College in Cambridge. 

K*— H^^ifc— ■■ • •• I I 'i 


I Printed f^r Sam. Harding, on the Pavement in 
f St. Marlines Lane. 1753. 

« / r 


1 . > r # 

^ ■ • 


. . > 


i <. M 







I Thing an ufual Complaint with thofe 
•*• who art unacquainted with Geometry j 
that they are vitfcouraged by the Mathe-^ 
matical DemonJirationSj from ferujtng 
Books of Natural Philofophy ; / ap-- 
prehended that fome Papers I had drawn 
up for the Ufe of my Pjipils in the 
Univerjityj would not he altogether un^^ 
acceptable^ if publijhed in fuch Pormy 
that the Propoftions^ or Subjiance of 
the Booiy might be read without Inter- 
ruption from the Mathematical Demon- 
ftrations. And therefore after a large 
Explanation^ and fometimes an llluf 
tration alfo^ of the P articular s^ as oc-m 
cafion feemed mojl to require^ t have 
endeavoured to Jhew the Truth of thent^ 
in a familiar and popular Manner^ 
without Geometry y by way of Text : 

A And 



And for the fake of thofe who are sill- 
led in Geometry^ have added the De- 
tnonfrationsy with fome occajional Re- 
fnarh^ by way of Notes. And whereas 
the JVr iters on this SubjeSi have appro- 
priated to themfelves a Stile too techni- 
cal for Beginners^ I have^ in hopes of 
being more eafely underjiood^ fometifnes 
chofe a different Method of ExpreJ/ton^ 
though perhaps not fo accurate. 



In the IntroduEiion to the fir fi Far t^ 
Notice is taken of the Method of Philo- 
fophifing made Ufe of ^ Des Cartes, 
and others before him^ fo far as the 
Defign of this Compendium required. 
I Jhall add here a few Confiderations 
relating to the Method which prevails 
at this Time. 

In the prefent Method of Philofophi- 
fing^ all Matter is confidered [with ref- 
peSt to 'its Subflance) as homogeneous, 
or of the fame Kind\ and no other Cdufe 
or Principle of AEiion in Matter is al- 

P R E F A C E, iii 

hme^ oft but what is well efiablijbed by 
FaBs. ■ ' 

Sofm Pbil<^Oiphers dM&wi^' Elementary 
Fire, as they caU ity among their Prin- 
ciples ; or which comes to the fame things 
they confider Fire as endowed with ac- 
tive Powers d^fiinB from thofe of other 
Matter, Keill, in his Letter to Dr. 
Cockburn, De Legibus Attradionis, 
aliifque Phyfices Principiis, makes uje 
of three Principles^ viz. i. Empty 
Space. 2. The infinite piyifibility of 
Quantity. 3. Tl^e Attraction of Mat- 
ter, .^nd afirmst that all Phyfics 
depepds thereon. 

., Xhefirfl of bis Principle the Reader 
may perhaps think ridiculous ; but he 
fffay confider y that at that time of I)ay, 
the Notion of a Plenum wqs f^ot wholly 
expkded: Th^lapng donpn pmpty Space 

as^, fiffi Prinf^iple^ wa^xmb: f^^^ 
in^ for Elbow-Rppm and.^^!^,^^ Stage 
-But, not\\to trouble, the lieader 
vifhoit ^ptyri- :^bave-:don0^^ f.ha've 
A 2 chofen 

iv P R E F ACE. 

cJ^ofen and every where Jluck to three ; 
and as oft as a Phaenomenon occurred^ 
which I coiitd not account for by thefrty 
I have given it up as a Difficulty ; not 
defpairingy but that when all the Cir-» 
cumjlances of the Phenomenon jhall be 
thoroughly known^ they alone may be 
found fufficient. Itfeems not confijlent 
with the Regard a Phihfopher fljould 
have to the Uniformity of Nature^ ev&^ 
,ry where obfervable^ to call in a new 
Principle at every knotty Point. • Thbfe 
which I make ufe ofare^ , ^ 

Firjly Attradion of Gravitation. 
Ihat isy a Difpofetion in Bodies to move 
towards each other ^ even when at great 
Dijiances af under. 

' Secondly^ Attradion of Gobefion. 
^hat isy a like Difpofition in Bodies to 
move towards each other^ but dfftii0 
from the former, in as' much as it is 
obferved to take 'Place otily 'whin the 
Bodies are very ntzi together, ■ 

Thirdly, RepuUion, or a Difpofition 

- in 



in Bodies^ whereby in fame Qafes they 
endeavour to . avoidy or fly from each 

The firft of thefe. is Matter of daily 
Obfervation. Thusj a Ball let go from 
the Hand f alii ^ to the Ground. 

Tbefecond may befeen in the follow* 
inglnflance. A f mall Portion of a 
Fluid f or m^ itfulf into a Sphere or Drop : 
Which can only happen from a Difpofi^ 
tion in the Particles of which it confifls^ 
to come as near as pofflble to each other. 

An inflame of the third is this. If 
Air inclofed in a Bladder;^ hefqueezd 
into a lefs Compafs^ the Air within^ when 
the Prejfure is taken offy reflores the 
Bladder to its former Size : A plain In^* 
di cation that the Particles of which tb^ 
Air conflflsy endeavour to avoid or fly 
from each other {a)* 

"Jbefe Difpofltions in Bodies ^^?^ot 
the Refult of any Mechanical Cdufe 

(a) 5^^ another tnftwice of this Piffojition^ in Part III. 
Page 1 6 1. Natim of this Compendium. 

whatever j 

vi PRE F A C E. 

whatever; that is, fucb as. may , arife. 
from the Effluvia^ Bodies,, or. tbeJJ(H 
tion of any other material Subftance (b)i 
They are therefore the A£i of an'mim2i' 
terial CauJfe, in Virtue of wbicb inac^ 
tive Matter performs . the Ofices fir 
which it was defigmA 

" . . From 

« s • * 

■ . « X. 

(b) Deftionftration. In the firji Blace it is zuell inaivn^ 
that if Gravity ai5fs\upon bodies wth the fame Degr^ 
ef Intenfenefsy wbeibsp- they be in Motion or at Refi i it 
may he demonjirated that Bodies^ when proje6ied^ will de* 
fmbel^z,f2hc\2^sx ^nd that whm. ^tffsHng in Cyirlpld^ 
their Vibration^ will ^^ ifocronous, ^c. In the next. Place 
it is as well knmfrt^ that Bodies iijhen prffjefhd'do d^fcribe 
Para4x)la*«, anef^ t^ i^ra vibr^tin^ ki Cycloi^, ^^hi^ 
Vibrations are ifocronous, £ffr. >. From i^bich two Propo* 
fititms it demohfl^ativify foilowsSi\at i/^Graifity he the 
caufe of the ah$yemett{ioned EffeSii;^ it muji a£t upon Bo- 
dies with the fame Porcey^ whether fhey ie in Mot'tpn or at 

Jgain^ it is:V^elJMown^ Afc/ jjf Attraftion of Cohe- 
fion aSfs upon Kayi df Lights ioith the fame Degree of 
h^enfenefs^ ^fbfii^er\he tke Vsh^ity they f^ove with} 
it may be demonjirated^ that tl:(e Ratio of th^ Sine of the 
Angle of Incidence to the Sine fif^ihe jfhgle of RefraSf:- 
ion^ will be given. But in Refra£fion of Lights the 
Mfitio, pf thafe* Sims is given in, -FaSl^ 'if therefor§ At- 
traftion of Cohefion he tht iu>aufe\of. the' Refraction of 
Lights it mufi aft tipon Rays fff Ifighp fvith ihejpm^. In:^ 
ttnfnefs^ whatever Velocity they movn ipith^ 

But no Effluvia $f Bodies^ w materia' Sabftance, ofid 

in Jhort na material Caufe whatever ^ can a£t tcith^ the 

. - . fame 

PR E F A C E. vu 

From thefirfl and third Principle (c), 
together with the Properties of Matter 
enumerated in the fir ft Chapter of this 
Compendmm^ which Properties mufl 
he always underfiood^ the Elafiicitj or 
Spring of the Air^ and from thence the 
Nature and Propagation of Sound are 
accounted for. j^^ from the Spring 
of the Air confldered as being augment-- 
ed by Heat^ and diminijbed by Cold^ as 

fame InUnfmefi^ or havt ibe fame EffeSf upon a Body in 
Motion J as upon the fame Body at ReJI ; becaufe as it is 
very well known to Mathematicians^ to whom I addrefs this 
Note^ Body can only aSt upon Body, according to the Sum 
^r Difference of their Motions. It remains therefoye^ that 
the two Difpojitions herein mentionedy are not the Refult of 
any material Caufe whatever: Which is one Part of the 
Pr&pofition to he demonjirated. 

As to the other Difpofition in Bodies^ their Repulfion, 
Jince Rays of Light are aljo affeSfed by it, as it appears they 
are by an Experiment of Sir Ifaac Newton' j, referred to in the 
foregoing Note, it may very reafonahly be ft^pofed, though 
we don^t at prefent know the exa£i Law of its A^ion, to 
affeB Bodies in Motion after the fame Manner that it 
would do the fame at Reft , a)ii that it therefore is alfo the 
Refult of no material Caufe whdtever. 

(c) TTje Law or Manner ivherein thefe Principles arf 
^bferved to aSf in different Circumftances, are determined ' 
from Fails, in Part I, Chap. 3, ^e Law of the third, 
fo far as it relates to the Air, will he found in Part II. 
Chap, 3. of this Compendium, 



// is ohferved to be^ and the Airs being 
at the fame time affeSied by the jirji 
Principle^ the Phaenomena of the Winds 
are explained. By the fecond P rincipky 
the Cohefion of Matter^ the various 
Degrees of Hardnefs obfervabh in it^ 
the Dijfolution of Bodies by Fluids^ 
with other chemical Operations ; and in 
particular the Phaenomena of Fermen- 
tation^ and confequently the Caufes of 
Thunder and Lightningy &c. By this 
Principle alfo the rijing of Fluids in 
fmall Tubes y and from thence the afcent 
of Sap inVegetahles are accounted for \ 
all "which Particular s^ except the two 
firjly are treated of in thefecond Part 
of this Compendium: as alfo the Re- 
fraSiion of Lighty and confequently all 
that Train of Phaenomena depending 
thereony which is the SubjeSi of the 
third Part. By the fir ft Principky the 
fever al Circumftaitces relating to falling 
BodieSy and to the Motion of Projec- 
tilesy together with the DoEtrine of 



"Pesydulumsi \{treaJ^cl of in th&jirfi) and 
lihssoijk . all ti>ofiwMehsfjsiat^ to ify 
Prejfttre of Eiuidsi ^trut^d, sf ir{ the 
facond Part) aj^determui^\Anda^^^ 

aU is dtd^ed'ik^ m&^xus^iomlko^rim 
i^Acentral Eorce©,. jufiimtehai upon^ in 
ii^firfi^ , huiiarg^y ttndfdUj^:£xfilamed 
in the fourth Pjzr/y i^ mhithipff^ 
fhaJL the J)eammly l^oMeT\^tre\at jirji 
put\sk^ Mati{m.\ky their Creatar) we 
are enabled to affign the.Cau/e of th» 
Continuation thereof ^ with all its Mo- 
difiaimis imd\Irregtdafit{es\. io dei er- 
mine::. the \ne^€^ry \Shaf^ \of thofe Bu^ 
diei ^ ^nd\to xuioount for the eiSing and 
fiomi^g af\£i^':i^eflj &c. . f^f^lties^ 
ii^rgreut fep^iii^ for 'M(f^i^ Reqfon 

waite^able tdg^ afatisfaEiory Account 
<fy from the abovementhned Principles y 
-arejthe RefieBf(m\^ Lights its Emif 
fon frj^m lukiinoilt^ Bodies ^ and the For^ 
motion >and i/i/ceAt of Vapour. 7 his 
. :: a way 

X P R E F A C E. 

may be is only owing to the want 
of better Acquaintance with the Cir" 
cumftances of thofe Phaenomena; that 
jsy more ^fuficient Data, or FaBs to 
found their Solution^ . upon : So that we 
are not- to conclude immediatet^^ that 
the Principles are infuffieient', but ra- 
ther to wait with Patience: *The Dili*- 
gence of others may render that eajy^ 
which our utfmfi Efforts at prefent are 
not able to furmount. 


However y as a Reader unacquainted 
with Studies of this Kindy may wonder 
that fo many of the Phienomena or Ap- 
pearances of Nature^ fhoUldbe account- 
ed Jor by fo few Principles', andbecaufe 
it may be a Means of giving him fome 
Infght into the SubjeB of thefe Sheets, 
/ nsoill here lay down the following Pro- 
pofitionsy which are immediately dedu- 
ciblejrom the Principles, and alfo near- 
ly conneBed with the Phaenomena to 
be accounted for by them ; by means of 



^bicby be will more readily perceive the 
Connexion or Relation between tbe one 
and tbe otber» 

Proposition I. 

Matter being an unaSiive ,Subflance^ 
is utterly incapable of putting itfelf in- 
to Motion in any Direiftion whatever ; 
and will therefore in all Cafes move, 
or endeavour to move in that Dire<9:- 
ion only, in which it is urged with the 
greateft Force. 

Hence we have the true Idea of the 
Gravity or Weight of Bodies belong- 
ing to tbe Earths Bodies are, here, 
by Virtue of the firfi Principle, attrac- 
ted towards the Sun, the Moon, tbe refi 
of tbe Planets, and the Earth', but to- 
wards this lafi more Jirongly than to- 
wards any of the refl', andfo they tend, 
gravitate, or are heavy towards that. 
The Reafon that they are attraSed more 

a 2v forcibly 

itfi 1^^ Ft B F- A <^- Et 

forcihU towiiMs the EdrihYthaH to^rd& 
ihofe of hhr Bodies i is^ thai dlihbtigh U 
he one of the Laius of the firft Prikci-^ 
pkj that it operates according to the 
^antiiy df Maftdr in. Bodiess and 
therefore the, AttraBion . of the Sun 
fiouid be the fHofl f>'imIeHt, in as mUch 
as that Body vpntains the mqfi Matter i 
yet it is anpth& Latv if that Principle 
6t DifpoftioHy thatlt aBs more JVr&hg- 
ty according to the nkaf^efs of Bodi-es to 
eadh other: This latter Cdnfideratibkin 
the prefent Cafe^ overbaiances the for- 
mer y andfo the Bodies about us tend 
tcrjoaf-ds the Barth. 

P k;o p 6 s I t 1 o N II. 

' If a targe rouad feod^ be covered 
every wh^t^ 'with ftnalUelr qn^s to aii 
ej^bal Hei^lit or Diftatice frorti its Sur- 
face; ahd if thofe teiliet bnts tend 
towards the large 5B6dy, by virtiS^ of 
ihefififtP"riitcit)!ef, and are, ait die feme 


i^me/ dirpaffd\ta.d)r>\£tom eack othec 
by yuttwVt'^^Hffd'} aod fuppofii^ 
^thtr, thdt wbea tibcy toiich or arcr 
very near each other, their Difpofitidkx 
to avoid each other exceeds their Ten- 
dency to the large JBgn^y^ and when 
they are at a certain greato* Diftance 
ftoih each other, that Diipo£iti6a is 
kfs than their Tendency to the Jarga 
Body: Then. will thbfe fmaller Bodies 
keep dt certain Diftanoes from each 
other^ and conftitute an elafiic, com-' 
frejjtbk Subfla^ce Surrounding that 
krge Body, gravitating towsuds it on 
all Sides. 

Hence an Ide4 of the Nature and 
C&nditim of the Atinofpherey«rro«»»af» 
ing the E^t^^'^th aU its Properties 

N. B. When I fay a Body tends fo 
andt^r, I don't mrnn that it moves t9* 
'ioarSi it ^ hut otdy that it 'Osould fnovie 
towards it, if^Aoihing ^revemed 2&uSi 
ii ^ird whik imuniiiig aloft inU tit 


^r, tends towards the Earth, as much 
as one that is falUt^ dtmn\ for the one. 
•would fall as well as the other, if tMh 
thing prevented* 

Proposition HI, 

If, while the abovementioned fmal- 
ler Bodies are in the State fuppofed in 
the foregoing Propofition, any one, or 
mxxt. of them, be made to move, (fup- 
pofe for Inftance half way) towards the. 
next, it will by virtue of the third 
Difpofltion, drive qr impel thofe it 
comes nearer to, clofer together j which 
Bodies, when that other moves back 
again (as it will immediately do, 
l^ng repelled by them) will re- 
cede from each other again: That 
is, a kind of tremulous Motion wiU be 
communicated to them by that other, 
and for the like Reafon, by them to the 
next; and fi> on through the whole^i 
or. at leaft to a great Diftance iron^ 
^ce it began. Hence 



• • • « 

Hence we ffiay form an Idea hem 
Sound h excited by the Tremors of a 
Body durif^ its FibratiMy and propa- 
gatid tbraUgb the Air, 

P R-O P O S 1 T I O N IV. 

Otifc of die Laws hf which the ^ 
cond Principle is obferved to ad, is, 
that Bodies ad upon one another, not 
in Proportion to the Quantity of Mat- 
ter they Gontainj as by the firft Princi- 
.ple ; but only according to the Breadth 
of their Surfaces, and the nearne^ of 
thie .Surface of one Body to that of ano- 

From hence we may underfiand, 

that fucb Particles of Bodies as are 

flat orfquarey and Jo fituated among 

each other as to touchy or he very near 

one another in many Points^ will con- 

Jlitute what we call an hard Body, 


x»i B a E. F A C E. 

and thofe Particles which are more 
rmnd, orfofituated that Itfs ForUoni 
^f their Surfaces are itear M^etber^ 
^iJJrattraSi' one another ^ith a Itfs 
Force^ and Jo .farm ^ ^(l|£ter Bod^r ; 
thoje which are round, or nearly Joy 
will AttraU (snfi -fimtherjli^l-lbjsi and 
aljo Jlide more eafily over one another^ 
•tihdjofofin whflt we call 4 ft vaid Bddy. 

P R O" P OS I T I ON V. 

I I « t , 


When two Bodies isneettogcchery if 
the PaFtiolies which conftitiite the on^, 
be difptjfed,' by Virtue ^f 'the le^ohd 
-Principle, to -mjove towards ehofe oif -4?lie 
other with a greater Degree of F^de, 
than the Particles of either Body are 
.difpofed to move towards' themfelves ; 
'thofe of the firft willleavse it, ai?.d jiin 
in among thofe of thefecond: And^fojr 
the fame Reafon, thofe of thefebond 
-will iever from that, leave it and enter 
,in between thofe of the firil. And if 
.. .. the 


PREFACE. xvii 

die Motion with which this is done, 
be very violent, and the Bodies be of 
the inflammable Kind, their Particles 
by thus rubbing and claQiing one againft 
another, will be fufficiently heated to 
take Fire, and will burft out into Flame. 

Hence Diflblutions, Fermentations, 
Explosions, Eruptions of Vulcano's, 
Thunder, Lightning, Aurora Borealis. 
With all other Phsnomena of that 


Proposition VI. 

If a Pipe, open at both Ends, and 
of a very fmall Bore, have one End 
dipped into Water, the Water will run 
up into the Pipe above the Surface of 
the Water on the outfide (being drawn 
up by the Tendency it has by the 
fecond Principle to that Part of the 
inner Surface of the Pipe, which is 
juft above it, as it rifes) till that inner 

b Surface 

xviii PREFACE. 

Surface which is ftill juft above it, be 
loaded with as great a Weight of 
Water, as that Tendency can fupport. 

Hence a right Notion of the Afcent 
of Sap in Vegetables^ the ,Su«9:ion of 
Fluids by Spunges: With all other 
Phenomena reducible to that Head. 

Proposit ion VII. 

If a Body moving right forwards, 
but obliquely with refped to the 
Surface of another Body, at length 
comes fb near that Body, as to be dif- 
pofed by the feeond Principle to tend 
towards it; inftead of continuing to 
go right on, it will turn out of its Way 
towards that Body, before it comes at 
it ; and confequently will ftrike or en- 
ter it in a nearer Place, and in a lels 
oblique Diredion, than it would have 
done, in cafe it had gone right on. If 
it enters the Body, it ilill keeps turning 




out of its Courle the fame Way as be- 
fore, till it has got fo far within it, that 
there ihaJi be as many Particles of tlje 
Body behind it to attract it backwards, 
as there are before it near enough to 
attract it forwards : After which it goes 
right on in its laft acquired Diredion, 
till it comes near the other Side ; for 
while it is furrounded with as many 
Particles to attract it one way as 
another, it is the fame thing as if it 
were not attracted at all. When it has 
got fo near the other Side, that there 
are fewer Particles before it to attra6l it 
forwards, than there are behind itj near 
enough to attrad: it backwards, it then 
begins to turn out of its Courfe towards 
the infide of the Body ; that is, from that 
Side of the Body towards which it is 
going; and continues to bend its Courfe 
the fame Way, till it has got fo far 
out of the Body, that there are no 
Particles of the Body behind it, near 
enough to it to attradl it any more. 

b 2 . After 

XX r^ R E F A C E. 

After which it purfues an undifturbed 
Courfe in the Diredion it acquired laft 
of all. 

Hence we have a jufi Idea of the 
Refradiion of Light with all the Phe- 
nomena arijing therefrom ; tvbicb are 
no other than fo many Cafes of this 

Proposition VIIL 

If feveral Bodies be moving right for- 
wards, and at length be attradied bjr 
another Body, as fuppofed in the fore- 
going Propofition, but fome with 
greater Degrees of Force or Intenfeneis, 
than others; thofe which are attracted 
with the greateft Force, will turn the 
far theft out of their Way towards that 
Body ; and confequently if all of them, 
before this happened, were moving in 
one Diredion, they will be made to 
part {jrom each other, and move dif- 
ferent Ways. 




Hence an Idea of the different Re- 
frangibility of the Rays of Light; 


If a Body be made to move from 
another Body, towards which by the firft 
Principle it tends, its Motion will be 
retarded continually; that is, it will 
move flower and flower: If it moves, 
towards that Body, its Motion will be 
continually increafed ; and unlefi it be 
made to move diredly to or from it, 
its'Couriie will always keep bending 
towards it, ib that it ihall defcribe a 
Curve, concave, or hollow, on the 
Side next the Body. 

Hence all the Phenomena £/* falling 
Bodies^ and of Projediles. 


xxii PREFACE. 

Proposition X. 

If a Body, that by the firft Princi- 
ple tends towards another Body, moves 
towards it on the Surface of an incli- 
ned Plane, its Motion (as in the fore- 
going Propofition) will be continually 
increafed; and if it moves from it on 
the fame Plane, its Motion will be re- 
tarded continually, but lefs in Propor- 
tion to the Obliquity of the Plane: 
(that is, le^ in Proportion as the Plane 
deviates from the Perpendicular) the In- 
terpofition of the Plane preventing in 
Ibme Mealiire the Effedt its Tendency 
to the other Body, would otherwife pro- 
duce. And the Velocity it acquires by 
rolling down one Plane, will by virtue 
of its InaBivity, or that Difpofition 
Bodies have to continue their State of 
Motion or Reft, inable it to roU up 
another fitly diipofed. 


PREFACE. xxiu 

Henct the Solution of the Phamo- 
mena of Bodies deiixading on incliqi- 
ed Planes, and the Vibration of Pen- 



Proposition XI. 

If a Body aded upon by the firft 
Principle, move to or from another 
Body with a competent Degree of Ob- 
liquity and Velocity, it will move quite 
roui^d the other Body without touching 
it at all, returning to the Place from 
whence it fet out: In which Cafe it 
will revolve round it over and over 
again in the fame Path ; for being in- 
different either to Motion or Reft, and 
meeting nothing to take off from, or 
diminifli its Motion, it will have the 
fame Tendency to move on after any 
one Revolution, as it had at £rft. 


xxiy PREFACE. 

From benct we have the Solution of 
the Motion of the primary Planets 
round the Sun, and of the iecondary 
ones round the Primary. 

Proposition XII. 

If a Body be revolving about another 
as in the laft Propofition, and a third 
Body approaches tnem> towards which 
they both fhall alfo tend, the Motion 
of the , revolving Body will be dis- 
turbed : That is, its Path will be al- 
tered, and Irregularities in its Courfe 
will enfue its Tendency to that 
third Body in fbme Parts of its Courfe 
con{piring with, and in odiers being 
oppofitd to its own Motion. And not 
only fo, but the Tendency it has to 
the Body about which it revolves, will 
in fbme Situations he increafed, and in 
others be diminifhed by the Adion of 
the third; which Thing alfo conduces 
towards altering its Courfe. 



Hence the Lunar Irregularities, and 
all other Difturbance$ in the Motion 
of the Heavenly Bodies on their tot 
near Approach towatdt each other. 

Proposition XIII. 

Imagine a large Body cover'd all 
over with fmaller ones tending to its 
Centq: : Suppofe alfo a diftant Body, 
towards which they all tend, but the 
little ones with le^. Degrees of Force 
than they do towards the Body they 
touch. Then will fuch of thofe 
fmaljer Bodies, as are neareft the dif- 
tant one, lofe Part of their Tendency 
to the Body they touch; and fo will 
thoie fmaller ones which are fartheft 
off, or placed on the oppofite Side the 
large Body. But, as to thofe fmaller 
Bodies, which are at the fame Dif- 
tauce from the diflant Body with the 
Center of the large Body itfelf, their 

c Tendency 

xxvi P R E F A C R 

Tendency to the Body they lie upon,^ 
will be increafed. The reft will have 
their Tendency increafed or diminifhed 
more or lefs, according to their Near- 
nefs to thofe whofe Tendency is in-^ 
creafed or diminifhed. (d) 

Hence arifes the DifFerence In the 
Weights Bodies have upon the EartFs 
Surface^ at the Approach and De- 
parture of the Heavenly Bodies^ {but 
chiefly of the Moon^) to or from that 
Side of the Earth where the Bodies are\ 
and confequently the ebbing and flowing 
of the Sea, the Water rifing where its 
Weight or Tendency to the Earth is di- 
mintjhed^ and finking at the fame Time 
in thofe Places where its Weight is nug^ 
mented. That the Approach and De-^ 
parture oftheMoonJhouldcaufe agreat-- 
er Difference in the Weight of Bodies 
on the Earth J than the Approach and 

(d) What is affirmed in this and the foregoing Propo£tioo, 
depends on a Train of Reafoning too long to be incerted herf . 
To underiland it throughly, read Chapters the i8th and 19th of 
fart the f^oifrtb. 



P R E I? A C Ei xxvii 

Depafiure of the other Heavenly BodieSy 
a owing to the nearnefs of the Moon to 
the Earth ; which Cdnfideration in this 
Cafe overbalances theConfideration of her 
Smallnefs, the above-mentioned Effe&s 
depending in a great Meafure^ on the 
Proportion the Diameter of the Earth 
bears to the Dijlance of the Heavenly 

Propos irioN XIV; 

If a Bodyi whofe Parts tend to the 
Center thereof, eonfifls wholly of a 
Fluid, Or b^ partly folid and partly 
fluids provided fame of the Fluid be 
at the Surface^ and very diftant Parts 
thereof communicate with each other j 
and the Body have no Motion about 
its Axis, it will fettle into a fpherical 
Form, the mutual Tendency of its 
Parts towards each other, contrading 
it into the leaft pofllble Shape. But 
if it reyolves about its Axis,- all its 

€ 2 Parts 

xxviii PREFACE. 

Parts will endeavour to fly off from 
that Axis; but fuch as are fartheft 
from the Axis, more than the reft : 
Confequently thole Parts in its Surface, 
which are the fartheft from the Ex- 
tremities of that Axis, being alfo far- 
theft from the Axis itfelf, will have a 
greater Endeavour to fly off^, than 
fuch as are nearer thofe Extremities ; 
befides, as is evident, the former will . 
endeavour to fly off^ diredly from the 
Center, but the latter not (o. The 
abovemcntioned Endeavour therefore 
in the former will take ofi^ a much 
greater Degree of their Tendency to 
the Center than the Endeavour of the 
latter v/ill ; and fince the fame may 
be laid of thofe which are at any other 
allignable equal Diftances from the 
Center, all thofe which lie between 
the Center of the Body^ and fuch, as 
are fartheft from the Extremities of 
the Axis, will have their Tendency to 
the Center much more diminilhed, 


piR E F A C E. xxix 

than thofe will, which lie between 
the Center and the faid Extremities : 
Thefe latter Parts therefoffe will prefs 
in towards the Cehter, overbalance the 
former, and faife them to a greater 
Diftance from it than they were at be- 
fore, reftctfiiig thereby ^xx^ Equilibrium 
of the Parts of the Body on^ among 
another. On which Account the Body 
will afTume a flattifh or oblate Form. 
That is, fuppofirtg Lines drawn thro' 
the middle of the Axis at right Angles ' 
therewith, thofe Lines will be lengthen'd 
and the Axis will be (horten d. 

* t 

Hefici the Figures &f the Heavenly 
Bodies. . . > 

Proposition XV. 

The Impetus or For<» wherewith a 
Body in Motion endeavours to pooeed. 
forwards, depends not only on the" 
Quantity of Matter in that Body, > but i 


XXX P tL E f A C E. 

Hkewiife on the S wiftnefs theBody moves 
with: Thusj the Stroke of an Hamiiier 
is not only according to the Bulk or 
Weight oF its Headj but is alfd accord- 
ing to the Swiftnefi of the Motion it 
ftrikes with. If therefore two Bodies 
of eqvlal Quantities of Matter, be fuf* 
pended at the Ends of a Lever of e(|ual 
ArnM^ each of them when the Lever 
turns bii its Center, having equal De- 
grees of Swiftnefs or Velocity^ will 
therefore have the fame ImpetUs or 
Force whereby thdy endeavour to pro- 
ceed (being in like Ciretimftances with 
refped to both thofe things, which 
a|one can givie the one a Force or Ten- 
dency to move on with, ftiperiot" to the' 
other) and consequently neither of them 
will pre-ponderate. If one of th^ 
Bodies be larger than the other, the 
larger Body having the fame Velocity 
with the other, but more Matter, will 
have the Advantage, and preponderate. 
If the Arms of the Lever are unequal, 


PREFACE. xxxi 

and the Bodies equal, that Body which 
is at the greateft Difiaiice from the 
Center of Motion, moving the quickef^ 
will have the Adv^tage over th^ other 
that way, and overpoife it. So that 
the leaft Body or Power, imaginable, 
may be made to equiponderate, over- 
poiie, or keep in Motion the greateft, 
by being applied to fuch a Machine, 
and in fuch Manner, that when the 
Machine moves, what it wants in 
Weight or Force, may be made out 
■t by the Vekjcity it has, compared with 
the Velocity the Body has at the lame 
Time, which is to be equiponderated, 
over-poifed, or moved by it. 

77>is holds equally in all Machines, 
and is the Foundation of their Theory. 

Proposition XVI. 

Imagine the Surface of a large round 
Body to be covered every where, or in 


xxxii PREFACE. 

Pairt, . with fmiall^r ones to an equal 
Height, and. tikat thefe fmaller ones 
tend .towatd^ the large Body hy tht 
firft Pfinciple ; imagine alio die whole 
Mzfs of fnialler ones dii^ided into jCor 
^liiDs readiing; from tcjp to bottom ; 
4Jioife Columns, if theirB^fes be equal, 
,will equiponderate, or. be an equal 
XiOUJQterpoife to one another} and (o 
theyiwill, if their, Eafes be unequal: For 
in this Cafe the Columnsr being of uiif 
.equal Size 'in iDiameter, -if a lar- 
ger Column ful^fides, the lower Parts 
.■of i^ajt .Column '( to find .Room for 
^themfelres ) will raife a fmaller Co- 
lumn farther than the larger one fet»- 
tied in the fame time, and in fuch 
^uc^brdon^ that, what the little Co- 
i^unn wajats ih^ Weight, will be made 
out to it in Velocity ; and confequent- 
ly, according ctQ what was fhewn in 
the foregoing Propofition, the little 
.Column will be a juA Balance to the 
greater. ... . ^ 

.•• _ Farther 

PREFACE. xxxiii 

Farther, if in the abovementioned 
Suppofitioni, there be a Body among 
thofe fmaller ones, heavier than a 
Bulk of them equal to its own Bulk, 
a Column of which that Body is a 
Part, will be heavier than any other 
Column of an equal Bale; it will 
therefore, permitting the_Body 
to come to the Bottom: if the Body 
be lighter than a Bulk of the fmaller 
ones equal to its own Bulk, a Column, 
of which it makes a Part, will be 
lighter- than any other ; the Body 
therefore will be buoy'd upwards, till 
it rifes fb far out above the Surface, 
that it, together with the Column be- 
low it, may be a Counterpoile .to ano- 
ther Column of equal Bale. 

Hence the Effeds of the Preffure of 
Fluids upon one another^ and upon So- 
lids immerfed in them. 

d Pro- 

xxxiv PREFACE. 

Proposition XVIL 

Imagine the Surface of a large 
round Body cover'd every where, or 
in Part, with fmaller ones to an equal 
Height; and that thefe fmaller ones 
tend towards tlie large one by the firft 
Principle, and that they are at the 
fame time dilpofed to fly from one 
another by Virtue of the third, eonfti- 
tuting thereby an elaftic Subftancc 
furrounding that large Body, as in 
Propofition the fecond ; and let them 
be divided into Columns, as in the 
lafl Propofition. And let it be far- 
ther fuppofed, that the Difpofition in 
thofe fmaller Bodies, whereby they 
endeavour to depart from each other, 
is capable of being increafed by Heat; 
and that at the Bottom of fome of 
thefe Columns, that Difpofition is ac- 
tually increafed, but no where elfe, 
or at leafl not in Co great a Degree : 



dien will the Bodies, where that Dif- 
pofition is increafed, diflufe them- 
felires into a larger Space, and fo tak- 
ing up more Room than an equal 
hfumber in the neighbouring Columns, 
a Column of which they are a Part, 
will become lighter than a neighbour- 
ing one of an equal Bafe. For, fince 
the Bodies in the lower Parts of this 
Column, are more diftant from each 
other, than fuch as are in other Co- 
lumns, this Column cannot contain fo 
many of them; that is, .it cannot be 
fo heavy as another of equal Bafe, un- 
lefs it be longer; that is, unlefs the 
uppermoft Parts thereof fland out 
above the Tops of the neighbouring 
Columns ; but this they will not do ; 
for by Virtue of the Tendency thofe 
Parts have to the large Body, they 
will immediately (like Water raifed 
above the Banks, which before con-^ 
fined it) fpread themfelves every Way. 
This Column therefore, which, ac- 

d Z' cording 

xxxvi PREFACE. 

cording to the forcgoidg Propofiton, 
before this happened, was a Counter- 
poife to thofe, which are round about 
it, being now become Hghter, is no 
longe'r fo. The Confequence of which 
is, that the lowermoft Parts of the 
neighbouring Columns, will prefs in 
under this from all Sides to reftore the 
Equilibrium. Neither can the Equi- 
librium be reftored, fo long as the 
Place we have been confidering re- 
mains hotter, than thofe which are 
•round about it. For, fince the Bodies, 
that come in, will fpread thcmfelves 
into a larger Space by Means of the 
Hea^ they receive there, and fill up 
more Room, than the like Number in 
another Column of equal Bafe, the 
Column to which they belong, will, 
for the Reafons abovementioned, al- 
ways be lighter than another of equal 
Bafe. And confequently, according 
to the Tenour of the foregoing Pro- 
pofition, the neighbouring Columns 


PREFACE. xxxvii 

will overpoife it, whatever Dimenfions, 
as to their Baies, we fuppofe them to 
be o£ . 


Imagine the like to happen to a Co-- 
lumn or Columns of the EartFs At^ 
mofphersy and the lower Parts of the 
neighbouring Columns rufhing in ac^ 
cordingly at the Bottom from all rounds 
and you have an adequate Idea of the 
Caufe and Nature of the Winds; 
every Stream of the Particles of the 
Atmofphere ru/hing in^ as ahave^ being 
a diftinSi Wind blowing from that 
Point of the Compafs from which they 
come. Andy if you conceive the Center 
of that warmer Space to Jhift its Place 
varioufly upon the Surface of the 
Earthy you then get the Idea of the 
feveral Sorts of them^ as the Trade 
Winds, Monfoons, ftff. For Inflance^ 
if it Jhifts regularly along the fame 
Pathj it caufes Trade Winds ; if now 


xxxviu PREFACE. 

forwards^ and then backwards^ Mon- 
foonSy &c. 

Thefe are the Principal Phaenomcna 
in Natural Philofophy that are inde- 
pendent of each other \ the reft are for 
the mo ft Part^ no other than fo many 
particular Cafes, Circumftancesy or 
Confequences of thefe, or, in fbort one 
way or other related to them. For the 
Solution^ of which I refer the Reader 
to the Book it f elf 

From a due Confideration of the 
Propajttions here laid down, the Reader 
will be able to form a true Judgment of 
the Nature and Bufinefs of Natural 
Philofophy; .will fee the Uniformity 
</W Cbnfiftency of the fever al Parts 
thereof with each other, and therein the 
wonderful Wifdom and Contrivance of 
the fupreme Being, in choofing fo fhort 
and eafy a Method of producing fo 
great a Variety of EffeEis, 


PREFACE. xxxix 

Tiere is one Thing more I think 
proper to he taken Notice of^ before I 
put an End to this Preface ; viz. l^hat 
it has been a Jianding OhjeEiion a^ 
gainji all Natural Philofophy in gene-- 
ral\ that 'whereas it afcrtbes EffeBs to 
natural or mechanical Caufes^ aUing 
by fixed and unalterable Laws, it 
therefore excludes a Providence and the 
immediate Care and ProteBion of the 
flipreme Being, making him no other 
than an Idle SpeBator of Tilings here 

In Anfwer to this^ it is to be conji- 
dered in the jirjl Place^ that the Prin- 
ciples of the Philofophv which is now 
received^ are fo far from being m^c\\^^ 
nicalCaufes, at leajl thofe which are here 
made Ufe of thatj as above demon- 
Jlratedj they are the very Reverfe \ and 
confequently can be no other than the con^ 
tinual aSiing of God upon Matter^ 
either mediately or .immediately. ^ Since 



then Natural Philofophy, by accounting 
for the Phaanomena of Nature by thqfe 
Principles^ tends to Jhew the Reality of 
them'y it is evident that it isfo far from 
excluding the 'Dtityfrom being concern^ 
ed in the Affairs of this Worlds that 
it tends to demonfirate that none are 
performed without his Order and Di- 
reEiion, Neither^ fecondly^ does Na- 
tural Philofophy inculcate, that the 
Laws by which thofe Principles aSiy are 
fixed and unalterable : H^e Accufation 
is therefore foreign^' But to confider 
this Matter a little more particularly. 

When, in Natural Philofophy, a 
Principle is faid to aSi according to a 
particular Law, • the Meaning is not, 
that it aBs necejfarily and unalterably 
fo\ but only^ that it does fo ordinarily, 
and in common Cafes. Doubtlefs the 
Author, both of Matter and of thofe 
very Principles by which it a£ls, can 
at any Time, in the Room of its ordina- 
ry Opperationf fubfiitute a different 



oncy and by that means produce Effe&s 
contrary to the common Courfe of Na- 
turey whenever he Jhall think proper. 
VCbat he has donefo^ when wife Ends r en- 
quired it ^ appears from Hijiory. That 
it may be done a Thoufand Ways^ un- 
perceived by us^ is evident ; the Ope-- • 
ration of natural Caujes [as they are cal- 
led) being to us almoji always out of 
Sight. For Infiance^ though Light- 
ning may be accounted for by thefe Prin- 
ciples ; and in all Probability is ordi- 
narily the Refult thereof *y yet who will 
affirm^ in any particular Cafe^ that 
thofe Principles formed that very Light- 
nings or that its Courfe was direBedby 
them f Upon the whole therefore^ to pre- 
fume^ that the ordinary and common 
Courfe of Nature is not fometimes aU 
teredy is hafty and unwarrantable. 

e THE 

ERRATAinthe Preface. 

T) Age 1 0, Line i ; dele U ; Page 24, Line 1 3 ; read, 
^ itijut } Page 26, laft Line but 2 5 read, inferied. 







rHE Jntrbduifkn^ Page x 

Chapter f. Of the Properties tf B^^ 7 

Cha?. n. OfVacuuniy 10 

-Chap. III. Of Attraefion and Repuljtm^ \% 
Chap. IV. Of the Laws pf Motim y ao 

Chap. V. OffaUingBMesy 14 

Chap. VI. 0^" ^Af Defcent of Bodies on oblique Planes^ 
and if Pendulums^ 1 g 

Chap. VII. OfProfe^liSy 55 

Chap. VIII. Of Central Foreesi 43 

Chap. IX. Of the Communicaiim of Motion^ 48 

Chap. X. Of the Mechanical Powers, 58 

A p p fi N p I X to P A R T L ' 

Chapter I. Of the Vibration of a Pendulum in a Q« 

Ch ap. It. Of the Centers ofOfcillation and Percidffi§Hy ' 

c 2 P ART 

ijtiiv CONTENTS. 

Hydroftatics and Pneumatics, 

Chapter I. Of the Phenomena which arife from the 

Chap. II. O/* /)&^ Eff'^^ Fluids have on Solids imfjurfed 

Chap. III. (^the Air^ 33 

Chap. IV. Of the M^an(;/LOf Fluids^ . 41 

DifTertation W^ OfSoind, - '• A ^ * 47 

Diflert. II. Of Capillary Tubes^ 57 

Diflert. III. 0//^^rv?«;^/iWf/M'^ 7$ 

Diflert. IV. Of the Barometer^ 83 

jDiflert. V. Of the Origin of the, mnis^, v - ^ . ii^ 

piffert. VI;:' ©/ ik^f^r^ti^. i'^/f'A^M ^^»rs\nd 

/ y /]b^/r Refolution mtp^ Kain^'^ow. fn^ Hatl^ 3190 

J5>iflert.^.y IL J^J\ the Miufe ^f !il^unS(^^ apif . Vt£htnings 

and of the Aupjra^tta|fs^ \ _;!'.*' . ' ,. j[4^ 

JDiflert. VIII. Of'Ferment^ttony ][ -}. .. ' / . , 17 f 

p A R ^^ ; _ Hi. 

yx. __0;^>T iXj'iSi,- ■ ■' ;•'■'■'■> 

**. f«v •»*•*»»>. *\ '.. V . /F./ 

^bnAPTER I. OfW/UatuNandPropagatiifnifLtgM 

Page 3 

ChaI». Ilr 9^ tfe Cauj^^of .^fra^ion and, the Law 
*" wperehy It %s performed^ .•./.... ^ 

e^AP, ill. rOfihe Refra^ion^f light in^ajtng throuj^ 

''• * '• plainmyphrUdl'Sn^ces, • v' - * ?8 

Chap. IV.. Of LenffSy ^nd the Aiqnner in which Rays 

* areaffeifediffffaffihgthroughrthe^f ' 44 

Chaf.V. Of the Eyey 55 

G^.\l\ Of the Nature of Vift9n^ ^ S6 


contents: ixlY 

'CtiAt. Vih OfthiAfpi&fmct\f.'Qhjia$fitn tiraugk 

Afedia of different Forms^ • j.% 

PllTertation I. OfikeHorhonialMo9H^ 86 

OlAf. Vin. Of fb0 Manner whetein Light is refleaiiy<)j 

€ii^A>. IX. Of fht R£fte£ii9n sf Light frm plain and 

fphertciil Skffaees^ lOo 

CtiAP. X, Of fUe Jfypearance of Bodies feen by Light r^ 

^ fisihd friMfhin and fm . n8 / 

<>rAP. XL Vf the different Refrangtbility in the Rays tf 

• . ^ Light \ of4he> Colours the dJ/iinii Species of them 

/ are difpofed to excite ; and of the Haufe of that Va^- 

^''^' riety of Colours which is obfii^aUeih Bodies^ '34 

Cm A P. XII. Of the Ratifications in Bodies^ which dif^ 

pofethem to reflM the Rays of different Colmrsy I4)r 

€itAp. XIIL OftheCaufeofCfpacityandTranfparenCy 

in Bodies^ * 15^ 

rlHflert. II. Of the Caufe of Rifraahn of LigU^ 158 

'Diflert. III. Of Mierofcopes and Telefcopes^ 169 

'Diffeit. IV. Of the Rainhoto^ ' 18^ 

Qfthe Qbfcura Camera^ and the Migic Lantern^ 9, im 

P A R T IV. 

the Introduaiony P^ 3 

Chapter I. Of the Bodies which compofe the Solar Syf 

tenty and their real Motion^ 1 1 

Chap. II. Of the fixed Stars^ 25 

£haP^ III. Of fuch of the apparent Motions of the hea^ 

venly Bodies^ as arifefrom the Motion of the Earth 

about its Axis^ 33 

Chap. IV. Of the apparent Motion of the Sun arifing 

from the EartVs revolving about itp 35 

Chap. V. Of the Earth* s annual Parallax^ the Nutation 

Xth^ Poksy and tb$ Preceffton of the EquinoSfial 
ints^ 5^ - 






Chap. VI. Of the ^hmmmena tohicb arifi from the 
Motion of the Earthy and of the inferior Planets 
Mercury jand Venus ^ conjointly^ rg 

Chap. VIL Of the Phanomena which are owing t& the 

Motion of the Eartbj, and that of the fuperior Pla* 

nets^ Mars Jupiter and Saturn^ conjointfy, 66 

Chap. VIII. Of the Phenomena ^f the Moon^ y% 

Chap. IX. OftheEclipfesoftheSunandMoon^ 86 

Chap. X. Of tie Ph^enomena of the Satellites of Jupiter 

and Saturn I thejr Eclip/es and Occulta tions: Jnd 

alfo ofSatstrn^s Ringy o^ 

Chap. XI. OftbeComets^ ^g 

Chap. XIL Of the Parallax of the hem/enly B^diesy 1I3 
Chap. XIII. Of the Refraaion of tbe.Atmofpherey and 
the CrepuTculum or Twilight ^ i ty 

Chap. XIV. Of the DoSlrine of the Sphere^ 125 

Chap. XV. The Defcription of the Orrery and the Ghbet^ 

Chap. XVI. Of the Equation of Ttme^ 178 

Chap. XVIL OftheDiviftonofTme, 18, 

Chap. XVlII. Of the Forces neceffary to retain Bodies 
revolving in circular and other Orbits^ 203^ 

Chap. XIX. TTfe Lunar Irregularities^ the P voce (f on 
of the EquinoSfial Points^ the Nutation of the Poles 
of the Earthy and the Ebbing and Flowing of the 
SeOy accounted for^ 24.0 

Ck A P. XX. Of the Figures 0/ the heavenly Bodies^ zja, 


Compendious Ststem 

O F 

Natural Phflofophy. 


Containing the Mathematical 
Demokstratxons and £bme 
occauon^ Remarks. 

P A R T L 
O P 

^^ Properties cf Bo Dims* 
^[ieir Laws •/ Mo t i o n* 

72i« Mechanical Powers* 


Footed at the UNxyERsiTT;F»if«i' 



*^ .> 


. i 

r • 


, ; » I. 

^ 41. 



» ' 

•' i 

•A |r ,» 


. » 

• . I -• >. 

« ." . .'- 

• ♦ » 


Compendious Systeac 

O f 

< < 

Natural Philofopby. 


. » * • • 


SO wild and extravagant have been the 
Notions of a great part of Philofophers, 
both ancient and modern, that it is hard 
to determine, whether they have been 
morediftant in their fentimcnts from trtith,or 
from one another 5 or have not exceeded 
the fancies of the mod fabulous Writers, even 
Poets and Mythologifts. This was owing to a 
precipitate proceeding in their fearching into 
Nature, their negleftingthe ufe of Geometry and 
Experiment, the moft ncceflary helps to the 
finding out Caufes and proportioning them to 
their Effefts, 

Their manner of Philofophizing was to 
give bodies certain arbitrary properties, fuch as 

A bcft 


bcft fcrv'd their purpose in accounting for the 
Phasnomcna * of Nature 5 from whence pro- 
ceeddd fo many various Sefts of Philofophers 1 
cvc^y one afcribing a different caufe to the 
fame appearance, as his particular genius and 
imagination led him. 

Th€ chief agreement obfcrvablc among moft 
of the Ancient Philofophcrs confifts in this, 
"wz. that they conceived -aH bodies as compo- 
fitions of Air, Earth, Fire, and Water, or fomc 
one or more of thefe, from whence they ac- 
€(uired the name of Principles or Elements,, 
"^ich they dill reuin. - 

Epicurus advanc'd a little farther, and a^(^ 
ierted^ that though bodies confided of fome 
one or more of thcfc, yet that they were not 
flridly Elements,, but that they themfelves con- 
iiAed of Atoms ^ by an accidental cpncourfe of 
which, (as they were moving through infinite 
fpace in lines nearly parallel) all things received 
their form and manner of Exiftcncef.. 

Dns Cartes has contrived an Hypothefis very 
different from the reft, he fets out with a fup 

* By a Phsenomcnon of Nature is meant any motion or 
fituation of bodies among one another, which offers it lelf to the 
notice of our fenfes, and is not the immediate rcfult of the adlion 
Tof an intelligent Being. 

f For the Opinions of the Ancient Philofophcrs confult Dioge- 
nes Laertiui and StanUfs Lives. 



yo/itjoa that .die Univetfe^at firft was entirely 
fiill of matcds tliat> from this matter when 
firft put in motion^ there would neceflarily be 
xubl^cd off (by the grinding of the fevcral parts 
one ^mft , aiiother). foode particles fuiSiciexijtf* 
ly fi«e to pafs: through the hardeft and xfioSt 
folji4 bodies without meeting with any rcfift- 
ance: of tjipfe conilfts hls^MAterm fuhtiU^ 0( 
MMffia^^£iff9ff7if4^^M^ imagined that &oa\ 
hence alfo would refuit other particles of a glo- 
bular form^ to which he ^gaye the nam^: of 4/^ 
feria Jecumii ^Elemenii. T\ip(c wh^ fq 

iFar lofe their firft figure, as to. cdplf under the 
denomination Qf'Mahtla prtmi oi fecundi Ele* 
mentis he call'd Materia tertn Elemeniii.znd, main- 
tained that all the variety, which appears in na- 
tural bodies was' owing to different combina- 
tions o/ thofe Elements* 


He like wife fuppofes that God created % 
certain quantity of Motion and allotted it to 
this roals of Matter, which therefore (being 
(reared) can no more be annihilated without 
an omnipotent hand, than JBpdy it felf $ \i\. 
confequence of which he wa? obliged to 
t^each, that, the quantity 6f motion is al- 
ways the fame : fo that if all the Men and 
4ninflals in the World weye inoving, yet 
ilill there would be no more motion^ than 
yh^n thev were at reft; the motion loft 

A ? being 


beltij tnttSfrtrdl to flM!^ jfiilM*. ■ So'iliisa- 
toufftaHe >it Iht «6iSbii» of <hfe ^tH' tfej- 
Mfojllitrj tfi* ft'is- flJjpriiiHg his *(B*it(* 
Blodld have ittct "Withi ffi£h"4«rvctfa WStiji"- 
lion, ana have gbt «< nfoft* s^ahy'* Pft& 
lofiiphcrs oti- MS Ale'/' iftW liiJfWRhlMrtii^ 
it *as radre ■ABxiiYhMii tW Sede^ltetlS 
tttjlMiliat ferim, tht% rtraftall fed HlplMSd 
fc rtakc teay for iis •in^'ni6tt*HJ^&h«!s-. 

(s b^eii .M by a late Wri- 

H 'to "his gtWt eeniir^ aft tx- 

itticHiatfts.vahd by M'uKi 

'nss^rogithcr ti' haVe, kWeR 

)f great iraptb+tlBeriK W thi 

Writer bugtit to hivtWen 

ibblt'd upon, ih t>ls tdtlcli 

Book of Principles as DeWanKratlOns, ait OBiy 

lUudtations, there not being a pemonftration 

from Geometry in all his tftilOfopliKal WotkS t-. 

■ Tiii picKht' tnct'hod'ofrtlloTotitliiitig cttai 
ifili'd'ty Sh.jfific^f/^yiim ii"t6 fiftd <»Ut-th« 
J^^w's pf Nature" byj'experitncnfS ^nd tjbf^a- 
tions/ J3,,<his. with a proper ap^titatrbn 6t 
Ccotnstry, is . owing the it?* adWWagi IhB 

• }XrWoi'min his Reiieitioiis on Aildelil? suid' SSWent 
Irfsniing; ■ ■ ' ■ - ■ ' ■• 

' + Set aisSobjeftdiltHfs'd wore at large jwiTo/^fttrodo^aw 
to hb Eiajninalion of Dr, Burnetii Tlieory ttf. Second Edition. 

-ptmrltSfRm -it Miii&fiftfif Bra^ft Hi m 

ijtetasii!^ diidii ilia m m-m/imcmst a 

at Viifttb iftigiilft AM a Sfttaii Wf mmfSl 
PhUbKpht ei* bt Wliritld Dj Shf tiffift fiie. 
thttd: fot -Withoat'oliffirtaibtft ft ft HHpbr- 
lible *e iWom (fifedWr tRir Pifehdftc'ia » 
Natritii *ii!ht)tt «i(ciHifthf4 Wt Aiftlt K^- 
norant of the mutual adions of bodies, and 
without Geometry we can never be certain 
whethet the eaufes aflign'd be adequate to the. 
dFefts wc would explain, as the various Sy- 
ftetns of Philofophy built on other foundations 
evidently fliew. 


iidering the difcoveries of that excellent Phi- 
lofophcr laft mentioned. To him it is prin- 
cipally owing, that wc have now a rational Sy- 
ftem of Natural Philofophy j 'tis he who, by 
putfuing the fure and unerring method of rea- 



JiMUBg from c;tpcrimcnt and obiTciyation. joyiv- 
^d iritb the moft pix>fpiiQd 5kiU in Geometry, 
has canycd his <uiquj^ies to the mo(l minute 
aod iavUtbIc patxs of mattcri as v^ell as to the 
moft rcmpce bodies in the Umveire, and has 
cfiaUifh'4 9 Sjflcm. aoc,rubje^ to the uncer- 
cnaty g<> i»ere Hypothefis, but which, fiaods 
i^on the fecurc baits of Geometry it fclf. 


C H A p. r. 

^e Properties of Body. 

IT being the de%Q of th^fics or Natural 
Fhilofophy to account for the Phenomena 
of the Material World* it mud be oar method 
to begin with laying down the known proper- 
tics of Body. 

These are i. Solidity, z. Exten/ion. j.Dt- 
vifibility. 4. A capaciry of being moved, ftotsi 
place to place. 5. A Paffivenefs orlnadiyity. 
Theie are all the eflential properties of Bodies 
that we arc acquainted with^ and that they are 
eifentialy appears from what follows. 

I. Solidity, called al fa Impenetrability, is 
that power which Body has of excluding all 
others out of its place. 

That Body, as fuch» mufl: be endued with 
this property follows fr<;>m its nature, for other- 
wife two bodies might exifl in the fame placc> 
which is ablurd. The fofteft are equally fo- 
lid with the hardeft, for we find by cxpcri- 
ment« that the itdcs of a Bladder filled with 
Air or Water, can by no means be made to 
come together *. 

* At Florence ^ hollow Globe of Gold was fill'cf with Water, 
and then exa^ly clos'd ; the Globe thus clos'd was put into si 
Prefs driven by the force of Screws ; the Water finding no room 
for a nearer approach of its particles toward each other, made its 
way through the pores of that clofe Metal (landing in drops like 
Dew on the outfidc, before the Globe would yield to the violent 
PreiTure of the Engine. V. Locked EiTay B. z. c 4. 

2. That 

& T^e Properties of Body. Part !• 

2. That Body is .cjtffljdFd,. )s fclf evident, it 
being impoffiWc to conceive any Body which 
has not Ici^^t^ b];eadjix an4 thickia«&> that is> 

3. It is no \^(% evident that Body is. divi- 
lible, for fince no two particles of Matter caa 
exift in the fame place, it follows that they 
are rea}ly diftind* from each other> which is a)i 
that is meant by being divilible. ♦ 

In. this fcnfc the Tcaft conceivable particle 
muft ftiU be divifiblc, fince it wiH confift 
of parts, which will be really diftinft * To 
illuttrata this by^ a familiar Ihftance: Let the 
Icafti imaginable' piece of matter be conceived 
lying on a fmooth plane furface, 'tis evident 
the furface will not touch it every where, thofc 
parts therefore, which it docs not touch, iriay 
be fuppofcd feparable from the reft, and io 
on as far as we pleafe $ and this is what is 
meant' when we fay matter is infinitely divi- 

. *. This Propofition is demonftiatcd Gcometncally thu», fup- 
pofe the Ime AD (Fig. i.) perpendicular to ^F and, another as 
G/f at a fmall diftance from it'alfo perpendicular to the Yamc 
line ; with the Centers CCC &c. defcribe Circles cutting the Ime 
GH in the points e, e, e, &c. Now the greater the Radius AC 19, 
the lefs is the part e H, But the Radius may be augmented in in- 
finitum,^creforp the part rfi may be diniiniihed in the fame 
manner 5 and yet it can never be rediicM to nothing, bccaufe the 
Circle caa never coincide with the rlglit. line -^^F; confeqi^^ntly 
the parts of any magnitude reprefented by GK m^y be diminiihca 
in infinitum. ^ E, D. V. KeiPs Introd ad Phyf. Prael. 3, 4, 5. 
Grayefand6\ Elem. Math.Piiyf. L. I. c. 4* Schol, 


Cfca|fc/3r. 7%e Prspertm of Body. 9 

, How • far. to^icr imay; aflually be divided, 
may ifi ionjc m^naer bccojop eiv'dfrom hoice *, 
that, a pietc of Wire, gilt with fo fmall a quan- 
tity as, ? gmins of Gqld, may be dtawaout to 
t^e Iqixgih of 13000 f?ct, the whole fujface of. 
it ftill.ftoiaiiwng cove?'d with Gold ,t* 

A quantity of Vitriol b,eing diffolved and 
mix'd with 9000 times as much Water, will 
tinge the whole, cojifeqfuen,tly the Vitriol will 
be divided into as many parts as there are vi- 
iiblc portions of matter in that quantity of 

Thj^i: arc Perfumes,, which, without a fen- 
fiblc diminution of their quantity, fhall fill a 
v?iy lwg€. ^acc with their odoriferous par- 
ticJ^s,: vfhieh muft therefore be of an incon- 
ceivably faiailnefs, fince there will be a fufficient 
nujnbcroili every part of . that fpacc, fenfibly 
to, ^|&:^:tl|L/& organ of fmcUing. 

]4, . TfliAT :all naatter is moveable follows from 
its h%\ti% finite : and to fuppofc it pofitively 


• We have a furprizing iuftance of the minutenefs of fome 
parts of Matter from thenatijire of Light and Vifion. Let a Can- 
dle be fitted and'plaqed in aii open plane, it will then be via- 
ble two mil^ round, confequently was it placed two miles above 
the furface of the Earth, it would fill with lui. .inous particles a 
Sphere, wh6fe diameter was four miles, and that before it had 
loft ^py fenfiblc part of its weight. The force of this Argument 
will appear* better when the Reader is acquainted with the caufe 
of Vifion. 

t ^^^ ' Introd. ad Phyf. Prxl. 5 . Religious PKilof. Con- 
tempi. 25. 
X Mc^. de r Acad. 1706. • 

B infinite 

lo f^acuunu Parti. 

infinite h abfurd, bccauft it' conMsof parts*. 
5. By the Paffivencfs or inaftivity of mat- 
ter, (commonly call'd its Vts Jnerm} is meant 
tlic propcnfity it has to cominuc itsftatc of Mo- 
tion or Reft, till Tome external force aOs upoii; 
it. This will be farther expUin'd under the 
fieft Law of Nature.- 

. ♦ ■ ■ 

C H A P. IL ..'.:... 


Of Vacuum. 

\ TpLACE void of Matter is cjird «ittptf 
II Space or Vacuum. 

II. It has been the opinion €)f feme Phi- 
lofophers, particularly the Carte fans^ that Na^ 
ture admits not a Kacuum^ but that the U- 
xiivcrfc is entirely full of Matter, in confeijuencc 
of which opinion they were oblig'd tix^flen?,- 
that if every thing contained in a veffel could^bc 
taken out or annihilated, the fide^€>f that vef- 
fel, however, ftrong, would come together 5 but 
this is contrary to experience, for the air may 
be drawn out of a vefiel by means of the 
Air Pump, which will ncverthelefs remain 
whole, if its fides are ftrong enough to fup- 
port the weight of the incumbent Atmosphere. 

III. Should it be objeded here, that it is im- 
foilible to extrad all the Air out of a VefleU and 

* See Mr. i^'s Tranilation of ABp. King d^Origtm Mail 

Note 3. 


Chap. 2. . Vacuum. x i 

that there will not be a Vacuum on that ac- 
count ; the anfwer is* that itncc a very great 
part of the Air that was in the Veflcl may be 
xlrawnx>ut^ as appears by the quick defoent of 
light Bodies in a Receiver^y there muft be ibme 
vacuities between the parts of the remaining 
Air : which is fufficient to confiitute a Vsuuum. 
Indeed to this it may be objeded by a Oirte^ 
fiany that thofe vacuities are fiird with Ma^ 
tcrU fuhtilis that pafles freely through the 
fides of the VefleU and gives no refiftance to 
the falling Bodies $ but fince the exificnce of this 
fame Materia fuhtilis can never be prov'd, we 
are not oblig'd to allow the objedion> espe- 
cially as Sir Ifreic Ntwtm has found, that alJL 
Matter afibrds a refiftance nearly in proportion 
to its denfity f* 

There are many other Arguments to 
prove this, particularly the motions of the Co* 
mcts through the Heavenly Regions without 
aay feo/ibie refiftance ; the different weight of 
Bodies of the fame bulk &c^ but thofe being 
ndt yet explained are not fo proper to b^ in* 
fifted on in this place. 

* By this Term is meant any VcSsX, oat of which we eztn^ 
4ie Air by the Air Pump, 
j* Nfwtom Opt. p. 310. 

8 z. . CHAP. 

12 AttraSiionand Rkpulfion. 'Pait/Ii 



Of AitraSiion and Repulfion^ 

. TTIESIDES the -fOTdiicntioned' prbper- 
X5 ^^s olF Maft^ri it has alfd certain pow- 
ers or adiive Principles, known by the names 
of Attrdiiion and Re^alftony probably iibt eif- 
fential or neceflary to its exigence,, but itn- 
pircfled upon it by the Author of its Being, 
for the better performance of the Oiffices for 
which it was defigri'd. 

II. Attraction is of two kinds, i, Co- 
hefion, or that by which the feveral particles 
whereof Bodies confift, mutually tcrid toward 
each other, z. Gravitation, or that by which 
diftant Bodies aft upon each other. 

III. The Attradion of Cohcfioh is prov'd 
from abundance of Experiments, of which fomc 
of the moft obvious arc as follows. 

I. LfeT a fmall glafs Tube (commonly call'd 
a Capillary Tube) open at both ends, be dipt 
into a Veflel of Water, the Water wiU im- 
mediately rife up in the Tube ,to a certain 
height above the level. This rife bf the Wa- 
ter is manifcftly owing to the Attraaion of 
thofc particles of the glafs which lie in the 
inner furface of the Tube immediately above 
the Water : accordingly the quantity of Water 

. raifed 

Chap* 3. AttrMlm amUtepulficn. ^13 

raifcd is iiway^ propprtioiiablc jd the lwg^is'£; 
of th^ futfacc *. " - 

2. Let t\teo fphbrcs of C^ickfilvcr be |)la- 
ced near each other and they vritl immedM^^ 
ly run together and form okke globule. 

IV. The Laws of this Attradioa are ifi. 
That it ads only upon conta^l ot at very 
/fliall diftances^ for the Spheres mehciotied in 
the laft experiment will not approach eatrlx 
other till they are plac'd very irear. 2. It 
afts according to the breadth of the farF;lcis 
of the Attrading Bodies, and not accord- 
ing to their quailtities of Matter. Let thste 
be two poiifh'd glafs Plates laid onb u^bti &- 
nother in fuch a manner, as to touch at otle 
end, and there, make a very fmall angle: 
if two unequal drops of oil be put betwefch 
thefe plates at equal diftances from the line 
of contad, fo that the leaQ; itiay touch both 
glaffes, they will then both mdve towards the 
ends that touch, becaufe the Attraction of the 

• The heights the Water rifes to in different Tubes,, are ol>- 
fcrv'd to be reciprocally as the diameters of the Tubes, from 
whence it fplfows that the quantities nifed are as the furfaces 
wlych raife them. 

Dem, Let there be two Tubes, the diameter of the iirft double 
to that of the fccorid, the Water will rife half as high in the firft 
as in the fecond^ now was it to rife equal)/ high in both, the 
quantity in the firfl would be four times as great a? in the fccpnd, 
(Cylinders of equal heights being as the fquares of their diameters ; 
II.. EL 14.) therefore fince it. is found .^Q rife bvi^t hf^lf ^13 ^h» 
the quantity is but twice as much, and therefore as the diameter ; 
but die furfaces of Cylinders are as. their diaiAeters, thereibre the 
quantities of Water hdfed are alfo as the furikces. ^ £• Z>«, 

See a Pillertation on thi« SubjciS;. FaK VU' 



14 AtiraSiion and Repuljton. Part h 

furfaccs incUnes that yay; but the lafgeft, 
touching the glailes in moft points^ will move 
the faftcft. 3. Tis obfccv'd to decrcafe much 
. more than as the fquares^ of the difiances of 
the AttraAing Bodies from each other in- 
creafe: that is» whatever the force of Attra- 
Aion is at. a given diftance, at twice that di« 
fiance it (hall be more than 4 times lefs than 
before *. 

V. FnoM hence it is eafy to account for the 
different degrees of hardnefs in Bodies ; thofe 
whofe conftitucnt particles are flat or fquare, 
and fo fituated as to touch in many points^ 
will be hard ; thofe particles which are more 
ix>und and touch in fewer points will conftitute a 
fofter Body; thofe which are fpherical will 
form a fluid f, 

VI. Attraction of Gravitation is that by 
which diftant Bodies ad upon each other. This 
is fecn every day in the falling of heavy Bodiesr 
toward the £arth« 

VII. The Laws of this Attradion are i. That 
it decreafes as the fquares of the diftances be- 
tween the Centers of the attrading Bodies in- 
creafe. Thus a Body at the fUrface of the Earth 
(/. e. about the diftaoce of 4000 miles from its 
Center,) which weighs J9 Pounds, if it was plac'd 
4000 miles above the fgrface of the Earth i. e. 
twice as far diftant from the Renter as before^ 

▼ V^ Keilii Opera Ed. 4/^. p. 626^ 
jf titmitomi Optic* p. 335. 

Ghap. 3. AttraEiiQn and Repuljton. 15 

\TOuld weigh 4 times Icfs, if thrice as far, 9 
times lefe &c^ The truth of this Propofitioa 
is not to be had from Experiments, (the titmdl 
diftancc we can convey Bodies to, from the 
farfacc of the Earth, bearing no proportion 
to their diftance from its Center,) but is fuf- 
ficiently clear from the Motions obferv'd by 
the Heavenly Bodies* 2. Bodies attrad one 
another with forces proportionable 10 the 
quantities of Matter they contain j for all 
Bodies are obferv'd to fall equally faft in the 
cxhaufted Receiver, where they meet with 
no refiftance. Prom whence it follows, that: 
the adion of the Earth upon Bodies is tx^Q^r 
ly in proportion to the quantities of Mat- 
ter they contains for was it to aft as ftrongly 
upoa a lefsBody as upon a larger^ the kaftBody 
being moft cafily put into motion would move, 
the ftfteft./ Accordingly it is obfervable that 
the weight of a Body is the fame, whether k 
be whole or ground to powder** 

Vlll. From hence it follows, that was a 
Body to defcend from the furfacc toward the 
Center of the Earth, it would continually bc^ 
come lighter and lighter, the parts above at- 
trading it as well as thofe below, in which 
cafe it is demonftrated by the Mathematicians 
that the Gravity, would decreafe with the di- 
ftance of the Body from the Center \. - 

* Grofvefande Uh. 4. Chap, IX. O^^/s Pre&cc to Nem;tojtU 
f Dm* Let there be a Body ^ P, (Fig. 2. J placed any where 


i6. AftrqBhn 0^d Rtpi^lfipn. Part L 

Scholium. It vcivj be pr/jpcr to observe here, 
that when Pbilpfpphers (peak of Bodies gravU 
taang t;6, or attifaaijQg eac^ ptfajer, th^t Body 
i? f^id to ^rAvitate to anpth^r, which moves 
tpw.atds it, while i;he other adually is> or ap- 
pears to be at reft^ an4 thjl^ other is faid to atr 
traft ttic formejc v tljiough i;icl,^ed the force be- 

within a concave fphere, as AB^ which fct us fuppofe divided 
irit6 an infinite niinlber of thin concentrit furfaccs; I fay the 
Body P will be atjtrafted equally each way by any one ofthefe, 
n),g, the interior IHKL, Let there be lines as /L, HKy &c. 
drawn through any point of the Body P, in fuch a manner as to 
form the furface of two fiihilir figures, fuppofe Cones, the diameters 
ofwhofebafes may be IH, KL^ which Itft be infinitely fmall. 
Thefc bafes (being as the fquares of the lines IHy KL) (20. Elem, 
br) will be diredlly as the fquares of their diftances from P (for 
the Triangles being infinitely fmall are fimilar.) But thofe bafes 
include all the particles of matter in the interior furface, . that are 
ojjpofite to each other; iheoppofite attractions are therefore in 
tl^e fame ratio with thofe bafes, that is as the fquares of the di- 
ftances P Hy P L But the attraction is inverfdy as the fquares of 
the diftances of the attracting Bodies, J. -j.i.e* inverfely as the 
i^uares of the fime diftances F A, P / 5 thefc two ratios deftroying 
each other, it is evident, that if the concavity of the Sphere was 
fill'd with Matter, that alone, which lies nearer the Center 
than the Body, can affeCt it, the refpeftive aftions of all the 
parts, that arc more diftant, being equal, and ih contrary di- 
rc(?rions, fmce the fame is decjionftrable of any of the remaining 
concentric furfaces. Let us then fee what jcffeft that which lies 
nearer the Center than the Body will have upon it, which may be 
confidered as a Sphere, on whofe furfacfc the Body is. pbc'd. The 
diflanccs of each particle of Matter from the Body, (taken collective- 
ly ).will be as the diameter of the Sphere, or as the Radius, i.e, as the 
diftance of the Body from the Center ; their aCtion therefore 
upon the Body will be inverfely as the fquare of that diftance : 
but the quantity of Matter will be as the cube of that diftance ; 
(18. Elem.^12.) the attraCtioh' therefore will bealfo in that propor- 
tion. Now, thefe two ratios being compoun4cd, the attraction 
will be only as th$ diftance of the Body from the Center. ^ E. Z>. 




itirg; itt&ltUal and eqaal on both iidcs (as will 
ht explain d uiider the id Law of Nature) the 
fame Term might be apply 'd to either the gra< 
▼iraflii^ of attraSEing Body. 

It is farther to be obHerv'd, that whch we 
afe the Ternis, Attradion or Gravitation; 
W6 do not thfereby determine the Phyfical 
Caiife of it, as if it proceeded from fome 
fuppofed occult quality in Bodies $ but only* 
riffi thofe Terms to fignify an Effed, the 
Caiife of which Iks out of the reach of out 
Fhilofophy. Thus we may fay, that the 
Earth attrads heavy Bodies ; or that ftfci 
Bodi^ tend of gravitate to the Earrh : though 
at the fame time we are wholly ignorant 
wheftiet this is effeftcd by fome power adu- 
ally exifiing in th^ Earth or in Bodies, or ex- 
t^naito both: fince it is impoflible any error 
in our reafohings can follow from hence ; it 
being evident, that all the confequences of 
fuch tendency muft be the fame, let the caufe 
ht where or what it will. 

X. Repulsiok is that property in Bodies^ 
whereby if they are placed juft beyond the 
Sphere of each others Attradion of Coheiion* 
they mutually fly from each othen 

Thus if an oily Subftance lighter thaii 
Water be placed on the furfece thereof, oc 
if a piece of Iron* be laid on Mercury, the 
furface of the fluid wiU be dcprefs'd about the 
Body laid on it.' Thi^e depicilion vs manifeft- 

C ly 

1 8 \Aitr€0idn and Repulfion. Part fc 

ly occaifon'd by a repelling po\^er in the Bo- 
dies^ which hinders the approach of the Fluid 
towards theqi. . 

But it is pofCble fn fonie cafes to prefs 
or force the repelling Bodies into the Sphere 
of one anothers attraction j and then they will 
mutually tend towards each other, as whea 
we mix Oyl and Water till they incorpo* 

XL Beside* the general Powers foremen- 
tioned there are fome Bodies that arc endued 
with another call'd EkHrtcity. Thus Amber, 
Jet, Sealing- Wax, Agate, Glafs and moft kinds 
of Precious Stones attrad and repel light Bo- 
dies at coniidcrablc diftances. 

The chief things obfervable in thefe 
Bodies are. i. That they don't aft but when 
heated. 2. That they ad more forcibly whca 
heated by rubbing, thsin by ifire. 3. That when 
they are well heated by rubbing, light Bodies 
will be alternately atrrafted and repeird by 
them, but without any obfervable regularity 
whatever, 4. If a line of feveral yards in length 
has a Ball or other Body fufpended at one 
end, and the other end be fixed to a glafs Tube 1 
when the Tube is heated by rubbing, the Eledri- 
cal Virtue of the glafs will be communicated 
from the Tube to the Ball, which will attrad and 
repel light Bodies in the fame manner as the 

• We have an undeniable Proof of this RepuUire Force in 
Sir Ifaac Ne^ion\ Qpticks, B^ 3. an J Q^f^tj 3i« 


Chap. 4. Laws of Motion. 19 

glafs it felf docs. 5. If the. glafs Tube be 
emptied of Air^ it lofes its Eledricity ^, 

XII. Lastly^ the Loadftone is obferv'd to 
have Properties peculiar to it felf, as that by 
which it attrads and repels Iron, the Power ic 
communicates to the Needle aiid fevcral o- 
jthcrs f. 


Of the Lanios of Motion commonly cal- 
led Sir Ifaac Newton'x Laws of Na- 

L A ^^ Bodies continue their ftate of 
x\ reft or uniform motion in a right 
linCf till they are made to change that ftate ( 

hy fome external force imprcflfed upon them. 
This Law is no other than that univer* 
fal property of Bodies, caird Paflivcnefs or In* 
aftivity; whereby they endeavour to conti- 
uuc the State they are in, whatever it be. 
Thus a Top only ccafes to run round on ac- 
count of the reitftance it meets with from the 
Air> and the fri£kioo of the plane whereon it 

• Sec Hauhhee^% Experiments. Fhilofiph. Tranfa3. Numb. 326. 

+ Several folutions of thefe Properties of Eledricity and Mag* 
ntltfm have been attempted by different Philofophers, but all of 
them fo onlatisfad^orv as not to dcferve a particular account in 
this Place. See Chambers'^ Didtionary in Eledricity, and De^ 
Caries Opera Philofophica. P. IV. $• 133. with fevcral others 
fitcd in ^4iiipnes Philofiphicji, 

C 2 moves 

to Le^s of Motion* Part'X 

snoyes* And a Pcnd ulum when left to vibrate 
in "v/vuo^ where there is notliing to flop it 
but the friction arifing £romthe motion o£ the 
pin on which it is fufpended^ continues to 
move much longer than one in the open Air. 

IL The change of Motioni'producd in any 
Body> is always proportionable to the ifbrcct 
whereby it is efTc&ed $ and in the fame dire- 
£tion^ wherein that force a As. 

This is an immediate confeque<ice of this 
Axiom, the Effeifl is always proportionable to 
itsCaufe. For infiance, if a certain force pro-^ 
duces a certain motioui a double force will pro- 
duce double the motions a triple force triple 
the motion (jrc. If a Body is in motion, and has 
a new force impreflcd on it in the dircftion 
wherein it moves, it will receive an addition 
to its motion proportional to the force im- 
preflcd 5 but if the force ads direftly contrary 
to its motion, the Body will then lofe a pro- 
portional part of its motion : agaiut if the 
force is imprefled obliquely, it will produce a 
new diredion in the motion of the Body» 
more or lefs different from the former in pro-» 
portion to its quantity and diredion. "^ 

^ • This cafe is cxprefled more accurately by Mathenuti- 
cians thus. If the proportion and direction of z forces a^ng 
upon a Body at the fame time, be reprefentcfd by the fides of a 
Parallelogram, the Diagonal of that Parallelogram will reprefent 
Ac proportion and direction of their united forcies. 

Dem, Let the ,Body A (Fig. 3 J be impeird with a forcc^ 
^hich would carry it to £» in the im^ time that anotner/ ading 


eadi Dtiier ate w^, <'Moi dn pmAzi^Jjiifo- 

to be dbra wn by ^k^ tiarfc $ the 'Load read^ 
upon tlic Hoi:t<b-k^ tiluch ds the Horfe 4€bs Up- 
oh the Load ^ for the harnefs, \(^hichlsftret<th*d 
equally between them both ways^ drafws the 
HQiric.towards thcStonet «3 lattdi iis the Stone 
tovfttds the~H€>rrei and the {urogceflive modolL 
^ the Hof fe ui as much i otudcd by the Load» 
as the motion cf the Load is p romoted t^ 
the endeavour of the Uorie*. This wiU 

upon it in the dirediOn j^D, would carry it to D. IttiApg^ 
that while the Body paffes to E, the line JD (in which the 'Ba\ 
6y mc^es by the other force) SK>ves to EB9 in a direAioit pa»Hd 
toitfelf; wken.theBody h^ advanpM to G m ^e line jfE^ the 
line JD will have got to GF,, and the Body will have paifed over 
fuch a part of it (7 H, as bears the fame proportion to the Wholb 
lioc GF, as JG does to JS^ that is GH Ithc fhoiDerfideof 
die Parallelpziam GM* ia to QF^ or, which is the £une ihin^ 
to £B (the porter jide of the Parallelograio ED,) as J 6 (the 
longer nde of the feriper] is to JE (the longer fide of tike Jbt- 
terj from whenpe th& Pj^)elQgnuns ajre fimikr. El 6. Z)^ t« 
and confequ$ntly» by 24. £/. 6. the point H is in the BiagpnaJ^ 
that is, the Body will always be found in the line ^J?-. QJE* |>. 

enroll. From hence we have an eafy method of refolving a ^vita 
notion into a^y two, pr niioi«diie£U(in&wjhatev)er; <vrjs. bjr die- 
fcnbing a Paralleiognan about th« given diredioaas^a^ Diag^Mal^ 
the two fides of whjjch wil} seprefent the diredtionst feugtit., Tku^ 
fuppoi^<; a Body was impelled in th(» Line JS^ w« majf ooiir 
ceiye it as afbd upon hv* tyro forces- at the fame tissey one lo- 
Wards £^ the other towards 2>» ojr my other two whatever, f^gx^ 
vided tbc^l4nes;be»dnkwi).pf fttc}i:lei^ptb,,tlut» when- dte Fajadk 
l^lo^nt is cpjnpleated,^ th^.given line JB fhall be its Diagpna^k 

* It may* be thou^t perl^ps tliat (tpro e^uaf and conti:trjF 



be bcttet «(|itain'dfrQmthe following ioftanccj 
let a "PtiUki^ fiitii^ in a Boat drav anothet 
equally, rheavy towaids huoi^ they- will both 
move towards each other with equal velocities - 
let the Boat he fits in be tfae lightcft, and it 
will move the fafteft}.:bccaiifc the adion be-o 
ing equal on both .fides, the f^c .quantity of 
motion v.'iU be given to each Boat, that is* 
tfae lelTcr will have the greater velocity *. 

We have a farther confirin^ion of this from 
Attr^on. Suppofe two Bodies dttrading one 
another, but hinder'd from meeting by ibme 
other Body placed between them: if their ten- 
dencies towards each other are not equals 
then the Body that Is between them, will be 
prefTcd on one fide more than on the other, 
and confequently the firongcr preflure over- 
coming the weaker, they cannot remain at 
reft, but wilt all move on continually in that 
dire£lion wherein the ftronger force aAs; which 
is both contrary to the iitftLaw of Nature and 
Experience. This may be try'd with a Load- 
ftone and Iron } which* being put into proper 
Ve0cls contiguous to one another and made to 

''-ic« deftroying one another] the Harfe will in this cafe not 
able to move Mall, becauTe the Load draws him back, as much 
be draws the Load forwards. But it is to be obferv'd that the 
Biigth of the Horfe is not properly exerted upon the Load but 
on the Ground ; confequently the Ground reacting and coati- 
ing at reft pdhea the Horfe forward with juft fo much force as 
: Horfe exert), above what is counteraAed by tfae Load. 
* See the diftinj^on betvreen Motion and Veloci^, Cl^p, 9. 


' { 






<Shftp..5' BdlUng Bodies. 2% 

ftoat o»^ wat^, .w^l be an cxa£k cQUOttrbilahcc 
159. .eac^ .other, ^ilndw^nain a,t reft, whatcv6: he 
tlie attraaivc jiewqr of the Loadftone, or the 
proportion of tUpiR rcfpeftive magnitudes. 

Thbse Law$\r^^iyc an abundant additid* 
nal^rQof jFrpqa hence, viz. that all the con- 
^uitpiis ith^t; arc drawn from themj in rela«^ 
tioti to the Phenomena of Bodies^; how oom^ 
pUqafcd rfpevcr J tiic^r Motions be,, arc always 
found to agree perfcftly with obfeirvation. The 
truth of which fuffifiently appears in all parts 
oC the itfJ?wft>w^»^Philofophy *. 

1 > 

G H A P. V. 

The Phenomena of Falling Bodies. 

' ' ' . ' 

L Tp H E Laws of Nature being thus explain- 
JL cd, we proceed to account for thofc 
Phaenomena, which are folvable by them. 

II. To begin with thofe of Falling Bodies* 
Conftant experience (hews, that Bodies have 
a tendency towards the Earth, which is call'd 
Gravity, the Laws of which were enumerated 

in Chap, j . §. 7* 

III. The height. Bodies can be let fall from,' 
bears fb fmall a proportion to their diftancc 
from the Center of the Earth, that it cannot 

* Sec thefe Laws explain'd more at large by Cheyne in hia 
Principle* of Philofophy. KeiN Introd. ad Phyf. PraeL 1 1, 1 2. 


^4 FuHif^ ^i^. . Vseth 

flcty . be c^n&^fidk' i» ^eoa^- conftam)^ and 
tttfifoiftniy updtf thMH dUrkij^ the wMtf tiftffe 
ofthc^fath' &dili-^}Wnc^^ fh<J^ ittuft necqfia^ 
jilf ac^ikW^fff' evcrf inlKiA«;^^aii equal degree 
o£ Vel««tt:^r \i4iilh*='<^ 't^S^^ wiU coA- 

ftfthdy iin€f?6afe ,' iri p¥6j[Jb«i6ii^ tc> VhieL' tibilS' 
ti» Boljf tat«^u)^itf Mingi' ' '•::... 

iVJ TWb fp^'ceff Bodi^ farf throttgh *' id dlf^* 
IbicnttTftJei; KckfotiWg^: ft^ the Stginriii^rg' 
0f ifhek^ fall, are as tht? f<!|iui¥cs^ of thofe tithes 5 
thus, a Body wiil fail 4 tirtiea^ ai fttf in V ix*-* 
nutes, as it does in one, and 9 times as far 
in 3i 16 times 45 far. in 4 &c.i^ 

• Inorderto demoirflratc tins Prqpolitipn, it writ be necefiary 

That the fpacc a Body pafles over, with an uniform motion, 
is in a ratio compounded, of the time and velocity. .For tha 
IbngcraSbdy^coiitlhtics' to* move- uMfdrmly, the ihore fpac^ 
it ^moyes ovcri ; and* the . ftft^ it moves, darix<g any inter- 
val of time, the fartji^r. it go^s y therefore* the fpace is in a ratio 
compotrndcd'oft^th; thit is, is hid by multiplying one into tke 

.. ConlL TJierefore tht area of a redlangle, one gf whofe fidea 
rcf relents" tke celerity a Body moves with, and the other the 
dmc of its 'motion, • will cxpreft the fpace it moves through. • 

This being premifcd, let jtHc line J.B (Fig -^J reprefent the 
time a Body takes up in falling, and let B C exprcfs tne pelenty 
acquired by its fall ; ferther, let the line JB be divided info ait 
iuQcfimte nmntner of iin&Ii portions, f/,tm, m/,.&^c. and'Iet ^ 
ii, mn,fqy ^c. be d^awn parallel to the bafe. Now it i« evident 
from §. 3. (*vV«. that the velocities are as the times in which they 
are acquirM) -that the lines e/, iij mh, />^, Set, hein^ to eacK other 
(4. £/. 6.) as the lines Je, Ai^ Anty Jpj kc. will reprefent tbe 
celerities in the times reprefented ^by thcfe : that is, <?/?" willbc as 
the velocity of the Body in the fmall portion of time^iV andiA 
"SviU be as the velocity in the portion of time im t in like oianne^ 

C\kp. S' ^FaBng Bodies. 2^ 

V. From this Prbpof?tion i^ follows, that 
a Body falls 3 times as far, in the fccond pof-> 
tipn of titoicf; as it does in the firftj 5 tirfics 
aS ht in the third 5 7 times in the fourth, and 
fo <m id the lerits'of the odd Numbers : for 
Whtfrwifc, it could not fall 4 l^aces in 2 mi- 
nutes; dnd 9 ill J, ' as the Propolition aflferfe. 

VJ. The fpaces defcrib'd 'by Falling Bodies 
in different tintes are as the fquares of thd 
laft ac^uir'd Velocities. For by §. 4. the fpa- 
ces' are as the fquares' of the times, and by §. 3. 
the vclotttrcs arc as the times j therefore the 
fpaccs arc ilfo as the fquares of the velocities. 

VIT. The fpace a Body pafies over from thd 
beginning of its fall in any determinate timc^ 
fe half what it would defcribe in the ftmc 


f<{ will be as the vclociQr in the portion of time po, which portion* 
of time being taken iiifaiitel)r fmall, the \;elocity of the Body 
may be fuppos'd the fame, during any whole portion ; and con- 
fcquently, by the Corollary of the foregoing Theorem, the fpace 
nmover in the- time ei with tht velocity efmxy be repreicnted 
by the redbmgic if: in like manner the fpace run over in the time 
m with the cderfty /;>, mzf be exprefs'd- by the PcAangle mk i and 
that run over with the celerity mn in the time mp, by the rettangle 
pni and fo ofihc reft. Thereforethe fpace run over in all thofc^roes 
willbe reprefented by the fum of all the reAangles,' that is, by the 
tmngfle ABCr for tbofe:little trrangular de§ci«icic$, at the end of 
,each redtanglc, would have vanifhed, had the lines <?/, i w, fnpy Sccm 
been infinitely fliort, as . the times they were fuppofed to re- 
prcfetit. Now as the fpace, the Body defcribcs in the fiAie JB, 
IS rct)refented by the triangle JBC, for the fame reafon the 
fpace pafs'd over in die time Jo rtay be reprcffehted by* the tri- 
angle JoK but thefe trialigfes being, fimilar are to each other, 
as tliie fquares of theirhomoTogOUs fides JB atidufo (20. EL 6.); 
that is, the fpaces rfepVefcnttfd by the triangles are to etch other, 
as the f(juares of the times reprefented by the fides. ^J^ E.D- 

D time 

ft 6 Bodies defcending Part I, 

time moving uniforcniy with its laft acquk'd 
velocity *. . . 

VIIL In like manner^ when Bodies are 
thrown up perpendicularly,, their velocities de- 
creafe* as the times they afcend in increafe; 
their gravity deftroying an equal portion. of 
their velocity every inftant of their afcent, ... 

IX, The heights Bodies rife to> when thrown 
perpendicularly upwards, are as the fquares of 
the times fpent from their iirft fetting out, to 
the moment thev ceafe to rife. That is, if a 
Body is thrown with fuch a degree of veloci- 
ty, as to continue rifing twice as long as ano- 
ther, it (hall afcend 4 times as high $ if thrice^ 
9 times as high, &c. 

. These two. are the converfe of the ^d and 
4/^ Scftionsf. 


Of the defcent of Bodies on oblique 
P lanes y and of Pendulums. 


H E N a Body defccnds on an oblique 
Plane, its motion is contiually acce- 

* Fop let the time be ABy and the laft velocity BC^ the fpacc 
the Body runs over, while it is acquiring that velocity, is ABCj 
fcut.the fpace it would pafs over in the time AB^ was it to move 
uniformly with the celerity B C, is, by the Theorem, (Note p. 
24.) the fpace ABCD^ double the former. ^E, D. 
. t See Keiti Introd, ad Phyf. Prael. ii. Grtevefande L. i* 
Ch. 17, 


Chap. 6. oh. oblique Planes. 27 

lerared by the aSbion of gravity^ but in a Icfs 
degree, than when h defcetids perpendicularly ; 
its free dcfcent in this cafe being hindcr'd by 
the interpoffHon of the Plane : ' from whence it 
follows, that what was faid in the laft Cliap^ 
t«, concerning* the perpendicular defcent of 
Bodies, is triie of fuch as fall on oblique 
PlaneSf allowance being made for the di^e« 
rence of acceleiation* ; . , 

IL The effeft of Gravity upon a Body fal- 
ling down an pblique Plane, is as : much lefs 
than the fame afting on another falling freely % 
as the perpendicular height of the plane is lefs 
than its length^. 

III. A Body falls through as much longer 
fpace perpendicularly, than it does obliquely 
in the fame time, as the oblique fide of the 
Plane is longec^ than the perpendicular height \. 

* Dem. Let AC [Fig. ^.) be die Iiic'Iiifd Plane, tlie Body at 
jf,.and the adtion of gravity, whereby it endeavours to fell pcr- 
pendiciilax1y» rcprefcnted by the line JB i let JD be pexpen- 
dicular*to AC^ AD wIH then reprefpnt the direAion by which 
xhe Plane acts upon the Body (for all Bodies a^ in lines perpendi- 
<mUr to their iurfaccs,) let then thofe two forces be refolvcd into 
one in the dirieftion AC^ (as Ihewn in Note to J. 4. Chap. 4) by 
compleating the Parallelogram B D whofe Diagonal will be AG. 
In order to diis i^G muf| be let fall perpendicularly upon AC 
(that it may be parallel to the opppfite fide of the Parallelogram 
AD^ confequently {8. Elem, 6 ) AG is to A3 as AB to AC^ 
that i&^ the tendency of the Body down the plane is to its per- 
^)cndicular tendency, as AB is to AC' ^ ^. 2>, 

f That is, fuppofing BG (Fig. 5. J perpendicular ;to ACf the 

Body would fall to G in the fame time it 'would &U to B, for, as 

was obferv'd Note'the laft, AB is as much longer than AG as 

^Ci^^Iongerdian ^*; "' ^ ' 

^ P 2 Dm. 

^* B^iif defymiing , . Part f. 

J1:J^\ ?^*^''^ * Body a^qu^wsj^f^jljflg 

It acquires by . falling oWicm^iy m tljc f^ 
«me. as rhc fpac< of ifs p* rpcoiicukr di^St 
« that n J, CKccds that pf Tt, .o^Iiqpe 51^^ 

w falhug down the oblique, ^ of a Pla^r 

than It doe^ the p„pett4Uul45.fee*gbt.of iC^ 
the obhquc fide exceeds ^\i^i, \ 

as the aaion of mvitv nn fkT b j ^ 1^*1^ "" *'^<«ne'titafe^ 

.per,e„4icuIar'aS L^°h: Z^l Jst^^ ^''^''^ 
toe;,ch other, fgV «• thff l«rf /^&^,?- 9^ *^« *^<m a« 
(dicular heiphf tL r ! '^ f "^^ obhqufl fide to the oerben- 

%SS '^i ^gf f^^«*'? f »^-<l>^fr wiU be in tTL. 

ling Sody paffeT'o^er ;„^ PnOhitL^^f, 7.) tfc^ ^aft 4.fel- 
run ovJilZ gZ^, '"^ *'"?*' " J»»'f that which it would 

Plane SS^;ff;°";>7„,'Jf th« Body fallifildovv' the'dbliiue 

■ ^itkit. iXSirKctit [^ ^f^'- ^^' "loving u«iWy 
in Which it3aS^^;t^v^r??^*^»'"««fc^ ^«-«^^ 

laft acquir'd velocity in .X, !-^* r'".^""^ uhiformly with its 

^G »ndT3misJiru-''''t'i'^^'^ double the imps 
are as the fpacesTn tiZ.l- •''"«' ,.'^««ftlv% which by |. ,. 
Pwpofitio/L 3^5 """^^ '" '^^ %»1l tJm^. from vrhi'^e 

^ / f f woai (». ^/,^. 6.J „ the Rjf^fff Qf^C to the 


^hap. 6. on obUqm Planes, 29 

VI. A Body acquires the feme, velocity in 
^ling dowa the obliqu^ fide of a Plane* ^ 
if it fell freely ibroogh the perpcndicul« height 
of it*. 

VII., A ^pdy taj;cp wp the fame ' time "ii> 
falling through the Chofd of a Ciiij^e, whe- 
ther it he Ipng Qt fhftrt, as it does m falling 
pcrpcndicuUriy through, thp diameter of the 
feme Pirclef. 

VIU. Uppn this is fpijfidfid the Theory of 
^enduluDW: fpr fr6q:i hence, if fpllowsj thap 
4;pgofii^ a Pcndpintn could be roaflp to vibrate 
ja a CboEd pf a Circki inftead of an' 4rcl^ all 
its vitifatiops would fc^aJfC ihe^ ^"^ ilwc, 
whether they were large or feiall:f.' ', : 

fquare of AB {by Def. lo. £/m. ;.) therefote tHe tinws diem- 
felves are as the lines AC ?nd AB, that is, as (he abBqne fide di 
the Plane to the perpendkubr height. ^ t.>^\ 

* ptm. The fqiMK of cIk vojo^it^ s Be 
to Q> if to the Jquare of the v^oeicy it m 
w t)w ffafe jfG to th.e fpace */C <fay Phs . „„ -^, __.^,-, 
»- jPVno 6. w>d iJ*^ 10. JEA*. j.) w ^Gj tp -.rfn- «"t Oacs 
jtG is nin ov^ in the ftme timf ^f j(, (fe , ) the 

wteei^ top iMo the vdodty in J, « .^P (. 4.) 

ao^ cesfv^eQ,!^ Ijftce tbf wiorilita.bodi ia m me 

%»^ liTOpowipB w ihit i« p, ihCT nail bs o other. 

+ flew. X« w»a dwooftnUfNt (i- 3.) di»t>,Sody will 
&I1 ft«n .rf to <r, (fig.f>.) "jn.tttf indin'd ptwe.^C, ia 
the &ne ttiM «todief wesld &I1 fi«t# ;o i^. provided ^G5 i» 
srlgkt wglf, i« which cifc AG (by 31. £/«». 3.) isaChoel 
cf tkit CiDcte df wluch .^5 is th« DiusWr : J^te&rc ? Boc^ 

:{ TJws may be illuftrwied by cMoemag th« Mi %ve Inveited 
(a> in fig. 7.), ivhnre %>(»&« ^ Sail fdpeadsd'M fuch > «un- 
nei> aa .t« fu'Jttii »> the ikhc lane G4 inflicad 6i tha Arch Gvl', 
it would always fall tbvuj^ it in tbt jGuoe tins Iwwcet Iwyf or 

3© Pendulums, Part. I; 

IX. From hence wc fee the reafon, why 
the Ihorter arches a Pendulum defcribes, the 
nearer its vibrations come to an equality, for 
fmall arches differ lefs from their Chords than 
large ones* But if the Pendulum is made to 
vibrate \ri a Curve, which Mathematicians call 
a Cycloid I each fwing wilLthen be performed, 
in the fame timei whether the Pendulum moves 
through a larger or Icffer fpace. For the na- 
ture of this ;ipurve is fudi, that the tendency 
of a Pendulum towards the lowcft point of it, 
is always in prpportlon to its diftancc from 
thence $ irid confequently let that diftance be 
more ot Ifels, it will always be run over by 
the Pendulum in the fame time *. 

|bpK ;t w&s, for the inclination of the line GA to the horizontal 
Ene BC^h not alter'd by inverting the figure. 

• The Defcription of a Cycloid. 

Upon the right line AB^ (Fig, %.) let the Circle HDE be f(y 
'|ila(fd, as to touch the line in die point ff, then let this Cirdc 
jolll along npon it from H to C, as a wheel upon the ground, 
then will the point H in one revolution of the Circle defcribe the 
Curve HKCy which is call'd a Cycloid. Now fuppofc two 
Plates of Metal bent into the form HK and JSTC, and placed in 
thefituati^n £H and LC^ in fuch manner, that the points H 
and C may be apply'd to Zfr-and the points anfwcring to Khtvp- 
:)>]y*d to H and Q. This done, if a Pendulum as IJ^t in length 
equal to £» H, be made to vibrate between the Plates or Cheeks 
of the Cyck^d I C and £ H9 it will fwing in the line C KH ; and 
the time of each vibration, whether the Pendulum fwings through 
a fmall or a great part of the Cycloid, will be to the time a Body 
takei up in ^ling perpendicularly through a fpace equal to I K^ 
(half the kngth of the Pendulum ;) as the Circumference of a Cir- 
cle to its Diameter, iind confequently it will always be the fame. 

They that Wjbuld fee a Demoxiftration of this and feveral other 
'things relating to this Curve, may confult ^i^q^^j Uor^LOfcil- 




chap. 6. Pendulums. 51 

X. The time of the defccnt and afcent of 
a Fendulum^ fuppofiiag it to vibrate in the 
Chord of a Circle, is equal to the tiiAe in 
which a Body falling freely would defccnd 
through eight time;s the length of the Pea- 

For the time of the defcent alone upon 
the Chord is equal to that in which a Body 
would fall through the Diameter of the Cir- 
cle (by §. 7.) ; that is, twice the length of the 
Pendulum: but in twice that time {viz. du- 
ring a whole vibration) the Body would fall 
four times as far ( Chap. 5 . §. 4. )^ that is, 
through eight times the length of the Pen^ 

XL The times, that Pendulums of diffe* 
tent lengths perform their vibrations in, are 
as the fquare roots of their lengths *• 

XIL The Center of Ofcillation is a point 
in which, if the whole gravity of a Pendulum 
was colle^ed, the time of its vibration, would 
not be alter'd thereby \ i this is the point from 

• Dem. Let there be two Pendulums A and B (Fig. 9. and 
I O.J of different lengths, the ti^ie the iirft vibrates in (fuppofe 
through a Chord) is equal, to the time in which a Bodjr 
would fall freely through DA^ the Diameter of the Circle {mL 
demonftrated $• 7.) ' ii^ ^^^ manner the time B vibrates in, is 
that in which a Body would fall through FB, Now the timet 
in which Bodies fall through differeBt fpaces are as the iquare 
loots of thofe fpaces, that is;^ o^DJ andl FB9 oi of therr baivM 
CA^siACBt <- ^* of the lengths of the Pendulums. ^ E* />• 

t The Rule fw finding the Center of Ofcilktion. 

If theGlobe AB (Fig. 1 1 . J be hung by the llring CD, whole 
weight b inconfiderable, the Center of Ofciliatlon is found thus; 



34 Ttndutufns* Pkrt t, 

wheftce the length of a Pendulam fe mea- 
fur'd, V^hich ill our. Latitude, in a l*endu- 
lum thdt.fvt^ings Seconds, i$ }#. 2. inches. 

Xin.. TiftE fqttarcs of the times ifl which 
P^nditfCihiS, a^ted updii by differetit degrees 
of gravity, perform their vibrations in> are tp 
icach othef, as the graviticsi *. 

ftppbfe i the Cemtcf of the Giobe, take the line G <rf' fiich a 
lengdi, that it fliall bear the fame proportion fx> tD u ED to 
EC, thAtk EH being mide e<}ual to ^ of G, the point H (hall 
be tho Center of Ofcilktion 

if the weight of the Rbd C /> be too cDnfiderable td be ncg-- 
lefted divide CP (.Fig. 1 2.) in /, fo that DI may be equal to f 
of CZ>, and inake a line as Ky in the fame propo^tipn t0 CI, thsrf 
^e weight of the Rod bears to that of the Globe, then having 
found H the Center of Ofcillation of the Globe, as before, divide 
/H in L, fa that IL fluy bear the {amt prbportion to LH, as 
the lino CH bears to the line K; then will L be the center of 
Ofcilktion of the whole "Pendulum. See Huygens'ttotol, Ofcillat. 
pag. 141, 142. 

• j9^iw. The fpaces faHing Bodies defeend through,^ are aft 
the fquarcs of the times, when the gravity by which ^ey arc 
impcird is given (Chap. 5. $. 4); and as the gravity when 
the tinae is given (for the Turn of the velocities produced in any 
time will always be as the generating forces) : confoqucntly 
when ndthcr is given, they are in a ratio compounded of both ; 
the fquares of the times are therefore inverfly . as the gravities- 

{Far if in 3 (pumtities a, b, c 5 a i^dshc, thin b : - , i< e: ^ a is 


gi'ven, as — or as c inn)efj!y,'] But if the fquares of* the times in 

' which Bodies fall throx^h given fpacea are iftvertfy^ atf ebe gra- 
vities by which thnr are adled upon ; then ^e (^u«ffis erf the 
times in which 'PenduhuBs of equal lengths, perform l^dir vibra- 
tions, will be alfo in the f^me rfttio, on accour^ of tbe conltMt equii- 
Jity between the thne of the vifc^ration of a Pendieiliini, and of the 
4lefcent of a Body through eight times its length ($< 12*) 





^ V- 



0mp^7' ProjeSiiles. ^^ 

Fkoj|i wbe|ice it foUow^i that a Pendulum 
^ill yij^rate. flawer when nearer the £quatorj» 
than the fame when Aearer the Poles $ foe 
the gravity of all Bodies is lefst the nearer the/ 
arc to* the Equator 3 viz,, on account of the 
iphcrddatikl Figure of the Earth, and its ro- 
tation . aboitf its Axis, as^ will be explained 
hcrcaftey. To which we may add the increafc 
of the length of the Pendulum occafion'd 
by the heat in thofe parts } (for we find by e^« 
pcrtaent , that Bodies are inlarged in every di- 
meaiion, in jp^roportlon to the degree of hcac 
that is given thim :) for which reafon (Chap* 
6. %. ii») the vibrations of the Pendulum 
will alfo be flower. 

Of ProjeBiles. 


I A BODY projeded in a diredion pa- 
2^L i^^Ucl or oblique to the Horizon would 
proceed on in infinitum in a right line, (by 
the iirft Law of Nature) but being continually 
accelerated towards the Earth by its Gravity, 
it will defcribe a Curve called a Parabola *• 

• Dem. Let us futmofe the Body thrown from A, in the diredlioft 
AB horizontally (Fig, ly) or obliquely (Fig. .14.I jt would 
fif not attra£led towards the Earth) in equal times defcribe cqital 
{arts of the line^i?, as -^-C, CP, D J?, &c. but if in the firft por- 
^*on of time, while Jt moves from -^ to C, it defcendsby icjGravi 
^ ar&r a»G> by a compoikioo of ^efe two Motions (Chap. 4. f . 2.} 



34 ProjeBiles\ .Part L 

II. The greateft diftancc, to t^hieh a Body 
can be thrown with a given velocity, isfatthtf 
elevation of 45 degrees*. 

It will btf found in //, and while it moves fr6ni A io D twice a< 
far, it will move downwards to M . 4 times as far as before (Ch^p. 
5. §. 4 ) .and will therefore be found in / fuppofing 2)/ 4 times 
as long as CH, Again, while it moves to E three times as far 
from yf 3is C is, it will have moved downwards 9 times as far as 
it did in the firft portion of time, and therefore will be found- 
in K, provided ^ AT be 9 times as large as C H &c. -that is- the lincf 
CHjD ly EKy Sec. will be to each other as thefquares ofthcrlines 
^C, JDy AEy &c. which is the property of the parabolic Curve, 
(De L' Hofpital^. I Prop. I. Cor. 2. and Prop. 3I Cor. 1.)' and 
confcquently the line AH IX, &c, which the 'Bodjr moves in, 
whether thrown horizontally or obliquely, is a Parabola. ^ E, D» 
* It is dcmonftratcd by the \Vritcrs on Conic Seftions, that 
the Quotient which arifeS from the divifion of * the f<^are of the 


line GH by the line AG «i//«. the quantity -rpir- (in 'either of 

the parabolic curves, (Fig, 13, or 14. J, or of the fquare of MI 

by the line AM, viz. -rr^ or of the fquare of NK by AN viz. 

— -^ &Q. provided thofe lines are all pscfallel to AB which 

touches the curve in the point A, is always the fame : which 
Quotient is call 'd the Parameter of the point A^ .' 

Now the velocity, with which the Body is projcAed from A^ 
being (ex hyfoth.) fuch as would carry it to C,' in the time it 
would ft 11 by its own gravity to G ; and to E in the time it 
would fall to Nl and fince it would move over twice the fpace 
AN in that time, had it moved uniformly with the velocity 
acquired at iV 5 it follows, that the velocity it 'moves with from 
A to £, is to that which a Body acquires by falling to iV, as 

AE to twice AN (Chap. 5. J. 7.) or as \ AE to AN, But the 

velocity a Body would acquire by falling through a. fourth part 


of the Parameter of the point A via. -■ ^-. is to the velocity 

it would acquire by falling to Ny 2isAE to zAN : (ice thi&de- 
monitrated in Note f ) therefore the velocity a Body ought to 
be projedted with from A to make it dcfcriba the given ParaboU 


Chap. 7. ProjeBiks. 35 

AHIKj is cqua} to the velocity it would acquire br ^falling 
through a fourth part of the Parameter belonging to tlut point 
of die Parabola from whence it is projefled. 
f Tiic f^fp of thjs velocity acquired by a Body in defccnd- 

-" AT Jf 

ing through a fourth part of the Parameter, or ^ ■• is to th€ 
fquarc of that which is acquir'd by falling through the linc^A^; as 

^ ' " '' to ^-JV, {Chap. J. ^. 6.), that is, multiplying both terms by 
JN» as -INKq^to^Nq^ and by extraftion of their fquare rootSj 

ts Ink to J N. q^E.D. . 

Corol, This affords us an eafy method of finding what dirc- 
ftion it is neceflary to throw a Ball in with a given velocity, in 
order to flrike an objcft in a given fituation. v.g. Let it be re- 
quired to ftrike anobjedfc as iT with a ball thrown from J with a 
given velocity. Here it is only neceiTary to make the triangle^ 

JNK (fuppofe a right line drawn from ^ to ^ fuch, that -ji^ 

or -which is the fame thing -^^ in the triangle J EK, may be 

equal to four times the fpace a Body muft fall through, to acquire 

fuch a degree of velocity as that with which it is intended to be 

thrown, and then JE will be the diredtton fought Tn order to 

tliis we muft lay down the folJowi;ig Lenjma. 

Let there be a Circle as JB C (Fig. 1 5 J j4K a Tangent in 

tbjp point J, JB perpendicular to the Horizon and parallel to 

KE or Kh I fay ^~ = AB. For the angle ^5 £ is equal todw 

^i^^(tEAK(lz.Elem. j J, and the angle 5-<^£ is equal to the angle 

JEfC^s alternate, therefore the triangles ABE and^fiTarc fimj- 

lar; ponfequently AB is to AE9 as AE to EK, and multiplying the 

atremc terms together, and middle terms together, ^^x EK=AEq 

and dividingbdth fides of the equation by EKy AB^ -^r- . Q^. D. 


By the (amc method of arguing j^ niay be proved equal to 

The Problem, 

Ut it be rejiuir'd to ftrike an objefl as K (Fig. l6.) with a Bill 
jrojc6tcd from A with a given velocity. 

E 2 Solution. 

••1 J 

36 ProjeBiks. Vzxt L 

III. if 2 Balls are thrown at different ele- 
vations (but with equal degrees of velocity), 
the one as much above 45 degrees as the other 
below, the horizontal diftances (or Randoms) 
where they both fall will be the fame *• 

. Solution. EreA JB perpendicular to the Horizon, and cqud 
to four times the height a jQodj muft fall from, to acquire the ve« 
loelty with which the Ball is to be thrown ; biie^'this in dm 
point G, through which draw HC perpendicular to JB, ^and 
meeting the line AC (perpendicular to AK) in C. . On C as a 
Center with the Radius CA^ defcribe the Circle -^:ffZ> ; laftly 
fixrough K draw the line KE I perpendicular to the Horizon, 
cutting the Circle in the points E and/s ICzy AE or ^/ will 
be the diredion fought. 

AEq Ala 
For by the Lemma AS =? «-«. or yj^ » ^^' (^^ conjiru* 

Sione) AB is equal to four times the height a Body mull fall 
from» to acquire the velocity with which it is to be thrown, 

AEq Alq 
therefore its equal rr^p- or yjp w the fame, which by the Co- 
rollary . was the thing required to determine the dircftion fought, 
ccnfcqucntly the Parabola, which the Body will defcribe, will 
pais through the point K. . Q^JS., D. 

CorolL I . From hence it is evident, that if the objef^ to be 
ftruck, be placed any where in the horizontal line AO ( 
.beyond ^, the "Problem is impoffible; for then ^Ji will not 
touch the Circle, and the Ball will not reach that point with anv 
dircftion whatever. And that when the Ball is diredled towarot 
"If, it will fall on j^the grcateft diiUnce it can poflibly be thrown 
to ; but the angle ^H being equal to ABH m the oppofite 
4cgmcnt ^32. E/em. 3.^ is equal to hsilf AQH at the Cfcntcr 
^20. EJem. y.j which as a right one; confequently ^AHlaza 
'angle of 45 degrees. 

* CoroU, 2. If the objeft is fituated in the horizontal line AO 
(Fig. 18.^ but nearfcrto'^, dian the greatcH horizontal (Kftancc 
at which it may be ftruck, iiippofe in JST ; the two direftions 
JE and A I with which it mav be hit, are equally diftant from 
the dirc£Uon AH 5 for the angles tAH and HAE arc equal, u 
Mfting on equal arches IH and fiE (iB^FUm. 3 J 


IV- Ttic hcigjit a.Body wMl, wfa«ii 
thrown perpendicularly upward?* |s sq^ 
half the greatcft horizontal diftance it c^n be 
thrpwn jtp with the fam? velppty *. 

From hence we tnay eafily know how/ai: 
a Mortar-Piece* or other Tuch Macbdne^ wiU 
carry a Ball. Let the Ball be thrown .pemekr 
dicularly upwards* note the time of its jalgent 
and defcent, half that is the time of dcfcent^ 
from whence we karn thb height^ to which 
the Ball is thrown, for Bo^iifs are obferyrd to 
fail in the firft fecond of time 1 6 feet, confe- 
quently in 2 feconds they fall 4 times 1$ feet 
(Chap^r 5. §. 4,) in 3> P times as much &c. 
but (§ 4.) the perpendicular height being dou. 
bled will give the greateft horizontal diftanc^ 
to which that Machine will carry the Ball with 
an equal Charge. 

V. The Randoms of two Projeftilcs, hay- 
ing the fame degrees of elevationi but thrown 
with different velocities, are as the fcjuarcs of 
the velocities : for by the laft, the Randoms 
are as the heights tp which ^e Bodies thtowa 
perpendicularly upwards will afccnd, but ,th? 

• Cordl 3. The altitude of a perpendicular projedion is 
equal io a fourth part of the height j^J^; for the vdocj^t/ widi 
^iuch thefiody is pr0j«£ted9 is (mx bpfoth,) fuch as it woul4 
^cqiiire by falling through a fourth part of the line AB i but a 
•forath part of die Kne A Bis equal to half «he line GH, or AJ^ 
(^*S' ^7-) ^t 13 ^^ die greateft horizontal diflance to which 
the fiqdy can bs thrown. 

Sc^Cot0s*s HfimiQW Monfurarum p* 87. Kd^s Introdud. a^ 
PhytPwl. i6. » " 


38 Proje&iles. Parti 

heights are (Chap« 5. §. 6.) as the (quares of 
the velocities. 

VI. Supposing the motion of the Earth, all 
Bodies, when thrown perpendicularly upwards, 
defcribe Par^oldsi notwithftanding they ap- 
pear both to afcend and defcend in the fame 
right line* 

This may very eafily be lUijftratcd in the 
following mannpr 5 let there be a Body car- 
ry ed uniformly along the line AB (Fig. ip.) 
by the inotion of the Earth from A towards 
B 7 as it paflcs the point C let it be projected 
upwards by fbme force ading underneath it 
Sn the direQLion CO perpendicular to the for- 
mer; the Body will not thereby lofe its mo- 
tion which it had in common with the Earth 
towards B (by the firft Law of Nature), but 
will be carryed by two motions, one towards 
B the other towards O 5 let us then fuppofc, 
that in the time it would have advanced for- 
wards to P in fhe line AB, it rifcs upwards 
to M in the line C O 5 it will then be found 
in D (Chap. 4* §• 2.) : in like manner fup- 
pofing it would have advanced forward to Q^ 
while it rifes to N, it would then be found 
in E, afterwards in F, then in G drr. de- 
Icribing the Curve CGL whiph (from what 
was demonftrated under §. i .) is a Parabola '^. 

* Dem, Suppofe die inotion the Body had in common with 
the Earth towa-ds B (Fig. zo.) and that with which it is pro- 
je6(ed tovr;uds 0>fach, as being compounded (Ch. 4. J. 2.) would 




Chap. 7* ^ PfojeSiikil > J^ 

The rea(bn why it appears to a Spedator 
to rife and fall perpendicalariy^ is becaufe he 
is carryed uniformly along with it by the mo* 
tion of the Earth in its firft dire£kion.^. 
Suppofe the Speftator at C at the inftant the 
Body is thrown from thence, when it arrives 
at D, he will be moved to P, .when the Body 
is at E he will be at Q^^^. as is evident from 
^hat was obferved about the motion of the 
Body in the Curye $ and they will both meet 
in L. Therefore itnce the Spedator imagines 
himfelf ftanding ftill, and itts the Body zU 
ways perpendicularly over his head* hemuftof 

courfc think th^t it rifes right up and falls right 

It may be proper to pbferve here, that 
Experiments relating to the motion ofprojed* 
cd Bodies, do not exadl-y anfwer the Theory ^ 
the refiftance of the Air deftrpy ing part of their 
motion : for which a fmall allowance is to be 

Have produced a motipn in the direction. CXi it will folloifr 
|rom thence, that the path dcfcribed by it will be the fame, as 
ifit had been thrown in that direction from a point as C at reft ; 
but in that cafe it would have defcrib'd a Paraboh as CGL (J. i.) 
therefore in this. ^E.D. 


4^ CefUral Forces^' Pdit'li 

G H A F; Viu; 


Of peniripj^M and Centrifugal Forces, 

. J t 

HJE N- a Bo^y is fi^^efted m ^^ hotu 
aofotaa^ dHredioa ^d by its Gravity 
iittde 'to <it@icrlbe a Parafbota^ as dcmonAratcd 
OdAfttt tke laft 5. the curVaraFe ef that Para- 
bola will vary in proportion 10 tbc velocity 
wkb i^^icb i!hd Body is thrown, and the^Gra^ 
itiiy ^t^hidh ibipdl^ it towards t-he Eai^rh. For 
the. le^is' dtts-Gcavity is in praporrioia to the 
quantity of matter it contains* or the g^eMer 
dievdociiy is With Whidh it is projc^dj the 
le&wiU ir deViaite from a ftrait line^and the 
fiitfher it Will gd> bcfbrc it Ms to the £arth<r 
Ibr inftahccfc if a Bullet be fhot out of a Gan- 
non^ from the ^p of a Mouiitaiil with a gi«> 
vcn velocity in an horizontal dire£tion» t^nd 
goes in a curve line, fuppofe to the diftancc 
of two Miles from the foot pf the Mountain 
before > it falls to the ground $ the iame Bullet 
fhot with ^ much greater velocity would: fly to z 
much greater diftance before its fall. And by 
cncreaHng the velocity, the diftance to which 
it is pro)e£ted> may be encreafed as much as 
you pleafe; fo that it will not fall to the 
ground, till it is arrived at the diftance of ten, 
or thirty, or ninety degrees 5 or till it has even 







Chap. 8. Central Porces. 41 

furroundcd the whole Earth, and arrives at the 
very top of the Mountain from whence it 
was projeded : in this cafe it will per- 
form a fecond revolution, and fo on in tnfi^ 
nitwn without a new projection , provided 
the reflftance of the Air Is taken away. Nay 
it may be projefted with fuch violencei that 
it will continually recede from the Earth, 
moving in a Curve, till at length it gets out 
of the Sphere of the Earth's Attraftion^ after 
which it will go on in a ftraight line with- 
out ever returning. Which may thus be illu- 

Let ABC {Tig. 21 J reprefcnt the Earth, 
,M the point from whence the Body is pro- 
jcfted in the diredion MQ^: it may bethrowa 
with fuch force as to carry it to B before it 
falls, or to C, or even to go round to M, 
dcfcribing the Circle MDM5 or laftly it may 
be made to defcribe the Curve MO, till it 
gets out of the Sphere of the Earth's Attra- 
ftion, fuppofe at O, going on afterwards in 
the infinite ftrait line OX, there being nothing 
to flop or alter its courfe. Farther, it may be 
projcded with fuch a force from M (Tig. zi.) 
as will caufe it continually to recede from the 
Earth, till it arrives at the oppofite point G, 
dcfcribing the curve MKG5 and if the point 
G is within the Sphere of the Earth's Attra- 
ftion, the Body will return to M, defcribing 
the Curve GLM exaftly fimilar to MKG5 

F and 

42 Central Forces. Part I 

and in moving nearer and nearer to the Earth 
till it comes to M, will regain what velocity 
it loft in going from M to G, its Gravity con- 
fpiring with its motion from G to M in the 
lame degree in which it oppofed it from M 
to Gj confequently the Body when at M 
^laving recovered the velocity with which it 
fct out) will be inablcd to perform a fecond 
revolution in the fame Curve as before, and 
ib on. 

Again, fuppofc it had been projefted from 
the point M with a lefs degree of force than 
would have carryed it round in the Circle 
MDM {IFig. 2 1 J, but greater than would have 
fuffcrcd it to have fallen to the Earth at the 
oppofite point F (Tig. 22 J 5 it would alfo in 
this cafe have arrived at the point M from 
whence it fet out; for the excefs of velocity 
it would have gained in F, by its tendency to- 
wards the Earth in its way thither, over and 
above that with which it was projeded from 
M, would be fufficicnt to carry it off again 
from the Earth, till it arrived at Mj and to 
make it defcribe the path FPM exadly fimi- 
lar and equal to the former, lofing in its way 
from F to M juft fo much velocity, as it gain- 
ed by pafling from M to F; and thereby it 
would be inabled to perform an infinite num- 
ber of revolutions in the fame Curve without 
requiring a fecond projcftion. 


Chap. 8. Central Forces. 43 

From hence ir follows, that fuppofing a 
Body projeded from a point at any diftance with- 
in the Sphere of the Earth s Attradion, with a 
force fufficicnt to carry it half round without 
falling to the furface, it is impollible it fhould 
fall u'pon any part of the other half 5 but will 
return to the point from whence it let out, 
making continual fuccefllve revolutions in the 
fame Curve; provided it meets with no re- 
fiftaace from the Medium through which it 
paffes, nor any other obftacle to obftrud its 

From hence alfo it is clear, that, the near- 
er the revolving Body approaches to the Earth, 
the fafter it moves 5 its velocity being conti- 
nually increafed during the time of its accefs 
towards the Earth, and as much retarded du- 
ring its recefs from it. And this acceleration 
and retardation will always be fuch, that thcN 
Body will defcribe equal Areas in equal times : 
the meaning of which is, that if we imagine 
a line conftantly extended from the Center of 
the Earth to the Center of the Body, that line 
will always defcribe or pafs through equal fur- 
faces or fpaces in equal times, for it conftantly 

• Gravity is here fuppofed to be inverfely as the fquares of 
die diftanccs from the Earth, for 'tis poffible that the force by 
which a Body tends towards another, may vary in fuch a manner 
at different diftances, that the projedted Body fhall defcribe a 
Spiral line, oonanually^appioaching to or receding froni that about 
ivhich it revolves. 

Fa becomes 



44 Central Forces. Part* I. 

becomes (horter the fafter it moves» and incc 
*versA *. 

And for the fame reafon that a Body pro- 
jcded with a fufficient velocity may by the 
forc^ of Gravity be made to dcfcribe a Curve 
round the Earth, and perform continual fuc- 
ceffive revolutions in the fame 5 it follows that 
the Moon, may by the fame force of Gravity 
be made to revolve about the Earth, or any 

* Dem, Let the time in which the Body performs one revo- 
lution be divided into equal parts, in the iirft of which let thq 
Body defcribe the right line AB (Fig, 23.^ : in the fecond part 
of time, if not prevented, it woula^go flraight on to f, dcfcribing 
the line Be equal to AB by thefirft Law of Nature; the lines 
SAy SB, Sc being drawn, the triangles SB Ay ScB will be equal 
to each other, their bafes AB and Be being equal and their 
heights 5 the fame (38. Elem, i). When the Body arrives at 
By let the Centripetal force by one fingle impulfe turn it out of 
the ftraight line Be into the line i^C : in which let it move on 
uniformly without receiving a fecond impulfe till it comes to C. 
Let Ce be drawn parallel to SB meeting ^C inC ; then at the 
end of the fecond part of time the Body will be found in C, 
having defcribed the Diagonal of the Parallelogram Ne (Chap. 4. 
i- 2.)- Draw SCy and the triangle SCB will be equal to the 
triangle SeBy (each having the fame bafc SB and being between 
the fame parallels Cc and SB) and therefore alfo equal to the 
triangle SB A. For the fame reafon, if the Centripetal force afts 
in the points C, Z>, E fuccellively, fo as to make the Body de- 
fcribe the ftraight lines CD, DEy EFy Sec, in fo many equal 
parts of time, the triangles SCDy SDE, SEE, Sec- will be all 
equal to' one another and to the triangle SAB. Confequently e- 
qual Areas are defcribed in equal times. Let us then fuppofe the 
bafes of thofe triangles, 'viz. AB, BC, CD, DE, Sec, diminiih- 
cd /« ififinitumy and likewife the times in which they are dc^ 
fcribed; then will the Perimeter Ay By C, D, Ey F, Sec. become 
a Curve, and any number of thofe triangles taken together, (or 
their Areas) will be proportionable to the times hx which they 
are defcribed, J^ £, />, 


chap. 9. Communication of Motion. 45 

other Planet by the like force about the Sun, 
if the velocities with which they move arc 
duly adjufted to the forces by which they ard 
aded upon. 

When a Body revolves about another in 
this manner, that force or power by which it 
is prevented from flying off (as it othcrwifc 
would do in a Tangent to the Curve which 
it defcribes) is call'd the Centripetal^ the coun- 
tcr-aftion of this, by which it endeavours to 
fly off, the Centrifugdi, thcle, by the id Law 
of Nature being equal to each other, are cal- 
led by one common name Central Forces^ that 
with which the Body is at firft projected, or 
continues its motion from any point, is the 
Trojeclile force 5 and the time in which it per- 
forms one revolution, the Periodical time. 

These forces properly relating to the mo- 
tions of the Heavenly Bodies will be more large- 
ly treated of in another place. 

Of the Communication of Motion. 

\.X\EliOK^ we proceed to explain the 
j3 Laws, by which Bodies communicate 
their motion from one to another, it is very 
necelTary to make a diftindlion between Mo- 
tion and Velocity 5 which ought to be well 

pbfcrv'd and is as follows. > \ 


46 Communication of Motion. Part I. 

By the Motion of a Body (fomctimes called 
its quantity of motion^ fometimes its Motneti- 
turn) is not to be underftood the veloci- 
ty only » with which . the Body moves ; 
but the fum of the motion of all its parts ta- 
ken together : confequently the more matter 
any Body containsi the greater will be its mo- 
tion, though its velocity remains the fame. 
Thus, fuppofing two Bodies, one containing 
ten times the quantity pf matter the other 
does, moving with equal velocity s the great- 
er Body is faid to have ten times the motion 
or Momentum that the other has: for 'tis 
evident th^ a tenth part of the larger has as 
much as the other whole Body. In fliort that 
quality in moving Bodies which Philofophcrs 
underftand by the term Momentum or mo- 
tion, is no other than what is vulgarly call'd 
their Force^ which every one knows to depenjj 
on their quantity of matter as well as their 
velocity. This is that power a moving Body 
has to affed another in all adions that arife 
from its motion, and is therefore a furidam^t^tal 
Principle in Mechanics, See it farther explained 
in the next Chapter. 

IL Now fince this Momentum or Force 
depends equally on the quantity of matter a 
Body contains, and on the velocity with which 
it moves 5 the method to determine how great 
it is, is to multiply one by the other. Thus 
fuDpofe two BodieSt the firft having twice the 

Chap. 9. Communication of Motion. 47 

quantity of matter and thrice the velocity 
\i^tiicb the other has} any two nunxbers that 
are to each other as two to one^ will exprels 
their quantities of matter (it being only their 
relative velocities and quantities of matter 
which we need confider)* and any two num« 
bers that are as three to one, their velocities $ 
now multiplying the quantity of matter in the 
firft viz,. 2 by its velocity 3, the produd is 6 ; 
and multiplying the quantity of matter in the 
fccond by its velocity, viz,, i by i, the pro- 
dud is one$ their relative forces therefore or 
powers will be as 6 to 1 5 or the Moment of 
one is fix times greater than that of the other. 
Again if their quantities of matter had beea 
as 3 to 8 and their velocities as 2 to 3, then 
would their Moments have been as 6 to 24, 
that is, as i to 4. 

This being rightly apprehended, what fol- 
lows concerning the Laws of Communication 
of Motion by Impulfe, and the Mechanical 
Powers will be eafily underflood* 

The Communication of Motion. 
I. In Bodies not Elaftic. 

III. Those Bodies are faid to be not Ela^ 
fiic^ which when they ftrikc againft one ano- 
ther do not rebound, but accompany one a- 
nother after Impaft as if they were joyned. 
This proceeds from their retaining the impreG* 
iion made .^upon their furfaces after the im* 
prcfling force ceafcs to ad. For all rebound- 

4$ Communication of Motion Part I. 

ing is Gcca(ioncd by a certain fpring in tlic 
fiirfaccs of Bodies, whereby thofe parts* which 
receive the impreffion made by the ftroke, im- 
mediately fpring back and throw off the im- 
pinging Body 5 now this being wanting in Bo- 
dies void of Elafticity there follows no repara- 
tion after Impad. 

IV. When one Body impinges on another 
which is at reft, or moving with Icfs velocity 
the fame way, the quantity of the motion or 
Momentum in both Bodies taken together re- 
mains the fame after Impad, as before; for 
by the id Law of Nature, the readion of one 
being equal to the adion of the other, what 
one gains the other muft lofe. 

Thus, fuppofe two Bodies one impinging 
with 12 degrees of velocity on the other at 
reft : the quantities of Matter in the Bodies 
being equal, their Moments and velocities are 
the fame; the fum in both 12; this remains 
the fame after Impad (§. 4.), and is equally di- 
vided between them (§. 3.); they have there- 
fore 6 a piece, that is the impinging Body com- 
municates half its velocity and keeps half. 

V. When two Bodies impinge on each o- 
ther by moving contrary ways, the quantity 
of motion they retain after Impad, is equal 
to the difference of the motion they had be- 
fore ; for by the la Law of Nature, that 
which had the leaft motion, will deftroy an 
equal quantity in the other, after which they 


ChsLj^k^ g.'.Comm^kation of Mottan. 49 

vnW hfiovisltogedKir vHlfih the remakdcr, that 
is.thic cUiflFdrcuce. ^ 

Thus fbct mftailce« let there be. two equal 
]B^odie$ moving tewatx^s each other, the one 
with > degrees of velocity, the other with 5, the 
diff€iteiice of their Moments or velocities will 
he 2 f^ tihis^ iremains the fame after Impad (§. $.) 
jwd is eqiarally divided between them (§. 3,) 
ttiey ftavc riierefore one a piece : that is, the 
Body which had 5 degrees of velocity, lofes 
}/>r as. much- as 4:he other had, communicates 
half the remainder, and keeps the othcjfhalf*; 

11. In Elaftic Bodies. 

VI. BoENTEs^ pctfeaiy Elnjiic are fiich as re* 
boand after Impa£k with a force equal to that 
witli which they impinge upon one another : 
thoTe pafts of theis fttrfaces, that receive the 
impt^:flion:^ immediarely fpringing back, and 
thro^mg off thie impinging Bodies with a force 
eqiKiI to that of Impad. 

• Frowi tlwfc pofitioas it is eafy to deduce, a Theorem,- that 
fcall fhew thq velocity of Bodies after Impaift in all cafes whaN 
ever; Let th^re be two Bodies A and By the velocity' of the firft 
tf of th6 other b^ then [^ x^) the Moment of J will bo expreffed 
hy-i «, and of 5 hy Bbi therefore the fnm of both will be Ja--¥ Bh j 
and A a — BB will be the difference when they meet. Now thefe 
quantities (by }. 4. and 5.) remain the iame after Impact ; but 
iuiowihg the quantities of motion and quantities of matter, w^ 
have the velocity (which J. 3- is the fame in both) by dividing 
the fbrmer by the latter, (as follows from §. 2.) therefore 

"3? — !s" ^^ '^ — 5" ^^^ ^ ^ exprefs the velocity ot 
Ae Jodici after Impaft* 


5 o Communication of Motitm. Part" L 

VIL From hence it foUovs that the aftioh of 
Elaftic Bodies on each other (that of the fpring 
being equal to that of the ftroke), is twice as 
much as the fanie in Bodies void of filafticity. 
Therefore when Elaftic Bodies impinge on each 
other, the one iofes and tho other gains twice 
as much motion as if they had not been £- 
laftic; we have therefore an eafy way of de« 
termining the change of motion in Elaftic 
Bodies, knowing firfl: what it would have been 
in the fame circumfiances, had the Bodies beeff 
void of Elafticity. 

Thus if there be two equal and Elaftic Bodies, 
the one in motion with 12 degrees of velo- 
city impinging on the other at reft, the im-^ 
pinging Body will communicate twice as much 
velocity as if it had not been Elaftici that is^ 
(by §.4.) 12 degrees or all it had 5 confe^ 
qucntly it will be at reft, and the other will 
move on with the whole velocity of the former. 

VIIL It fomctimes happens that in Bodies 
not Elaftic, the one Iofes more than half its 
velocity, in which cafe fuppofing them Ela- 
ftic it Iofes more than all $ that is, the etcefs 
of what it Iofes above what it has, is negative, 
or in a contrary diredion $ thus fuppofe the 
circumftances of Impaft fuch, that a Body 
which has but 12 degrees of velocity, Jofes* 
1 6 5 the overplus 4 is to be taken the contrary 
way, that is, the Body will rebound with 4 
degrees of velocity. ^I'.^.Lctit be required to de- 

JChap. 9. Communication of Motion. 51 

rermine the velocity of a Body after Impaft 
againftan immoveable objed. Let us firft fup- 
pofc the Objed and Body both void of Ela- 
fticity : 'tis evident the impinging Body would 
be ftopt or lofe all its motion » and commu- 
nicate none i if they are Eiaftic, it muft lofe 
twice as much (by §. 7.) and confcquently will 
rebound with a force equal to that of the 

IX, It is fufficicnt if only one of the Bo- 
dies is Elaftic, provided the other be infinitely 
hards for then the impreilion in the Elaflic 
Body will be double of what it would have 
been, had they both been equally Elaftic : and 
confcquently the force with which they re- 
bound will be the fame as if the imprcfj[ion 
had been equally divided between the two 

X. There are no Bodies that we know 
of, either perfeftly Elaftic or infinitely hard ; 
the nearer therefore any Bodies approach to 
perfedion of Elafticiiy, fo much the nearer 
do the Laws they obferve in the mutual 
communication of their motion, approach to 
thofe we have laid down. 

XL Sir ^^ Newton made trials with fe- 
veral Bodies, and found that the fame degree 
of Elafticity always appeared in the fame Bo- 
dies, with whatever force they were (truck; 
fo that the Elaftic power in all the Bodies he 
9a4e trial npon, exerted it felf in one con* 

Q * ftani 

54 CommunicatioH of Motion. Part !• 

XIV^ To this wc may add the following 
Propofition, relating to oblique forces, ^iz,. 
that if a Body is drawn or impelled three dif- 
ferent ways at the fame time by as many for- 
ces ading in different diredions $ and the quan- 
tity of thoft forces is fuch that the Body is 
kept in its place by them : then will the for- 
ces be to each other as the feveral fides of a 
triangle drawn rcfpeCtively parallel to the di- 
ledions in which the forces aft "^^ 

• Dem, Let the lines JIS^ AD, JE, (Fig, 26.) reprcfent the 
3 forces adting upon the Body A in tHofe dircdions, and by that 
means keeping it at reft in the point A. Then the forces EA 
and DA will be equivalent to BA otherwife the Body would 
be put ]nt9 inotion by them (contra Hypoth.) But thefe forces 
are alfo equivalent %o A€ (Chap. 4. $. 2 ) confequcntly AC 
tnay ezprefs the other fbroe, and EC, which is parallel and equal 
to ADf mxy expi«& that force : bat ACE is a triangle whofa 
fides ase aU parallel to the given diredions, therefore the fides of 
this triangle will exprefs the relation of the forces by which th^ 
Body^is kept at reft. ^J^/>, 

C H A K 

r ' 


■ 1 





Qlazp. 10. Mechanical Powers. 53. 


Of the Mechanical Powerf^ 

L IT TAVING in the foregoing Chapter 
J[ X d^counted for the Commanicatiofi 
of Motion by Impulfe $ we proceed next to 
conftder motion as communicated without Im- 
pulfe ; which is done by means of certain In-i 
ftrumentS) commonly known by the names 
of Mcchimcal Powers. The ufe of thefe Pow-^ 
ers confifts chiefly in managing great Weights 
or performing other Works with a determi* 
pate force. 

U. Thby are ufually reckoned five, viz^l 
The Lever, the Wheel and Axis, the PuUy, 
the Screwi and the Wedge j to which fome 
idd the Inclined Plane. To thefe all Machines 
how complicated foever are reducible. 

III. Th£SB Inftruments have been of very 
ancient ufe $ for we find that Archimedes^ was 
well acquainted with the extent of their Power, 
as may be inferred from that celebrated faying 
of his, Ao$ *7r8 ra, ^rtoJ yltZ icwW. By which, 
he meant that the greateft imaginable Weight 
might be moved with the fmalleft Power. 

IV. That Body which communicates mo- 
tion to another, is called the Power i that which 
receives it, the Weighp. 

^6 Mechankat P(m^s. ^ V%rt L 

V. That point in a Body which remains 
at reft, while the Body is turning round, is 
called the Center of Motion. Befidesthis, there 
are two othes Centers in Bodios^ i. that of 
Magnitude^ which is a point, as near as pofli- 
ble, equally diftant from all the external parts 
o£ titc lodiy ; 2. that of Gravitjy or that abomi 
which atU tlui pares of the Body, in whatever 
ittuatioa it is placed^ exa^ly balance eacb 

Vi Wbekt a Body communicates motion; 
to another, rt lofes juft fa much of its own> 
as. is communicates to that other ; the a^ioti» 
of ODc beio^ equat to the rea^kion of the orher* 
Sec Chapteir the laft §. 4. a:nd 5 • 

VII. When two Bodies have fuch relatioa' 
to each other (fuppofe them fixed to different 
partsf of the fame Machine) that if one be put 
into motion, the other will thereby have ne-^ 
celTariiy fuch a degree of velocity given it,, 
that their Moments* will be equal; it will 
rixenr ho impoifibie that one fhould begin to 
move without communicating to the other a* 

* It was propofed (Chapter the laft) to give fome farther ex- 
plication of the term Mementwn in this place, and to fh'ew that 
the Force or Power any Body has (extept fuch as does not pro- 
ceed from motion) wholly depends upon it : it being then intended 
to treat this Subjed in the ufual way. But the method here made 
ufe of renders fuch explication unneceflary ; 'tis fufEcient if the 
Reader underftanda by it the quantity of motion in a Body, 'or 
its qiuntity of matter n«ilti|di€d by its velocity, as defined in 
that Chapter. 


Chap. to. Mechanical Power s^ 57 

qiuatitf of motion equal td its own ^ 'tis evH 
dent therefore from tlie lad Fropofttion, tliat 
if we fuppofe it to begin to move i in tliac 
Very inftant it muft lofe all its own motion by 
communicating it to the other Body : and con-* 
fequently will remain at reft, communicating 
none at alL Now the Moments of two Bo-^ 
dies are equal (Chap. 9. §. 2.) when the velo- 
city of the firft is to that of the fecond, as the 
quantity of matter of the fecond to that of the 
firft, for if wie fuppofe their quantities of 
matter as t to 3^, then by the fuppoittion their 
velocities are as 3 to i $ and if we multiply 
the quantity of matter in the firft viz. i, by 
its velocity 3, and that of the other viz. 3 by 
its velocity i ; their produds are equal $ f heit 
Moments are therefore by the Definition (Chap. 
9. §* I. and 2.) equal. They will alfo be c- 
qual, when the fpaces the Bodies pafs^ over arc 
ki that proportion; for; the times ttiey both 
move in , bdng the famc^ the fpaces will always 
be as the velocities. 

Viri. From hence it follows, that in any 
Machine whether fimple dr compoundi the 
Power however fmall may have a Moment 
equsil to that of the Weight; provided the 
Machine be fuch^ that when it is in mo«< 
tion, the velocity of the Power fnall exceed 
that of the Weight, as much as the Weight 
is larger than the Powers for then what the 
Power wanj;$ in quantity of niattcr or wcighc 

H will 

^8 7%e Let)er Part L 

will be made up in velocity; confcqucntff 
their Moments wiU be equal by §. the laft, and 
therefore by §. 7. they will exadly balance each 
other 5 or be in MquUibria. 

IX. But if the Power bear* a greater pro- 
portion to the Weight, than the velocity ©f 
the Weight to that of the Power 5 it will then 
have a greater Momcmum than the other, and 
confequently may communicate fuch a Mo 
mentum to it at it will receive, without lofing 
all its own ; the remainder therefore, if fuffi- 
cieni to overcome the fridion of the Machine, 
will put it into nwtidnv We proceed now to 
treat of each Mechanical Power in its order, and 

I. Of the Lever. 

X. The Lever is a right line (or bat whofe 
weight in Theory is not confidered) moveable 
on a Center, which is called its Fulcrum^ or 
fixed Point. 

XL The i^quilibrium in this Machine is,, 
when the diftance of the Power from the fix- 
fd point is to that of the Weight from the 
iame, as ^e quantity of matter in the Weighr 
to that in the Power. 

For fuppofrng the Lever placed on its Ful- 
crum with the Weight to be raifed at one 
end^ and the Power applied to the other ;^ 
'tis evident the farther the Power is placed 
from the Fulcrum or center of motiOHt the 
larger will be its fweep when the Machine isr 
put in motion i that is^ it will move ever A> 


Chap* iQi The Lever. 59 

much mor^ '/pace in the fame time tlian the 
Weight to be railed : now if it is placed ;u(i: 
fo much farther from the Fulcrum^ as it is 
Icfs than the Weight, it will move juft fi> 
much faft^c $ their Moments therefore will be e^ 
qual (§.7.) and confequently the Power and 
Weight will cxaftly balance each other, or be 
ia iEquUihrio *. And if the Ppwcr is fuffi- 
cicntly augmented to overcome the friction of 
iheMachine, it will put it in motion. 

The X^ver is of 3 kinds, i. When the 
fixed point is between the Weight and the 
Power, as in the laftcafe. 2. When the Weight 
is between the fixed point and the Power. 
J. When the Power is between the fixed point 
and the Weighs 

Int all which cafes the ^Equilibrium will be, 
when their diftances from the fixed point arc 
fuch, that their velocities (hall be inverfely as 
their quantities of mattpr j for then by §. 7. 
being at reft, ijeither of them will commu- 
nicate any motion to the othen 

* Geometrically thus. Let AB (Fig. zj.) reprefent the 
Lever, F tlie Fulcrum, W the Weight, P the Power, the one 
fufpcnded at the extremity of the Lever Ay the other at By and 
let 5 F be to FAzs W to P i then while the Lever moves from 
the fituation i/^ into that of CD, the poSn^ B which fudains 
the Power will move as much farther than A which fullains the 
Weight (and confequently as much fafter iince they perform 
their motions in the fame time) as the arch BD is longer than 
AC ; that is, the triangles BFD and AFC being fimiiar, as the 
arm BF is longer than AF^ which (ex Hypotb/j is as much Jl« 
0ic Weight exceeds the PQwel", they will therefore (J. 7.) be In 
i£^ttiiib|rio. ^H.D. 

H ^ The' 


6o The Wheel and Axis. ^ Part I. 

Thb common Scales may be confidcr* 
ed as a Lever of the firft kind* 'Where the 
Weight and Power are applied at equal idiftau^ 
ces from the fixed point. 

The Steelyard is alfo a Lever of the firft 
kind, whofe arms are unequaL 

The difference between the ufe of the 
Scales and the Steelyard conffifts in this; that 
as in one you make ufe of a larger Pow- 
er (or more Weights) to eftimate the weight 
of an heavier Bodyj in^thc other you ufe the 
fame Power, but give it a greater velocity 
with^ refped to that of the Weight by apply- 
ing it farther from the "fixed pointy which by 
§. 7. will have the fame efFcd. 

II. The Wheel and Axis. 

XII. This Machine is a Wheel, that turns 
round together with its Axis \ the Power in 
this is applied to the Circumference of the 
Wheel, and the Weight drawn up by means 
of a Rope wound about the Axis. 

XIIL In this there will be an iSquilibrium, 
when the Weight is to the Power, as the Dia- 
meter of the Wh^el to the Diameter of the 

Tis evident^ the velocity of the Power will 
exceed the velocity of the Weight, as much 
as the Circumference of the Wheel exceeds 
that of its Axis ; becaufe the fpaces they pafs 
over in one revolution will be as thofc Cir*' 
cumferencesj that is, as much as the Diameter 


Chap. lo. T7ye PuUey^ 6# 

oi one exceeds th^ of the ochcr> (the Circum; 
ferences of Circles being as their Diaineten »)i 
what therefore in this cafe the Power wants in 
weight will be made up in velocity* fix>ni 
whence (§. 7.) there will be an ^quilibriunjL** 
The ufe of this Machine is to raife 
Weights to greater heights than the Levet caa 
do, becaufe the. Wheel 1$ capable of being 
turned feveral times roand, which the Lev^ 
is not 5 and alfo to communicate motion £rom 
one part of a Machine to another 3 accordingly 
there are few compound Machines without ir« 


XIV. A Pulley is an Inftrument compofed 
of one or more Wheels moveable on their 

XV. A fimple Pulley, if its Axis is fixcd» 
is of no other ufc^ than to alter the dire- 
^ion of the Powers for the Power and 
Weight will both move through an equal 
fpace in the fame time. But in a Pulley noc 
fuedt as in J^^. zg^ where the Rope runs un« 
der itt or in a combination of FuUies as ia 
fig* 30. the ^Equilibrium will be> when the 

* Geometrically thus. Let JS (Fig* z%.) be the Diameter 
Df the Wheel, DE that of the Axis, #^ the Weight, and P the 
Power ; when the Wheel begins to move, the point B and D 
will defcrihe fimilar Arches about the Center C, in the. fame 
manner the point ji and ^ in the Lever were ihewn to do about 
the fixed point F (Pig, 2^) that is the point B will move as 
much fafter than Dt as C J? is longer than CD ot JB than D E^ 
the motion therefore of P ($. 7.) will be e^ual to tih^t of W. 
f torn wh^Qce the Piropofiti ji^ 19 clear* 


6* ^The Pulky : Part 1. 

Power is to the Weight, as one to the num- 
ber of Kopest thu pafs between the upper and 
lower Pullies. 

Suppose one end of the Rope fixed in B 
(rig. 29J the other fupported by the Power 
3P, it is evident, that in order to raife the Weight 
W one £bot> the Power muft rife two, for 
both Ropes nnz^ B C and C P, will be (horten- 
cd a foot apiece, whence the (pace run over 
by the Power, will be double to that of the 
Weights if therefore the Power is to the Weight 
as I to 2, their Moments will be equal : for 
the fame reafon if there be 4 Ropes pafling 
from the upper to the lower Pullies as in Ti^. 
JO. the velocity of the Power will he quadru- 
ple to that of the Weight, or as 4 to i. &c. In 
all cafes therefore when the Power is to the 
Weight, as one to the number of Ropes paf^ 
foig from the upper to the lower Pullies, {%. 7.) 
there will be an iEquilibrium. 

XVI. If the Pullies be difpofcd as in Figure 
the 3 \fiy each having its own particular Rope« 
the adion of the Power will be very much xxnr 
creafed ; for here every PuUy doubles it, where- 
fore the Power is 4 times greater with 2 Pul- 
lies, 8 times with 3, 16 times with4e^<r. For 
it is evident from the conHderation of the Fii* 
;ure, the firft will niove half as fafl: as the 
^ower, the fecpnd h^lf as faft as that, 4nd fo on ; 
wherefore (§, j.) the Power is doubled by 
each Pulley, 


Chatp. ro. 7%e Screw* 63 

The ufc of the Pulley is nearly riic fame 
ti^ith that of the Wheel and Axis, but it ii 
more portable and eaiter to be fixed ap» 

IV. The SCRE^^ 

XVn. In this Machine thtf iGquiltbriuM 
*rill be, when the Power is to the Weighft 
as the diftance between any two contiguous 
threads or fpirals in the Screw> to the way de- 
faibed by the Power In one whole revolit* 
f ion. It is manifeft ' from the form of the 
Machine (Fig. ii.) that in one revotntion of 
the Screw, the Weight will be moved through 
a fpace equal to the diftance of two contiguous 
threads, and that the Power will rtm througEi 
a fpace equal to the compafs it takes in one 
revolution, therefore (§• 7.) if the Weight 
exceeds the Power in this prop<^on> thcr6 
will be 9n iGquilibrium* 

This Machine is of great forcct and 
very ufeful in retaining Bodies in a comprefled 
ftare, becaufe it wHl not run back, as the 
three foregoing will when the Power is re^ 
moved. This arifes from the great fri&ibn 
of thofe parts in the Sctew^ which durii^ its 
motion ilide upon thofe, that are at reft. 

V, The Wedgb. 

XVIII. This Infirument is formed t^ two^ 
equal redangles joined at their low^r bafes^^ 
and feparated at their upper ones, by a third i 
which is called the 9wk of the Wt^ s the o^ 
Ifeer two> m SidcT. 

. XIX. 

64 X^ Wedie. Partv L 

;^ XIX. Ik. the foregoing Mechanical Pow-* 
Its we have all along conliclered the Weight, 
as moved in the fame dircdion with that in 
which it is aded i^pon by tb^ Machinci as is 
commonly the cafe^ but in this, the Weight 
is generally applied in fuch a nuAner as to 
jbe made to move in a dircdion different from 
that iu which it is protruded by the Wedges 
hence it is, that Mathematicians have difl^red 
in ti^ir determination of the Power of this 
Machine* ibme confidering the Weight as mo- 
ved by it in oae ddredion and fome in another^ 
Kay there are Tome (I fpeak of late Writers) 
that have differed from Truth it felf. We will 
therefore la.y down the feveral Proportions they 
have given us for the determining the Power 
of this Machine and examio^ them one by onc« 
I . It is demohftrated by fomc, that the Power 
will be equivalent to the refiftance of the 
Weight, when it bears fuch proportion to it, 
as the. breadth of the Bade of the Wedge, does 
to the fum of its Sides ^ or, .which is the 
fym% thing, as half that breadth to one of ics 
3ides. 2. Others make it fomewhat larger* 
and demonftrate that it ougiit to be as half 
the breadth of the back to the perpendicnlar 
height of the Wedge. 3. Some arc of opi- 
nion, that there will not be an Equilibrium 
jlji this Machine^ unlefs the Power is to the 
Weightf as the whole breadth of the Back to 

the perpendicular height. Wallih ^^^ &^ 4* 


Chap. 10. 7^e WedgL 65 

Gravefande in his Elements (L. I. Ch. t j.) gives us 
the fame proportion with the laft i and in hisr 
SchoUumde Ugmfindefulo, tells us^ that when the 
parts of the wood are feparated no £irther thaa 
the Wedge is driven in, the :/^quilibrium will 
be, when the Power is to the Refiftance, as 
hatftkc breadth of the Back of the Wedge to 
one of its Sides. 

TfiiosB who lay' down the firft Proportion 
for determining the Power of this Machine,^ 
fiippofc the parts, which are feparated from 
each other thereby, to recede from their fiirfl: 
iituation in diredions perpendicular to the 
fides of the Wedge. Thus let A C B (Fig. j 3 .) 
rcprefent a Wedge j P, P^ two Bodies to be fe- 
parated by it, the one to be moved towards 
I, the other towards F, in the diredions CI 
and C F petpendicular to A C and C B i then 
'tis evident that when the Wedge is driven ia 
to the fituation M N O, the two Bodies will 
be moved to Q^ and Qj that is, one will have 
paiTcd through the fpace C K the other through 
CL, but thefc fpaces being equal, their velo- 
cities are the fame as if they had both palTcd 
over one of them. v.g. CL, or which is equal 
toitDG (drawn perpendicular to CB)s there- 
fore tlie Power which we fuppofe applied at 
D moves through DC, while the obftacle 
moves through DG^ confequently (§. 7.) when 
the Power is to the Weight as DG to DC, 

I that 


66 Tie Wedge. . : Part D 

that is, as DB to CB*, or half the Back of 
the Wedge to one of its Sides, they will be in iE- 
quilibrio. This proportion therefore, whea 
the parrs of the Weight are naovcd by the 
Wedge in the diredions CI and CF, may be 
admitted as true. 

2. The fecond proportion is alfo tfuc^ifup- 
pofing the Bodies P, P, to Recede from each 
other in the diredbons C N, C M, parallel to 
AB the Back of the Wedge 5 for when the 
Wedge is driven in between them, to the 
fuuation MNO, the Bodies will have moved 
through a fpace as CN, or which is equal to 
it D B, half the Back of the Wedge, and the 
Power through a fpace equal to its height as 
before 5 coniequently (§. 7*) in this eafe, the 
-Equilibrium will be, when the Power is to 
the Weight, as half the Back of the Wedge 
to its height f. 

* For (8. Elem, 6.) the triapgles DCG? and DCB arefunilar, 
and confeqiiently DC : DC : :DB : BG. 

f The fartie may be othcrwife demonftra ted from Seftion 14. 
Chapter^ thus, Let'therebea Body as L (Fig, 34.^ drawtt 
againft the Wedge JBC by the Weight ^, in the diredlion LF; 
parallel to the back of the Wedge ^5 ; but prevented from Aiding 
down towards C by a Plane (whofe upper furfece we may fup- 
pofc reprefented by EF) lying under it. I fay, the Power 
will be to the Weight, when they ar6 in iEquilibrio, ixs D B 
to D C. 

Dem. The Body L is here afted upon in three diredlions, i;/«. 
by the force of the Weight fF in the direftion LFy by the two 
Planes CB and EF, in the diredlions AG and LI, perpendicular 
to their furfaces ; let GjP be drawn parallel to LI, then will 
the triangle LGE have all its fides refpediively parallel to thofe 
dircdions; epnfequently (Chap. 9. J. 14) if we fuppofe LE to 


Ghap. 10. TheB^edge. 67 

3. THOdE, who imagine there iv ill not be 
an ^Equilibrium, unlefs the Power be to the 
Weight, as the whole breadth of the Baxrk of 
the Wedge to its height, fuppofc as in the laft 
cafe, that the Bodies to be feparated, recede from 
each other in direftions parallel to the Back 
of the Wedge; and endeavour to fupport 
their opinion by the following Argument: 
w^. that, \^hen the Wedge is driven in to iiie 
Uruation M N O (Fig, 3 3 J as before, each part 
of the Weight having moved through a fpacc 
equal to half the Back of the Wedge, the whole 
Weight has therefore moved through twice 
fo much, or a /pace equal to the whole Back : 
as much as to fay, the whole has moved far- 
ther than its parts $ which is abfurd. 

cxprcfs the force of the Weight W, GL will repa«fent th^ prcf- 
^ure of the Body L againft the Wedge; and if that is^ reibWejJ 
into G^ and GH the one perpendicular to the diredidn of the 
Power, the other parallel and contrary to it j the lalt, viz. GT?, - 
will exprefs the whole force of the Weight to refill the motioii [ 
of the Power ; but G^ is to £Z, as DB to DC (for the triangle 
£GL and D BC zvt fimilar, the fides of one being ex Conflyu3. * 
rofpeftiveiy. perpendicular. to thofe in the other ; v. g. ,LGxo^B9* 
EL to DC and GE to DB) -, confcquently the Pojyer.isto thc^ 
Weighr, when they balance each other, as half the breadth of* 
tke Back df the Wedge to its height. ^E, D, ' 

CW. Suppofe f he Body L had been drawn again ft the Wedge, 
in the direction GL perpendicular to its furface, and to be mo- 
ved by the Wedge in the contrary diredlion towards G, as in' the 
firft cafe ; then if GL exprefles the force with which it is 4ra\vn 
towards the Wedge, GE will be that with which it refills the 
Power; but Gi? is to GL as Z>-B to J? C, the triangles £GL and ' 
i)^C being fimilar ; confcquently in this cafe, the Power will? 
be to the Weight, as half the breadth of the Back ^f, th«. 
Wedge to pne. of it^ fides ; as was before dembhllr^ed. ^ V "^ ' 


68 Tie Wedge. . Part I. 

4. This is Gftwefmdei miftake in )iis £Zr- 
tnems^ the fame he has alfo made in his Schth 
liuifft de ligno findendo^ and thereby determined 
the Power in both places to be twice as bigt 
as it ought to be* If he had proceedipd in the 
following manner, his Argument would have 
been eafter, as well as the Conclufion jufier. 
Suppofe the Wedge ABC driven into the 
Wood QLQi (as reprcfentcd Tig. 35-) which 
is fplit no farther than the point of the Wedge, 
or however no farther than is juft fuificient to 
give it room to move* I fay that in this . fitua- 
tion of the Wedge, the Power is to the Weight, 
as one fourth part of the Back of the Wedge to 
one of its Sides. For it is evidenti tfiar when 
the upper ends of the Wood^ which prefs a- 
gainft the Wedge in the points G, H, are put 
into motion by the Wedge, they will move 
in the diredions HI and GF, perpendicular to 
the iides of the Wedge^ becaufe they turn as 
it were upon a joynt at L, which we fuppofc 
contiguous to C : again, fince only the upper 
ends of the Wood are put into motion, and 
not the lower ones, which remain at L s 'tis 
evident that the motion of each piece (fup* 
poiing their thicknefs the fame from end to 
end, and their fubftance uniform) will be 
but half, what it otherwife would have been. 
Now were all the parts of the Wood to have 
the fame degree of velocity, the Power would 
be to the Weight, as in the firft cafe, viz. 


Plltc Vllt. Paa.e%. 

■ — 1 


. Chap. '1 0* Th^ Inclined Plane. 69 

as DB to BC (Tig. 3 3.; 5 therefore in thi$ 
cafe^ it is as half DB to BC, or as one fourth 
part of the Back of the Wedge to one of its 
Sides. Which was to be proved. 

XX. The form of the Inclined Plane being no 
other than that of half a Wedge, as is mani* 
fed from the reprefentation of ij {Fig. 16.) it 
follows that what has been d^monltrated of 
the one, may be applied to the other, and 
the properties of both will be the fame. For 
inftancc, if the Weight W is to be raifed up 
the Plane C B, by the Power P, in a dircdion 
parallel to the Plane j inftead of that, we may 
fuppofe the Weight prevented from running oif 
the Plane by the String WB, and the inclin- 
cd Plane driven under it like a Wedge in the 
dircftion DC^ then will the Weight rife to- 
wards G in a diredion perpendicular to CB, 
for wc muft always fuppofe the String C B 
parallel to the Plane, as it would haye beent 
if the Weight had been drawn up by it j then 
will the adion of the Plane upon the Weight 
be fimilar to that of the Wedge in the firft 
cafe; and confequently the Power will bear 
fuch proportion to the Weight, as DB to BC j 
that is, as the height of the Plane to its length. 
! Again, fuppofe the Weight was to have been 
draw|i up the Plane by a String in the dire- 
aion WF parallel to the bafe'pf the Inclin- 
ed Plane CB; t^en if the Plane be driven un- 
der the Weight as before, it muft rife in a 



70 7ha Conclujton. J^art I. 

dircdion perpendicular to CD, that is parallel 
to DB : then the cafe will be analogous to the 
^d of the Wedge 5 confequently the Power 
will be to the refiftancc of the Weight, when 
there is an ^Equilibrium, in the proportion of 
DB to DC, as there demonftrated. 

XXI. These arc the Powers or Machines, 
which under different forms, conftitute all o- 
thers how complicated foever 5 and as the M- 
quilibrium in aay one of thpfc is, when the 
Power and Weight are invcrfely as their ve- 
locities 5 fo in a Machine howeycr compound- 
ed, the Power and the Weight will exadly 
balance each other, when they are in this 
proportion; for by §. 7. their Moments will 
then be equal, ^and the Machine, if at reft will 
continue in that ftatc; and if put into iiiotion 
by an external force, will gradually lofe it, 
when that force ceafes to ad \ on account of 
the unavoidable fridion of the Machine, and 
the refiftance of the Air, which it muft necef- 
farily meet with, unlefs its motion could be 
performed in la pcrfed Vacuum. From hence 
we fee the impoflibility of contriving an En- 
gine, w^hofe motion Ihould be perpau^l^ 
that is, fuch as does not owe its continuance 
to the application of fome external force ; a 
Problem that has given birth to an almoft 
infinite number of Schemes and Contrivances. 
For unlefs fome method could be found out 
of gaining a forcc^ by the artful difpoiition 


chap". lo. . 7he Conclupdn. yt 

and combination of the Mechanical Fowtrs^ c- 
quivaknt to that which is continually dcftroy- 
cd by fridion, and the rcfiftance of the Air, 
the motion which was at firft givicn to the 
Machine mi^ at length be neceflarily loft. But 
ve fcci that thofe Inftrumcnts are only diffe- 
rent means, whereby one Body communicates 
its motion to another $ and not defigned to 
produce a force which had no exiftence be- 
forc, A given force may be difpofed be- 
tween the Power and the Weight an infinite 
number of ways 5 but can never be augment- 
ed by any Mechanifm whatever : fo much as 
we place in the Power will always be loft to 
the Weight, and what we attribute to the 
Weight will never be found in the Power. 
Tis for want of a due confideration of this, 
ttiat To many Mechanical DeHgns have proved 
abortive, fo many Engines unequal to the 
performance for which they were defigned, 
and fo many impoifibilities attempted. 

" If it were poffiblci fays Bp. Wilkins, to 
" contrive fuch an invention, whereby any 
" conceivable Weight may be moved by any 
'* conceivable Power, both with equal velocity 
'' (as it is in thofe things which are immediately 
" ftirred by the hand, without the help of any 
'* other inflrument) the works of Nature 
'' would be then too much fubjeftcd to the 
" power of Art 5 and Men might be thereby 
^ encouraged (with the Builders of Babel, or 

" the 


^2 The CoHclufion. Rut L 

^ the r€bc* Giants) td fuch bold dcftgns, as 
<' would noc becoinie a created Being. And 
*^ therefore the Wifdom of Providence has fo 
^^ confined thefc haman Arts, that jwfaat an 
^^ invention hath in the firength of its mocioa» 
^' is abated in the fiffumefs of k ; and what it 
^* has in the extraordinary qmehnfs of its mo- 
^' tipn. muft be allowed for in the great 7?m^/i» 
^ rcquifice in the Power, whidi is to move 
" it*. 

• WtlkiTui Mathcm. Magick. p. lo^^.. 


', ■ ^^ 

( I ) ■ 

AppENDixto Part L 

i» * '■■''■ " ifii 


Of the Vibration of a Pendulum in a 


Proposition I. 

IF a Pendulum be made to vibrate in a 
Cycloid, all its Vibrations however une- 
qual, will be ifocronous ; that is, they will be 
performed in equal Times (^). 

(a) In order to demonftrate this Propodtioti, it will be pro- 
per to lay down the following Lemma^s. 


If a Body defcends from A along the Line AX^ (Appendix 
Plate, Fig. i .) hy virtue of a Force which decreafes in Proportion 
as the Diilance of the Body from X> decreafes; that is, if when 
the Body comes to M, N, O, 6f^. the Adion of that Force 
upon the Body, be as the Diftanccs XM, XN, XO, l^c, ref- 
pcftively : And if the laft acquired Velocity of the Body j that 
is, its Velocity when i tcomes to X, be exprefTed, or fet off, by 
the Perpendicular XB equal in Length to the Line AX, and its 
Velocities at M, N, O, ^c, be fet off there by the Lines MD, 
NP, OC^ bfc, in Length proportionable to each other and to 
the Line XB, as the Velo<;ities of the falling Body at M, N, O, 
i^c. are to each other and to its laft Velocity at X : And if 
through the Extremities of thefe Lines, the Curve ADB be , 
drawn ; I fay, that Curve will be a Pcfrtion of a Circle : And 
the Time in which the B^y will defcend through the whole 
Space or Line AX [or any Part of it, as MO] will be fuch Time, 
as would be requifite for it to defciibe the whole Arch AB [or 

A 11^ 


PL : LD : : DM 



2 Appendix to Part I. 

any Part as DQ^ correfponding to MO] 'm, with its laft acqoi*. 
rca Velocity at X. 

DeftanJIration of the Lemma, Parallel and contigoous to the 
Line MD, draw NP, in which Cafe the Line MN, becomes a 
I'ointy and the Arch DP a Tangent to the Curve : Produce PD 
till it meets XA produced, in T; draw the Line XD; and let 
fell the Perpendicular DL. Then the Lines DL and TM being 
parallel, the Angles PDL and DTM are equal, as being alter- 
nate ( by 27 Elcm. 1 . ) 5 and the Angles at L and M. as being 
right ones ; the Triangles therefore PDL and DTM are fimilar, 
which for the Sake of referring to it afterwards, let us mak^ the 
firft Step of the following Proccfs i The Triangles PDL and 

DTM arc fimilar 
From the firft Step we hive this 

Proportion (5 Elcm. 6.) 
By the Figure 
But MD being the Velocity when 

the dcfccnding Body comes to 

M, the Point MN ia dcfcribed 

with that Velocity; for there 

is no Acceleration during the 

Paffage of a Body over a Point ; 

confequentlyMN is proportion- 
able to MD: that is, 
Comparing ihe fccond, third and 

fourth Steps 
But MD and NP 'being the Velo- 
cities of the dcfcending Body at 

M and N, LP the Difference of 

thofe Lines, expreffing the In- 

creafe of Velocity in the Body, 

will be proportionable to the 

moving Force at the Point MN ; 

that is, by the Suppofition, to 

the Diftance XM j therefore 
Comparing the fifth and fixth 
Confequently (5. Elem. 6.) 



MN is as MD. 

PL : MD : : DM : MT 

PL is as XM 
XM : MD : : DM : MT 
The Triangles XMD and 
DMT are fimilar. 

And therefore, fince their Angles at M are right ones, the 
Triangle TDX is (by the Converfe of Prop. 8. Elem. 6,) right 
angled at D. Confequently fince the fame is true of any other 
Point of the Curve, as well as D, the Arch ADB is a Porliom 
•f a Circle (16 Elem. 3.), Which is the firft Part. 


Appendix to Part L 



LD : DM : : DP : DX 


MN : DM : : DP : XB. 

Secondly, comparing the firft and 

dghthSteps, the Triangles POL 

and XMD are fimilar ; therefore 
ADB being a Portion of a Circle, 

as already proved 
Comparing the 3d, 9th and loth 


Since then the Point MN bears the fame Proportion to MD, 
or the Velocity it is defcribed with by the falling Body, that 
the Point DP does to the lafl acquired Velocity XB, it follows 
that the former, MN, is defcribed in the fame Time with the 
Velocity the Body has when there, that the latter, DP, might 
be with the laft acquired Velocity XB. And iince the fame is 
trae of every other Part of the Arch ADB, it is obvious that 
the Time in which the Body will defcend through any other 
Part of the Space AX, [or the whole of it J will be fuch as 
would be required for it to defcribe any correfponding Part of 
the Arch ADB, [or the whole of it,] with the laft acquired 
Velocity XB. Which was the other Part. 

CorolL Hence it follbws, that if a Body defcends along the 
Line AX, by Virtue of Forces afting upon it at A, M, N, O, 
l^c, proportionably to the Length of the Lines XA, XM, XN, 
XO, Csfr. and if on X as a Center, and with the Radius XA a 
Portion of a Circle, as ADB, be defcribed ; and if the Radius 
or whole Sine XB, be put to reprefent the Velocity of the Body 
when it comes to X, the other Sines MD, NP, OQ, £sff. will 
reprefent the refpedive Velocities of the Body at the feveral 
Points M, N, O, fcfr. And converfely, if one of the Sines, 
as MD, be put to exprefs its Velocity at M, the other Sines 
NP, 0(^ and the Radius or whole Sine XB, will exprefs the 
Velocity of the Body at thofe other Points N, O and X, 


If a Body moves along the line AX, (Fig. 2.) and be urged 
all the Way by Forces proportionable to its Diftance from the 
Point X ; whatever Point or that Line it fets out from, it will 
come to the Point X in the fame Time. Which Time will bear 
foch Proportion to the Time it would move over the whole Line 
AX in, with the Velocity it ihall acquire by filing through the 
whole Line AX, as the Semicircumference of a Circle does to its 

A 2 Dem. 

A'PJP E N D I X to /Part L 

Dem, Let two Bodies A and P fee out from the Points A and P 
at the fame Time } and let them br urged by Forces poportioi^^' 
able to their Piftknte;^ from the Point X : I fay, thofe Bodies 
will come to X at the fame Inflance of Time; that is, they will 
overtake one anothjer at that Point. On X as a Center, and 
with the Radias's XA and XP deferibe the two Qi|adrants AB 
and PQ ; and draw the line SX, and the Sines RS and MN s 
ai\d let the whole Sine or Radios XB exprefs the Velocity the 
Bpdy A will acquire by felling to X : Titen by Corollary of 
Lemma i . will the Sine RS, if taken as near as poffible to A, 
exprefs the firft Velocity of the Body A. But the Force, which 
oiges the Body A is fuppofed to be to that which urges the Body 
P, as XA to XP (or becaufe the Archs AS and P^^ are iimilar) 
as RS to MN ; As therefore RS expre&s.the iirft Velocity oF A, 
MN will exprefs the firft Velocity of the other Body P : And 
therefore by the fame Corollary, its Velocity when it comes to X, 
will be expreffible by XQ^ Farther, the Time the Body A fells 
to X in, is by Lemma i . equal to the Time the Arch AB would 
be defcribed in with the" Velocity XB; and the Time the other 
Body fells from P to X in, is equal to the Time tl^e Arch PQ^ 
woMd be defcribed in, with the Velocity XQ. But a Body will 
be as long in moving over the Arch PQ with the Velocity XQ^ 
as over the Arch AB with the Velocity XB, the Lines Xv^anJ 
XB having the fame Proportion to each other, that the Archs 
have. Therefore the Time the Body A falls to X in, is equal 
to the Time the other Body P would fell to that Place in. 
Which was the firll Part. 

The Time a Body would fall from 
A to X in, is equal to the Time 
it would move over the Arch AB 
in, with its laft acquired Velo- 
city at X. 
The Time a Body would move 
over the Arch AB in with the 

Again by Lemma i . 

Axiom, or felf evident 

Comparing the firft and 

acquired Velocity itt X, is 
to the Time it wotild move over 
AX in with the fame Velocity, 
as AB is to AX. 
The Time a Body would fej} from 
A to X in. is to tjie Time it 
would move oyer with 
the laft acquired Velocity^ 
AB is to AX. 



Appbnoix to Part I. 


Bjr die Figure 

Comparing the ^d, 4th 
and fifth Steps. 

AB is (oAX US liriceABisto 

twice AX. 

Twice AB is to twice AX as the 
Semicirciunference of a Circle it 
to its Diameter. 

The Time a Body would fall from 
A to X in» is to the Time it 
would move over AX in with 
its laft acquired Velocity , as the 
Semicircumference of a Cirde 
is to its Diameter. Which was 
the fecond Part. 


If from the lowermofl Point of a Circle, as X (Fig. 3.)^ he 
drawn the Chords XQjmd XO, the Power of Gravity whereby 
it ihall canfe a Body todefcend along the former, will be to the 
Power whereby it fhall caufe it to defcend along the latter, at 
the Length of the former is to the Length of ^the latter.' 

Dem, Draw the Diameter XD, the Ferpendiculars QR and 
OS; and join the Points QD and OD. Then (by 31 £lem. 3.) 
the Triangle XQD is right*anglcd at Qj and therefore (by &•. 
Hem. 6.) 1 i XR : XQj : XC^.: XD. 

And for Uke Reafoas a XS : XO : : XO : XD 

But by Part I. Chap6. S 2. 3 The BShA or Power of QrMritf 

opon a Bodv defcending alone 
the Chord QX, is to that vMek' 
it exerts upon another fidling 
freely ; that is» tb its whole Pow* 
er, as XR to XQ^ 
The Power of Gravity upon aBo* 
dy defcending along the Choid' 
OX, is to its whole Power, at 
XS to XO. 
The Power of Grayity upon a Bo- 
dy defcending along the Chord 
QX is to itt whole Power, «s 
X^to XD. 
The Power of Gravity upon a Bo- 
dy defcending along the Chord 
OX is to itt whole Power, at 

XO to XD. 


And alfo 

Comparing the i ft and 3d 

Cbmparing the 2d and 4th 

Appendix to Part I. 

Compiriiig the jth and 
6ta Steps 7 The Power of Gravity upon a Bo- 

dy defcending along the Chord 
QX, is to the Power of Gravi* 
ty upon a Body ddcending along 
the Chord 6x» as XQ to XO. 
<^E. D. 

The Defcription of a Cycloid, with the Definitions relating 
thereto. If a Circle as FCH (Fig^ 4.) be rolled along the Line 
ABt till it has turned once round ; the Point C in its Circumfe* 
rence, which at firft touched the Line at A, will defcribe the 
Conre line ACXB, which Curve is called a Cycloid. The right 
Line AB is its Safe : The middle Point X is its Vertex ; And a 
Perpendicular, as XD, let &I1 from thenoe to the Bafe, is its 
Jxis : And the Circle FCH, or any other as XGD, equal there- 
to, 18 called the Generating Circle. 


If on XD, the Axis of the Cycloid, as a Diameter, the ge- 
nerating Circle XGD be defcrib«l ; and if from a Point in the 
Cycloid, as C, the Line CIK be drawn Parallel to the Bafe, 
the Portion of it CG, will be equal to the Arch GX. 

Dem. Draw the Diameter HF, then the Circles FCH and 
DGX being equal 
Adding GI to each of them 
By the Figure 
0)mparing the two laft 
By the Defcription oi the Cycloid 
By the Figure 
Comparing the 5th and 6th 
By the Defcription of the Cycloid 
Comparing the 7th and 8th with 

the Figure 
Comparing the 4th and the 9th 










KI = CG 

KI = DF 

CG = DF 

The Arch CF = AF 

The Arch CF c= DG 

AF = DG , 


FD = GX 

CG = GX. Q^E.D, 


The fame Things being fuppofed as in the foregoing Lemma, 
a Tangent to the Cycloid at the Point C, is parallel to GX a 
Chord of the Circle DGX. 

Dem. It appears from the Defcription of the Cycloid, chat 
Snce the Angle FCH is a right one, (as it is by 31 Elem. 3.) 
the Chord CH is .a Tangent to the Curve at the Point C, but 



Appendix to Part I. 7 

CH is parallel to GX ; a Tangent therefore at the Point C, ib 
parallel to GX, the Chord of the Circle DGX. Q. E. D. 


Things remaining as before, if from a Point of the Cycloid, 
as L, the Line LMK be drawn parallel to the fiafe Afi, the 
Arch XL of the Cycloid, will be double of XM the Chord of 
the Circle correfponding thereto. 

Dem. Draw the Line SQj>arallel and contiguous to LK, crof- 
fine the Circle in R, and the Chord XM' produced, in P, then 
win LS, MR and MP become Points, the firft having the Pro- 

?Tty of a Tangent to the Cycloid at LS, the fecond that of a 
angent to the Circle at MR, and the third, the Properties of a 
Produdlion of the Chord XM. Join the Points X and R, and 
on MP let fall the Perpendicular RO : Produce alfo the Point 
RM, till it meets XN, a Tangent to the Circle at X. Then 
will the Lines XN and QS, being each perpendicular to the Dia- 
meter DX, be parallel ; and the Triangles MNX and MPR will 
be iiotilar ; as having their Angles at M vertical, and at P and 
X alternate. But the Tangents NX and NM are equal (by 36. 
Elem. 3.) the correfponding Lines therefore PR and RM in the 
other Triangle, are fo too : This laft Triangle is therefore an 
Ifofceles one ; and therefore RO being perpendicular to its Bafe 
MP, MP is equal to twice MO. The Tangent LS is parallel 
to MP, (as being by Lemma 5. parallel to MX) and therefore 
equal to it, the Lines LK and SQJ)eing parallel : It is therefore 
equal alfo to twice MO. But LS is the Difference between the 
cycloidal Archs XL and XS ; and MO is the Difference between 
the Chords XM and XR, for fmce XO and XR are dofe toge- 
ther, RO which is perpendicular to one of them, may be con- 
fidered as perpendicular to both : The Difference therefore between 
any two Archs of the Cycloid is twice that which is between 
two correfponding Chords of the Circle ; and confequently any 
Arch, as XL, is double of the correfponding Chord XM. 
Q: E. D. 

CoroiL Since when the Arch XL becomes XB, the corref. 
ponding Chord XM becomes XD the Diameter of the Circle 
DMX ; its obvious, that the Semicycloid BX, or AX, is equal 
to twice DX the Diameter of the generating Circle DMX. 


If a Body defcends in a Cycloid, the Force of Gravity (fo fkr 
as it zSts upon it in caufing it to defcend along thQ Cycloid) will 


8 Appendix to Part 1. 

Proposition II. 

The Time in which a Pendulum vibrating 
in a Cycloid, performs a Vibration, is to the 

be proportionable to the Diftance of the Body ftoln the loweft 
Point oi the Cycloid. 

Dem, Let the Cycloid be AXB (Fig. 5.) whofe Bafe is AR, 
and its Axis DX, on which lafl as a Diameter^ defcribe the ge- 
nerating Circle DQX : Draw the Chords OX and QX ; throagk 
the Points O and Q» and parallel to the Axis AB, draw the 
Lines LS and MR ; draw alfo the Tangente LV and MY. Then 
becaufe by Lemma 5. the Tangent LV is parallel to OX/ and 
the Tangent MY parallel to QX, its obrious that Gravity exerta. 
the.fame Power or Force upon a Body defcending in the Cycloid 
at L. (becaafe it then defcends in the Tangent LV) as it would 
do upon the fame Body defcending along the Chord OX : And 
for the like Reafon, it exerts the fame Force upon it when it 
comes to M> that it would do if it were defcending along QX: 
But (by Lemma 3.) the Power or Force of Gravity upon Bodies 
defcending along the Chords OX and QXj are as the Lengths of 
thofe Chords ; that i$« hy Lemma 6. (halves being proportion- 
able to their wholes) aa the Length of the Cycloidal Archs LX 
and MX. The Force therefore of Gravity upon a Body def- 
cending in the Cycloid at the Point L [or any other] is to its 
Force upon the fame when at M [or any other Point] as the Space 
or DiHance it has to move over in the former Cafe> before it gets 
to the loweft Point X, to that it has to run over in the latter^ 
before it arrives at the fame Point. Q^ £. D. 

Demonfiration of the Propofition in the Text to HvJ^icb this 

Note refers. 

By Lemma 7. The Force of Gravity fo £ir as it caufea a Body 
to defcend in a Cycloid is proportionable to the Diftance of that 
Body from the loweft Point ; imagine then that Body to be a 
Pendulum vibrating in the Cycloid, then whatever Point it feta 
out from, it will by Lemma 2. come to the loweft Point in the 
fame Time : And confeqaently ilnce the like is true as to its ai^ 
cending from that Point, all its Vibrations be they large or 
finally will be performed in the fame Time. (^ E. U. 



A p p £ K i> I X to Part I. 9 

Time in which a Body would faU freely thro^ 
half the Length of the Pendulum, as the Cir- 
Ctimfcrenee of a Circle is to its Diameter (^). 

Pro b. 

(b) To deraonftratfe thisi the following Lemma^s will be of 


If in a right-angled Triangle, as BFG (Fig. 6.) the Perpen- 
dicular PI be let iaXl from the right Angle to the Hypothenufe 

BG, the line BI multiplied by BG will be equal to BFq. 

Dem, By 8. Elem. 3. the Triangle BFI and BFG are fimilar^ 
confequendy BI is to BF, as BF is to BG^ and therefore BI X 

BG = BF^. Q. E. D. 

L E M M A IX- 

If a Body defcends along a curve Line, iis AX (Fig* 7.) it 
irill acquire the fame Velocity that another, or the fame Body^ 
would do, by falling from an equal perpendicular Height in the 
Line DX. 

Dem, Parallel to the hori:£ontal Line AD^ ditiw the Lines BM 
and FN coiltiguous to each other ; in confequenCe of which^ 
the Lines MN and BG are Capable of being confidered as Points ; 
and therefore the Velocity tRe defcending Bodies pafs over them 
With, as uniform ; and the .curve Line BG, as a flraight Line 
alfo, and as a Tangent to the Curve AX at the Point BG. 
Things being thus, let it be fuppofed that the Bodies begin their 
Fall at B arid M, or, which comes to the fame Thing, that they 
have equal Velocities at thofe Points : Then the Velocities of 
the Bodies being uniform and equal to each other, (for there is 
ho Acceleration in a Ppint) the Lines BG and MN may repre« 
fent the Relation the Times they are pafTed over in bear to each 
' bther. Parallel to DX draw BF, and let the equal Lines BP 
and MN reprefent the Force of Gravity adding perpendicularly 
at thofe Points \ and let the Force BF be refolved into two others, 
hisc, BI and IF, the one parallel, the other perpendicular to the 
Curve of the fiody at B : It Is only the former of thefe, v/z:. 
BI, that accelerates the Body algjjg the Curve BG ; the other, 
^iz. IF, neither accelerates it nor retards it, but is wholly fpent 
in preffing the Body dofe to the Surface BG, if it be a Surface ) 
or in ftretching the String which keeps the Body in the Courfe 
ABX, if it be a String. Now the Velocity a Body acquires by 
moving over any Space, is proportionable to the Force that adls 

B apofli 

lo A p p E N D I X to Part I. 

upon it, maltiplied by the Time that Force a£b. Since then 
BI reprefents the Force in one Cafe, and MN the Time in the 
other, it follows that the Velocity generated in one Cafe, is as 
BI X BG ; and in the other, as MN X MN ; or fince BF and 
MN are equal, as the Quantities BI X BG and BF X BF, (or 
BF^) which Quantities by Lemma 8. are equal to each other. 
The Velocity therefore the one Body acquires by defcending along 
BG. is equal to that which the other acquires by idling through 
MN : But the Lines BM and GN being parallel, it is obvious 
there is the fame Number of BG^s in the Curve AX., as of MN's 
in the perpendicular DX j the Velocity therefore which a Body 
would acquire by falling through one, is equal to that which it 
would acquire in ^ing through the other. Q^ £. D. 

Demonftration ef the Fropofition. Let AXB (Fig. 5.) ^ t^* 
Cycloid the Pendulum vibrates in. Then by Lemma 2. com- 
pared with Lemma 7, we have 

The Time a Body would defcend 
from A to X in, is to the Time 
it would move over the fame Space 
in with its laft acquired Velocity, 
as the Semicircumference of a Cirr 
cle is to its Diameter. 

AX is equal to twice DX. 

The Velocity a Body acquires by fal- 
ling from A to X, is equal to the 
Velocity it would acquire by fal- 
ling from D to X. 

The Tioie a Body would defcend 
from A to X in, is to the Time it 
would move over twice DX in, 
with the Velocity acquired by a 
Fall from D to X, as the Semi- 
circumference of a Circle is to it^ 

The Time a Body would move over 
twice DX in, with the Velocity 
acquired by filing from D to X, 
is equal to the Time it would fall 
from D to X in. 

The Time a Body would defcend 
from A to X in, is to the Time it 
would fall from D to X in, as the 
Semicircumference of a Circle is 
to its Diameter. 

, Froii 

By the Corol. of Lem- 
ma 6. 
By Lemma 9. 

From the three 


By Part 


L Chap. 5 

Comparing the 4th and 


Appendix to Part L 1 1 


To make a Pendulum vibrate in a given 


Sokt. Let AXB (Fig. 5.) be the given Cy- 
cloid i its Bafe AB, its Axis DX, and its ge- 
nerating Circle DQX, as before : Produce XD 
to C, fill DC be equal to DX : Through G 
draw the Line EF parallel to AB, and take 
CE and CF, each equal to AD or DB ; and 
on the Line CE as a 6afe, and with the gene- 
rating Circle AGE equal to DQX, defcribe the 
Semicycloid 'CTA, whole Vertex will there- 
fore touch the Bale of the given Cycloid in A. 

Prom the Figure 

From the Solution of 
the following Pro- 
blem it will appear, 

Comparing the thret 
lad Steps 

Doubling the Antece- 
dents of the laft Step 



The Time of Defcent from A to X 
is half a Vibration. 

DX is half the Length of a Pendu- 
' lum, which in vibrating (hall de- 
fcribe the Cycloid AXB. 

The Time of half a Vibration is to 
the Time in which a Body would 
fall freely through half the Length 
of the Pendulum, as the Semicir- 
cumference of a Circle is to its 

The Time of an whole Vibration is 
to the Time in which a Body 
would £ill freely through half the 
Length of the Pendulum, as the 
Circumference of a Circle is to its 
Diameter. Q;, £. D. 

B a And 

12 A p p E K D J X to Part I. 

And on the Line CF alfo as a Bafc, defcribc 
an equal Semicycloid CB. On the Point C, 
hang the Pendulum CTP equal in Length to 
the Line CX : And let the upper Part of the 
String of it, (as CT, in its prefent Situation in 
the Figure) as it vibrates this way and that, 
apply itfclf to the cycloidal Cheeks CA and CB ; 
Then will the Ball of it P ofcillate in the gi- 
ven Cycloid AXB. C^ E. F, (c). 


(c) DravvTG and PH, each parallel to the Bafe*AB; an4 
join the Points AG and DH. Then by the Corollary of Leni<p 

ma 6. 

By the Figure (DC being. equal 

Comparing the ift and 2d Steps 
By Conftruflion 
Comparing the 3d and 4th 
From the 5 th Step compared with 

the Figure 
(The String touching the Cycloid 

at T) by Lemma 5. ' 

By Conftruftion 
From the two lafi Steps compared, 

GATK is a Parallelogram, 

confequently ' 

By Lemma 6. 

Comparing the two lail Steps 
Comparing the 6th and 1 1 ch 
From the 12th Step compared 

with the Figure 
Comparing the lafl Step with the 


From the lait compared with the 

Comparin^j; th^ lafi with the Fi- 




AC=2 AE 

2 AE = CX 
^C = CX 
f AC = CTP 


GA is parallel to TK 
GT is parallel to AK 









GA = ^ TA 
TK = I TA 

TK = KP 

The parallel Lines GT 
and Pfj are equally dif- 
tant from AD 

The Arch GA =: the 

The Chords GA and DH 
are parallel, andG£= 
HX. From 

Appendix to Part h 13 


0/ the Center of Ofcillation and P?r-# 


TH E Center of Ofcillation is that Point 
in a Pendulum, in which, if the Weight 
of the fcveral Parts thereof were eol- 
leded, each Vibration would be performed in 
the fame Time, as when thofe Weights are 

The Toint or Center^ of Sufpenfion is the 
Point on which the Pendulum hangs. 

jti general Rule for finding the Center (f 


If feveral Bodies be fixed to an inflexible 
Rod fufpended upon a Point, and each Body 

KP is parallel to DH. 

From the 7th and i6th Steps com- 
pared with thie Figure 17 
And therefore (KD htmg by Con- 

ilra^lion parallel aHb to PH) 

KDHP is a Parallelogram, oon- 

fequendy 1 8 

By I^mma 4. 19 

Comparing the 9th and 19th 20 

By the Defcription o# the SeiDi- 

cycloid CTA 21 

From the two laft compared with 

the Figure 22 

Comparing the i8th and 2 2d 23 
Comparing the i6th and 23d 24 

But by Lemma 4. if PH be equal to HX, P is a Point In the 
Cycloid AXB j the Ball of the Pendulum CTP therefore being 
at that Point, is in the given Cycloid. The Problem therefore 
vn& rightly fol?ed. (^ E. D. 


KD = PH 

GT =3 the Arch AG 

AK ;7 the Arch AG 


KD=: GE 
PH = GE 
PH = HX. 

14 Appendix to Part L 

be multiplied by the Square of its Diftancc 
from the Point of Sufpcnfion, and then each 
Body be multiplied by its Diftance from the 
lame Point ; and all the former Produds when 
added together, be divided by all the latter 
Produds added together, the Quotient which 
fliall arife from thence, will be the Diftance of 
the Center of Ofciilatioh of thofc Bodies from 
the faid Point. 

Thus, if CF F%.. 8; be a Rod on which 
are fixed the Bodies A, B, D, eirc. at the fc-^ 
veral Points A, B, D, ^c. and if the Body A 
be itiultiplied by the Square of the Diftance 
C A, and B be multiplied by the Square of the 
Diftance CB, and ib on for the reft: And then 
if the Body A be multiplied by the Diftance 
CA, and B be multiplied by the Diftance CB, 
and fo on for the reft j and if the Sum of the 
Produfts arifing in the former Cafe, be divided 
by the Sum of thole* which arife in the latter, 
the Quotient will give CQ, the Diftance of the 
Center of Ofcillation. of the Bodies A, B, D, 
t$c. from the Point C (ii). 

(d) Dim, That the Proc^fs may be lefs complicated, let us 
fuppofe bat two Bodies, as A and F, fixed to the Rod CF ; and 
let A I and FL be the Archs which the Bodies A and F defcribe 
when the Pendulum vibrates, and let the Pendulum be removed 
into the Situation CL. Contiguous to the Line CL draw CR; 
then may the Archs IP and LR be confidered as Tangents at 
the Points I and L, and thofe Tangents as inclined Planes, down 
whkh the Bodies I and L are to roll : Thefe Tangents beii^ 
each perpendicular to CL, are equally inclined to the Horizon, 
the Bodies therefore will endeavqur to roll down with equal Ve- 
locides } but this they cannot do^ becaufe being "fixed to the in- 

Appendix to Part L 1 5 

flexible Rod, they will defcribe the unequal Arch IP and LR in 
the fame Time. That is, the Body L will oblige the Body I 
to defcribe a lefs Arch than it otherwife would have done ; and 
the Body I will occafion the Body L to defcribe a larger Arch 
than it would have done. And the EfFedls of the Forces by 
which they adt thus upon each other, like thofe of Aflion and 
Rea£lion, will be equal. It remains to determine thefe £fie6ls. 

In order to which, parallel to LI draw MN, and let the 
equal Spaces LM and IN be thofe the Bodies would move over 
in the leail Time polTibk, had they, been independent of each 
other. And let the Archs LR and IP be thofe which th« Bodies 
joinM to the Rod defcribe in the fame Time. For the Reafoa 
juft mentioned, the former of thefe <i;/k. LR, will be larger, 
and the latter, viz^ IP, will be lefs than LM or IN ; and the 
Arch >$rhich the Center . of Ofcillati«n defcribes will be equal to 
LM or IN, becaufe the Center of Ofcillation defcribes that 
Arch, which the Bodies would defcribe in the fame Time, if 
they were both together^ and neither of them an hindrance oif 
furtherance to the other. Confequently the Center of Ofcilla- 
tion is at Y, where the Lines MN and PR crofs. 

Now the Motion which the Body I Idfes by being retarded, 
is its Motion over the Arch PN ; and the Motion the other Body 
gains by being accelerated, is its Motion over MR : The Force 
. or Moment of the firft of thefe Motions, is the ProduA of the 
Body I multiplied by the Space PN ; and the Force or Moment 
of the laft is the Produft of , the Body L multiplied by the Space 
MR. Thefe are the Forces,. Moments or Adions, which retard 
the one Body, and promote the Motion of the other. But ob- 
ferve, that thefe Forces or Moments, in as much as they a6l at 
difFerent Diftances from the Center C, about which the Bodies 
I and L, when the Pendulum fwings, do revolve; have each 
their Mechanical Advantage ; but the one a greater than the 
other: For inftance, L ha^ an Advantage which is as LC, its 
Diftance frdm the Fulchrum C; and I only the Advantage IC. 
As then in determining the EiFed of a Power applied to a Lever, 
we multiply it by its Diftance from the Fulchrum ; fo the above- 
mentioned Forces or Moments (i;/«. I multiplied by PN and L 
multiplied by MR) muil be niultiplied by their refpedlive Dif- 
tances from C ; and then we have I multiplied by PN multiplied 
by IC, and L multiplied by MR multiplied by LC for the Ef- 
fefls^ which, as things are circumftantiated, thofe Forces er Mo- 
ments have upon the Bodies I and L. But, as obferved above, 
thofe EfFefts are equal, confequently we have for\he firft Step 


i6 Appendix to Part t 

The Center of ^ercuffhn 5s that Point in 
t^endulUm, or in an inflexible Rod movin 

But the Triangks PNY 
and MRY are fimilar, 

Comparing the two laft 

Or taking the Pendulum 
in the Situation CPR, 
in which 1 coincides 
with F, and L with R, 
we have ■ 

Or, which is the fame 






AX AQjt AC = F X FQ^X FCi 
That isy in Words, if one of the Bodies were multiplied by 
its Diftance from the Center of Ofcillation, and the Produd ari- 
fing from thence were multiplied by the Diflance of the fame 
Body from the Center of Sufpenfion, this laft Product would be 
equal to the Produfl of the other Body multiplied by its Diftance 
from the Center of Ofdllation, multiplied by its Diftance fironi 
the Centev of Sufpenfion. And, fince the fame would be true 
if there were more Bodies, if each Body be multiplied by its 
Difbmce from the Center of Ofcillation, and that ProduA by thd 
Diftance of the fame Body from the Center of Sufpenfion, all 
the Produdls relating to the Bodies on one Side the Center of 
Ofcillation taken together, will be equal to all thofe which re- 
late the Bodies on the other Side thereof taken together. Let 
then the Diftances of any Number of Bodies, as A, B, D, F^ 
from the Center of Sufpenfion be called a, b^ d^f, rcfpedlively, 
and the Diftance of the Center of Ofcillation Q from the Center 
of Sufpenfion C, be called x : And fuppofe the Diftances of the! 
Bodies A, B, D, lefs than the Diftance CQ^ or x ; and that of 
the Body F greater, as in the Figure : Then will the Diftances 
of A, B and D fit>m the Center of Ofcillation be expreftible by 
9c — a^ jr^—i, and x — d; and the Diftance of F, hyf^x ; mul- 
tiplying then each Body by its Diftance from one Center, and 
the Produ^ arifing therefrom by the Diftance of the fame Body 
from the other Center, we (hall have Aax — Aaa + Btx — * 
Sih^Ddx — Ddd=:F/jf-TFfie, which reduced gives xzr: 

•^- — \ ^, . » .., / ^ ' . Which latter Equation is the Scnfc 

Aa ^[- Bh 'f' Od '^^ t/. ^ 

of the Rule above laid down. 


A p p E N^;^ ?^;to Pgrj I. %J 

round a Point, with which, if the Pendulum 
or Rod ftrikf s agaipft jn Obfbclc, no Jar or 
Shock at the Point of Sufpenfibn fliall be oc- 
cafioijed thereby. . 

Thus,' let CF (Fig. 8j be an inflexible Rod, 
Jiavipg |he Bodies' A^^B, D, ^t.^fiit^ in it 
at'the'roints A, B, D,. (jyc. ^nd let O be an 
Obftacle againfl: wfiich', as it vibrates* tj; fwings 
round tlie Point of Sufpenliop Cj' it rnay 
ftrike againft : then, if there bie no Jar or 
Shod^ pcjpafjoned thereby at the Point C, the 
Pokit that ftrifces atgaioft. O, (as tfee Ppinj: Q^ 
luppofe) is called the Ocptcr of Perfcuffion. 

The Center of FdrGufflon is thirfjmK with 
the Center of .Qpllatlori ; ari.d„;cpnfequcntly 
may be det^niwea.iby(4i)be*iaaie,aCuk.<^^J. . 

• • «.' ;i. :.'■•. '"^ ■-> t'j'j .'^'J ^..'. 

(#) Drm. Frxm .the DefloiftW! 9f thf ftfn^ rf[/^rqiff9n 

above kid down, it iipp^rs^.(that,:iiep ^rm^ iHm .v*ii^ ^k^ 

ilodies A; B and D, wihi^ wocrid pafs ftb^Qi ;,inoyc ; ^rnvjOb 

be a GounterbaUnce to :the Kof<;e Qt t)ve Bo(^.^^ jK^hic^ wo^td 

.pafs below it : and that the Fi^ge of F laajft. te 9^ Couot^erbak^iGe 

to them. But the Forces whei^fwi^h, thoie Bpdies move^ are as 

^tbciff MafSss moltiplied by tbev Piftaaces frpig C, .^hdr Yelp- 

cities beini; as the(e Diftances. Farther, y/hi^ tl^ Point Q^ 

comes to O, aad i? ftop( th^re, the Bodies A^ fi and D, en- 

deavoaritig j(o go on, Iwiiy or bear againft F^ and F agai^ 

them ; juft as if ihey yretfi ixed to g Lever« as AF» havij^ its 

Faldirunt at Q^ Coofeqvieiiily the Forces of the fovmpr ^odie?, 

fo^as ^cy s£^ againft the lattcar, areas their Diftanoes fro^i 

the Point Q x jan4 the Fojjce of thf latter, (b far as it a^s againft 

. . C . th« 

i8 ApTtNDix to Part L 

Let it be required to find the Center of 
Oicillation, or Percuifion of an inflexible Rod 
AB (Fig. 5^. as a fiar of Iron, or the tike) 
every where of equal Size, and vibrating id, 
or revolving round the Point A, as a Center of 
Suipenfion. (/) 

cHe former, is as its Diftaace al(b from Q^: xht abovenftn^oAed 
Foroes muft cherdbre be maltipUed by the Difiances of tile 
Bodies from Q : hot the former of them, as obfenred above^ 
balances the latter ; and the latter them. So many therefore of 
the laft Produ£b as relate to the Bodies above Q uken together, 
snoft be equal to that which relates to the Bodv (or Bodies) below 
it. Bat tne like Prodadb wer6 equal to each other, when the 
Point Qjvas looked upon as the Center of Ofcillation (as in the 
Cth Step of the'tbregoiiie Procefs) oonfequently the Center of 
^eicuffion is xhe.fame with that of OfdUation. Q^ £. D. 

(f) SwUa. Imagine the Rod to be divided into the leaft poiS- 
Ue Buts i, C, D, &<. each of which call On. Tkefe Parts, 
we may oonfider as fo many Bodies contiguous to one another ; 
fo that the Center of Ofcillation or Percuffion of thefe Bodies 
will be the Center of Ofcillation or Percuflion of the whole Rod. 
To find thn, we ue by the Rule above laid down in the Text, 
16 multiply eadi ef thefe Bodies by the Square of its DiihUice 
fe>m A. The fhrfl of thefe ProduOs then will be & (or One) 
multiplied by A 6 fquared ; but one multiplied by AB iquared^ 
is the fame with AB fquared ; now AB fquared is a fquare Area 
or Surfiice, one of whofe Sides is AB. In like manner the 
Body C, ^hen multiplied by the Square oiits DiAanee from A. 
is a Squafcf Area, one of whofe Sides is AC, fomewhat lefs than 
the former. Imagine this Area laid upon the fornier ; and the 
next, which will be lefs ftill, laid upon that i and fo chi till 
' you come to the leail of all. Thefe will make a Pyramid, whofe 
Bafe is the firfl Area, and its perpendicular Height will be 
e^ual to the Tliicknefs of them all together; which Thicknefs 
Will be as the Length of the Line BA. The Value or folid Coa- 



Appendix to Part I. 19 

tent of this Pynunid will be AB^^ {wx. its Bafe) multiplied by 
a third Fart of AB (its perpendicular Height). In the next 
Hao^ we are to multiply each of thofe Bodies by iu Diftance 
from A : Now the Body B (or One) multiplied by AB, give a 
Live, as AB ; fo the Produa of C, multiplied by its Di^nce 
AC, give a Line, as AC ; thefe Ijnes heaped one upon ano- 
ther (as the Areas were bdfore) will make a Triangle, who& 
Bafe will be AB, and its perpendicular Height alfo AB ; the 
Value, or Area of which, wUl be AB multipUed by i AB. la 
the laft Place, by the Rule, we are to divide the Sum of the 
ProduiSls in the firft Cafe, by the Sum of the Produds in the 
latter; that is, the Content of the Pyramid by the Area of the 
Triangle ; that is, ABf x f AB, by AB X 4 AB, which gives 

^-t — ; that is, ^ AB, or two Thirds of AB: fo that, the 

Pittance of the Center of QfciUatibn or Percuffion, (as E fopp^^) 
frgm A the Center of Sufpenfion, muft be equal to two Thirds 
of AB, the whol^ Length of the Rod Q^^E. I» 

c ^ 





* < • < 

* \ > 











O F 

Natural Philofophy. 


0)ntaining theMATHEMAxrcAf 
Demonstra tions and fbme 
occafional R £ m a r £: s. 





To which arc added fome DissERTATioWf 
relating to thcfe Subjcds. 


C A M B K I t>^G E. 

Printed at the Universitv-Pre««^ 


• I 


r, ■.. 

,' t I 


O F 

Natural Philofophv 



'^ . 'M ' * - •^ M 





C H A P. I. 


Of the Phanomepa which arife from 
the mutual ABion of the Particles of 
Fluids upon <me another. 

N the former Part of this Eifay, I have 

laid doxy^n and explained the general 

L^ws (^ Jtt^iure^ and j4educcd from 

thence thoife Phapnomena which are ia 

a ftrid and proper Senfe"^ dcttominated Me-- 


• In a hrgtr Senfe all the Effefts and Operations of natural 
Jpdfe u^tf one another may be ealled Mechanical 5 as be- 
ing all fiJbjea to the general Laws of Modon* In Hydroftatics 
Fittid[9"'are> governed by the iJaWs of Mechanifm', asmudh a9 
' thfc'MediaificAl ?dvvcrs are; -the fimc holds of the Rays of 

% The AStton of Fluids Part It 

chmicali I proceed now to an Explanation of 
fuch^ as Fhiiofophers have comprehended un- 
der the Name of Hydroftatics 5 the Intentioa 
of which is to explain the Nature of Fluids^ 
and the Manner in which they a^ upon one 
another and upon Solids. 

II. The Nature of a Fluid "^^ as diftinguifli* 
cd from that of a Solid ot hard Body* confifts 
in this> viz. that its Particles are fo loofel/ 
connefted togethert that they readily move 
out of their Places, when preflcd with the 
leaft Forc^ one way more than another f* 

Light, as will be feen when we come to Optics ; and fn Ac 

larger Bodies of (he Planetary Syftem, Mechanifm equally pre- 
vails, as has been demonftrated by So* Ifiuic Newton ; which we 
ihall endeavour to make out (when we treat of Aftronomy] ib 
fir as the Nature of our Defign will permit. 

* Some Philofophers make the following Diftinftion iq 
Fluids i thafe which flow or fpread themfehres till their Sur- 
"ficc becomes level or horizontal, they call Liquid; in conr 
tradiftindlion to Flame, Smoak, Vapour Vc. which arc alfb 
Fluids, but do not acquire fuch a Sur^ce. Thofe which are 
capjible of exciting in us the Idea of Moiftnefs, as Water, fefc. 
they call Hutnid^ diilinguiihing them thereby fibm Air, Quick* 
iilver and melted Metals. But thofe piftin^tions are quite un-^ 
xiecc/Tary in a Philofophical Senfe : all Fluids being equally 
Liquid,' when not prevented from putting on that Appearance 
by the Bodies about tbcm i and as to Humidity, that is only a, 
relaii've Quality; for though Quicklilver will not moiflcn, or 
Hick to a Man^s Fingers, it will to Silver or Gold. 

f The common Definition, Tl^i4um ijt cujus faftes impref- 
fioni cuicMxque teduiU, ^ cedendo fitcillimk mo^entur inter Je^ 
though it exprefles very well the Nature c^ ^comprefihle Fluids 
9« Air, yet does not anfwer to that of Water, whofe Parts have 
been ftniad to yi^ld to ^o Forc«^yith which they h^ve been com- 
j>reired> unlcfs it was grga^ on one |i(ie dui^ 9a the other* 

Chap. 1. among tbemf elves. - ^ 

Trom whence Philofophcrs conclude, that 
they are exceedingly minute, fmooth, and 
round* 5 it being otherwife impoffiblc they 

The Definition tliereFore feems impcrfedt as not exprefllng tKe 
Inequality of PrcflUre which is requifite to move the parts of fomc 
Flujds one among another. 

* It is commonly obferved, that the Roundnefs of the Par- 
ades conduces very much to Fluidity upon this Account, «»/«• 
becaufe round Bodies touching oiic another in but few Points, 
the Force with which they mutually attraft each other is the 
weaker. Btit upon this Suppofition the Particle/? of a Fluid 
ought to move with lefs Freedom one among another, by 
how much the greater the Weight is with which they are 
^omprcfTed, (for it is the fame thing in this refpcdl, whether 
they prefs againft each other hy virtue of their own Attraiaion, 

.or by fome external Force) but that they do fo, we have no Ex* 
perience. A Diver, upon plunging out of his Bell at the bot- 
tom of theSea, never finds the Water lefs fluid, notwithftanding 
the great preffure from above. Mr. Boyh having caufed a Tad- 
pole to be put into a Veffel of Water, and to be prefled with a 
very great Force, tells us that in appearance it found no Incoa* 
vehience from thence, but fwam about with the fame Freedoxa 

. and Briiknefs as ever. 

Quaere, whether the particles of which Fluids confill are m 
Contadl with each other, or not \ Perhaps they arc prevented 
from approachipg, nearer than to a certain Diilance, by a re- 
pelling Power difiufed around each fmgle Particle. The Obfcr- 
vation, that Water is not rendered lefs fluid by Preflure, i^^rm 
to favour this Opinion » and the Property Ayhich the Air has of 
exjxinding or contra^ng it felf, according to the Weight which 
it fuHains (as ihall be (hewn Chap. 3.) proves beyond contra- 
diction, that its Particles are endued with fuoh a Power, Bat 
if the Particles of all Fluids have this Power, it will follow that 
they ought to be in fome meafure capable of being reduced 
into iefs Space by PreflTure, as Air is, which they have not 
as yet appeared to be. Further fince it has been proved (Part 
j. Chap. 3.) that if the parts of Fluids arc placed juft be- 
yond their natural Diftances from each othe^, they will ap- 
t^roach and run together, and if placed ferthcr afunder ftill, will 


6 The ASiion of Fluids Part XL 

fhould move with fuch Freedom one amoi^ 
another upon the leaft Inequality of Preffurc. 

icpel cack other; it fbllotvs upon the foregcMhg'Suppofirioiv 
that each Particle of a Fluid is furrounded with three Spheres 
of Attra6Uon and Repulfion one within another : the innennoll: 
of which is a Sphere of Repulfion, which keeps rfiem from ap- 
proaching into Conta^, the next a Sphere of Attraftion dif^ 
fufed around this of Repulfion, and beginning where this ends, 
by which the Partjcles of , Fluids are difpofed to run together 
*5nto Drops ; the outcrmoft of all a Sphere of RepuKon, ^yhere- 
•t)y they repel each other, when removed out of that of At- 

' * • , 

If this Wicre aOqwedi ^nd we might go oa» anlfuppofe the 

.Particles of all Bodies to attrad and repel each, Q^er iltemateijff 
%t 4ifferent piftanccs, perhaps ifve might be able xp fo^ve a great 
inany Phsenoniena relating to f^iaU Bodies, which are now hs^ 

^ yond the reach of our Philofophy • However upon the Suppo>- 
iition of the three Spheres of Attra^on and RepuUion jufl 
juentioned,. nothing is more eafy than t* fee hQW Solids may^ 
be converted in^to Fluids, iind Fluids into Solids (as is done ia 
Xique&^ipn and Freezing) ; for allowing that the firll or in* 
fucrmodl Sphere of Repulfion, is capable, like that of the. Partides 
4>f Air, of being augmented by Heat, and <iiminiibed or totally 

. iufpended by Cold, it follow^ that Bodies muft be more or le& 
fiaid in proportion to the degree in which they are affedled by- 
Heat or Cold ; for when the Adtion of the firft Sphere of Re- 
pulfion is diminifhcd or deftroyed by Cold, the Particles of the 
Fluid muft neceflarily be brought into cloler Contact with each 

' other by the Force of the circumambient Attraction, and by that 
means conftitute an harder Body than before. But we muft not 
dwell too much upon an Hypothefis which wants Proof ; I fliall 
only add, that although fome Fluids; as Water, have not beea 

• M yet contradled in their Dimenfions, or made to take up kfs 
Space than they naturally do, by any Force with which they 
have been comprefled by Art ; yet there are none but are na- 
turally contra^ed by Cold, from whence it feems reafonable to 
infer, tkat their Particles arp at leaft cafahle of being brought 
into clofer Contaft, which is fome Confirmation of this Do^inc. 

It is an obvious Objedlion to this, that Water by freezing is 
augmented in its Bulk ; but this may be owing td thqfe Bubbles 
OX Vacuities obfcrvable in the Water after it is frozen, which 


chap* li among ihemfehes. ^ 

IIL Those Particles confidered fcparately 
ire cftdocd with all the common Properties 
Of Matter, and fubjeCt to the fame Laws of 
Mbtidn and Gravitation with larger Bodies* 
To enquire therefore into the Nature of Fluids, 
is to confider what Appearances a Collcfkion 
of vcfy fftiall round Bodies, fubjcd to thofci 
Laws, will exhibit under different Circuni^ 
dances. In order to which, it is ufual with 
hydroftatical Writers to conitder a FIuid> as 
divide<i Ifito feveral perpendicular Coludins 
contiguous to each other. Sometimes it is 
convenient to conceive it divided into thin 
Plates or Strata lying upon one another. In 
fome Cafes, the fame Fluid is confidered as 
diftinguifticd both thefe Ways, viz>^ into per- 
pendicular Columns, and alfo into thin Strata 
or Plates. Figure i. rei^refents a VcflTel filled 
with a Fluid to the Height £ F, and divided 
into the Columns GH, IK, LM &c. and alfo 
into the Strata R S, T V, X Y e^r^ 

IV. From this Obfervation concerning the 
Properties of the Particles confidered fcparatc- 
iy, immediately refults the following I?ropo- 
lition, viz. that in a VelTcl whofc Form is 
fuch as is repref ented by A B C D, (Fig. i .) the 
Quantity of PrcfTure which each Stratum fu- 

Were not in it before } and not to any general and uniform rd- 
jnovsil of th^ Particles of the Fluid from each other, which the 
Qbjedion, if it is of aP7 Force againft what has been advanced^ 
inuft fuppofc. 


^ "The ABton of Fluids Part IL 

ftains from the Weight of the incumbent 
Fii)td, is in Proportion to the Number of thofc 
Strata which reft upon it, that is^ as the Height 
of the Surface of the Fluid ; for if we fup- 
poie the Strata of equal Thicknefs, the Quan^ 
tity fuftained is proportion9ble to the Number 
of ^Strata of which it conMs. 

V. W H B N the Surface of a Fluid is ho- 
rizontal or level, each Particle thereof is dif* 
pofcd to continue in its Place, being fufiainr 
cd therein by the contiguous ones. 

Let the Fluid be fuppofed to be divided 
into Strata, each of the Thicknefs of a Parti- 
tide of the Fluid, and if the Truth of this 
Fropofition is denied, let the Particle mn be 
one of thofe which is not fudained in its 
Place by the contiguous dues, but is nraving 
from thence towards fome other Part of the 
Veflcl, V. g. towards D. Now fince all the 
other Particles of that Stratum are at an equal 
Depth below the Surface of the Fluid with 
this, they alfofuftain an equal Degree of Prcf- 
fure (by the laft Fropofition,) confcquently for 
the fameRcafon that one of them is moving 
towards D, the reft may all be faid to be 
moving in the fame Diredion : but this can- 
not be true of the whole Stratum, while the 
Veflcl is entire, . and therefore of none of its 
Parts. Now the like Reafoning will hold a- 
gainft the Motion of the Particle mn towards 
any other Part of the Vcfiel, from whence it 

folio vfs. 

I « 

Cna.p. I. ^itfHdhg . ihemfehesi ^ 

follows* that' each Particle of the- Fluid, is 
fuftaincd ill its-P}a<:e by the contiguous One^i 
and^hdi-cfofc- difpofcd tacontinuc at Reft *i 

VL'. From hence is derived a fundamental 
Propo/tffion in Hydroftatics, njit. That when 
fhc Sc^rfacfc of a Fluid is level, whatever Prc(^ 
furc any fingle Particle or fmall Portion of it 
fuftains from the contiguous ones on one 
l^iart, k filftiins the fame on all the reft, that 
is, it is prefled by them with an equal Degree 
cyf -Force on- all Sides |. 
- For by the Definition of a Fluid (§. 2.)* 
tach Particle is difpofed to give Way, and 
move oat of * its Place, when the Prefliire is 
not equal on all Sides 5 and (§'.'5.) cadi Par- 
ticle is prcflcil by the contiguous ones in fuch 

^ a manner that it is fuftained in its Place there- 

j f by, it is therefore prefled with ah equal Dc- 

j grc€ of Force on all Sides. 

I • Corhl. From hence it follows that each 

' • Tliifi ih^wsi'us the Abfundify of fome Philofophers, wha 

place the fole Difference betweea Solid^ :and Fluids in this,, 

•u/jK. that tile Particles of thefc are ever in "Mguon, while thofc 

of the other are always at Reft. ' * -: . 

t This Propofition with its Corollary is not ftVidly fpe:iking 
^iie, unlefs the Particle or Portion of Fluid we fpeak of is fup- 
jiofed void oF Gravity, for it preffes downwards with a Force 
c^uaF to the Weight of thofe Particles which reft npon it added • 
tVi'its own, whereas the Force with which it prefled upwards is7 
^^y equal to th6 Weight it fuftains, ^i%. that of the incumbent 
Wuid. But the Particles of Fluids are fo exceedingly noinute, . 
aM the Gravity of each fo very fmaU, tliat the Error arifing 
f'Oiti kence can never be fenfible. i , . ,. -* 

•i r B PartiQlc 

%c> T^e ASiioH: of Flui4s . Part Ifi 

Panicle or fmall Portion of a Flui4 prefles 
with the lame Degree of Force in all Direct 
tions on thofe j^ich are cootiguous to it. 
For by the thiijj^piw of Nature,, every Par- 
ticle preQ~cf upoRhe contiguous ones with 
the fame Degree of Fotce. with. . Vi^hich it is 
prcffed upon; by them. 

\.\\. The Surface of a Fluid becomes le- 
vel by its own Gravity, when no external 
Force prevents it _ from being foi, , , 

For the Particles of Fluids pjcfe in,alir>i:% 
le&ions wit[h, Forces proportionable to^ the 
Height of thcix Surfaces (Cor. §. 6. and §. 41^ 
^ then the Surfacp is not level, ^thc; ,<UfFe|€ni( 
Parts of thc.f^Q^ ipferics Stc^tt^ wil} be 
Breflcd not only downwards, but fidcw^ys; 
againft each other with uneqiial Forces j ihe 
greater PreflTure, tl)erefore overcoming the weak- 
er, the Particles which .fuftai»ithc leaft Pref., 
I)ire will be driven out of: th<eii Places and 
raifed up, till the Surface becomes level; the 
Surface being level* each Particle will be c- 
qually prefled' in every Dircdion, {§. 8-) all 
therefore will remain atRt^, and the Surface 
continue in that. State*. 

• This Demonft ration, aa alfo the foregoihg, is foupdej- 
upon a Suppofition, that Bodies tend downwards by their Gra-. 
vity in Lines parallel to each other, which though fhyficaify 
true, is not ftriflly fo, their Tendency being toWai3» the Cen- 
ter of the Earth, and confequently in Lines which meet in % 
Point: and therelbre if we would be accurate, the Fluid contained 
itt a VeSel thould be conlideped, a« divl^^ inw Column* and 


Oiap. I. -0mong themf elves. li 

VIII. Fluids gtavitatc in Fluids of th^ 
iamc Kind. 

•This Propofition is a; ncccflary Confer 
^uencc of what has been' bt>ftrvcd about the 
-Nature of the Particles of which they confift, 
n/iz. that they arc folid, and endued with 
the fame Properties with other Bodies. The 
Reafon why their Gravity is not fcnfible 
in the Fluid, is becaufe the lower Parts fu- 
ftain the upper, and hinder them from dc- 
fcending. But h does not follow from thence, 
that their Gravity is entirely taken away, as 

Strata, as rcprefcnted Figure the fecond, where ABD is the 
Earth, C its Center, EFQH z Fluid • contained in a Veffel, 
and divided into Columns, which if continued down to the 
Center of the Earth, would there terminate in a Point C ; and 
into the concentric Strata aB, cdy &c. having the . Center of the 
Earth for the C-enter of their Convexity. And then confider- 
ing the Strata to be of this Form, ana arguing from thence, 
in the fame manner ae before, w^ fhall find that the Particles 
of the Fluid will not be in ^quilibrio with «ach other, till 
all the Parts of its Surface are at equal Diftances from the Cen- 
ter of tfee Earth, forftimg thereby the Surface £F, concentric to 
that of the Earth. , Cotifeqiiently the S(ur£iees of Fluids are ra^t, 
Jevcl or plain, but convex, having the Center of the Earth for 
the Center of their Convexity. 

This Convexity bv reafotoof the gfeatdilUnce of the Sardinia 
Center approaches fo near to a Plane, that in fmall Portion^ 
of it the Difference is not fenfible, and therefore may be neg- 
lefted; but at Sea Ui? evident to Senfe,: for when the Mariners put 
to Sea, the Shcu^ firft di&ppears, then t^e low^r Buildiogi, after- 
wards the Towers, M^untams ^c. ; in like Manner, when they 
approach a diftant Ship, the top of the Maft and Sails appea:^ 
lirft, while the Ship it felf is intercepted from their View, by 
the Oonvexitv of the Water b^ween .them, but wk^a tl^e/ ftfc^a^ 
ihsMiSt of cLeir oyfn Ship, it may eafily JDc^&en. 

12 The ASlion of Fluids . Part ir. 


fome "^ Phiiofophers have imagined ; for by 
fo much as the lower Parts prefs upon thofc 
which are above them, juft fo much additio- 
x\al Weight do they receive from the Readion 
of the other upon them: Thus their Weight 
)s communicated to the Ve0ely which upoa 
this Account weighs according to the Quantity 
of the Fluid it contains. 

IX. The Prcffure of a Fluid is in Propor- 
tion to its perpendicular Heighti and the Quaa- 
tity of Surface againft which it preflfes. 
This Propoflcion admits of four Cafes, 
I. When the Fluid is contained ina Vef- 
fel of the lame Dimcnftons from top to boti- 
tom, and held in an ered PofitioUf as that 
reprefcnted Fig. i. it is evident the Preflfurc 
of the Fluid upon the bottom will be in Pro^ 
portion to its Magnitude, and the perpendi- 
cular Hcis^ht of the Surface of the Fluid above 
it. For conceiving it divided into Columns, 
the Preflure upon the Bottom by the fourth 
Fropofition, will be as the Length or Height 
of the Columns : and it will alfo be as the 
Number of them, becaufe the Quantity of 
Fluid which prcffes upon the Bottom is in that 
Proportion, that is> as the Magnitude of the 
Bottom prefled upon. But when the Veflcl 
is inclined or irregular, the Truth of this Pro- 

- * This w» the Notion of the Cartefians^ who held, that 
^hen a Fluid if mixed with another pF the fame Kind, it lo^ 
i^ own \y?ig^t thereby. 

;7: wi / . pofuion 

Chap. I. among themfelves. ij 

poiition is fo far from being evidtntt that it 
jias been commonly looked upon as a Paradox* 
. 2. Let the Vcffel ABCD (tig. i.) be 
filled with n Fluid to the. Height EF^^ and 
lield lA an inclined Pofition, as there repre«> 
fcntcdj I fay thePreffure of this Fluid ispro? 

* fortionable to the Magnitude of theBafe CD, 
^and FG or HD the perpendicular Height of 
the Surface of the' Fluid above it. 

For fuppoitng the Fluid divided into the 
Strata EI, KM, LO, c^r, fo far as the firft 
Stratum EI is prevented from preffing upon 
KI the Surface of the next inferior Stratum^ 
by being in fome Meafure fupported by the 
Side of the Veflcl F I, fo far is its PrclTupe 

\ augmented by the Reaftion of the oppoiite 
Side EK upon it, which is exa£tly equal to 
the Adion of the former, becaufe the Fluid 
preffing every Way alike, at the fame Depths 
below the Surface, exerts an equal Force 
againft both thefe Sides. The Surface there* 
fore of the fecond Stratum is preflcd with the 
fame Degree of Force with which it would be, 
if the Quantity of Fluid contained irf the for- 

\ mer Stratum was included within the Space 
HKQJ, which is exadly equal to it, as having 
the fame Safe KI and the fame perpendicular 
Height QI *. Now this being true of each Stra- 
tum, their Prcffufe upon CD the Bafe of the Vcf- 
fel is the fame as if they were all placed pec>- 

P 31. £/. 11. 


J4. TTie Mim of Fluids Part II. 

pcndicularly over, k, and filled the Space 
RHCD; which thby would do, fincethcfuoi 
of their perpendicular Heights QI, KS, LT and 
iN V is equal to H D the perpendicular Height 
of this Space, and each of thdc Bafes KI, LM, 
C^r. is equal to C D its Safe "^^ But by the for& 
going Cafe, if the Space RHCD was filled 
with a Fluid, the Preflfure of it would be pro- 
portionable to the Dimenfions of the Bafe C D, 
and the pet^endicular Height DH* therefore it 
is the fame in the inclined Tube ABCDf. 

3. Let the Veflel ABC be irregular, as 
rcprcfcntcd Figure the J^fht and filled with a 
fluid to the Height D, I fay the Preffure of 
the Fluid upon the Bafe C, is proportionable 

' • 31. EL II. 

f Perhaps it may be thought more Geometrical to demm^ 
ftratc this Propoiition with the Generality of Authors from the 
Property of the inclined Plane. They conlider B D the lower 
iSide of the Tube, as an inclined Plane, on which the Fluid 
contained within it refts, and argue that it lofcs thereby a Part 
p^ its Weight in Proportion to the Length of. the Plane, and 
therefore bccafions no greater Preffure upon the Bafe, than if 
Ae Veflel was held ere<9i, and filled only to the fame pcr- 
.peudicvilar Height, as when inclined. 9ut this D^nonftration 
proves" too much, for by this Way of Reafoning, one might 
Ihcw, that the Preflure of the Fluid EFCD upon the Bafe 
•C/^.is ^^i than x\t Pre%ro of RHCJ) a Column of the 
fame Fluid having an . equal Bafe aijd perpendicular Height 
■with 'If. Fot both the inclined* and -the perpendicular Co- 
-Hiinn contain the fame .Cfeantityof Fluid, upon account of 
the equality ot the;r Bifes, , ajid perpendicular Heights, but 
that r6fts upofi an inclined Plane, wfiich this does not; atfd 
ihdr^fore. preffes . lefs upoa the. Bafe. . . But this is contrary both 
to Demoftration and Experience, this Argument therefore proves 
too much. 

Chap. !• ^ifmng thmfeheSi. ' || 

tpthe Magnitude •of the Ba^i and CD thf 
peqpcndicular Height of the: .3urfa€e of th^ 
|li^id above it^ . :> ^ 

[, I K Ordci:. ife^t thjc PropC of ;Khis Propq5tM>|i 

mi be Xh% beftcr ua4c.i;ftp94 jj^fg.pauft:pi5$ir 
igHfe rhQ fpUfO^ving /:«!W»^. :.,\m r 
I, Ihat whgp 4 ,F4iHdrj?§ff^ th.^WghaPi5ft 
ai AB, (^-F^. 5>J! which ip fpi^e Patts is large? 
diania q^herSji the AioiQent^ or JE^orce ^itH 
which itr iqpv«s^ is eveiry jyhcrc tjljc -faipe^ . i^oi 
vhiU. the pijiiM> w; P^fliOK tfeej«gb the Tul>fit 
ilss Velocity; iiv.eyery Papjr w-ill'bq: ^cciprcxyiHi; 
a$ theQ^aijtity pf Matter; forinftancejt.M^lU 
be^ much^ grater at Cth^it i$/atD, anhe 
Quantity puffing through C af any loft^uit; qC 
Time is iefs than at P> and fo of the reft i 
becaufe a Iefs Quantity wiqulcl : ^c . convey cd 
through the fmaUcr P^rts of thc;Tqbe ip the 
iame Tioie, qnlefs it fhoul}irn;ipye:M'^r. there 
ia Proportion to the Smalnc^^ of rhcrp. )JSIqw 
t^c Momenti«n of Bodies i$; partly; owiflft {A 
the Quantity of JMattciv and paftlj^ to tfhey;?-^ 
Ipcityj (as explained Part J.iCh^. 9- §•. i<i 
cpnfequently what the Fluids rwhich is ady^j^ 
ly paffing thrpugh the narrower Parts of thfe 
Tube,: wants in Quaptity, is coHipcnfated bp: 
its Velocity in thofe Parts, and what it wants 
ijti Point 'of .Velocity . in I'he other Parts is 
made up by thct Quantity pafling through 
tticm 5 fo that t4ie Monaent is the ftmfe in 
€vcry Piart of the Tujt)?,-, ,.W- he ther larger oi 
: . 1 nar- 

t6 The ABhn of fluids PartH- 

narrower* The fame is tru6. whatever be the 

JPofition the Tube is held in.- - 

Let us now conceive the Fluid in the 
Veffel ABC (f^g.^.) to be diftihguiflicd in- 
to the- Strati EF,GH,IK c^h Let us alfdf 
imagine the Bottom of the Veflfd C to btf 
moveable* that is» capable of (liding- up and 
down the narrow Part of the: Veflel, v. gl 
from C to XjfH; (without Tetting any of the 
Fhiid run out.) - Let it further be fuppofcd 
that- this moveable Bottom is drawn up or let 
acfwrt witK a'^iVen Velocity, while the Vef- 
fel it 'felf is fixed -artd immoveable; it is evi- 
dent' the lowetobft Stratum which is conti-- 
jguou^ to th<? Bottom will' 6c raifed or let 
down- With 'the (artic Velocity, and will there- 
by have a Moment proportibnablc to that 
Velocity and the Quantity of Matter it con- 
tains: Butby Wc Lemma, all the reft of the- 
Strata 'wiir have the fame Moment, con- 
fcqiicntly the Moment of all taken togcthef*- 
(that is, of.'th'elwhole Fluid,)'- is* the fame* 
as -if .the Veffel had been no Islrger in any 
one Part, than it is at the Bottom, (for- 
then the Moment of each :Stratiim would 
alfo have bce^i ^s great- as tli^t- of the lower- 

* Thus we inaVjObferye in a River or C^naJ, .that by hovr 
much the Breadth or l)epth is lefs iri jiriy Paf^' fo much the 
more rapid' is the-StTcarii in that Part? landV^h f^d contrarf ' 
where it is widor apd; 4eeper, the Motion; lof ^% Water is*^ 
rhore gcntk . and * lane:ai'dr ' So that the' Alomcnt with' which. 
K irows 15 the fauae in etery Parti • * * - • ^ •. • • * 

- » tnoft}) 





! J 

Chap. I. among the mf elves. ^ 17 

moftj) the Prcflurc therefore, or Adion of 
the Fluid Vl^ith which it cndcaVoiif^ to force the 
Botrom out of its Place, is as the Number of 
Strata, that is, the pctpcndicular Height of the 
Fluid, and the Magnitude Of the Ibwcrmoft 
Stratum, that is, the Bottom. 

4. Again, fuppofe the Veflcl K\^C(Fig. 
6) filled with a Fluid to Dj I fjy the Prcl- 
fure upon the Bottom BC, is proportionable 
to the Dimenfions of the Bottom, and DE 
the perpendicular Height of tiiv/ Fluid, 

For if wc fuppofe tlie Bottom moveable, 
as before, and raifed up or let down with 1 
given Velocity, the Moment of every Stra- 
tum will be the fame with the lowermoft 
by the Lemma ; therefore the Moment of all 
taken together, is the fame as if the Veffel 
had been no lefs in any one Part than it is at 
the Bottom j confequently the Prcflure is pro- 
portionable to the perpendicular Height, and 
the Magnitude of the Bottom. This Cafe is 
the Convcrfe of the former *, 

• upon this Propofition is founded the Praftictf of convcjr*- 
itig Water through Pipes from Place to Place, ^c. For front 
hence it follows* that if one end of a Pipe is laid in a Refervoif 
of Water, the Fluid will run into the Pipe till if rifes to a Level 
at the other End with its Surface in the Refervoif . Thus let 
ABC (Fig, S.) reprefent a Rcfervoir or Bafon of Water^ DGS 
a Pipe laid from thence to i5. If £ the end of the Pipe is 
placed above the Litie JBF the Level of the Water in the; 
Refervoir, the Water will run into the Pipe till it rifes in 
the other End to F the Levdl with AB, at which time the 
Water in the Pipe will be in iEquilibrio with that in the Re- 
fwvoir, and remain at Rea. • But if the End of the Pipe is 

C b«lofr 


1 8 1%e AEiion of Fluids^ Part iL 

From hence it follows, that if a Veffcl isf 
made of fmih Form, as is rcprcfentcd (Fig. 7.) 
by AECDEFG, and filled with a Fluid to 
the Height C, the Weight which the Bottom 
fuftains, is as^ great as it would be, had the 
Form of the Vcilelbcen IKFG, which is every 
where of the fame Dimcnfions. that the othet 
is of at the Bottom, and filled to the Top 
IK. Bccaufe the Preflure by the Propofition 
is proportionable to the Bottom and perpen- 
dicular Height, which in both Cafes arc the 

The Reafonwhy thcVeflcl ABCDEFG 
>^ith the Fluid contained in it, does not weigh 
fo much, as the Veffcl IKFG when full td 
the fame Height IK, notwithftanding the 
Preffure upon the Bottom is the fame in both, 
is becaufe ABDEthe upper Part or Cover 

twlow the Surface erf the V/ater in the Reicrvorr, it will con- 
tinue to run dut, till they are reduced to a Level. For let 
GH be the lowcfl Part of the fipe, then fince F the perpen- 
dicular Height of the Fluid on one Side, is equal to B the 
perpendicular Height of the Fluid on the other, and GH4 
^vhich (being the Place where the Fluids prefs one againft 
another,) may be conlldered as a Ba(e to both, is common ; 
it follows from this Propodtion that the PreiTures on eisich Side 
are exaftly equal, and therefore being in contrary Directions 
will neceUarily deilroy each other, and the Fluid will remain 
in iEquilibrio. But while the End E is below the Level,. 
this .^Equilibrium cannot be obtained ; and therefore the Fluid 
will continue to run out. 
i* For the fame Reafon, when two or more Tubes commu- 

^ liicate with each other, the Surface of the Flvnd they contaift 

will iiand at the fame Level in all. 


Chap. I. among thetnf elves. 19 

of the former VcflTcl, is prcflfcd upwards by the 
Fluid below it with a Force equal to the 
3£ndeavour the Fluid in tiae fmall Tube BCD 
has to dcfcend. Which Endeavour is the 
fame that k would be, if the Tube BCD 
comprehended alfo the two Spaces ICBA 
and CKED, its Moment being the fame ija 
jboth Cafes by the Demonftration % the Coyer 
therefore is preffed upwards with a force e- 
4}ual to the Weight of as much Fhiid as would 
fill the two Spaces ICB A and CKE D 5 confer 
quently the VeiJeU whofe Form is A B C D E F G, 
is fo much lighter than the other^ that is, as 
much as the Fluid it contains is lefs. 

F&OM hence arifes this Paradoxi that thff 
Icaft Quantity of Fluid may be made to raife 
any Weight how great foever it be. 

For by the Propofition the Cover ABDE 
is preffed upwards with a Force equal to the 
Weight of as much Fluid as would fill the two 
Spaces ICBA and CKED 5 now thofe Spaces 
may be enlarged at Pkafure in Height, by lengths 
ing the Tube BCD (which at the fame timp 
rauft be made proportionably fmaller, other- 
wife the fame Quantity of Fluid will not fill 
Vl) 5 it follcjws therefore that the fame Quan- 
tity of Fluid may be made to prefs the Co- 
ver upwards with a given Force 5^ if that Co- 
ver then is made moveable, any Weight thg* 
\& l^id upon it ma^ be fupported thereby. 

C a X. 

20 The j^Bion of Fluids Part IL 

X. Thb Velocity with which a Fluid fpouts 
out at an Hole in the Bottom of a Vcfld, is 
equal to that which a Body would acquire 
by falling freely from the Level of the Surface 
of the Fluid to the Hole. 

Let there be a large cylindrical Tube 
A B C D (Fig. 9.) \\\ the upper Part of which 
let us imagine a Cylinder of Ice FGHl cx- 
adly fitting it ? let it further be fuppofed that 
HI the lower Surface of the Ice is continually 
melting, fo as to afford a Stream of Water 
running down the Middle of the Tube. Now 
the Form of this Stream of Water will ne- 
ccflarily be fuch as is rcprefented in the Fi*- 
gure by HLI, for the Water falling freely 
will defccndfafler and fafter like other Bodies^ 
caufing thereby the Stream to become nar- 
rower and narrower. Now let it be fuppo- 
icd that the Tube has a Bottom as CD with 
an Hole in it at K jud lUiBcient to let the Stream 
pafs freely, it is evident there will be no Ob- 
ftrudion on this Account, but that the Fluid 
will pais through the Hole with fuch Vcloci^- 
ty as it naturally acquires by falling from HI 
the lo\ver Surface of the Ice. And if we fup- 
pofe M and N the empty Parts ^f the Tube 
to be filled with Water, the Water will prefs 
equally upon* the Sides of the Stream in eve- 
ry Diredion (§. 6.) and therefore will be no 
Impediment to its iMotion on that Account. 
Laftly let us fuppofe the Ice raken away, and 


Chap. I. among themf elves, it 

the Stream fupplycd from the Water at the 
Sides, as is the Cafe when a Fluid runs out 
through the Bottom of a Veflcl 5 then will 
the Velocity with which the Water flows 
through the Hole continue the fame? for fo 
far as the Water coming from the Sides en- 
deavours to dclcend it Iclf, fo far it obftrufts * 
the Defcent of the Stream, and no farther; 
and conlequently caufes no Alteration in the 
Velocity or Quantity of Fluid running our. 
The Velocity therefore with which the Fluid 
pafles through the Hole, is equal to that which 
a Body would acquire by falling freely from 
the Level of the Surface of the Fluid to that 

If the Hole is made^ in the Side of the 
Veflcl at the fame Diftance below the Sur- 
face, the Velocity will be the fame, on Ac- 
count of that equal Tendency Fluids have to 
move every Way alike*, 

• upon this Principle is founded the Praftice of making 
artificial Fountains. For if to a Veflel or Refervoir ABCD 
filled with a Fluid to the Height EF, be fixed the Pipe CH, 
(as reprefented Fig, lo.) with a fmall Aperture at JT, th^ 
Fluid will fpout up from thence to FL the Level of the 
Surface of the Fluid in the Veflel. For by this Propofitioa 
it will fpout from K with fuch a Velocity, as a Body would 
acquire by falling from FL the Level of the Surface to the 
Aperture at K, that is, fuch as will carry it from the Aper- 
ture to the Level ; becaufe that Velocity which a Body acquires 
by falling from a certain Height is I'ufficient to carry it back 
to the fame Height from whence it fell. 

But in Pradtice the Height the Fluid rifes to, is lefs than 
that uf the Level of its Surface in the Refervoir ; this is ow- 
jn^ to the RcSftance it meets with from the Air, its Fridion 


22 Tie ASiim of Fluids Part II. 

XL The Velocity with which a Fluid 
fpouts out from the Bottom or Side ofi Vef- 
icl is as the fquare Root of the Height of its 
Surface above the Hole *. 

The Caufe why a Fluid fpouts out through 
an Hole made in the Bottom or Side of a Vef«» 
(el is the PrcflTure or Weight of the Fluid in- 
cumbent upon the Holes from whence it 
(hould fecm, that the Velocity ought to be 
as the PrefTure; but if fo, then the Quan- 
tity run out would alfo be as the Preflure 
{for the farter the Liquor flows the greater is 
fhe Quantity thrown out in a given Time^ 
;^nd vic^ versa) confequently upon this Sup^* 
portion we (hould have two Effeds, each de* 
pending on the facbe Caufe, and equal to it, 
which is abfurd^ Tis not then the Quantity 

^tgainft the Sides of the Pipe CsTr. It is found impoiible to 
make it much exceed the Height of an hundred Feet : For 
when it fpouts out of the Aperture with a Velocity neceflary 
CO carry it higher, the Stream is immediately dalhed to Pieces 
hj the Refiftance of the Air, whereby it lofcs its Force, an4 
ifi prevented from riling to any conuderabl^ Height. 

• This Propofition may be otherwife demonftrated from 
the laft in the following Manner. For lince the Velocity 
ivith which a Fluid fpouts out through an Hole in the Bot- 
tom or Side of a VefTel, is equal to that which a Body would 
acquire by falling from the Leyel «f the Surface of the Fluid 
to the Hole, arid the Velocities Bodies acquire by falling are 
as the fquare Roote of the Heights they fall from (Part I. 
Chap. 5. S- 5) it follows that the Velocity, with which « 
Fluid fpouts out from an Hole in the Bottoih or Side of 
9 VefTel, is as the fquare Root of the Heig^ of the Lev^} 
j&f the Surface of the Fluid above the Hole, 


Chap. T- among themfehes. ^23 

of Fluid run out, nor the Velocity with which it 
flows, but its Moment or both thefe multiplied 
together, (Part I. Ch. 9« §• i •) that is the true 
and adequate EfFcd of the PrefTurc. Thefe there- 
fore being ever in the fame Ratio, will each of 
them be as the fquarc Root of the Preflure : 
For then being multiplyed together, their Pro- 
duct or the Moment of the fpouting Fluid 
is adequately as the Preflfure which occafions 
it$ but the Preflure is as the perpendicular 
Height (§. 4.) therefore the Velocity and alfo 
the Quantity of Fluid fpouting out is as the 
fquare Root of the Height of its Surface above 
the Hole. 

T o give an Inftance or two ; fuppofe two 
Holes made in the Side of a Veflel^ the one 
an Inch below the Surface of the Fluid it cbn-^ 
tains, the other four 5 the Velocity with which 
the Liquor flows out of the lower Hole, will 
not be four times as great* as that with which 
it flows through the upper, notwithflanding 
the Preflure is four times greater : for if it 
Ihould, the Quantity run out in a given Time 
would alfo be four times greater, confequent- 
ly the EiFed produced would be fixtecn times 
greater than it is at the upper Hole, that is, 
four times greater than the Caufe, which is 
abfurd. Whereas the Velocity and Quantity 
of Matter will each be only twice as great as 
they arc above, producing thereby a Force or 
Moment only four times as great^ which is 


24 3^^ ASiion of Fluids Part II 

tionablc to the Caufc. So if an Hole were 
made fixtccn times lower than the firft, the 
Velocity and Quantity of Martcr will not be 
each fixteen times greater than at the other, but 
only four times greater apiece, and fo the Mo- 
ment fixteen times greater, as the Prcfliire is*. 

• From hence we may fee the Error fome of die foreign 
Mathematicians have f-Jlcn into with Regard to the Forces 
of moving Eodiesji who contend that they are as the Squares 
of the Velocities multiplied by the Quantities of Matter. For 
from thb Propolition it is, that one of the principal Argu- 
ments brought in Favour of this Opinion is* derived. They 
argue thus, EffeSs are ever proportionable to their Caufes^ 
the Frejfure oS the incumbent Fluid is the Caufe of it^ 
fpouting out, the Force with which it fpouts out, is the Ef- 
feU^ but by this Propofition the Frejfnre is as the Square of 
the Velocity it flows with, therefore the Force is likewife as 
the Square of the Velocity, True, it is fo ; but let us fee the 
Confcquence. The Force with which the Fluid fpouts out 
is not only owing to the Velocity, but the Quantity run out 
in a given Time, they have each their Share in producing 
the Force, confequently the Force is in a Ratio compounded 
of both, or as the Produ<ft of one multiplied by the other, 
or, which comes to the fame Thing, (fince as was obferved 
before, they are in the fame Ratio with each other) as the 
Square of either of them ; from hence it is, that the Forces* 
of Fluids in Motion are faid fo be as the Squares of their 
Velocities ; not that they are fo in Virtue of thofe Velocities, 
as fuch, but in Virtue of them, and the Quantities cf Matter 
taken together, or becaufe the Squares of the Velocities is 
the fame Thing with the fimple Velocities multiplied by the 
Quantities of Matter. . Therefore when it is faid, the Force* 
of Fluids are as the Squares of the Velocities, that Part of 
the Force which arifes from the Quantity of Matter is really 
taken into Conlidcration. How ridiculous then muft it be 
in thofe Gentlemen to fetch an Argument from hence to 
prove, that the Forces of Bodies in Motion are as the Snuares 
of the Velocities and Quantities of Matter too, when^ the/ 
are as the Squares of the Velocities, only becauic the Quan- 
tities of Matter are implied in them. 






Chap. I. among themf elves. 25 

XII. When a Current of Water or other 

JFluid falls perpendicularly upon the Surface 
t)f a Plane, or flows againft it, (as the Wind 
againft the Sail of a Ship, or the like) the 
Force, which the Fluid c:fertsupon it, is equal 
to the Weight of a Column of the fame Fluidt 
whofc Bafe is equal to the Plane, and its 
Height fuch, that a Body falling freely through 
it would acquire the fame Degree of Veloci- 
ty with which the Fluid moves *. 

In Order tp demor>ftrate this Propofition, 
let us fuppofe t^he Veflcl ABCD (Fig. iij 
filled with a Fluid, and havin? a lar2;e Hole 
EF in tiie* Bottom, then'Vill the Prcflure of 
the Fluid caUcfe a Stream to flow out,, which 
in the. Hole it felf will have . fnch a De2;rec 
of Velocity, as a Body would acquire by fall- 
ing freely from the Surface of the Fluid ia 
the Veflcl to the Hole (as demonftrated §. 10.) 
In the midft of this Hole, and confcquently 
in the Stream, let us fuppofe a Plane as PQ^ 
fufpended, but fomcwhat lefs than is fufiicient 
to fill the Hole, lead it flop the Current of 
the Water. Now 'tis certain this Plane fup- 
ports. a Cbluhnn of the ,Fluid equal to that 
vvhich prcfles upon any other Part of the Bot* 
torn of the Veflel of equal Dimenfions with. 

* Prom this Prdpofition is deduced the Method of computing 
the Power of a Machine, which is 'to be moved by Wind or 
Water ^c. See an Inftance of fuch a Calculation in the Mc- 
- fiioin of the Royal Academy of Sciences for the Year 1725* 

D it 

26 7%e ASlion of Fluids Part 11. 

k fcif (for being thus placed^ it may be look- 
ed upon as a Part of the Bottom) but every 
Part bears a Column, whofe Bale is equal to 
its own DimenHons, and its Height the fame 
with that of the Surface of the Fluid in the 
VeflTcl : Confequently this Plane fupports fuch 
a Column, that iSt it is refifted by the Stream 
with a Force equal to the Weight of a Co- 
lumn« whofe Bafe has the fame Dirnenftons 
with it fclf, and whofe Height is equal to that 
of the Surface of the Fluid In the Veflel, that 
is, fuch an Height as a Body by Falling freely 
from, would acquire ia Velocity eqiial to that 
with which the Fluid moveis. 

XIII. The Prcflurc of a Fluid agatnft a per- 
pendicular Bank or Sluice (^c. is equal to the 
Weight of a Column of the fame Fluid, whofe 
Bafe is equal to fb much of the Bank as is 
below its Surface, and which has half the 
Depth of the Fluid for its Height*. 

If the Prcflurc upon every Part of the Bank 
from the Surface to the Bottom was as great 
as it is at the Bottom, the Preflure againft it 
would be equal to the Weight of a Column 
whofe Bafe is equal to fo much of the Bank 
as is under the Surface of the Fluid, and 

• From hence we fee the Reafon, why the Water of the Sea 
ti great Lakes is as eafily kept within thdir Banks (fctting 
afide the Force which arifes from the Motion of the Waves 
^c.) as that of the narroweft Canal, w«. becaufe the Preflure 
of Fluids is not in Proportion to their Surfaces^ but their 


Chap. 2. ufm Solids. 57 

which h?is the 'whole Depth of the Fluid for 
its Height 5 for the Prcflure upon every Part 
of the Banic at the Bottom is equal to the 
Weight of a Column, whofe Bafe correfponds 
to the Part prcflcd upon, and its Height is 
that of the Depth of the Fluid 5 confcquent* 
I ly if the Preflure was the fame evcfy where 
from Top to Bottom, it would be equal to 
the Weiglif of as many fuch Columns as would 
anfwcr to all the Parts qf the Bank : But the 
Prcffurc every where diminifhcs in Proportion 
as we approach the Topt where k is Nothjng; 
it is therefore but hdf^ what it woiild ho. 
in the other Cafe 5 from whence the Propo- 
Ation is dear. 

' C HA P. II, 


Of the Effe&s Fluids have on Solidf 

immerfed therein* 

*^HE specific Gravity of a. Body is that, 
JL by which it is faid to be heavier or 
ligh'ter than another of a different Kind : Thus 
Lead is faid to be fpecifically heavier, thaa 
Cpr>:^ bejcaufe fuppofjng. an equal Bulk bC 

^ • Bccaufe the Sam of a Number of Terms in Arithme- 
dcai Progreflion- beginmng from Nothing, is half the • Suitt *of 
an equal Nu^[>ber' of Teims^. each p^ Mr)kifh is equa] to 4^e 
laft in the^rogrcffion. 

2 8 The ABion of Fluids ' Part II. 

^cach,,thQ one would be heavier than the other. 
Trpm hence it follows that a Body fpecifically 
heavier than another is alfo more denfe, that 
is, contains a greater Quantity of Matter un- 
der the fame Bulk, becaufe Bodies weigh in 
Proportion to the Quantities of Matter tiicy 
contain (Part I. Chap. 3. §. 7.) 
. II. If a Solid is immerfed in a Fluid of 
'the fame fpecific Gravity with it felf, it will 
remain fufpendcd therein, iii whatever Part 
of the Fluid it is put. 

Let the Body FGHI (Fig. iz.) be im- 
merfed in the Fluid AB CD to the Depth MN, 
or ariy other whatever; I fay, it will continue 
in the fame Part of tlic Fluid when left to it 
felf, without either rifing towards the Surface, 
or finking towards the Bottom. 

For the Body being (by the Suppofition) of 

equal Gravity with the Fluidi the Weight of 

the Column KL HI, which confifts partly of 

Fluid and partly of the Body, is the fame as 

if it had .been all Fluid 5 confcqucntly HI, that 

,^art;pf the Surface of the Stratum MN which 

J'lipi' immediately under the Body, is prcflfed 

'^ with'tlie fame Degree of Force, that any other 

*'Part 'of ,thc fame Dimenfions is, and there- 

' fore the whole Column KLHI will be fup- 

..port/ed in its Place. Now the fame being true 

of the Column KLHI whatever be its Length, 

'tis evident the Body will be fufpended in its 

Pl§ce at any ^^^x\ 


c Ju: 

Chap. 2. upon Solids. 29 

Ifl. B u T if the Body is (pccifically^ heavier 
than the Fluid in which it is immcrfed, it 
will fubfide to the Bottom : For then in what- 
ever Part of the Fluid it is pur, the Column 
KLHI, will always be heavier than an equal 
Column, that confifts all of Fluid 5 confequcnt- 
Jy HI, that Part of the Stratum MN, which 
lies immediately under the Body will fufFef 
a greater Preflurc, than any other Part of the 
fameDimenfionsj and therefore will give way 
and permit the Body to fubfide continually 
till it reaches the Bottom. 

IV. On the contrary if the Body is fpcci- 
ftcally lighter than the Fluid, it will rife to 
the Top in what Part of the Fluid focver it 
is put. For then the Column KLHI will 
always be lighter than an equal Columa 
which is all Fluid 5 confcquently H I will be 
Icfs prcffcd downwards than any other Part 
of the fame Stratum of equal Dimenfions, aiKl 
will therefore continually rife up carrying the 
Body with it, till it, arrives at the Top. 

V. A Body being laid on thie Surface of 
9 Fluid fpccifically heavier than it felf, finks 
into it, till the immerfed Part takes up the 
Place of a Quantity of Fluid, whofe Weight 
is equal to that of the whole Body. 

Let EFGH [Fig. ij.; be a j^ody floating 
on a Liquor fpccifically heavier than it felf, 
\l will fink into it till the immerfed Part 
IKGH takes up the Place of io much Fluid, 



30 n^e AStion of Fluids Part 11, 

as is equal to it in Weight. For in that Cafe 
GH that Part of the Surface of the Stratum 
iipon which the Body refts, is preflcd with 
the fame Degree of Force as it would be, 
Vas the Space IKGH full of the Fluid; that 
i^^ all the Parts of that Stratum are prelTcd 
alike, and therefore the Body after having 
iUnk fo far into the Fluid is in Mydlibm 
with \ij and will remain at Reft. 

f R o M hence it follows, that the Body is 
as much fpecitically lighter than the Fluid on 
which it floats, as the immerfed Part is lefs 
than the Whole. For by how much the left 
the itfimerrcd Part % fo much the lefs Fluid 
|s equal in Weight to the whole Body 5 that 
IP, the Body is fo much the lighter inRefped 
pf the Fluid. And if the fame Body is made 
to float fucceffivcly in Fluids, whofe fpccific 
Gravities differ among thcmfelvcs, (but all ex- 
ceed that of the Body), the lighter the Fluids 
are, fo much greater will be the Part im- 
merfed *. 

VL A Body fufpended in a Fluid fpeci- 
fically lighter than it felf, lo ies a Part of its 
Weight (or rather communicates it to the 

• This Pha?nomenon is what gave Rife to the Hydrome- 
ter, an Inftfument- of great Ufe in afccrtaining the Genuincfs 
of Liquors ; for it rarely happens, that the adulterated and 
the genume Liquor, ^however they may agree ip Appearance) 
arc of the fame fpecific Gravity. 



Chap. 2^ upon Solids. 3 1 

Fluid) equal to that of a Quantity of Fluid 
of the fame Bulk. 

Let us inftead of fuppofing the Body fuf- 
pended in the Fluid, imagine it to be away» 
and its Place filled with the Fluid 5 now 'tis 
evident, this being of the fame fpccific Gra- 
vity with the circumjacent Fluid, will be en- 
tirely fupportcd by it, or if we fuppofe the 
Body to be of the fame fpccific Gravity with 
the Fluid, it will be wholly fufpended by it 5. 
we fee therefore the Preffiire of the circum- 
ambient Fluid, whereby it endeavours to buoy 
up the Body, is equivalent to the Weight of 
fo much Fluid, as would fill the Place the 
Body takes up. But fince the Fluid preflcs 
only on the Surfaces of the Body, that Pref- 
fure is the fame, whatever be the fpccific Gra- 
vity of the Body 5 the Body therefore lofcs fo 
much of its Weight as the Fluid would natu- 
rally buoy up 5 that is, fo much as \% the Weight 
of a Quantity of Fluid of the (ahie Bulk. 

This Propofition affords us a Method of 
determining the Relation which the fpccific 
Gravities of Bodies, whether Fluid or Solid, 
bear to each other. For whereas by weigh- 
ing a Solid in a Fluid, fpccifically lighter than 
it fclf, we find the abfolute Weight of a Quan- 
tity of the Flpid equal to it in Bulk {yiz,. the 
Weight the Solid lofes) the Relation, that 
' Vl^cight bears to the Weight of the Solid, is 
the Relation of their fpccific Gravities; bc- 


g2 Tl^e ASlim of Fluids Part IL 

caufc the Weights of Bodies, whofe Bulks 
are equal, are as their fpecific Gravities : con- 
lequcncly if the fame Solid is weighed luc- 
ccffively in different Fluids (all lighter than 
it felt) we gain the Relation which the fpe^ 
cific Gravity of each bears to that of the So- 
lid, and therefore to one another. Again, 
if different Solids are weighed in the tame 
Fluid, the Relation which the fpccific Gravity 
of that Fluid bears to each Solid is had, and 
therefore alfo the fpccific Gravities of the So- 
lids among themfclves** 

• Upon this is founded the tffe of the hydroftatical 6a- 
lance for determining the fpecific Gravities both of Solids and 
Fluids The Praftice is thus. Firft let the Solid be weigh- 
ed in Air, that is> out of the Fluid ; afterwards in it (this ought 
to be done by fufpending it at one End of the Balance by \ 
String that is as nearly of the fame fpecific Gravity with the 
Fluid made Ufe of as poffible> and letting it link into the Fluid, 
till it is wholly immerfed below the Surface ; if the Fluid 
is Water, an Horfe Hair is moft convenient to hang the Body 
at the End of the Balance by) then fubftrad its Weight in the 
Fluid from its Weight in Air, the Difference is what it lofcs in 
the Fluid. This" done, fay, hy the Rule of Proportion, as the 
Weight loft in the Fluid is to its Weight in Air, fo is Unity, 
or an/ Number taken* at Pleafure, to a Fourth, which by its 
Relation to the former, will exprcfs the Rehtion of the fpc- 
cific Gravity of the Fluid to that of the Solid. Thus the Re- \ 
lation which the fpecific Gravity of the fame Fluid bears to that 
of various Solids, or of the fame Solid to that of various Fluids, 
and confequently the Relation of the fpccific Gravities of all 
among themfelvcs may be obtained. 


Chap. 3. Of the Air, jt 

CHAP. ill. 

0/ the Air. 

LTHHAT Part of Natural Philofophy; 

X which treats of the Properties of the 
Atr^ and the EfFefts of its 'Prejfure and Elafti^ 
city^ is called Pneumatks. 

IL Air is a thin tranfparent elaftic Flaid 
furrounding the Earth to a certain Heightt 
which taken together^ is called the Atfnojphere. 

IIL That Air is a Fluid, is evident from 
the eafy Pafiage it affords to Bodies moving 
in it : for this (hows it to be a Body^ 
whofe Parts eaHly yield to a PrcfTure that is 
greater on one Side than on the other* which 
is the Definition of a Fluid. 

IV. Air gravitates towards the Earth, or 
is heavy like other Bodies. 

T o prove this, we have Abundance of Ar-* 
guments both from Senfe and Experiment. 
Thus, when the Hand is applied to the Ori-^ 
ficc of aVcficU it readily perceives the Weight 
of the incumbent Atmofphcre, as foon as the 
Air included in the Vcflel begins to be drawn 
out. Thus» Glafs Vcffcls exhauftcd of their' 
Air (if not ftrong enough to luftain the Prcf- 
furc of the incumbent Atmo(phcrc) arc crufh- 
cd to Pieces by the Weight of the Air with- 

E out. 

J/t Of the Aif. Part It 

out. When the Air is cxhaafied out of a 
Vcffel, the Vcffcl weighs Icfs than bcforc- 
With a great many more Experiments gene- 
rally mentioned by Authors on this Subjed ^# 
V. T H E exaft Weight of the incumbent 
Air is determined by filling a Tube with Mer- 
cury» and immerging the open End in a Vef- 
fel of the fame Fluid : for then the Mercury 
will run down the Tube, till its Surface is fallen 
only to the perpendicular Height of about twen- 
ty nine or thirty Inches above the Surface of the 
Mercury in the VeiScli if the fame Experi- 
ment is made with Water, the Surface of it 
will (land at about the Height of thirty two 
Feet above the Surface of that in the Veffel y 
the Column of Mercury in one Cafe, and the 
Column of Water in the other exadly ba* 
lancing the Weight of a Column of Air, which 
reaches to the Top of the Atmofphere, and 
prefTes upon the Surface of the Fluid in the 
Veflels. This is what is called the Torricel- 
lian Experiment, from Torrictlli the Inventor^ 
and is the fame with the common Baro' 

) meter. 

r • 

From hence it follows, (Chap. I. §. 9.) 
that all Bodies at the Surface of the Earth 
fuftain as great a Weight from the Preffure 
of the Air, as is that of a Column of Water, 
whofe Height is thirty two Feet» and its 

* Sec Boylh Ti»as> or Grmieftmii Libi II. P, III. 


Chap. 3. Of the Air. 35 

Safe equal to the Surface of the Body prefled 
upon *. 

VI. That the Sufpcnfion of the Mercury 
in the Barometer depends on the PrelTure of 
the external Air, is beyond all Doubt 5 for if 
the Barometer is included in the Air Pump, 
the Mercury falls in the Tube in Proportion 
as the Air is exhaufted out of the Receiver ^ 
and if the Air is let in again gradually, the 
Mercury reafccnds proportionably, till it reach- 
es its former Height. 

VII. That the Atmofphcre is extended to 
a determinate Height, appears from hence; 
niiTu. that when the Torricellian Tube is re- 
moved to a more elevated Place, the fufpendp 
ed Colurpn, of Mercury becomies {horter, 
w.hich is, becaufe a (horter Column of Air 
prefles upon it, or, that the Tube in this Si- 
tuation is nearer the Top of the Atmofphere* 

• The PrelTure of the Atmpfphere Ujpon every fqnare Inch 
Bear the Sar&ce of the Earth is about fifteen Pounds, being 
eqisU to the Weight of a Column of Mercury* whofe Height 
is thirty Inches and its Bafe one fqoare Inch. Now fuch % 
Column of Mercury would weigh about fifteen Pounds. The 
\ Weight of the Athiofphere therefore which preHes upon a Man*s 
^ Bo^yis equal to fo n>any Tinges fifte^i^ Pound* as the Sux&ce 
of his Body contains Tquare Inches. 

The Reafon why a Perfon- fufFers no Inconvenience from ^(^ 
gieat a PrefTu/e i$ low^ to the Air included within the Pores 
and Fluid-*: of the Body* which by its Readlion is a Counteipoiie 
to the PrefTure of the tztemal Air : as we fhall explain more 
iully, when yfA come to fpeak of the Diving Bell, and the Maor. 
Xicr^of ufing iC , 


E *. ym; 



36 Of the Air. Part IL 

VIII. The Elafticity of the Air is that Pro 
perry by which it controls it fclf imo Icfs 
Space, when an additional PreflUre is laid up- 
on ity and recovers its former DitnenAonSf 
when the Preflure is taken off. This is ac- 
counted its diftinguifhing Property, all the reft 
being common to it with other Fluids. 

Of this we have numerous Proofs. Thu$, 
ft Bladder full of Air being comprefled by the 
Hand, the included Air gives way s but whea 
the Prefliire is taken off, the Air expands it 
felf, and readily fills up the Cavity or Im- 
preflion made in the Surface of the Bladder. 
And if a larger Quantity of Air, thati is na- 
turally prefled into a Veffel by the Weight of 
the incumbent Atmofphere, is forced into it 
by the Condenfer (an Engine for that Purpofe) 
and if that Air is afterwards let out by open- 
ing the Vetfel, the Remainder is found to be 
of the fame Weight as at firfl: \ from whence 
it follows, that the Air by means of its Ela- 
fticity or Spring drives out all that which was 
forced in by the Condenfer, recovers its for^ 
VMX Dimenfions, and fills the Veffel as before, 

IX. From hence, together with what 
has been obferved about the Preffure of the 
Atmofphere, it follows, that the Air near 
the Surface of the Earthy i$ comprefled 
into a much narrower Space by the Weight 
pf the Air above, than that which it would 
naturally take up^ was it freed from that 

Chap. 3. Of the Air. 37 

PrcfTurcs accordingly it is found by Expe- 
riment, that when the Prellure ot the At- 
mofphere is taken off from any Portion of 
Air, it immediately ielt into avaft 
Extent. Hence it is, that thin Glafs Bubbles 
or Bladders filled with Air, being included ia 

^ the Receiver of the AirPump, arc broke in 
^Pieces by the Spring of the Air they contain 
within them, when the Preffure of the exter- 
nal Air is taken off. Thus a Bladder quite 
flaccid containing only a fmall Quantity of 
Air in it, fwells upon the Removal of the ex- 
ternal Air, >wd appears diftended as if it con- 
tained as gre^t.a Quantity as poflibie. The 
fame EiFeft is found in carrying a Bladder 

. ibmewhat flaccid to a more elevated Place, 
for there the external Preflure being icfs, the 
Air included, iq the Bladder is in fome mea« 
fure freed from the PrcflTure of the Atmo- 
fphere, it therefore dilates it felf, and diftends 
the Bladder as in the former Cafe. 

X. It is fpund by Exp^iment» that the 
greater the Force is with which a Quantity 
of Air is cotnprcfledi lb much lefs is the Space 

L into which it is contra&ed. From whence it 

' follows, that the Denfity of the Air is pro- 
portionable to the PreiTure which it fuflains. 
As to the tttmoft Degrees of Expanfion and 
Contradlion which the Air is capable of, they 
are as yejt unknown. In feveral Experiments 
fli^de by AJr. Boyte, Air in its natural Srarc, 




3^ Of the Air, Part H. 

that is, pccficd only with the Weight of the 
incumbent Atmofphere, dilated it felf, when 
that FrelTure was talsien off, into more than 
thirteen thoufand Times the Space it took up 
before. And he was able fo £ar to compre^ 
it, that it fhould take up more than five hun- 
dred and twenty thouland Times iefs Space 
than that into which it would dilate it felf 
when freed from its PreflTure *. 

XL From this Property it ' ft>llows» that 
the Air in the inferior Parts of the Atmo- 
fphere is more denfe, than that which is at 
great Heights in the fame ; or, that the Den- 
fity of the Air dccreafes ccmtinually as we 
approach the Top of the Atmofphere. Foi: 
the Deniity of the Air is proportionable to the 
£Qrce with which it is compreired, and that 
Force continually decreafes as we approach 
ihe Top. 

• Sec Boyle^s Tra&s and Experiments on the Spring and 
FrcfTure of the Air. 

' Various have been thcf^pinions of Philofbphers concerning the 

Caufet>f this prodigious Spring in- the Particles of Air ; fome hold- 

ipg it to depend on their Figure, which they fuppofe to refem^ 

bfe in fome Manner* little Bundles of Twigs or the Branches of 

Trcfis I 'fome think them like Fleeces of Wool, others conceive 

them, as. rolled up like Hoops, or the Springs- of Watches, and 

endeavouring to expand themfelves by Virtue of their Texture. 

Bot Sir Ifaac Ne'wi(ht is. of Opinion, that fuch a Texture i» 

by, no Means fuffici^nt to account for that vaft' P&wer of Ex* 

panlion obfcrved ^bove : but that each Particle is endued with 

I a \ repelling' Force, which encreafcs as they approach one ano- 

1 thcri and accordingly keeps them afunder at Dlftanc^ red*' 

I procally proportionable, to the PrefTure they fuibin. 

• /Se'c Halei^ Staticar iSflays. Vol. I. Chap. 6. 

i .- i Was 



3. Of thi Air. ) tf 

I r- 

W A s the Dcnfity of the Atmofphcrc every 
Inhere the fame, as it is near the Surface of 
the Earth, its Height (as is computed from 
the Quantity of Preffure it exerts in raiiing 
the Mercury in the Barometer) would be a- 
bout five Miles. But whereas its Denlity con- 

f^ tinually decreafes* as we approach the Top, 
and it is uncenain how far the Particles may 
expand themfelvcs where there is little or no 
Preflure, the true Height cannot be obtained. 
It is computed to continue of a fenfible Den- 
sity to the Height of about forty five or fifty 

XIL The Elafticity of the Air produces 
the fame £ffe£b with its Preffure. 

^ For Adion being equal to Readion> the 
Borce which the Spring of the Air exerts in 
endeavouring to expand it felf> is equal to 
the Force with which it is compreflcdj juft 
as it is in the Spring of a Watch, which ex- 
erts no Force, but in Proportion as it is wound 
up 5 confequently a Quantity of Air in fuch 
a State of Contradion, as it would be com- 
prcffed into by the Weight of the incumbent 
Atmofphere, exerts a Force' equal to that 
Weight. If a Quantity of Air therefore is 
included in a Veffel, and is of the fame Den- 
fity with the circumambient Air, its Preffure 
againft the Sides of the Veffel is equal to the 
Weight of the Atmofphere. Thus Mercury 
is fuftained to the fame Height by the elaftic 


40 Of the Air. Part If. 

force of Air included in a GUfs VefTel no 
way communicating witla the external Air, as 
by tiie Weight of the Atmofphere it fclfr 

XIII. The Elafticity of the Air is aug* 
mcntcd by Heat and diminirticd by Cold"^- 
Por if a Bladderi which is about half filled 
wirh Air, is laid before the Fire» it will, 
whin it is iufficiently heated, be diftendcd 
and burft. Thus, Glafs Bubbles being laid 
upon the Fire immediately burft with great 
Violence by the augmented Spring of the in- 
cliidcd Air. . 

XI V, The Denfity of the Air thus conti-' 
tinually varying, according to the different 
Degrees of Hear and Cold, to which it is ex- 
poled, makc!» it difficult to afcertain its true 
fpccific Gravity. Ricciolus eftimatcs it to be to 

* This Propeity is found in all bodies both Solid and 
Fluid, but in a much lefs Degree, than it is in Air. Thus, 
if a Flafk is filled with Water only to the lower Part of 
the Neck, and is then fct upon the Fire, the Water, when it 
begins to grow warm, will rife into the Neck, and continue 
to afccnd, as the Heat« is increafed. And when a Wire of 
Bur of Iron is heated, it is augmented both in Length and 

Upon this Property depend the Phsenomena of the Thef- 
mometcr, which is a Glafs Bubble with a fmall hollow Stem 
a fifing from it This Bubble and Part of the Stem is ufually 
filled with Mercury, or Spirit of Wine, which will rife oi 
fall in the Stem as they are affected by the Heat or Cold 
of the external Air. U a fufficient Degree of Heat is fud- 
denly applied to this Inilrument, the Liquor is obferved td 
defccnd a little before it rifes, becaufe the Glafs difl^ding 
it (^\f, the Capacity of the Bubble is augmented, before the 
included Liquor is atfe^led by thQ Heati. 


t)hap, 4. 7i5^ Repftance of Fluids. 4 1 

that of Water, as one to a Thou fa nd : Mer 
fennus as one to one Thoufand three Hundred • 
tMr. Boyle by more accurate Experiments found 
it to be, as one to nine Hundred and Thirty 
eight, and thinks, that, all Things confidered> 
^ the Proportion of one to a Thoufand may be 
r taken as a medium 1 for there is no fixing any 
prccife Proportion, beeaufe not only the-fpe- 
cific Gravity of Air, but that of Water alfo is 
continually varying. However by fome Experi- 
ments made fince with more Accuracy before 
the Royal Society^ the Proportion has been fix- 
ed at about one to eight Hundred and 
XV. Air is neceffary for the Prefervation 
f of Animal and Vegetable Life 5 neither will 
Pire fubfift without it. The Reafon of this 
is as yet unknown to Philofophers. Mr. HaUi 
by fevcral curious Experiments in his Statical 
Eflays makes it probable, that 'tis owing t6 
its Elafticity, See his Jnalyfis of it* Statical 
Effays Vol. I. Chap. 6. 


Of the Reffiance of Fluids. 

1. '"Ip^HE Refinance a Body meets with ill 

JL moving through a Fluid, is of three 

kinds. The firft arifes from the Friftion of 

th€ Body againft the Particles of the Fluid j 

F thel 

42 lloe Reftftance of Fluids. Fart 11 

the fecond, from their Cohefion or Tenacity 
among themfelvcs : the third, from their In- 
adlivity, or the Tendency they have, in com- 
mon with other Bodies, to keep the Places 
they poflefs. 

The firft, viz. that which arifes from the 
Fridtion of the Body againft the Particles of 
the Fluid is very inconfiderablc 5 for whatever 
the Weight is, which preflTes the Particles of 
a Fluid together, the Freedom, with which a 
Body moves through it, is not fenfibly di- 
minifhcd thereby. As was obfervcd Chap. i. 
§. 2. in the Notes. 

The feeondj or that which arifes from 
the Tenacity of the Particles of the Fluid, is 
as the Time tiie Body takes up in pafling 
through it * 5 for the fliorter the Time is in 

* We have a very curious Argument in Confirmation of this, 
and which at the fame time illuftrates the Manner in which a 
Body makes its Way through a tenacious Fluid, by Sir Ifaac 
2^€^ton himfelf, in 'Si Poilcript to a Letter in the Philofophical 
Tranfadions N"". 371. It is as follows. ' Suppofe Pieces of 

* fine Silk, or the like thin Subftance, extended in parallel Planes, 
« and fixed at fmall Diilances from each other. Suppofe then a 

* Globe to ftrike perpendicularly againft the Middle of the 
< outcrmofl of the Silks, and by breaking through them to lofe 
' Part of its Motion. If the Pieces of Silk be of equal Strength, 
' the fame Degree of Force will be required to break each of 

* them ; but the Time, in which each Piece of Silk refifts, will 

* be fo much (liorter as the Globe is fwifter ; and the Lofs of 
' Motion in the Globe confequent upon its breaking through 

* each Silk, and furmounting the Refiftance thereof, will be pro- 

* portional to the Time in which the Silk oppofes it felf to 

* the Globe's Motion ; infomuch that the Globe by the Re- 

* filtance of any one Piece of Silk, will lofe fo much lefs of its 

* Motion as it. is fwifter. But on the other Hand, by how 

* much 

Chap. 4. T^e Refinance of Fluids. 43 

which the Force of Cohefion is broke through* 
the Icfs EfFcd it has in refifting the Motion 
•of the Body. This Species of Refiftance is 
alfo very fmall except in glutinous and vifcid 
Fluids, whofc Parts arc not cafily feparated. 

The third Species is the principal Refiftance, 
that Fluids give to Bodies, and arifes from their 
Inaftivity or the Tendency the Particles, of 
which they confift, have to continue at Reft. 
The Quantity of this Refiftance depends on the 
Velocity the Body moves with on a double Ac- 
count. Fpr in the firft Plape, the Number of Par- 
ticles put [into Motion by the moving Body in 
any determinate Space of Time, is proportion- 
able to the Velocity wherewith the Body moves i 
and in the next Place, the Velocity with which 
each of them is^moved, is alfo proportionablp 

' much fwiftcr the Globe moves, {o many mare of the Silks it 

* will break through in a given Space ef Time ; whence the 

* Number of the Silks, which oppofe themfelves to the Mo- 

* tion of the Globe in a given Time, being reciprocally pro-* 

* portional to the Effedl of each Silk upon' the Globe, the Re- 

* fiftancc made to the Globe by thefe Silks, or the Lofs of Mo- 
' tion the Globe undergoes by them in a given Time, will b^ 

* always the fame. 

^ Now if the Tenacity of the Parts of Fluids obferves the 

* fame Rule, as the Cohefion of the Parts qf thefe Silks; name- 

* ly, that a certain Degree of Force is required to feparate and 

* difunite the adhering Particles, the Refiftance arifing from th^ 

* Tenacity of Fluids muft obfcrvc the fame Rule, as the Re- 

* fillance of the Silks ; and therefore in a given Time the Lofs 
' of Motion, a Body undergoes in a Fluid by the Tenacity of 

* its Parts, will in all Degrees of Velocity be the fame ; or 

* in fewer Words, that Part of the Refiftance of Fluids, which 
■• arifc3 from the Cohefion of their Parts, will be Uniform. 

44 5r&^ Refiftance of fluids. Part II 

to the Velocity of the Body; this Species 
therefore of Refiftance is in a duplicate Pro- 
portion, or as the Square, of the Velocity, 
with which the Body moves through the 
Fluid *. 

II. Farther the Refiftance a Body mov- 
ing in a Fluid meets with from thence, may 
be confidered with Regard to the Fluid \ and 
then it will be found to be more or lefs, ac- 
cording to the Denfity of the Fluid. For by 
how much denfer the Fluid is» fo much the 
greater Number of Particles are to be put in- 
to Motion by the Body in Order to make its 
Vl/'ay through it. 

III. The next Thing to be confidered 
is, the EfFeds of the Refiftance of Fluids upon 
Bodies moving in them $ that is, the Retar- 
dation which they caufc in the Motion of a 
Body by their Refiftance, Or the Quantity qf 
Motion they deftroy. 

* This may be otherwife demonftratpd from the twelfth 
SefJ^ion of the foregoing Chapter ; for from thence it follows, 
that the Refiftance a Fluid gives to a Solid againft which it 
jnoves, .is proportionable to the Height a Body muft fell from, 
to acquire fuch a Degree of Velocity as the Fluid moves witlj : 
but the Heights Bodies fajl from are as the Squares of the Ve- 
locities they acquire by falling ; confequently the Refiftance a 
Fluid gives to a Solid, againft which it moves, is alfo as the 
Square of its Velocity, Now it matters not, as to the Re- 
fiftance, whether the Fluid moves againft the Solid, or whether 
5t be at Reft, and the Solid moves in it ; the Refiftance there- 
fore which a Fluid gives to a Solid moving in it, is as the 

Square of the Velocity, \yith which it moves, 

» • • ■ . 

Chap. 4. "The Refinance of Fluids. 45 

And this in fimilar Bodies of equal Mag- 
nitudes is invcrfely as their Dcnfitiest or the 
t^antity of Matter they contains for by how 
niuch the greater the Quantity of Matter in 
any Body is, fo much the more eafily doe^ 
it overcome the Refiftance it meets with from 
jhe Fluid. Thus we fee the Refiftance of the 
Air has a much lefs Effed in deftroying the 
Motion of an heavy Body, than of a light 
one which has the fame Dimeniions. 

IV. In fimilar Bodies of equal Denfities, 
but different Magnitudes, ithe Retardation is in* 
verfcly as their homologous Sides. For the Re* 
liftance Bodies meet with in a Fluid, is inverfely 
as the Quantity of Matter they contain (by the 
laft,) that is inverfely as the Cubes of their 
homologous Sides \ and it is alfo diredly as 
their Surfaces, becaufe 'tis by them that they 
move the Fluid put of its Place, that is, di* 
redly as the Squares of their homologous Sides; 
con(equently the Retardation is inverfely as 
their homologous Sides*. 

Having given the fundamental Princi- 
ples of HydroftaticSy and fliewn how Fluids 
both comprefllble and incompreflible are dif- 
pofed to ad upon each other, and upon So- 
lids by their Preflure, Motion, Elafticity and 

* Bccaufc ^e inverfe Ratio of the Cubes of any Numbers 
being compouhded with the dirafi: Ratio of the Squares of the 
iamc, gives the inverfe Ratio of the Numbers (hemfelves. 


^6 The Refiflance of Fluids. Part II. 

Re/illancei I proceed now to account for 
fome of the more temarkable Fhxnomena 
of Nature* in which they are in Fart or al- 
together concerned : and this I deiign for 
ihc Subjcft of the following Diflcriations. 


DIffeit. I. Of Sound, 47 


Of Sound. 

y ¥ Tjyr HEN the Parts of an claftic Body arc 
^ V r pu^ ii^^o ^ tremulous Motion by Per- 
cuflion o\ the like, fo long as the Tremors 
continue, fo long is the Air included in the 
Pores of that Body, and likcwife that which 
prcflcs upon its Surface, affeded with the like 
Tremors and Agitations: now the Particles 
of Air, being fo far compreffed together by 
the Weight of the incumbent Atmofphere, as 
their repulfivc Forces permit, (as has been ex- 
plained Chap, 3.) it follows, that thofe which 
arc immediately agitated by the reciprocal 
Motions of the Particles of the claftic Body, 
will, in their Approach towards thofe which 
lie next them, impel them towards each other, 
and thereby caufe them to be niore condchfcd, 
than they were by the Weight pf the incum- 
bent Atmofphere, and in their Return fufFcr 
[ them to expand thcmfelvcs again 5 whereby 
the like Tremors and Agitations will be pro- 
pagated to the next, and fo on, till having 
arrived at a certain Diftancc from the Body, 
they ceafe, being gradually deftroyed by a con- 
tinual fucceflive Propagation of Motion to 
frefli Particles of Air throughout their Pro- 



48 Of Sound. Pari 11. 

Thus it is that Sound is communicated 
from a tremulous Body to the Organ of Hear- 
ing. Each Vibration of the Particles of the 
founding Body is fucccilively propagated to 
the Particles of the Air, till it reaches thofc 
which are contiguous to the Tympanum of the 
£ar> (a fine Membrane diilended acrofs it,) arid 
thefe Particles in performing their Vibrations 
impinge upon the Tympanum, which agitates 
the Air included within it, and that being put 
into a like tremulous Motion, afFeds the au- 
ditory Nerye, and thus excites in the Mind 
the Senfation or Idea of what we qaW,. Sound. 

Now fince the repulfive Force of each 
Particle of Air is equally diflFufed around it 
every Way, it follows, that when any one ap- 
proaches a Number of others, it not only re- 
pels thofe which lie before it, in a right Line 5 
but all the reft, laterally according to their re- 
fpedive Situations 5 that is, it makes them re- 
cede every Way from it fclf, as from a Cen- 
ter : and this being true of every Particle, it 
follows, that the aforefaid Tremors will be 
propagated from the founding Body in all Di- 
redions, as from a Center: and farther, if 
they are confined for fomc Time from (pread- 
ing thcmfclves by pafling through a Tube or 
the like, will when they have paflcd through 
it, fprcad thcmfelves from the Erid in cVery 
Dircdion. In like Manner, thofe which paft 
through aii Hole in an Obftaclc they meet 


Diflert. I. Of Sound. 49 

With iti their Way, \^'iii iafterwards fprcad 
thcmreives from thence, as if that was the 
Place where they began; fo that the Sound 
which paflfes through an Hole in a Wall or 
the like* is heard in any Situation whatever*, 
that is not at too great a Diftance from it. 
Something analogous to this we may oblcrvc 
in the Motion of Waves upon the Surface of 
a Fluid, which are propagated equally through 
all Parts of the Surface in a Circle, though 
occafioncd not by a circular, but reciprocal 
Motion and Agitation of the Finger in a 
flraight Line. 

Since the repulfive Force with which the 
Particles of Air ad upon each other, is reci« 
procally as their Diftances, (Chap, 3.§. lo.) 
it follows that when any Particle is removed 
out of its Place by the Tremors of a found- 
ing Body, or the Vibrations of thofe which 
are contiguous to it, it will be driven back 
again by the repulfive Force of thofe towards 
which it is impelled, with a Velocity propor- 
tionable to the Diftance from its proper Place, 
becaufc the Velocity will be as the repelling 
Force. The Confequence of this is, that, lee 
the Diftance be great or fmall, it will return 
to its Place in the fame Time 5 (for the Time 
a Body takes up in moving from Place to Place 
will always be the fame, fo long as the Ve- 
locity it moves with is proportionable to the 
Diftance between the Places.) The Time there- 

G fore 

50 Of Sound Part IL 

fort in which each Vibration of fhe Air is 
performed, depends on the Degree of Repul- 
iion in its Particles, and fo long as that is not 
altered, will be (he fame at all Diftances' 
from the tremulous Body 5 confequently, as 
the Motion of Sound is owing to th6 fuc- 
ccflive Propagation of the Tremors of a found* 
ing Body through the A if, and as th^t Propa- 
gation depends on the Time each TrcftWr \i 
performed in, it follow*, that the V<l0cit/ 
of Sound varies as the Elafticity of the Air, 
but continues the fame at all Diftance^ from- 
Che founding Body. 

And as the Velocity, with which Sound is 
propagated, depends on the Elafticity of the 
Air, (b it docs alfo on its Denfity 5 for when^ 
the Denfity of the Air is augmented, while; 
its Elafticity remains the fame *, a greater Num- 

* Perhaps it will not appear to every one, how the Dcnfitjr 
of the Air can be augmented without a proportional Pncreale 
of its Elafticity, becaufe cs.terii parihusy the nearer the Parti- 
cles approach each other, the ftrbnger is the Adlion of their 
rcpulfive Force. 

But it is to be confidered, that when the Air becomes, cold- 
er, its Elafticity is diminifhcd, and then the Particles are 
brought clofer together by the Preflure of the Atmofph'erc, 
till they acquire an Elafticity equal to what they had before, 
'viz, fuch as anfwers to the Preflure they fuftain (Chap. 3. J. 12 ) 
From hence we may infer, that the Propagation of Sound if 
llovyer in Winter tlun in Summer, when the Mercury in the 
Barometer is at the fame Height ; for the Preflure of the Air 
being the fame, its Elafticity which depends upon it, is fo too ; 
but the Air is denfer by Reafon of the Cald* Mid therefore 
its Vibrations flower. 


Diflert i. Of Sound* 51 

bcr of Particles will move forwards and back* 
wards in each Vibration 5 now fince we fup. 
pofe the Caufe by which they put each other 
into Motion, {^iz,. their Elafticity,) the fame, 
they will each receive a lefs Degree of Ve- 
locity} and fo the Vibrations will be per- 
formed in a longer Time, whence the Succef- 
fion of them will be flower and the Progrcfs 
of the Sound proportionably retarded *• 

Whereas the undulatory Motion of the 
Air. which conftitutes Sound, is propagated in 
all Dircftions from the founding Body, it will 
frequently happen, that the Air in perform- 
ing its Vibrations will impinge againft vari- 
ous Objeds, which will refled it back^ and 

• The Method of detcrminine the Velocity with which 
Sound is propagated, is (by the help pf a fliort Pendulum) to 
cftimate the Time which paflcs between feeing the Fire of a Gun 
at a Diftance, and hearing the Report. Its great Velocity makes 
it difficult to be determined exadlly ; accordingly Authors differ 
much in their Accounts. The moft accurate Obfcrvcrs Dr. 
Ualley and Dr. Durham have found it to be about one Thou- 
jand one Hundred and Forty two Y^^^ which is almoft a Quarter 
of a Mile in a Second. 

The ufual Experiments to prove that the Air is necelfary for 
the Propagation of $pund, are fuch as thefe. A fmall Bell 1^* 
ing put into the Receiver of the Air- Pump may be heard at a 
coniiderable Diftance before the Air is cxhaufted out of it, but 
when the Air is much rarified by exhaufting, can fcarcely be 
heard ap all. When the Air is condenfed, the Sound is aug- 
malted in Proportion to the Condenfation. Thefe Experiments 
do not only fuccecd in forced Rarefactions and Condeniations, 
but in fuch alfo as are Natural ; Sound being be much 
weaker on the Tods of high Mountains, where the Air is lefs 
condenfcd by the Weight of the incumbent Atmofphere» than in 
the Valleys below. 

52 Of Sound Part IL 

fo caufc new Vibrations the contrary Way; 
now if the Objcfts are fo fituatcd, as to rc- 
flcd a fufficient Number of Vibrations back 
{viz,, fuch as proceed different Ways) to the 
fame Place, the Sound will be there repeated, 
and is called an ^cho"^. And the greater the 
Diftance of the Objeds is, the longer will be 
the Time, before the Repetition is heard* 
Therefore when the Spund ija its Progrefs 
meets with Objeds at different Diftances fuf- 
ficient to produce an Echo, the Sound will 
be repeated feveral Times fuccelfively, accord- 
ing to the different Diftances of thofe Dbjcfts 
from the founding Body ; and diis makes what 
is called a repeated Echo. 

If the Vibrations of the tremulous Body 
are propagated through a long Tube, they will 
be continually reverberated from the Sides of 
the Tube into its Axis, and by that means 
prevented from fprcading, till they get out of 
it ; whereby they will be exceedingly ip. 
creafed, and the Sound rendered much loud* 
cr than it would ptherwife be f • 

• In Wwdftock Park in Oxfordjhirey there is an Echo which 
repeats diftindly feventccn Syllables, by Day and twenty by 
Kight The Reafon why it repeats more Syllables by Night 
than by Day, is becaufe the Air being colder at that Time, is 
more denfc ; and therefore the Return of the Vibrations is flower. 
Which gives Time for the Repetition of more Syllables. Sec PMx^ 
Natural Hiftory of Oxfordjbire. 

f This is the Cafe in tb; Stentorofhonic Tube or Speaking 


Diflert. T. Of Sound 53 

The Difference of MuficalToncs depends 
on the different Number of Vibrations com- 
municated to the Air in a given Time by the 
Tremors of the founding Body; and the 
quicker the SuccefHon of the Vibrations is, 
the acuter is the Tone, and e contra. 

A mufical Chord performs all its Vibrations, 
whether great or imall in the fame Time^ 
For if a String is flretchcd between two Pins, 
and a Force is applied to the middle Points 
to draw it out of its reftilineal Situations it 
is found by £xperiment> that the Diftance (if 
it be fmall) to which it is drawn, is as the 
Force applied 5 confequently the Velocity, 
with which it returns when left to it fclf, will 
be as the Space it has to move over $ it will 
therefore perform all its Vibrations in the fame 
Time : this is the Reafon, why the fame Chord 


Trumpet. Sec Kircber de Re MuficS. Lib. 9. Par. 4. Od$ 
Philof. Natur. Princip. p. 293. 

Upon this Principle it is, that Sound is conveyed from one 
Side of a Whifpering Gallery to the oppofite one, without be- 
ing perceived 1^ thofe who Hand in the Middle. The Form of 
a Whifpering Gallery is that of a Segment of a Sphere, or the 
like arched Figure ; and the Progrefs of the Sound through it majr 
be illuftrated in the following Manner. ^ 

Let JBC (Fig, 1.4.^ reprefent the Segment of a Sphere^ 
and fuppofe a low Voice uttered at />, the Vibrations expand- 
ing themfelves every Way, fome will Impinge upon the Points 
Bj Ef &c, from thence be refledled to the Points F, from thence 
to G, and fo on, till they all meet in C» and by their Union 
there caufe a much Wronger Sound, than In any other Part of 
the Segment Wl^atcY^r, even at D the Point from whence 
it^Qy came. , 


5& ^f ^^^ P^^ ^^ 

however firucjc produces the fame Note. It 
is alfo found by Experimenty that when Strings 
of equal Diameters, but different Lengths, 
are equally ftretched, the longer they are, fp 
much the lefs Weights will draw them from 
their rcdilineal Situation to the fameDiftance} 
the Forces therefore by which they return 
arc lefs, and the Times of their Vibrations 

When two Chords perform their Vibra* 
tions in equal Times, the Tone produced is 
called an Unifon. If one performs two, while 
the other one, 'tis an oilm)e. If one three, 
while the other two 5 'tis a Ttfth. If one 
three, while the other fours '^^s called a 
fourth &c. 

To make an Unifon Sound, it is not ne- 
ceflfary, that the Vibrations of the two Strings 
fhould actually concur, but only that they 
fliould be performed in equal Times 5 fo that 
they would always concur, if they began at 
the fame Inftant. For the Ear perceives not 
the fingle Vibrations diflindly, but only finds 
that Difference which proceeds from the In- 
tervals of Time, that pafs between them*. 

• Upon thefe Principles wc may account for that remarkable 
Phaenomenon in Mufic, that an intenfe Sound being raifed, either 
with the Voice or a fonorous Body, another fonorous Body near 
It and in Unifon witli it, will thereby be made to found. For the 
Vibrations of the Air, which correfpond to the Tremors of 
the firit founding Body, agreeing exadbly in Point of Time with 
thofe which arc capable of being given to the other Body at 


Diifert. I. Of Sound 55 

Uriifon with it ; wKcn, they have by their firft Tfflpulfe com- 
inunicated' a finall Degree of Motion to it, will, by confpiring 
with it as it moves forwards and backwards continually increafe' 
ifs Motion, till it becomes ftnfible. The contrary happens in 
Strings" which ar^ in DSfcord with each other; for in this Cafe, 
though the fiffl Vibration of one may give Motion to the other, 
yet their Vibrations not being pcrlbnned in equal Times the 
ie'corid will come unfeajonahlj^ /. e. when the other is moving 
the contrary Way, and obftruCl its Morion*. It is farther ob-' 
lervable that in two Strings, oxit of which vibrates twice, while 
the other once ; if the firil be founded, thi tvj^o extreams of the 
o~ther will each found an Unifon with it, while the middle 
Point remain^ at Reft. So if one vibrates rhric6, while the other' 
Once, the laft will be divided into three Parts, ea'ch' of v^hich 
will found an Unifon with it, and the two Points between thofe 
farts" will remain at Rcf!. For other\<'ife that w^hich vibrates* 
twice, while the other once, rouft necelfarijy interfere with it at 
iytry fecohd Vibration j and that which vibrates, thric^ while 
the' other oricei would ihterfere Vvith it at every third ; ib thalf 
It would not be' put into a fufficient Motion to produce a Sound* 
But when it is divided by the quiefeenf Poincs, it becomes fo* 
many Strings at Unifon with the former, each of which cafily 
receives its Vibrations from thence. 

From hence likewife it is, that if we take two or three Drink- 
ing Glaifes and put fome Water or other Fluid into each of 
them and place thcrii nesh* to each otheri takifig Care to fill 
them, to fuch Heights, that (when ftruck) their Tories fhall be in 
Unifon ; arfd then if we Hide the Finger along the Brim of one 
of the GlaiTcs preffing pretty ftrongly upon it, (which will caufe 
it to found) we fhall fee the Surftice of the Fluids in the other 
GlalTes begin to tremble \ which fhews that the Vibrations of 
the £rft Glais caufe the like in the other at y nifon with it, though 
not perhaps in a Degree fufficient to produce a Sound llrong c- 
nough to be heard diflind^ly from the former. 

Thus it is that fome Perfons are able to break a Drinking Glafs 
by a Tone of* their Voice at Unifon with it. They firft try the 
Tone of the Glafs by ftriking it, then applying their Mouth 
near to the Brim of it, found the fame Note with their Voice ; 
this fets the Glafs a trembling ; they then- continually raife their 
Voice, founding ftill the fame Note ; this cncreafes the Tremors 
of the Glafsi Which by that Means (if it is not too ftrong) ia 
broke in Peices. 

The Effect of Mufic upon Perfons bit with the Tarantula^ (if 
the Accounts we have of it from aWoad may be credited) is very 


55 Of Sound Part IL 

furprifing. A Pcrfbn bit with the tarantula after fomc Timtf 
loles both Scnfe im] Mocioa, ind dies irdeilitute of Help. The 
moil effcftual Remedy is Mujic. TheMufician trict Variety of 
Airs, till he hits upon one that aJTeCU the Patient, who upon thit 
begins to move by Degrees, and keepi Time with his Fingers, 
Anns and Legs, afterwards with his whole Body i he then 
raifcs himfelf up, begins to dsnce, and increases in Aaivity 
every Moment ; till after five or fix Hours, being very much Ei- 
tigucd, he is put to Bed to recover Strength. The next Day the 
lanie Air brings him out of Bed for a new Dance. Which Rx- 
ercifc lieing thus continued, the Diftempcr is abated in the Spacs 
of four or five Days, the Effccls of the Bite being in Ibme 
Meafure carried off by Sweat, and the Patient begins then to re- 
cover his Senfe and Knowledge by Jittle and little. 

The Reafon why the Patient is thus affected by the Mujie, it 
becaufe the Nerves of his Body are fo difpofod in that Diltem- 
~'r, as e^tly to be agitated by the Vibratiotu which are occa- 

med by the principle and ftronger Noi«s of what is played. 

See on the Subjeft of this DilTertition, Philofoph. Tranlaa. 
N". 134. 243. 302. 313. 319. 337. Hill, de 1' Acad. 170*. 
1708. Grrtv's Cofmolog Sacr. Book I. Chap. j. Mtad upoa 
Poifons p. j9. KeiPi Anatomy p. 214. 



Difleit. 2. Of Capillary Tubes* 5 7 


Of Capillary Tubei. 

BY a CafilUry 7i/^f is generally underftood 
a Glafs Pipe, the Diameter of whofe Bore 
is at mod but about one tenth of an Inch i 
though any Tube whofe Cavity does not ex- 
ceed that Magnitude^ may be fo called. 

The Phasnomena of Capillary Tubes be* 
ing fuch as contradiA a known Law in Hydros 
flaticsy viz. that a Fluid rifts in a Tube to the 
fame Height with the Level of its Source^*, and 
likewife of Affinity with the Afcent of the 
Sap through the Stems of Plants for the 
Nourifliment of their Fruit, and with divers o* 
ther Operations of Nature : it has been thought 
of no fmall Moment in Philofophy to find 
out and eftablifh their true Caufe ; which af- 
ter numerous Experiments and feveral Con- 
jectures about ic> is found to be no other than 
the Attradion of Cohefion, by which fmall 
Particles of Matter mutually run together and 
fomi larger Bodies f. I fhall lay down the fe- 

• See Chap. I. §. 9. Cafe 4. in the Not^s. 

f See Haukshee*s and Power's lExperimcnts. Mujffchenhroeck 
4^Edit. Philofoph. Tranfaa. N°. 355. Mem. & 1' Acad. 
1 70^ , 1714, 1 7 22, 17 24. With others r^fcr'd to in Quaeftiontfs 

H Ycral 


58 Of Capillary "Tubes. Part It 

Vcral Phxnomcna, as fo many Matters of Fad, 
and fbbjoin to each a Solution from that 
Caufc. In order to which, it may nor be 
improper. to premife the following ConHdera- 
tion by way of Lenmia. 

Let us fuppofe the Vcflcl ABCD (Fig. 
IS.) filled with a Fluid to the Height LM, 
and let it be conceived as divided into the e- 
qual Portions EFGa GHIK, IKLM, &c. 
farther, let it be fuppofed, that each Par- 
ticle of Matter in the inner Surface of the 
Veflcl, has a Sphere of Attraftion, whofc 
Semidiameter is equal to the Thicknefs of 
three of thofe Portions 5 that is to fay, that 
the Attraction of the Particle M reaches up- 
wards as far as F, and downwards as far as S ; 
and that of the Particle O upwards as far as 
H and downwards as far as U ^ and To of all 
the reft quite round the Tube. From hence 
it will follow that every Particle of the inner 
Surface of the Vcflcl, which lies between EF 
and RS conlpires in endeavouring to raife the 
Fluid towards AB the Top of the VeflTel, and 
that the Fluid is not afFcftcd by any other : for 
Inftance, the Particle S, and all below it, will at- 
trad downwards three Strata of the Fluid (fuch 
as are contained in three equal Divifions* of the 
^Veflcl) from above, and as many upwards 
from below, and therefore will have no Effcft 
at all in raidng or depre fling the Fluid : But 
the Particle (^ will attract only two Strata 


Diflert, 2. Of Capillary Tubes • 59 

downward$> becaufe there are no more above 
it| and three upwards, and therefore will in 
feme Mcafurc tend to raifc the Fluid 5 fothe 
Particle O will attraft but one downwards 
and three up wards » the Particle M, none down- 
wards* and three upwards \ the Particle K two 
upwards, and H only one : all which tnay clearly 
be feen by their Situations in the Figure with 
Rcfpe^ to the Surface of the Fluid, There- 
fore in every Veflcl, where there is a mutual 
Attradipn between the Fluid it contains and 
the Particles of which it is conipofed, there 
will Ifk a certain Number of Particles difpofed 
around it in Form of a broad Periphery or 
Zone Ss reprefented by AB Tig. 16, half of 
which lies above the Surface of the Fluid and 
half below it, that will tend to make it rife to- 
wards the Top*. This being underftood, the 
' following Phasnoqiena will not be difficult* 

* I have been tjic more particular in explaining this Lem- 
ma^ becauie it is not a bare Periphery of no Breadth, to 
which the Afcent of the Fluid is oiling, but a Zone or Cingulum 
of Particles diflended equally JA Breadth both ways from the 
Sur&ce of the Fluid ; and becaufe it is upon the Breadth of this, 
that fome of the following Solutions depend. As to the 
Thickncfj of it, that undoubtedly is equal to the Scmidiameter 
of the Sphere of Attraction in the Particles of the Veffel ; and 
therefore VefTcls whofe Sides are of difFerent Thickneffes (provided 
thofe Thickneffes be lefs than that Scmidiameter) muft have diffe- 
rait Effedts upon the fame Fluid, thqugh no one has as yet been 
fo accurate as to obferve it. The Rcafon why a Fluid will not 
riie in a large Veilel, as well as in one that is Capillary, is be- 
, caufe the Attrat^ion of its Particles does not reach far enough into 
the Middle of the Ve^el; and therefore it only riies abott( 

Ha th« 

6o Of Capillary Tubes. Part It 

I. Let there be two Capillary Tubes AB 
and CD (fig. 17.) open at both Ends, and 
having their lower Orifices A and C im*- 
merged below the Surface of the Water con- 
tained in the Veflel FGHI: the Water will 
immediately rife up in each Tube above the 
Surface of that in the Veflel, beginning with 
a fwift Motion, which will gradually decrcafe, 
till as much Water has entered the Tubes, as 
they are able to raife : and the Heights to 
which the Water will rife in them, will be 
reciprocally as their Diameters. 

That the Water ought to rife in both 
Tubes is an immediate Confequence of the 
foregoing Lemma 5 becaufe the Column of Wa- 
ter within the Tube is rendered lighter than 
an equal Column on the outfidc, as being at- 
traftcd upwards by a Portion of the interior 
Surface of the Veflel 5 and therefore will rife 
till it becomes as much longer than the exter- 
nal ones as it is made lighter, that the j^qui^ 
librium which was deftroyed by the Attraftion 
of the Tube, may be reftored by the Weight of 
the Colunin, The B^eafon that the Velocity with 
which it rifes, ought conftantly to decreafe, 
. is becaufe th? heavier the Column is, the lefs 
is the EffeftpftheAttraaion, which is always 
the fame in a Tube of the fame Diameter. 

' /the Sides, Handing higher there than in the jniddle : as may be 
feen in a Drinking Glafs, when a Quantity of Water is put into 
- |t^ fomcwhat leis thaq is fufficient to Jill it. 


Pwt.II. Hlte.ln.i^.fo, 











Dii]fert. 2. Of Capillary Hibes. 6i 

And the Heights' to which the Water rifcs ia 
them, will be reciprocalty as their Diameters; 
for then the Quantities railed Ml^ill be dircdly 
as the Diameters "^5 but the Peripheries that 
raifc them, (being always of the fame Breadth 
and having their Lengths equal to the Circum* 
ferences of the Tubes») are as thofe Diameters s 
the Quantities of Water therefore being in the 
fame Ratio, are as the Peripheries, i.e. as the 
Caufes by which they are raifcd. 

II. I F the Tubes before they are immerged 
in the Water, are filled to greater Heights, 
than thofe to which it would naturally rile in 
them, and then have their lower Orifices im- 
merged in Water, the Water will fubifide till 
itftands in each at the fame Height to whidi 
it would have rifcn ; but if they are held ia 
a perpendicular Pofition without being im- 
merged, the Water will not fubfide in the 
Tubes quite fo fan 

The Reafon why the Water in the Tube 
when its lower Orifice is immerged, fubftdes 
to the fame Height it would have rifcn to, had 

• The Heights to which the Water'rifes, being in a recipro- 
pl Ratio of the Diameters ; and the Contents of Cylindrical 
Tubes being in a dire A Ratio of their Heights, and of the 
Squares of their Diameters ; the Quantities of Water raifed in 
this Cafe will be in a reciprocal Ratio of the Diameters, and 
a diredl one of the Squares of the fame. Now thefe two 
Ratio's being compounded together, give the dire6t one o£ 
the Diameters tbcmfelves ; becaufe the fimple reciprocal j?.a- 
tio deftroys one of thofe, which arc 9ontaincd in the direft 
fnc of the Squares. 


62 Of Capillary Tutes. Part 11. 

the Tube been immergcd vhen empty, is 
becaufe the Column is fufpended in one Calc 
by the fame Caufe, by which it is raifed in 
the other $ but when the Tube full of Water 
is held erei^, without being immerged, Jt will 
•not fubfide qmtc fo far, becaufe the lower 
End of the Tube which the Water leaves bo- 
hind it 9s \x, drops out* attrads it the coa- 
ttary Wayi fo that the Column in this Cale 
is fufpended ,not; only by the inner Surface of 
;fhe Tube at the Top, but alfo by its lower 
£nds and therefore a greater Quantity of 
. Water \% fufpended than in the former Cafe» 

III. I F a Tube having its lower Orifice im- 
mergcd in Wafer, be held obliquely, it will 

.raife the Water to the fame perpendicular 
Height, as ^hcn held ere£t. 

For fiucp Fluids prefs according to their 
perpendicular Heights, the Weight of the Co- 
lumn raifed will not be proporticHiable to the 
attra£tive Force of theTjibp, till it has arrived 
at the fame perpendicular Height, to which it 
would have rofc* if held ered. 

IV. If a Tube, when the Water is ;i[ca 
into it to its wonted Height, is laid in an 
Horizontal Situation, the Water will move 
towards the Middle of the Tube, leaving the 
End which was immerfed a little behind. 

The Solution of this Phaenomenon de- 
pends on what was obferved in the Lemma 
about the Breadth of the attrafting Periphery, 


DilTert. 2. Of Capillary Tubes 63 

and ks being equally fituated on each Side 
the Surface of the Water 5 for from thence 
it follows, that if the Water fhould not run 
from the full End of the Tube, after it \% 
laid in an Horizontal Situation, but remain 
contiguous to it, that End of the Column of 
Water would be attracted only by fuch a Por- 
tion of a Periphery as lies within the Surface 
at that End $ becaufe the End of the Tube co* 
inciding with the Surface, the other Half of 
the Periphery is wanting. Whereas at the other 
End of the Column there is a Periphery whofc 
Breadth is intire, which overpowering the o^ 
ther, caufes the Water to move towards the 
Middle of the Tube, till the Breadth of the 
Periphery at each End of the Tube is the fame, 
after which the Water being attracted equally- 
each way, remains at Reft^ 

V. Let there be a Tube {¥ig. 18 J con- 
fifting of two Parts DR and RCK, of diffe- 
rent Diameters, it follows from what has been 
faid^ that DR the fmaller Part of the Tube 
is able to raife Water higher than the other : 
let then the Height to which the larger would 
raife it be TF, and that to which it would 
rife in the leflTcr (was it continued down to 
the Surface of the Fluid) be XL. If this com- 
pound Tube be filled with Water and the 
larger Orifice CK be immcrfed in the fame 
Fluid, the Surface of the Water} will fink no 
farther than XL, the Height to which the 


64 Of Capillary Tubts. Part If* 

IclTer Part of the Tube would have raifed 

But if the Tube be inverted as in Fig. 19* 
and the imaller Orifice XL be immerfcd^ the 
Water will runout till the Surface falls toTF, 
the Height to which the larger Part of the 
Tube would have raifed it. The Size of the 
lower Part making no Alteration in the 
Height, at which the Fluid is fufpcnded in 
cither Cafe. 

In order to account for thefe Phsenomena^ 
it niuLl be confidered, that when a Body is 
fo difpoled, that its different Parts fhall move 
with different Degrees of Velocity, the great- 
er Proportion the Velocity of that Part to 
which a moving Power is applied, bears to 
that of the reft, fo much the more effedlual 
is the Power in moving that Body ; or that 
the fame Power applied to different Parts, will 
be equivalent in Effeft to different Powers 
applied to the fame Part : as is the known 
Cafe of the Ltver^ and all the other Mechanu 
cd Powers. 

N o w let us conceive the Tube D R. (Fig. 
i8.> continued down to HI, and let it be 
fuppofed at prefcnt that the Fluids contained 
in the Tube XLHl and the compound one 
XLKC, are not fufpended by the Periphery 
at L, but that they prcfs upon their refpedive 
Bafes HI and CK. Let it farther be fuppofed, 
that thefe Bafes are each of them moveable* 


Diflert. 2. Of Capillary luhs. 65 

and that they are raifed up or let down with e« 
qual Velocities; then will the Velocity with 
which XL the uppcrmoft Stratum of the Fluid 
XLCK moves> exceed that of the fame Stratum^ 
coniidered as the uppcrmoft ofthe Fluid in the 
Tube XLHI, as much as the Tube RCK 
is wider than DR (by the Lemma Chap. i. 
^. p.) that is, as much as the Space M N K C 
exceeds XLIH ; confequently by the foregoing 
Obfervation, the Effed of the at trading Pe* 
riphery XL, as it ads upon the Fluid con* 
tained in the VeiTel XLCK« exceeds its EfFcd^ 
as it a&s upon that in XLHI, in the fame 
Proportion. Since therefore it is able (e:c 
Hjfoih.) to fuftain the Weight of the Fluid 
XlHI by its natural Power, it is able under 
this Mechanical AdvantagCt to fuftain the 
Weight of as much, as would fill the Space 
MNKC : but the Preflure ofthe Fluid XLCK 
is equal to that Weight, as having the lame 
Bafc and an equal Height (Chap. i. §.9.) its 
Preflure therefore, or the Tendency it has to 
dcfcend in the Tube, is equivalent to the . 
Power of the att rafting Periphery XL, for 
which Reafon it ought to be fufpended by it. 
Again the Height (Fig. 1 9 >) at which 
the attrafting Periphery in the larger Part of 
the Tube is able to fuftain the Fluid is no 
greater than N F, that to which it would have 
raifed it, had tiiC Tube been continued dowa 
to MN. For here the Power of the at- 

I traftin^^ 

66 Of Capillary Tuhes.^ Part tt 

trailing Periphery a&s under a like Mech^ticM 
Difadvantage ; and is thereby diminidied in 
Proportion to the Capacity of the Tube T F N M 
to that of HIXL5 bccaufe if the Bafes of 
thcfe Tubes arc fuppofed to be moved with 
equal Velocities, tlie Rife or Fall of the Sur- 
face of the Fluid T F X L would be fo much 
icfs than that of TFMN. And whereas 
the attrafting Periphery TF is able by its na- 
tural Power to fufpcnd the Fluid only to the 
Height NF in theTubcTFMN; it is in this 
Cafe able to fuftain no greater Preflure than 
what is equal to the Weight of the Fluid in 
the Space HIXL: but the Preflfurc of the 
Fluid TFXL which has equal Height and the 
fame Bafe with it, is ^qual to that Weight 5 
and therefore is a juft Mquipondium to the at- 
trafting Power- 

VI. From hence we may clearly fee the 
Reafon, why a fmal I Quantity of Water put in- 
to a Capillary Tube, which is of a Conical 
Form and laid in an Horizontal Situation, 
will run towards the narrower End. For let 
AB (Fig. zo.) be the Tube, CD a Column 
of Water contained within it 5 when the Fluid 
moves, the Velocity of the End D will be to 
that of the End C reciprocally as the Cavity 
of the Tube at D, to that at C (by the Lem- 
ma Chap. i. §. 9.) that is, reciprocally as the 
Square of the Diameter at D, to the Square 




Diflert. 2. Of Capillary Tubes. 67 

ctf the Diameter at C * 5 but the attrafting Pe- 
riphery at D is to that at C, in the fimplc Ra* 
tio of the Diameter at D, to the Diameter at 
C. Now fince the EfFeft of the Attraftion 
depends as much upon the Velocity of that 
Part of the Fluid where it afts, as upon its 
Natural Force, ^its Effcd: at D will be greater 
than at C J fot though the Attradion at D 
be really left itt its fcTf than at C, yet its Lofs 
of Force upon that Account* is more thaii 
£ompeii(ated by the greater Velocity of the 
Fluid in that Part j the Fluid will therefore 
move towards B. 

VII. From hence I ike wife it follows, that 
ifa VdTel' as ABC (reprcfented rig. zi) of 
any Forni whatever, Kavc its upper Part drawQ 
oiit into a^ Capillary Tube as B 5 and if this 
Vcffel is filled Vi^ith Water, and have its lower 
Orifice placed on FGthe Surface of the fame 
Fluid 5 then the Water will; remain fufpended id 
theVeffel, proVidcd^tlie Capillary at the Top 
bcfmair enoiigh, (was' it cohtinued down to 
the Bottom) to raife ttic Fluid to the Height 
B. Becaufe by the foregoing Propofitioh' the 
lower Part of the Tube makes no Alteration 
in the Height at which the Capillary B is able 
to fuftain the Fluid. 

VIIL And if the fame Veflfel be filled only 
to the Height DE (fig. 21.) and a Drop of 

I » Watcf 

6S Of Capillary Tubes. Part IL 

Water be put into the Capillary at B, (the in* 
termcdiace Part BD£ being full of Air) the 
Water will continue fufpended at the Height 

Fon although the Fluid ACD£ is not in 
Contaft with the Drop of Water in the Ca- 
pillary Tube* and therefore not immediately 
iupported by its yet the PrefTure of the Atmo^ 
fphere upon the Surface FG, and againft the 
upper Part of the Drop in the Capillary B 
keeps the Fluid AD£ C^ and the Drop and the 
intermediate Air from feparating. )uft as in 
the former Cafe the Attradion of Coheiioa 
in the Particles of the Water prevented a 
Separation between that in the Veflfel and 
that in the Capillary. Confequently as the 
W^tcr in the Capillary was able in the former 
Cafe to fuftain as much Fluid as the Veflel 
could contain, it is now fufficient to fuftaia 
the Fluid A DEC* 

IX. Let there be a Capillary Siphon^ as 
that reprefented lig. 23, 24 or 25. and let £F 
be the Height, to which Water might be raifed 
by a Periphery equal to that at A Now iince^ (as 

• This happens quite othcrwlfe in Vacuo, bccaufc the Pref- 
lure of the Air, which as it were connedb the Drop with the 
Water JDEd being wanting,, it immediately fejls for Want 
of a Support. Whereas|the. former Phaenomenon equally fucceeds 
in Vacuo ; which Ihews that the Parts of the Fluid in the Veffcl 
axe conne^ed with each other« and with that in the Capillary 
by their own mutual Attra6li6n of -Coheiion» there being 
ikpthing elfc whereby they cam be fupported« 





Dlfiert- 2. Of Capillary Tubes. 69 

Hifas obrerv$d§. 2.) the lower End of aXube whea 
it is not immergcd) caufes a longer Columa 
to be fafp^jided than otherwifc would bei 
tb^t is, it lupports a fhort Column beiides 
that which is fuftaincd by the atrading Peri* 
phery \ let H I be the Height of fuch a Co- 
lumn as might be fufpended by the £nd C : 
then if any of thofe Tubes are filled with 
Water, and held as in the Figure (neither End 
being immcrged) the Fluid will run out of 
the Tube at Ci if C D the Difference of the 
Legs exceeds £F and HI added together, 
other wife not. 

F on the Column AB is a Countcrpoife 
to B D, being of the fame perpendicular Height \ 
and therefore it is only the Weight of the 
Column CD which determines the Fluid to 
move$ unlefs that Weight therefore exceeds 
the Force of the attrading Periphery at A 
(which the Fluid AB muft leave in riftng up 
the Tube) and alfo what may be fupported 
by the End C, that is, (ex Hyfoth.) two Co- 
lumns whofe Heights are £ F and H I, it (tan« 
pot run out at C \ otherwife it will, as bc-^ 
iug deftitute of a fufficieht Support. 

X. I F the End A is immcrged in Water (fop- 
pofing the T^ibe full as before), it will ma 
out, though C D the Difference of the Legs» 
pnly exceeds H I. For then the Attra£tion at 
4 ceaf^s^ and thcr? i$ nothing to fupport the 


JO Of Capillary 7u3es. P&rt Hi 

Column CD, but the Power the End C hai 
to prevent Drops from falling off it. 

XL Again if the End C is immerged in' 
Water» (and the other not) it will run oik ai 
A> if C D exceeds E F, otherwife not, 

Fo R in this Cafe, there is nothing to fup* 
port the Column C D, but the- actr^ing Pe- 
riphery at A, whole Power is fuppofed able 
to raife a Column as E F« and no more. 

XiL And if both End j arc.immeried (the 
Tube being fuppofed full as be^re) the Wa-^ 
ter will run out at the lower> which ever it is. 
For then the Attradion of both Ends ceafes ; 
and the longer Column over-Balancing the 
(horter^ the Fluid is determined thcfreby to run 
out at the lower End. 

'Xillf If either of the Tubes f//^. 2) or 24/ 
jtfe fmall enough to raifc the Water frbnl A to 
Bf and if the Orifice A is immerged, the Fluid 
will rife to B, pafling on ta C, where it will 
ran out or be fufpend^d according to thefore^ 
going Cafes : but if the Periphery at G (Fig. 
ZiSJ is fuch as would not fupport the Fluid 
highctthan AM^ it will flop, when it comes 
at G. and only the Part ABG will be filled 
with it. 

For that Fluid which has pafled B aflifts 
by its Weight the attraftirig Periphery in rai- 
fing the Column A B, and therefore runs down; 
to^C. But if when it comes to G, the Peri- 
phery' there is nor able to fupport more than 


Diilert. 2. 0/ Capillary \tubes 71 

A M the DifFercnce of the Legs A B and B G> 
the Fluid muft necefiarily fiop there ; fince B G 
is no more than a Counterpoife to M B, and 
A M is fuppofed to be as much as the Periphe- 
ry at G can fuftain. 

XIV. Tho' a Capillary Tube be fliorter than 
the Height to which its attrafting Periphery \% 
able to raifc a Fluid, v. g. tho' the Tube A B 
(Tig. 26.) be finall enough (was it of fufficicnt 
Length) to raife Water as high as C 5 yet when 
the End A is immerged the Fluid will not run 
out at B, but only be fufpended at that 

For when the Fluid is rlfcn as high as B^ 
it has then no more Periphery to attrad it any 
farthers and if it was forced up a little higher. 
It would be attracted back again by the 
End *. 

XV. The Afcent of different Fluids in the 
fame Tube is various. Mujfcheniyoek has found 
that in a Tube in which Water will rife to 
the Height pf twenty fix Lines, Oyl of Worm- 
wood will rife but eighti:eii or nineteen, 
whereas Urine will rife thirty three or thirty 
four. The Reafon of which is becaufe fome 

• Hence we fee the Abfurdity of fuppofing that a Fhiid may 
be made owtinually to flow from a lower Place to an higher by 
a Capillary Tube as fuch j for whether the Tube be of fucn 
Form, as is reprefented Fig, 23, 24, 25, or 26. the Fluid will 
always flop when it comes at the higher End; becaufe the 
Attrad^ion is then in a Diredlion contrary to its Motion, and 
the Weight of the Fluid contained in DC the Difference of the 
Legs is likcwiic an Impediment to it« 


7^ Of Capillary Tuhs. Part II 

Fluids are attracted more flrongly by Gla(s 
than others are. Mercury exhibits Phxnomc- 
na juft the Reverie of the former j for the 
Height it rifcs to iti a Capillary Tube is Ie(s 
than that of the Level. This is becaufc the 
Particles of Mercury attrad each other more 
forcibly than they are attracted by thofc of 

f See jKrtVi Differt. Philofoph. Tnhf. N"; J63, 
Abcording to Mujckenirteti the Length Of the upper Part of 
a Tube, which is above the Height to which it h able to raife 
i Fluid, conduces fomcthing towards the Railing it; and there- 
fore in a longer Tube a fluid rifes hig^r chan in one of the lame 
Dimcniioas that is fiiorter; and that if a Tube, with fo much 
Fluid contained in it, as it is »blc to raife, be Uid in an Hori- 
zontal Situ^ition, the Fluid will run to the Middle of it. But 
cf this I have had no Experience : 'tii poflible that ingenious Pro 
IcfTor though very accurate in making Experiments, might hare- 
in be deceived. He acknowledges, (Experiment the fifteenth,} 
that it fometimes happens atherwife. 

Other Authors befidea thofe already referred to, (hat have 
treated on this Subjea, are Jay// Ezper. Phyf. Mech. Eip^ 0. 
Slurniiat CoUeg. Cur. Tentam. 8. Btrnoulli Gravit ^th. 
hoiike Microgr. Obferv. 6. tteutumlwi ConliAuat. Arcan NiC 
£|^lt. 131. Sinclairt Art. Gravit. ' 


Difiert. 3. T^e Origin of Fountains. 73 


Of the Origin of Fountains. 

MANY have been the Conjcftures oif 
Philofophcrs concerning the Origin of 
Fountains; and great Pains have been taken 
both by the Members of the Royal Society, 
and thofe of the Academy of Sciences at ?^ris^ 
in order to afcertain the true Caufe of it. It 
was Arijlotles Opinion, and held by nioft of 
the ancient Philofophers after hifn:; that the 
Air contained in the Caverns ^f the Earth, 
being condenfed by Cold neai>ifs Surface, was 
thereby changed into Watet 5 and that it made 
its Way through, where it could find a Pal- 
fagc. But we have no Experience ofany fuch 
Tranfmutation of Air into Water. 

Those who imagin, that Fountains owe 
their Origin to Waters brought from the Sea 
by fubterraneous Duds, give a tolerable Ac- 
count, how they lofc their Saltnefs by Perco- 
lation as they pafs through the Earth ; but they^ 
ijnd great Difficulty in explaining by what 
Power the Water rifes above the Level of the-. 
Sea, near to the Tops of Mountains, wlicrc 
Springs generally abound 5 it being contrary 

K t« 

74 ^^ Origin of Fountains. Part IL 

to the Laws of Hydroftatics^ that a Fluid (hould 
rife in a Tube above the Level of its Source. 
However they have found two Ways, where- 
by they endeavour to extricate themfelves from 
this Difficulty. The one is that oi Des Cartes^ 
who imagines that after the Water is become 
frcfti by Percolation, it is raifcd out of the 
Caverns of the Earth in Vapour towards its 
Surface ; where meeting with Rocks neu the 
Tops of Mountains in the Form of Arches or 
Vaults, it (licks to them, and runs down their 
Sides, (like Water in an Alembic) till if 
meets with proper Receptacles, from whicli 
it fupplics the Fountains. Now, this is a 
isiere Hypothejis without Foundation or Pro- 
bability ; for in the firft Place, wc know of 
no internal Heat of the Harth to caufe fuch 
an Evaporation ; or if that were allowed, yet 
'tis quite incredible, that there (hould be any 
Caverns fo fmooth, and void of Protubc- 
xanccs, as to anfwer the Ends of an Alembic, 
in collecting and condcnfing the Vapours to- 
gether, in every Place where Fountains a- 
arife. There arc others (as FArenius &c. ) 
who fuppofe, that the Water may rife thro"^ 
the Pores of the Earth, as through Capillary 
Tubes by Attraction 5 but hereby they (hew, 
that they are quite unacquainted with what 
relates to the Motion of a Fluid through fuch 
Tubes* For when a Capillary Tube opens in* 


Diflert. 3. T!he Origin of Fount aim. 75 

to a Cavity at its upper End, or grows larger 
and larger, fo as to ceafe to be Capillary at 
that End 5 the Water will not afcend through 
that Tube into the Cavity, or beyond where 
the Tube is Capillary 5 becaufe there the Eoroc 

I pf Attradion is exerted the contrary Way; 

I Nay, if the Cavity is continually fupplied with 
Water, it will be attraded into the Capillary 
Tube, and run down it, as through a FunncL 
if the lower End is immerged in the fame 
Fluid, as in this Cafe it is fuppofed to be *. 

It has been a generally received Opinion, 
and much jefpoufed by Marriotte (a diligent Ob- 
ferver of Nature,) that the Rife of Springs ij 

; owing to the Rains and melted Snow. Ac^ 

\ cording to him, the Rain Water which falls 
upon the Hills and Mountains, penetrating 
the Surface, meets with Clay or Rocks con^ 
tjguous to each other, along which it runs, 
without being able to penetrate them, till be* 
ing got to the Bottom of the Mountain, or 
to a confiderabic Diftance from the Top, it 
breaks out of the Ground and forms Springs. 
In order to examine this Opiniont Mr. 

^ Perraultj Dc U Hire and D. Sideleau endeavour- 
ed to make an Eftimate of the Quantity of 
Rain and Snow, that falls in the Space qf a 
Year, to fee whether it would be fufficicntto 
afford a Quantity of Water, equal to that 

• See the latter Part of the foregoing pifTcrtafion. 

K 2 which 

7 6 T'he Origin of Fountains. Part 11^ 

which is annually difchargcd into the Sea bf 
the Rivers. The Refult of whofc Inquiries 
was, that the Quantity of Rain and Snow 
which fell in a Year into a Cylindrical Veflel, 
would fill it (if lecurcd from evaporating) to 
the Height of about nineteen Inches. Which 
Quantity D. Sideleau * fhewed, was not fuffi- 
cient to fupply the Rivers 5 for that thofc of 
England^ Ireland and Spain difchargc a greater 
Quantity of Water annually, than the Raiq, 
according to that Expcrimeiit, is able to fup* 
ply. Bcfidcs which, another Obfervation was 
made by them at the fame Time, viz. that 
the Quantity of Water raifed in Vapour one 
Year with another, amounted to about Thirty 
two Inches, which is thirteen more than falls 
in Rain : a plain Indication, that the Watef 
of Fountains is not fupplied by Rains and melt- 
ed Snow. 

Thus, the true Caufe of the Origin of 
Fountains remained undifcovered, tijl Dr.fli*/- 
ley in making his Ccleftial Obfervations upon 
the Tops of the Mountains at St. Helena^ about 
eight Hundred Yards above the Level of the 
Sea, found that the Quantity of Vapour which 
fell there (even when the Sky was clear) was 
io great that it very much impeded his 01?- 
iervations, by covering Jiis GlafTes with Water 
every half Quarter of .an Hour j and upon that 

• Memoirs of the Royal Academy of Sciences for the Year 
1693. ^ • . 


Differt. 3. The Origin of Fountains. 77 

attempted to determine by Experiment the 
Quantity of Vapour, exhaled from the Surface 
of the Sea, as far as it arifes from Heat ; in 
prdcr to try, whether that might be a fuffi- 
cient Supply for the Water continually di& 
<:harged by Fountains. The Proccfs of his 
Experiment was as follows. He took a Veflcl 
of Water faltcd to the fame Degree with that 
of Sea Water, in which he placed a Thermo- 
meter, and by means of a Pan of Coals, 
brought the Water to the fame Degree of 
Heat, which is obferved to be that of the Air 
in our hottcft Summer : This done, he affix- 
ed the Veflcl of Water with the Thermome- 
ter in it, to one End of a Pair of Scales, and 
fxaftly counterpoifcd it with Weights on the 
other. Then at the End of two Hours he 
found by the Alteration made in the Weight 
of the Vcflel, that about a toth Part of an Inch 
pf the Depth of the Water, was gone off ia 
Vapour; and therefore in twelve Hours, one 
tenth of an Inch would have cone off. 
Now this accurate Obfervcr allows the Me- 
^diterranean Sea to be 40 Degrees long and 
4 broad (the broader Parts compenfating for 
fhe narrower) fo that its whole Surface is 
160 fquare Degrees, which according to the 
Experiment mufl; yield at leaft 5280 Millions 
of Tons. In which Account no Regard is 
Jpd to the Wind* and the Agitation of the 


7 8 77)e Origin of Fountains. Part IL 

Surface of the Sea \ both which undoubtedly 
promote the Evaporation. 

I T remained now to compare this Quantity 
of Water, with that which is daily conveyed 
into the fame Sea by the Rivers. The oniy 
way to do which, was to compare them with 
fonie known River ^ and accordingly he takes 
his Computation from the River Thames, and 
to avoid all Objections, he makes fuch Al^ 
lowances as are probably more than the 

The Mediterranean receives the following 
confiderable Rivers viz. the ibfrusy the Rhone, 
the Til?ur, the Pa, the Danube^ the Neifter^ the 
SoryfieneSy the Tanais and the Nile. Each of thele 
he fuppofes to bring down ten Times as much 
Water as the Thames, whereby he allows for 
fmaller Rivers, which fall into the fame Sea, 
The Thames then he finds by Menfurarion to 
difcharge about 20300000 Tons of Wafer a 
Day. If therefore the abovefaid nine Rivers 
yield ten Times as much Water as the Thames 
doth, it will follow, that all of them together 
yeild but 1827 Millions of Tons in a Day; 
which is but little more than one Third of what 
is proved to be raifed in Vapour out of the 
Mediterranean in the fame Time. We have 
therefore from hence a Source abundantly fuf- 
ficicnc for the Supply of Fountains. 

Now having found, that the Vapour ex- 
haled from the Sea, is a fufRcient Supply for 


piflert. 3. The Origin of Poufitains. yg 

the Fountains} he proceeds in the next Place 
to con/ider the Manner in which they aro 
raifed, and how they are condcnfcd into Wa- 
ter again, and conveyed to the Sources of 

I N order to this he coniiders, that if an 
Atom of Water was expanded into a Sh^ll 
€^r Bubble, fo as to be ten Times as big in 
Diameter as when it was Water, that Atom 
would become fpecifically lighter than Air 1 
^nd therefore would rife fo long as the Warmth 
which firll Ceparated it from the Surface oi 
the Water ftiould continue to diftend it to 
the fame Degrees 9nd confcquently that Va- 
pours may be raifed from the Surface of the 
Sea in that Manner, till they arrive at a cer-^ 
tain Height in the Atmofpherc, at which they 
find the Air of equal fpecific Gravity with 
thcmfcves. Here they will float, till being: 
condenfed by Cold, they become fpecifically 
heavier than the Air, and fall down in Dew 
or being driven by the Winds againft the Sides 
of the Mountains, (many of which far furpafs 
the ufual Height to which the Vapours ivould 
of thcmfelvcs afcend) are compelled by the 
Stream of the Air to mount up with it 
to the Tops of them: where being con-* 
dcnfed into Water they prefenily precipitate, 
and glecting down by the Crannies erf tlic 
Stone, Part of them enters into the Caverns 
Qf the Hills J which being once filled, all the 


8o The Origin of fountains. Part IL 

overplus of Water that comes thithcrt runs 
over by the lowcft Place, and breaking out by 
the Sides of the Hills, forms (ingle Springs. 
Many of thefc running do'*^n by the Valleys 
between the Ridges of the Hills» and coming 
to unite, form little Rivulets or Brooks : many 
of thefe again meeting in one common VaU 
ley, and gaining the plain Ground* being grown 
lefs rapid, become a River ; and mapy of thefe 
being united in one common Channel, make 
fuch Streams as the Rhine and the Danube i 
which latter, he obferves, one would hardly 
think to be a Colledion of Water condcnfcd 
out of Vapour, unlcfs we conHder how vaft a 
Trad of Ground that River drains, and that 
it is the Sum of all thofe Springs, which 
break out on the South Side of the Carpa- 
thian Mountains, and on the North Side of 
the immenfe Ridge of the Alps, which is one 
continued Chain of Mountains from Switzer^ 
land to the Black-Sea. 

Thus one Part of the Vapours, which arc 
blown on to the Land, is returned by the Ri- 
vers into the Sea, from whence it came j ano* 
ther Part falls into the Sea before it reaches 
the Land 5 and this is the Rcafon, why the 
Rivers do not return fo much Water into 
xhz Mediterranean as is raifed in Vapour. 
A third Part falls on the Low-Lands, and is 
the Pabulum of Plants, where yet it does not 
reft, but is again c;(halcd in Vapour by the 


Aftton of the Sun, and is either caitied by 
the Winds to th€ Sea, to fall in Rain or Dew 
there, or elfe to the Mountains to be there 
turned into Springs. 

However it is not to be fuppofed that 
all Fountains are owing to one and the fame 
Caufe, but that fome proceed from Rain and 
melted Snow, which fubfiding through the Sur- 
face of the Earth, makes it Way into certain 
Cavities and thence iflues out in the Form of 
springs; becaufe the Waiters' of fcvcral aire 
found to increafe and dimi^i(h in Proportion 
to the Rain which falls : ^^at others again, 
efpecially fuch as are fait, and fpring near the 
Sea Shore, owe their Origin to Sea Water 
percolated through the Earth, and fome to 
both thcfe Cajjfts: though without doubt 
moft of aU, ^nd efpecially fuch as fpring near 
the Tops of high Mountains, receive their 
Waters from Vapours, as before explained *« 

* There is a certain Species of Springs which ebb ind fl<n^ 
alternately, and fome that ceafc to flow for a Time, ahd front 
thence are called reciprocating or intermitting ones. Their Rc- 
tiprocations may be accounted for in the following Manner. 

Let JB C reprefent one Side of an Hill iii which there is a 
Cavity DEF^ and from this a fubterraneoiis Du6t IKL. Now 
as this Cavity fills with Walter (fuprofe from Vapours perco- 
lating through the Surface of the Hill, or in any other Manner 
whatever) its Surface will rife in the Du€t as it docs in the Ca- 
vity, till it arrives at Af, the Level with the upper Part of the 
l)ud ; a t which Time it will ruu over at K^ filling KLA th^ 
other Part of the Dud^. Now if the Column KL is ionger than 
K I it will overpoife the other, and fo caufe the Water to run 
•ut at ^, till its Surface in the Cavity finks ns f^.r as /, (pro- 
vided the DixCt is large enough to convey the Water aWay fa iter 

L tiun 

83 ■ The^ Brigin-ofF^uApams. Part II. 

than it enters the Cavity) it which Time the FouoCain n A 
will ceaB to pfay, till the Soffecc Of the Water, in the Ca.vity 
rifes ^ia to M, toA nuu over at K as before. The Rearoii v/Ky 
die Water continues running (when tbt Dad , is opce full) till 
its Surface finks to 7, is b^caufc'the Air' preiGng againft it as it 
runs oat at G and alfo upon its Sur&ce in the Cavity, keeps the 
Duft fiitl, as long. as the Water in tht Cavity is high enongh 
(o feed its Orifice at /. 

See more on this Subjed' in Philofop. Tranfaft. N'. 119. 189. 
192. 384. 424. Hiftory de 1' Acad. r693. 170;. 1713- Gv- 
lielmim della NatuTa da Fiumi. Ddt^i Hiftory of HartuUh. 
Marrhttii Hydroftitics. Niewwentyt Contempt. 19. Vartniui 
Geograph. Cap 16. .^igaaiJl \o\. i-Camrs^x. 6-' Haltd 
Statical Ellays Vol. 1. Experiment 19. MiAeltttut in Appoid. 
dd y. Btrmullii de Effcrvefc. 









w * 


f=l \ 


Compendious SysteSt 


Natural Philofbphy^, 

With >ra,rES. 


Containing the M ^t^^ » e ma t i b a C 
Demonstrations^ andibme$, 
occalional REMiWRKSf 


PART II.- Continued. 
Confiftingof 6m^ DISSERTATION^^ 

X Of the Sarometer. *^. 

II. Of the Caqfe and Origin of the W?/>rf/^ 

III. Of thfe Afcent of FapourSy and thei^f Rcfolution int(| • '; 
H Raiftj Hail^ Snonny SiQ. 

f; 4 V. Of the (^\xf^s^o£ T'hunder^i Zightnhg^^^ith^ 
Solution of the 'PhdPncmena of the Aurora porealiu 
y. A Htw Theory of Fermenranon* 

By y. KowNiNQ^M. A. ^ 

tFellow oi Magdalen College In CamhrUgei 

^J^rinted for the Author ^ and fold byS^HARD^i^d) 
J^QoMdier^ <m the Pavemeot hxSu MattiriiirLan^ 




» r — 

• ♦ 

♦ I 


• - * « 

T t •- . 


3piffert4* Of the Sardmetcr, 8 J V^ 

Of the Barometer^ 

I.N treating of the Properties of the Aif 
(Chap. III.) I have already taken No- 
tice of the Conftru6lion of the common Ba^ 
rometer 5 and proved^ that the Afcent and 
Sufpenfion of the Mercury therein^ is owing 
to the PrefTure "^ of the Air. I proceed now 
to a more particular Inquiry into the Ori- 
ginalj and Ufe of this Inftrument ; and the 
different Forms under which it has appeared, 
iince the Time of its Inventor T^orricelli. 


* To fay the Afcent and Sufpenfion of the Mercury is owing 
to the PreUure and Elafticity of the Air, as is commonly done, is 
inaccurate. The Variation, indeed, in the Heiglitof the Mercury, 
may be afcribed to the Elaflicity of the Air, but no otherwife, 
than as to its remote Caufe ; viz, as it occafions an Alteration ia 
the Quantity of Air, impending over the Place where the Varia- 
tion happens ; which alters its Weight, and fo the Mercury is 
proportionably railed or depreffed. To illuftrate this, let it be 
fuppofed, that the Air is every where in JEquilibrioy quite round 
the Globe, and at perfeft Reft ; and then, that its Elafticity^ in 
feme one Place near the Surface of the Earth, is augmented by the 
Heat of the Sun, all the Reft of it remainmg as before. The Con- 
fequence of this will be, that the fuperior Part of the Atraofphere, 
over this Place, will be raifed higher by the ExpanGon of the infe- 
rior Air •, and therefore, being unconfined, will fpread itfelf, like 
boyling Water, over the neighbouring Columns, which we fup- 
pofe to retain their former State. The Quantity of Matter there- 
fore in thole Columns of Air, in whofe lower Parts its Elafticity 
yr9iS iacieafed^ will be dioainiftied, and that of the neighbouring 
" ' ' "' M ones 

84. Of the Barometer. Part IL 

In the Beginning of the laft Century, it was 
a prevailing Opmion among Philofophers, that 
the Univerfe was full of Matter ^ and that Na- 
' ''ture (as they expreffed it) abhorred a Vacu- 
um : Accordingly they imagined, that if a 
Fluid was fucked up a Pipe with a fufficient 
Force, it would rife to any Height whatever ^ 
fince Nature would not fuffer any Part of the 
Pipe to remain em^pty. GaliUo^ who flou- 
rilhed about that Time, found upon Trial, 
that the common Pump would not raife Wa- 
ter, unlefs the Sucker reached within three and 
thirty Feet of its Surface in the Well * : From 


ones augriiented. A Barometer therefore placed in thofe Regions, 
where the Air was rarified, will fubfide ; while one in the neigh- 
bouring Countries will afcend ; and they will continue at different 
Heights, till the denfer Air mfhlng in upon the ratified, reAores 
the Jl: equilibrium. Thus, we fee, the Variation of the Air*sElaf- 
ticity is not the immediate Caufe of the Variation in the Barome- 
ter ; it firA aftedks the Weight of the Air^ by altering the Quan- 
tity incumbtnt over any Place, and that afteds the Barometer. 
But, if we may have Recourfe to remote Caqfes, we may, if we 
pleafe, go one Step farther; and fay, the.Afcent and Sufpenfion *' 
of the Mercury is owing to the Heat of the Sun ; for, by the * 
foregoing Inftance, a Variation in the Heat of the Sun may fbme- 
times be the Occafion of a Variation in the Height of the Mercury. 
Neither is the Sufpenfion of the Mercury, in a Tube, that is 
kep: within Door*, to be afcribed to the Elafticity of the Air ; for 
that exerts no Force, but as the internal Air is preflT^d by the exter- 
nal, which endeavours to get in, where-ever it can find a Way, 

* It is a common Notion, that a fucking Pump will not raife 

Water above thirty-three- Feet, whereas it ^yiJl raife it to any 

Height whatever, if the Sucker reaches within thirty-three Feet of 

. the Surface of the Water ; as will be evident to any one that con- 

ilders the Strufture of the Pump : For all the Water, which has 


DiiTert. 4. Of the Barometer, 85 

hence he judicioufly inferred, that a Column 
of Water thirty^-three Feet high was a Coun- 
terpoife to a Column of Air of an equal Bafe, 
whofe Height extended to the Top of the At- 
mofphere; aud that, for this Rcaibn, the Wa- 
ter would not follow the Sucker any farther. 
^orriceUi obferving this, took the Hint i and 
confidered, that, if a Column of Water, of 
about thirty-three Feet, was equal in Weiglit 
to a Column of Air, of the fame Bafe * ; a 


oncepafled through the Valve in the Sucker, is fiipporced by tbar, 
as the Sucker is drawn up, and refts upon a Valvi; placed in the. 
Pump below, as it is let down ; To that it can be no Impediment 
to the rifiiig of the Water below the Sucker, whatever the Length 
«f the Column, which it forms, may be. The placing one Piimp 
above another, where ' From great Depths, is 

lather for Strength and ut of NecelTny. 

* Perhaps it may b it comes to paK, that 

the Column of Air, w Aagnant Mercury in 

the Bafon, is always fu al Bafe with the fuf- 

peoded Column in th i Reality, iti Bafe is 

equaVco the Surface ; ury. The Reafon is, 

thit^as the Bafe of th( afes, in theiame Vn- 

T»igS|i the Velocity \ j, decreafes, when it 

i<^^down the Surface i Bafon ; confequently 

its Moment, or Preffure ypoii the Surface of the flagnant Mercury 
((b far as it relates to the fufpending of it in the Tube) is no great- 
er, than it woirid have been, had its Bafe been eijual to that of 
the fufpended G)lumn ; and therefore, in conliderin" ic as fuf- 
pending a Fluid in x Tube, it is properly enough faid to be a Co- 
lumn of fuch a Bafe. 

Neither is this SuppoiTtion inconfiflent with the ninth Propofi- 
tion of the firft Chapter, where it is demonfirated, that the I'ref- 
fcte ofa Fluid is in Proportion to its perpendicular Height, and 
Ihe Quantity of Surface, againfl which it prefles. For, as the 
Surhce of t)i« Mercury may be conHdered as a Bafe on which the 
M 2 Column 

86 Of the Barometer. . Fart It 

Column of Mercury, no longer ' tfcan drout 
twenty-nine Inches and a half, would be fo tooj 
fuch a Column of Mercury being as heavy, as 
thirty-three Feet of Water. ' Accordingly he 
tried the Experiment in a Glaft Tube (in the 
Manner laid down. Chap. III. §. 4.) and found 
it to fucceed *, .The Apparat^s he made Ufe 


Column of Air refls, & the Bafe of the Coluoij^ of Air may be con- 
fid ered as a Surface againft which the Mercury prefles. Thefe 
two being equal, 'tis clear, that only the Relation of the Heights 
of the Columns are to be confidered, and not that of their Bafes. 

* Notwithftanding this clear Proof of the PreiTure of the-^of. 
phere, the Aflferrers of a Plenum would by no Means be prey^W 
upon to allow it to be fuch ; but tried all Ways to account fo^s 
Thanomenon from fome other Caufe. The moft chimerical Solution, 
and which at the fame Time gave the adverfe Party the greateft 
Pifficuky to overthrow, was that of Lin^s. He contended, that 
in the upper Part of the Tube, there is a Film, or Rope of Mer- 
cury, extended through the feeming Vacuity, and that the Reft 
was fufpended by it^ and kept from falling into the Bafon ; and 
that this Film is able to fupport about twenty-nine Inches of Mer- 
cury. He confirms his Hypothefis by the following Experiment/ 
Take, fays he, a fmall Tube, open at both Ends, fuppofe about 
twenty Inches long ; fill ,this Tube with Mercury, (lopping the 
lower Orifice with your Thumb : Then clofing the upper with 
your Finger^ and immerging the lower in ftagnant Mercury, you 
Jhall perceive^ upon the Removal of your Thumb, a .manifeft Suc- 
tion ofyour Finger into the Tube ; and the Tube and Mercury 
will both flick fo clofe to it, that you m^y carry them ahjout the 
Room. Therefore, fays he, the internal Cylinder of Mercury ia 
the Tube is not held up by the preponder^t Air without ; for if 
fo, whence comes fo flfong a Sudion, an<i h firm an Adhefion of 
the Tube to your Finger ? . - . ' 

' Or if you fill the fame Tube almofi full of* Mercury, leaving % 
httle Space of Air within, and then immVrg^ \t in the flagnant 
Mercury, you will find, that, notwithftanding its Surface is ac 
fome D;ftance f^om your Finger, there wiil be a confiderabJe Sue- 


IJiffert, 4. Of the Barometer: 87 

of, is now the common Barometer or Wea- 
ther Glafs ^ 

The Mercury ftanding at a lefs Height, the 
nearer it is carried to the Top of the Atinofphere, 

tion of it, as before. From hence he infers, thtt the Finger fup- 
ports the Mercury, by Means of the above-mentioned Film, and 
that the Freffure of the Atmofphere is not concerned. 

But, when it was found, that the Mercury would not fland fo 
high in the Tube, On the Top of a Mountain, as below ; and 
would quite fall, when the circumambient Air was extracted from 
it by the Pump, all Objedions vanifhed ; and Li»fis\ fiinicular 
Ifypotbfjis (as it was called) though it iS^emed to folve all other 
fhdtnomenay relating to the Sufpenfion of the Meicury, was with 
Jufti'ce rejefted. 

Kifchety When this new Dodririe of a P'dcuum was firft advan- 
ced at Rome, contended, that the Authors of it were eftablilhirig 
Principles not only repugnant to thofe of Nature, but fuch as 
would be prejudicial to the Orthodox Faith ; as endeavouring to 
evince by thisL^iibtle fix^eriment, that there might be in Nature 
locatum fine JocQj accidentia, fine fubje^o , and therefore made the 
Experiment with Water, in the following Manner. He caufed a 
fmall Bell to be fixed in the uppeir Fart of the Tube, imagining, 
that, if there (hould be a Vacuum^ the Bell would not be made 
to found : !l^ut in making the Experiment, ibme Air got into the 
Tube- (for he tells us, that but ten Feet of Water remained in the 
Tube, after, it was inverted) the Bell thereibre was heard to 
found ; and fo the Notion of a VacHum^ till more accurate Expe- 
jfiments evinced the conti-ary, was exploded with Contempt. 

* Huygens obferved, that, if a Tube feventy-jBve Tnches long^ 
was filled with Mercury well purged of its Air, the whole Quan- 
tity of Mercury would remain fu^endM \ whereas, according to 
the Torricellian Experiment, the Mercdr^ ougho to^ h^vQ fabuded 
|o the Height of about twenty- nine Inches. 

The Caufe of this Fbanomenon^ feems to be, that, by the great 
Weight ofib'Jong a Column of Mercury, it was pref&J into fo 
clofe Coata^ with the Glals in pouring In, that by the mutual 
Attra^ion of Cohefion between the Mercury and the Glafj, the 
i¥hole Colunon was fuftained . after the Tube was inverted; 

: ' ■ ' (Chap. 

88 Of the Barometer. Part IL 

(Chap. III. §.7.) renders it ufeful in determin- 
ing the Height of Mountains ; and finding out 
the different Elevation of one Place above ano- 
ther. Accordingly, Dr. Halley has given us a 
Table for that Purpofe, in the Philofophical 
Tranfadions N ^ . 1 8 1 , flie wing how many Feet 
the Defcent of the Mercury each Inch anfwers 
to, as it is conveyed to the Top of a Mountain, 
or other elevated Place. And Dr. Nettleton 
has done the like in the Philofophical Tranfac- 
tions N^» 388, fliewing what Number of Feet 
anfwers to each tenth Part of an Inch, from 
twenty-fix to thirty-one Inches of Mercury. 

But the principal Ufe of it is, to eflimate 
the Gravity of the Air at different Times, in 
Order to lorefee the Alterations of the Wea- 
ther, which are confequent thereon. To this 
End, Dr. Halley in the fame Tranfaftion has 
-alfo laid down the more remarkable Tban(h 
rnena^ relating to the different Heights of the 
Mercury at different Times, together with the 
Solution of each ; which are fo jufl, and fo 
agreeable to true Philofophy, that I doubt not 
but the Reader will excufe me for giving his 
Account in his own Words,' rather than to 
render it imperfedl, by endeavouring to vary 
from it, or abridge it. 

*^ I. In calm Weather, when the Airis in* 
*^ clined to Rain, the Mercuiy is commonly 

'[ low. 


Differt. 4, Of the Barometer. 89 

^^ 2. In ferene, good^ fettled Weather, the 
" Mercury is generally high. 

" 3. Upon very great Winds, though they 
^^ be not accompanied with Rain, the Mercury 
*^ finks ioweft of all, with Relation to the 
!^ Point of the Compafs the Wind blows upon. 

*^ 4. Ceteris paribus^ thegreateft Heights 
^^ of the Mercury are found upon eallerly and 
*^ north-eafterly Winds. 

" 5. In calm frofty Weather, the Mercury 
!' generally ftands high. 

" 5. After very great Storms of Wind, 
" when the Mercury, has been low, it gene- 
" rally rifes again very faft. 

^^ 7. The more northerly Places have great- 
*^ er Alterations of the Barometer, than the 
^^ more foutherly. 

" 8. Within the Tropics, and near them, 
" thofe Accounts we have had from others, 
^' and my own Obfervations at St. Helena^ 
^^ make very little or no Variation of the 
^^ Height of the Mercury in all Weathers. 

^' Hence I conceive that the principal Caufe 

^^ of the Rife and Fall of the Mercury, is from 

'^ the variable Winds, which are found in the 

temperate Zone, and whofe great Uncon- 

^ ftancy here in IBjngland^ is moft notorious. 

*^ A fecond Caufe is the uncertain Exhalation 

and Precipitation of the Vapours lodging in 

the Air, whereby it comes to be at one Time, 

much more crouded than at another, and 


*' con- 


90 Of the Barometer. ; PartIL 

confequently heavier, but this latter in a great 
Meafure depends upon the former. Now, 
from thefe Principles, I fliall endeavour to 
" explicate the feveral ^bdiiomena of the Ba- 
" rometer, taking them in the lame Order I 
^' laid them down. Thus, 

I . The Mercury's being low, inclines it 
to rain, becaufe the Air being light, the Va- 
pours are no longer fupported thereby, being 
become fpecifically heavier, than the Medi- 
um wherein they floated, fo that they delcend 
towards the Earth, and in their Fall, meet- 
*^ ing with other aqueous Particles, they incor- 
porate together and form little Drops of 
Rain ; but the Mercury's being at one Time 
lower than at another, is the Effed of two 
contrary Winds blowing from the Place where 
the Barometer ftands i whereby the Air of 
that Place is carryed both Ways from it, 
and, confequently, the incumbent Cylinder 
*' of Air is diminifiied, and accordingly the 
'^ Mercury finks: As for Inftance, if in the 
^^ German Ocean it iLould blow a Gale of 
wefterly Wind, and at the fame Time an 
eafterly Wind in the Irifh Sea 5 or, if in 
France it iliould blow a northerly Wind, 
and in Scotland a foutherly ,• it muft be 
granted, that that Part of the Atmofphere 
impendant over England^ would thereby be 
*' exhaufled and attenuated, and the Mercury 
** would fubfide^ and the Vapours, which be- 

" fore 






>Biflert 4. Of the Barometer, 9 1 

jt»' fore floated in thofe Parts of the Air of 
; equal Gravity with themfelves, would fink 
" to the Earth. 

" 2. The greater Height of the Barometer 
*' is occafioned by two contrary Winds blow- 
*^ ing towards the Place of Obfervation, where- 
*' by the Air of other Places is brought thither 
" and accumulated j fo that the incumbent 
" Cylinder of Air, being encreafed both in 
" Height and Weight, the Mercury preffed 
*' thereby muft needs ftand high, as long as 
" the Winds continue fo to blow ; and then 
" the Air being fpecifically heavier, the Va- 
*^ pours are better kept fufpended, fo that they 
*' have no Inclination to precipitate and fall 
" down in Drops, which is the Reafon of the 
ferene good Weather which attends the 
greater Heights of phe Mercury. 

3 . The Mercury finks the loweft of all by 
** the very rapid Motion of the Air in Storms 
of Wind. For the Trad or Region of the 
'' Earth*s Surface, wherein the Winds rage, 
" not extending all round the Globe, that 
ftagnant Air which is left behind, as like- 
wife that on the Sides, cannot come in fo 
faft as to fupply the Evacuation made by fo 
" fwift a Current, fo that the Air muft necef* 
farily be attenuated, when and where the 
faid Winds continue to blow,*and that more 
or Icfs, according to their Violence y add 
to which, that the horizontal Motion of the 

N ** Air 




9 1 Of the Barometer. Fart It. 

•' Air being ft) qukk as it is, may, in all Pro- 
^ bability, take off fome Part of the perpendi- 
•* cular Preffure thereof* ; and the great Agi- 
*• tation of its Particles is the Reafon why the 
•* \'apours arc diifipated, and do not condenfe 
^ into Drops, to as to form Rain, otherwife 
• the natural Confetpience of the Air*s Rare- 

^ 4* The Mercury (lands the higheft upon 
the eafterly and north-eafterly Wind, be- 
caufe in tte great Jtlantic Ocean, on this 
Side the thirty-fifth Degree of north Lati- 
tude, the Winds arc almoft always wefter- 
ly or fouth-wefterly ; fo that whenever 
here the Winds come up at ea^ and north- 
eaft, *tis fure to be checked by a contrary 
Gale as foon as it reaches the Ocean ; where- 
** fore, according to what is made out in our 

* Thu is confirined hy Expcrioieiit. Fhilofophkal Ttanfadions, 

Mo. z^iHi 

t The Reason the Dodor affigas for the finking of the Mercury 
the lowefi^of all in violent Storms of Wind^ feems not fu&ienc. 
Perfaajis it may be better accounted for thus; the Caufewh)Pthe 
Wind blows at all^ is in Order to reflore the JEquilihrium of the 
Atmofphere, when lofl (as may be inferred from what was laid in 
the firit Note of diis^ and will be more lat^gely explained in the 
following DiHertation) ; it therefore always blows towards that 
Toint, where the Air is moR rarefied and ligbteA. Now the 
Ait in its Progreis to that Point, muft certainly move fafter and 
frfter ;''.fpr theCaufe, which gave it Motion at firft, continues to z6l 
upon ic all the Way. Confequently, in whatever Place thefWiod 
blows with great Rapidity, that Place is at, or near the Point, 
where the Air is inoft rirefied^ lOid Bghtefl ; which is A fiiffitient 
lUsion for the Mercury's fimding lew at thM Place; 

• » 

* *^ fecond 




Di^rt. 4» Of the Bcardmcter. 9 j 

*^ iecond Rjemark^ the Air mnft needs &e heE][^ 
^ ed over this Ifland, and ccxifecpently the 
** Mercury muft ftand high, as often as thefe 
^* Winds blow. This holds true in this Conn- 
** try, but is not a general Rule for others, 
^ where the Winds are under different Cir^ 
^^ cumflances ; and I have ibmetimes feen the 
^ Mercury here, as low as twenty-nine Inches 
** upon aa eafterly Wind, but then it blew ex-^ 
^ ceeding hard, and fb comes to be aocoonted 
^ for, by what was obfervoi upcm the third 
** Remarks 

" 5. In calm frofty Weather the Mer<:tiry 
^ generally flands high, becaufe (as I con- 
^ ceive) it feldom freezes^ bat when the Winds 
^ come out of the northern, and nortb-eaff ern 
•* Quarters ; or^ at leaft, unleft thcrfe Winds 
^ blow at BO great Diftafioe dSi For the 
^ north Parts dF Germany^ ^Dmmarky Swe- 
^^ deny I^wayy and all that Traci frcMcn 
^ whence north -eaftem Winds come^^ are 
^ fubje^k to almoft continaal Froft all the 
^* Winter j and ther^y the lower Air is very 
^^ much copdenfod, and in that State h brought 
^^ thitherwards by thofe Winds^i and bemg ac^ 
^ cujijiilated by the Oppofition of. the Wie^^ 
^^ ly Wind blowing 19 the Oceanp the JSi^Br- 
"^ emy mtSk, needs be pe0ed to a more t^an 
'^ orcfinary Height ; and, as a opBCorrkig 
^ Caufe, the Ihrinking of the lower Parts of 
!^ the Air into leffer Roon^ by Cold, muft 

94- Of the Barometer. PartIL 

•^ needs caufe a Defcent of the upper Parts of 
^* the Atmofphere, to reduce the Cavity mad^ 
^' by this Contradion to an Equilibrium* 

" 6. After great Storms, when the Merr 
^^ cury has been very low, it generally rifes 
^^ again very faft ; I once obferved it to rif? 
^^ one Inch and a half in lefs than fix Hours, 
" after a long continued Storm of fouth-weft 
" Wind. The Reafon is, becaufe the Air be- 
*• ing very much rarified, by the ^reat Evar 
^^ cuations which fuch continued Storms m^kQ 
*^ thereof, the neighbouring Air runs in the 
*^ more fwiftly, to bring it to an JEquilihri': 
'^ umi as we fee Water runs the fefter for 
^^ having a greater Declivity. 

" 7. The Variations are greater in the mor^ 
northerly Places, as at Stockholm^ greater 
than that at ^aris (compar'd by M. P^/: 
^^ chat) j becaufe the more northerly Part^ 
" have ufually greater Storms of Wind than 
the more foutherly, whereby the Mercury 
fhould fink lower in that Extream ; and 
^^ then the northerly Winds bringing the more 
?^ denfe and ponderous Air from the Npigh- 
^^ bourhopd of the Pole, and that ^gaiii being 
^^ checked by a foutherly Wind at no great 
^^ Diftance, and fo heaped, muft of Necelfity 
make the Mercury in fuch Cafe ftand highef 
?f in the other Extream, 




Differt. 4- Of the Barometer, <>< 

^^ 8. Laftly, this Remark, That there is 
^^ little or no Variation near the EquinoUiaiy 
^^ does above all others, confirm the Hypothec 
*^ fis of the variable Winds being the Caufe of 
^' thefe Varktions of the Height of the Mer- 
*' curyi for in the Places above-named, there 
*^ is always an eafy Gale of Wind blowing 
^^ nearly upon the fame Point, !^i;s. eaft^north* 
*^ eaft, at \Barhadoe5^ and eaft-fouth-eaft at 
^^ St. Helena *, fo that there being no contra- 
^^ ry Currents of Air to exhauft or accumulate 
^' it, the Atmolphere continues much in the 
^^ fame State : However, upon Hurricanes 
" (the moft violent of Storms) the Mercury 
^^ has been obfervcd very low, but this is but 
^* once in two or three Yeirs, and it foon re- 
^^ covers its fettled State about 29-i Inches. '' 

Monfieur Leibnitz accounted for the De- 
fcent of the Mercury before -Rain, upon an- 
other Principle t> '^iz* as a Body fpecifically 
lighter than a Fluid, while it is fufpended b/ 
it, adds more Weight to that Fluid, than 
when, by being reduced in its Bulk, it be- 
comes fpecifically heavier, and defcends ,• fo 
the Vapour, after it is reduced into the Form 
o£ Clouds, and defcends, adds lefs Weight to 
file Air^ than before ; and therefore the Mer- 

* See the following DiiTertatiottt 
I Memoir. 4e TAcad. i7Mt 



^ Of the Bafomtter. FsatJh 

cory falls. To wiuch it is anfwerecl, ifi^ 
That when a Body defcends in a FIoLd, its Mo- 
tion^ in a very iitJtle Time^ becomes nniferm^ 
(or nearly fo) a farther Accel^ation of it be- 
ing prevented by the ReGftanoe of the Fluid ; 
ai^ then> by the third Law of Nature, it prei^ 
i^ the Fluid downwards, vdth ^a Force e<|ual 
to that whereby it tends to be farther accele- 
rated, that is, with a Force equal to its whol^ 
Weight, t/fy^ The Mercury, by ixs Defcecit, 
feretells Rain a BHicb k»^r Tiiae before it 
comes, than the Vs^cMir, ^tj&r it is condenied 
into Clouds, <^ii be fuppofed to take up in 
felling . ^{i/y. SuppoHng that as many Va- 
pours, as lall in Rain, diariog the Space (^ a 
whojle Year, were at once to be cond^i&d 
into Clpuds, and even quite ceafe to gravitate 
upon the Air, its Gravity would fcarce be di-^ 
ninliked thereby, lb much a^ i$ equivalent to 
the Defeent of two Inches of jStoxury in ihe 
Barometer. Farther, in many Places between 
the Tropics, the Rains fall at certain Seafons, 
in very great Quantities "*", and yet the Baro- 
meter ihews tlv^re very little or no Alteratioa 
m the Weight <£the Air, 

ThefoUowing are Mr. P^r^i&*s Ob/ervasr 
tion$ oh the Filing and ^llit^pf the Merctry^ 
They arfe wry jufti m4 are :tj(> ^^ fcgqifljted 


. • ^ 

* Sec Differtation the 6th. . - * 

' .J 




Di(reit.4. Of the Bttrwieter. 97 

for on the feme Principles with thofe t>f Dr^ 

** !• The rifing of the Mercury prefages ia 
^ general fair Weather ; and its falling, foul 
*^ Weather ; as Rain, Snow, high Winds 3s\d. 
^ Storms, 

2. In very hot Weathef, the falling of 

the Mercury forelhews Thunder. . 

*^ 3* In Winter the ri/ing prefages Froft ; 
** and in frofty Weather, if the Mercury falls 
*^ three or four Divifions, there will certain-- 
^ Jy follow a Thaw* But In a continued 
*^ Froft, if the Mercury rifes, it will certain- 
ly fnow. 

4. When foul Weather happens foon after 

the Falling of the Mercury, exped but lit- 
^ tie of it. And, on the contrary, expedbut 
** little fair Weather, when it proves feir 
" fliortly after the Mercury has rifen, 

** 5* In foul Weather, when the Mercury 
^ rifes much and high^ and fo continues for 
"* two or three Days before the foul Weather 
" is quite over, then expert a Continuance of 
" fair Weather to follow. 

** 5. In fair Weather, when the Mercury 
•* falls much and low, and thus continues for 
** two or three Days before the Rain comes ,• 
" then exped a great deal of wet, and pro-^ 
** bably high Winds. 



8. The 





98 0/ the Barometer. Part IL 

7. The unfettled Motion of the Mercury 
^ denotes uncertain and changeable Weather. 

8. You are not fo ftridly to obferve the 
Words engraven on the Plates (though, for 
the moft Part, it will agree with them) as 
the Mercury's Rifing and Falling : For if 

•* it ftands at Much Rain^ and then rifes up 
to Changeable^ it prefages fair Weather, al- 
though not to continue fo long, as it would 
have done, if the Mercury were higher : 
And lo on the contrary, if the Mercury 
flood at Fair^ and falls to Changeable^ it 
prefages foul Weather i though not fo much 

** of it, as if it had funk down lower. *' 

From thefe Obfervations, it appears. That 
it is not fo much the Height of the Mercury in 
the Tube, that indicates the Weather, as the 
Motion of it up and down ; wherefore, in Or- 
der to pafs a right Judgment of what Weather 
is to be expefted, we ought to know, whe- 
ther the Mercury is actually Rifing or Fall^ 
ing^ to which End, the following Rules are 
of Ufe. 

1 . If the Surface of the Mercury is convex, 
{landing higher in the Middle of the Tube than 
at the Sides, it is generally a Sign that the 
Mercury is then riling. 

2. If the Surface is concave, or hollow ia 
the Middle, it is (inking. And, 

3- If 


Difliert 4* Of the Barometer ^ 9 9 

3. If it is plain, the Mercury is ftationary, or 
rather, if it is a little convex^ for Mercury 
being put into a Glafs Tube, efpecially a fmall 
one, will naturally have its Surface a little 
convex ; becaufe the Particles of Mercury at- 
tra& each other more forcibly than they are 
attradked by Glafs. Further, 

4. If the Gkfs is finally fliake the Tube ; 
and if the Air is growing heavier, the Mercury 
will rife about half the tenth of an Inch higher, 
than it flood before ; if it is growing lighter, 
it will fink as much. This proceeds from the 
Mercury's flicking to the Sides of the Tube, 
which prevents the free Motion qf ifc> till it is 
difengaged by the Shock. And therefore, when 
an Obfervatipn is to be made with fuchaTube, 
it ought always to be Ihaken firft, for.fome- 
times the Mercury will not vary of its own Ac- 
cord, till after the Weather, it ought to have 
indicated, is pafl« 

. The Ufefiilnefs of knowing, whether the 
Mercury is adually rifing or falliiig 5 and the 
Advantage that would arife from perceiving 
the moft minute Variations in eflpiating the 
Heights of Places, have given Occafion to the 
Invention of feveral Kinds of Barometers differ- 
ent from the TorrtceiUani though founded on 
the fame Principle J wherein the Scale of Vari- 
Utioi^ which ip that is not above three Inches, 

<* 4 


loo Cf the Barometer, PartlL 

ihoold be condderably larger. 0f which I am 
now to give fome Accoont. 

I, Thefirftisthat of 2)^JrC^rf^^5 which was 
made in the Form expreifed Fig. 28. where 
AB is a Tube hermetically * fealed at A, and 
having its lower Orifice immerged in ftagn^it 
Mercury EF^ and filled with the fame Fhiid 
to G, firom thence to H with Water, and emp- 
ty from thence to the Top. Now, when the 
Mercury rifes in this Tube, iuppofe from G to 
L,, the Water will be raifed in the Imall Tube, 
perhaps from H to M, i^iz. as many Times 
fiirther, as the Tube C A is fmaller than CD 5 
by which Means the Variations become much 
more fenfible, than they are in the common 
Barometer. The Inconvenience of this was, 
that the Air, included in the Water, getting 
loofe by Degrees, filled the void Space at the 
Top, and fo fpoiled the Machine. 

2. He then contrived it thus, ABC (Fig. 29) 
is a bent Tube hermetically fealed at A, filled, 
with Water from F to D (titled with J^/ua 
jkegia to prevent its freezing), from D to E with 
Mercury, and empty from thence to the Top* 
pThen, upon the Mercury*^ rifing, fuppofe from 

"^ A Tube Ii ftid to be hermetkatty fealed, when die End is f^ 
cloCed, that nothing can pofllbly evaporate through it. And, be- 
caufe this is bed done, when it is dolbd up With its own Sub- 
fiance ; or when its Bore does aoc teach ^nice ibrough k, ic 1$ 
||m fiOd to be i«rmlM/i||r fealed* 

•0 ««> 

DlfTect 4* Of the Baremetef. i o I 

B to M, ^d falling as much at D, the Surface of 
the Water at F would fink fo many Times hx^ 
ther than the Surface of the Mercury at D, as the 
Tube CG was fmaller than GH. The Water 
here is liable to evaporate, though that may, 
in fome Meafure, be prevented^ by pouring a 
few Drops of Oyl of fweec Almonds upon it. 
Upon this Account, others have contrived 

3* The Horizontal or Re(5tangular Barome- 
ter (Fig. 30) hermetically fealed at A, and 
filled with Mercury from D to E ; then as the 
tipper Surface of it rifes in the Tube^ fuppofe 
from E to F, the lower will be driven from D 
to G, as many Times farther, as this Part of 
the Tube is lefs than that at E. But it often 
happens, that fome Parts of the Mercury break 
off from the reft in the Leg BC, and are left 
behind. This Inconvenience is remedied in 

4. The Diagonal Barometer ABC {Fig. 3 1 ) 
wherein the Mercury, inftead of rifing from B 
to D (fuppole that fpace to correfpond to the 
Scale of Variation in a ftrait Tube) will rife 
from B to A ^ for it will always ftand at the 
fame perpendicular Height, whatever be the 
Inclination of the Tube ; becaufe Fluids prefs 
only according to their perpendicular Alti* 
tude*. But the Tube AB muft not be too 
^qch inclined, left the Mercury break in it, as 
in the former. 

t Ctopier t. §. ^ 

O i 5 , AB 

loi ■! Of the Barometer. .Part HI 

y. AB, {Fig. 33;) is Dr. Roolt% Wheel-; 
Barometer, wherein A B D is a Tube filk^ 
with Mercury from ^ to E ; ^ is an Iron Ball, 
fwimming on the Surface of the Mercury y this 
as it fubfides with the Surface of the Mercury, 
draws the little Wheel m n round, to whofe 
Circumference it is fixed by Means of the 
String ^^*: This Wheel carries the Index 
PQ^, which points to the graduated Edge of 
the Circle K L, and by its Motion ihews 
the moft Minute Variations of the Mercury. 
When the Ball a is raifed by the Mercury 
on which it fwims, the Index is drawn the 
contrary Way by a lefler Ball hy which hangs 
on the other Side the Wheel. The FriiStion 
in this Machine^ unlefs it be made with great 
Accuracy indeed, renders it ufelefs. 

6, The pendent Barometer is another Con* 
trivance to render the Variations more fenfible. 
It confifls of a fmall conical Tube, (reprefented 
Tig. 33.) hermetically fealed at A, and filled 
with Mercury from C to D, and empty from 
thence to A. Now, fuppofing the Gravity of 
the Air encreafed3 it will raife the Mercury 
•higher in the Tube, and fo force it into a narr 
.r9wer Part i by which Means the Column be-r 
coming longer, its perpendicular Preffure upon 
the h\\ belpw will be proportipnably increafed* 


* The Tube is imaller at a thaa at E, that the greatefi Var}a«> 
t ioo ' may l>e ^ (hat l^urface of the Mercu7 qq ^bich (be ^11 


Differt, 4. Of the Barometer. i b :} 

©n the cpatrary, when the Air becomes lighter, 
the Mercury defceads into a larger Part of the 
Tube, aj»d by that Means has the Length of 
its Column proportionably contracted. The 
Inconvenience that attends this Barometer, is 
that the Tube miift be very finall, otherwife 
the Merciiry will fall out ; or the Air will be 
apt to get into it, and divide the Column iir 
feveral Places ; and when the Tube is very 
fmall, the Fri<aion of the Mercury againft the 
Sides of it, will hinder it from rifing and fall- 
ing freely. 

7. Dr. Hooky obferving how unfit the com-* 
mon Barometer was to be ufed on Board of 
Ship, by Reafon its Pofition ought to be 
fteady, contrived the following one, called, 
from its Ufe, a Marine Barometer. A B 
{Fig. 34.) is the common Spirit Thermometer, 
C D is a Tube filled with Air from C to E, 
and from thence to the End D with tinged 
Water. This End is immerged in the fame 
Fluid contained in the Veffel G F ; and hav- 
ing its Surface expofed to the Preffure of the 
external Air. Now, the laft of thefe Ma- 
chines will be affeiSted both by the Warmth of 
the external Air, and alfo by its PrelTure: The 
former dilating the Air included in C E, and 
by that Means driving the Water downwards 5 
the latter prefling it up higher in the Tube: 
Whereas the other, ^iz. AB, is affeded by 
the Warmth of the Air alone. Cpnfequently, 


1 04. Of the Barometer. Part IL 

vseve thefe Inllruments graduated 'm fiich » 
Manner, that, if the Gravity of the external 
Air ihould always remain the fame it was, 
when the Inflruments were made, their Varia* 
tiOTS (then only depending on its Warmth) 
ihould exadly correfpond with each other; 
that is, when the Spirit in the Tube A B» 
ihould afcend to i, the Water in C D) ihould 
defcend to i , drcm Then, whenever their Va- 
riations ihould be obferved to diffi^ from each 
other, the Difference could only be afcribect 
to feme Alteration in the Preflfure of the Air 
upon the Surface of the Water in the Veffel 
G F. In Proportion therefore as this Diffe* 
rence is greater, or left, fo is the Alteration in 
the Gravity of the Air, from what it was 
when the Inftruments were adjufted. For In- 
ilance, when the Water (lands above the 
Divifion, which correfponds to that, which 
the Spirit points to in the otha: Machine, it is 
an Indication, that the Prefliire of the Air is 
greater at that Time, than when the Inibru*- 
ments were graduated, and vice verfd. 

This Machine is not only more ufefril at 
Sea, than the common one, as not requiring 
a fteady Pofition ; but may have its Scale of 
Variation confiderably enlarged, by making 
the Bore of the Tube CD very fmaU, in Prc^ 
portion to the Capacity of its Head C. 


Differt. 4. Of the Barometer; 105 

But it is obferved, that in long keeping this 
Inftrument, the included Air lofes fomewhat 
of its Elafticity ,• whereby ^ in Procefs of Time, 
the Water ftands higher than it ought, and 
therefore indicates the Gravity of the Air to be 
greater than what it is. 

In the Phiiofophical Tranfaftions N^. 427* 
I have given an Account of a Barometer^ 
wherein the Scale of Variation may be en- 
creafed ad Infinitum, The Defcription of it 
is as follows: A B C t), {Fig. 35O is a cy- 
lindrical Veffel, filled with a Fluid to the 
Height W5 in which is immerged the Baro- 
meter S V, confifting of the following Parts : 
The Principal of which is a Glafs Tube T P 
(reprefented feparately at //>) whofe upper 
Bna T is hermetically fealed: This End 
does not appear to the Eye, being received- 
into the lower End of a Tin Pipe G H, which 
in its other End.G receives a cylindrical Rod, 
or Tube ST, and thereby fixes it to the Tuba. 
TP. This Rod ST may be taken off, iti 
Order to put in its ftead, a larger, or lefTer, 
as Occafion requires. S is a Star at the Top 
of the Rod ST, and lerves as an Index^ by 
pointing to the graduated Scale L A, which is 
fixed to the Cover of the Veflel ABCD*. 
MN is a large cylindrical Tube made pf 
Tin (reprefented feparately at m n) which 
receives in its Cavity the fmaller Part of 
the Tube* TP, and is well cemented to it 

. at 


1 06 Of the Barometer. Part II. 

at both £nd$3 that none of the Fluid may get 

The Tube TP, with this Apparatus, being 
filled with Mercury, and plunged into the 
Bafon V, which hangs by two, or more Wires^ 
upon the lower End of the Tube M N, muft 
be fo poized, as to float in the Liquor con- 
tained in the VefTel ABCD, and then the 
whole Machine will rife, when the Atmofphere 
becomes lighter, and c^ice t'erfd. 

I ihall here add a Computation, in Order to 
fliew the Poflfibility of the Variation being 
infinite, upon a given finite Variation of the 
Weight of the Atmofphere, and withal, the 
Keafon why it may be fo. And for the Sake 
of thofe who would fee a Mathematical 
proof of it, I ihall give the Demonftration ia 
a Note below* * 


* Let the fpecific Gravity of QuickGlver be to tBat of Water, 
or to the Liquor the Barometer floats in, as J to i ; and if it be 
fropofed, that the Variations in this compound Barometer ihall be 
to the contemporary Variations of the common Barometer in the 
given Ratio of iv to i , this £SeA will be obtained, by making the 
Piameter of the Rod ST to the Diameter dT'the Cavity of the 

Tube H T, as 4^-— ^ to i, which may be thus demonflrated. 


Let us fuppofe, that the Variation in the Height of the Quick* 

filver in the common Bammeter, called v^, is ftich, that a cubic 

Inch of Quickiilver fhall rife into the Vacuum X T ; in Order to 

which, a cubiclnch of Quickfilver muft rife from the VefTcl V; 

that is, the Surface P inuft fubfide fo far, that a cubic Inch of W«« 

ter (if that be the Fluid made Ufe of) fliaH enter the Veffd V, hjt 

which Means the Barometer with the Pacts aimexed will be hea* 

vier by a cubic Inch of the Fluid, 

:.: Now 







Diflert4* Of the Barometer. 107 

Let it be fuppofed, that the Fluid made life 
of is W ater, and that the given Variation in 
the Weight of the Atmofphere is fuch, that, 


Now this additional Weight of a cubic Inch of Fl>iid, will 
make the whole Barometer fubfide (according to the Laws of Hy- 
droftatics)* till a cubic Inch of the Rod HS, immediately extant 
above the Sur&ce at W, fhall come under it ; but the Length of 
fuch a Magnitude of HS will exceed the Length of an equal Mag-* 
nitude of Quickfilver in the larger Tube X, as many Times as the 
Square of the Diameter at X exceeds the Square of the Dl^etef 
at H (the Lengths of equal Cylinders being reciprocal t^ their 
. Bafes). That is, the perpendicular Pefcent of the compo^id Ba- 
rometer "Will be to V, the perpendicular Afcent of the M^cury in 
the common Barometer, ais d to i (fuppofing this the Ratio^of th«i^ 
Safes) and confequently will be equal to dv* "*! 

But, by this pefcent, the Diftance PW, between the Surface of 
the ftagnant QuickfUver and the Top of the Fluid, will be aug- 
mented by a Column, whole Height is dv^ the Defcent of the 
compound Barometer ; and confequditly the Weight of the whole. 
Column of the Fluid preffing on the lower Surface of the Qu ck- 
filver (to which the Height X is partly owing) will be encreafed 
by a Column of that Length ; and this Increafe would produce a 
fecond Afcent of the Mercury at X equal to itfelf, namely, dv^ 
were the Fluid as heavy as Quickfilver ; but fince it is fuppofed to 

be lighter in the Ratio of i to i, the Afcent of the Quickfilverj 

on this^ Account will only be — ^ 

But now, as in the former Cafe, when the Afcent of the Mer- 
cury was Vy the Defcent of the compound Barometer was fhewn 

to be ^v ; &> here, the Afcent of the Mercury being — the De- 

fcent of the common Barom«er^will be '-^^ and thl next De- 

fcent and the next — p- anid fo on to Infinity. There- 

fore the whole Defcent of the compound Barometer, is to the AC- 

cent of the Mercury in the common Barometer, that is, 91 is to z 

^ ,dd , ddd . d"*- . ^ ds , 

ajrf4-*- — h H ■ , 1 ' fiPc. to I, or as ; to 1 ; be- 

^ s ss s^ ^ s-^d 

caufe the Terms of the Series being in geometrical Froportiop^ the 

' r Sum 

I oS Of the Barometer. Part II. 

by prefllngupon the Surface of it atW, the Sur- 
face of the Mercury at X may be raifed an Inch 
higher, (meafuring from its Surface at P) than 
before ; and that the Breadth of the Cavity of 
the Tube at X, and of the Bafon at P are fuch, 
that by this Afcent of the Mercury^ there may 
be a cubic Inch of it in the Cavity X more 
than before, and confequently in the Bafon a 
cubic Inch lefs. Now, upon this Suppofition, 
there will be a cubic Inch of Water in the Ba- 
fon more than there was before i becaufe the 
Water will fucceed the Mercury to fill up its 
Place. Upon this Account, the whole Ma- 
chine will be rendered heavier^ than it was 
before, by the Weight of a cubic Inch of Wa- 
ter, and therefore will fink, according to the 
Laws of Hydrbffatics, (Chap. 11. $. 5.) till a 
cubic Inch of that Part of the Rod WS, which 

Sum of them all is ;. Hence we have n= -. and there- 

fore ffi = rff + ^i» ; that is, r : i : : » + J • w : : --I- : i ; 


and therefore, by extrading the fquare Roots of each Term in the 
Proportion, i : P^d, (that is, the Diameter of S T to the Diame* 

ter of HI) as f/— I— to i. J^ E, D, 

Example i. Putting 1=14 and if=i, *the Variation in each 
Barometer will be equal, by taking the Diameter of ST to the 

Diameter of HL as i/— to i, that is, as 20 to 29 nearly. 

Example 2. Ifn be put infinite^ the Diameter of ST wHl be 

to the Diameter of HI, as f/— Co I, or i to f^J4 ; that i% » 
I to 5 i nearly^ ^ 


Plflert. 4* Of the Barometer] 1 09 

was above the Surface of the Water at W^ 
comes under itf Then, if we fuppofe this Rod 
fo fmall, that a cubic Inch of it ihaii be four- 
teen Inches in Length, the whole Machine 
will fink fourteen Inches lower into the Fluid 
than before, and confequently the Surface of 
the Mercury in the Bafon will be preffed more 
than it was before, by a Column of WatCT 
fourteen Inches high. But the PrefTure of foiff- 
teen Inches of Water is equivalent to oiie of 
Mercury, (becaufe Water is about fourteen 
Times lighter than Mercury) this additional 
PrefTure therefore will make the Mercury af- 
cend at X, as much as the fuppofed Variation 
in the Weight of the Air did at Er&. This 
Afcent will give Room for a fecond cubic Inch 
of Water to enter the Bafon ; the Machine will 
therefore be agaiii rendered heavier by the 
Weight of fo. much Water, and accordingly 
will fubfide fourteen Inches farther. Thiis will 
occafion another additional Preifure of Water, 
which will raife another Inch of Mercury, and 
make the Machine fink fourteen Inches mor^ 
and fo on, without ever approaching nearer to 
an ^Equilibrium with the external Air : and 
therefore a Scale anfwering to the Variation 
of this Barometer ought fbidly and properly 
tp be of an infinite Lengthy becauf^ after this 
Barometer has rif^-thoufands of Miles (if thac 
;- were poifibl^) it would flill have the fame 

Tendency to rife od^ as when it firil fet out. 

no Of the Barometer. Part IT* 

Now, was the Rod W S fo fmall, that a 
cubic Inch of it ftiould be more than fourteen 
Inches Jong (the other Parts remaining as was 
fuppofed above) the Variation in this Barome- 
ter would be more than infinite^ or negative 
with Refpecl to thofe of the common Barome- 
ter. The Meaning of which is, that whereas 
in the common Barometer, the fufpended Co- 
lumn of Mercury, by its rifing or falling, ap- 
proaches nearer to an ^Equilibrium with the 
external Air, this Barometer would continually 
recede from an Equilibrium with it 5 fo that 
the farther it fliould move up or down, inftead 
of acquiring by that Means a lefs Tendency to 
move on, as the. Mercury in the common Baro- 
meter does, it would acquire a greater. 

On the contrary, when a cubic Inch of the 
Rod is lefs than fourteen Inches in Length, the 
Variation will be finite ^ and may be made to 
bear any Proportion to thofe of the common 
Barometer whatever, as demonftrated in the 
foregoing Note, 

While I am writing this, another Method 
occurs to me of making a Barometer, wherein 
the Scale of Variation fliall bear any Propor-^ 
tion to that of the common one. It is this ,• 
Let there be a compound Tube, as ABC (JPig. 
36.) hermetically fealed at A, and open at C, 
eijipty from A to D, filled with Mercury from 
thence to B, andj&pm thepce to E with Wa- 
ter ( 

• Dlffert. 4. Of the Barometefl 1 1 1^ 

ter : Then, if the Tube FC be a little more 
than five Times lefs in Diameter than the Tube 
FA, the Variation in the lower Surface of the 
Water at E will be infinite, if it be above fo 
many Times lefs, it will be more than infinite^ 
otherwife it will be finite. See the Demon* 
ftration in the Note "^^ 


* Let V denote a given Variation in the common Barometer^ * 
the correfpondent Variation at £ fought. Let the Ratio of i» to 
I, exprefe that of the fpecific Gravity of Mercury, to that of Wa« 
ter; and ^ to i, that of the Diameter of the Tube FA to FC 
Then the Variation at E, the lower Surface of the Water, being 
fuppofed Xy the Variation of it at B, the upper Surface of it will 


be — and confequently GE, the Pifference of the Legs EK and 


KB, will vary ^H-r-. Again, the Variation of the Sur&ce of 


the Mercury at B will be the iame with that of the Water in the 
fame Place, viz. ■— ; and, iftheTubcis ofthefame Dlametet 


at D, as at B, the Variation of the Surface at D will alio be the 


iame, that is, 73: The Sum of both Variations, or the Variation 

da 2.x 

of HD the Difference of the Legs, will therefore be -- . Now the 


Freffure of the Mercury and Water together upon the Air at £, li 
owing to the Lengths of HD and G£ ; and -fince one of thefe will 
always fhorten, when the other lengthens, the Variation in their 
PreiTure will depend on the Variation of the Difference of their 
Weights, that is, of the Difference between the Weight of jr*i» 

25 and of — . But the Weight of *-Ht 0>«flg ^^^ Weight of 

a Column of Water) compared to th$t of a Column of Mercury xf 

the iame Length, is only *"* *^ . The Difference therefore bo^ 

yween ^, TS and ^ wiU alw»]p be ctpil to the Viriacioo it 


1 1 a Of the Barometer. Part IL 

That the Variation in this Barometer may 
fce infinite, may be fliewn in the following 

Let the Proportion between the Bores of the 
Tube A F and FC be fuch, that when the per- 
pendicular Height of the Column of Mercury is 
augmented one Inch, GE the Difference of the 
Legs, wherein the Water is contained, fliall be 
diminiihed fourteen j then, as much as the 
Prelfure of the Mercury is augmented, that c^ 
the Water will be diminifhed, and fo the 
PreflTure of both taken together will remain ^s 
it was^ And confequently, after it has began 
to rife, it will always have the fame Tenden- 
cy to rife on, without ever coming to aa 
jEpii/ibrium with the Air. 

How far this Barometer will fucceed in Prac- 
tice, muft be left to Experience to determine* 
Probably, if the Bore of the Tube FC be made 
very fmall, ^iz* about the twentieth Part of 
an Inch Diameter,, the Air will not afcend 

tiie common Barometer, and therefore 7-;— ' -ssgg, and by 

tliecommon Method of Reduft ion, *= — • That is, x 1 


« :: mdd : zm — dd—i. Now, ifweput «i=i4, andi/=5,», 
' — dd and — i will be as much as ziw, and therefore zm-^dd—^t, 
w 11 be equal to nothing ; and fo jr being by the Proportion as 
many Times more than «, as mdd is than nothing, 'tis infinite. 
And if m be put =31^, and <^=5, mdd will be equal to 550, 
and xm'^dd — 1=1 ; and therefore the Variations in this Cafe, 
Will be to thofe in the common Barometer, as iJS'to onc» 



Diflert. 4. Of the Barometer. 115 

through the Water, as it is apt to do through 
the Mercury in the pendent Barometer ; and 
the fmallnefs of the Bore will not prevent the 
Water, from moving, near fo much as it does 
the Mercury in that Barometer. 

There is an Improvement of another Kincf 
in the common Barometer, whereby it is ren^ 
dered portable. The Tube containing the 
Mercury, inftead of haying its lower End im- 
merged in a Veflel of that Fluid, has it tied 
up in a leathern Bag, not quite fiill of Mercu- 
ry. And though the external Air cannot get 
into the Bag to fufpend the Mercury in the 
Tube, by prefling on its Surface, as in the 
common one ,• yet it has the fame EfTed: by 
prefling on the outfide of the Bag, which being 
pliant, yields to the Preflure, and keeps the 
Mercury fufpended in the Tube at its proper 
Height. This Bag is generally inclofed in a 
little Box, through the Bottom of which pafles 
a Screw ,• with this Screw the Bag may be 
comprefled, fo as to force the Mercury up to 
the Top of the Tube ^ which keeps it fteady, 
and hinders it from breaking the Tube by dafh- 
ing againft the Top when it is carried about, 
as it otherwife would be apt to do. 

See more on the SubjeA of this Diflertation, 
JVeidleri InftitutionesMathemat. p. 568. MeU 
cbior Verdries Phyf. Pars fpecialis, Cap. IV. 
$• I J. Mr. Tafcbah Traite de Tjiquilibre 


114 Of the Barometer. Part II 

des Liqueurs. Sriclair^s Ars magna gravJtatis 
& ievitatis. Mariottea Second tflay de k 
Nature de I'Air. Fhilofoph. Burgund. Tom.II. 
p. 850. ^^'./s 'ircatife on the Barometer. 
Regimult\ Philoioph. Converfat. 21. Clares 
Motion of Fluids, p. 141. Mem. de I'Acad. 
^705, 1711. Philofophical Tranlaftions N**. 
j>, 10, II, 55, 86, 91, 165, 18 ij 185, 208, 
229, 236, 237, 240, 243, 26pj 351, 365, 
385, 388, 405, 406, 427. With feveral 
other Authors referred to in Mr. Johnfons 
Quiftiones Philofophical, Cap. VI. Qusft. 36, 



Differ t. 5. Of the Origin of the Winds. 1 1 5 

Dftbc Origin of the Winds. 

THE Wind Is no other, than the Mo- 
tion of the Air, upon the Surface of 
the Globe. Some of the Ancients took it 
to be Air, rufliing out of the Bowels and 
Cavities of the Earth ; And others thought it 
an Exhalation from its Surface, But thefe 
are Hypotbefes too chimerical to ftand in 
Need ol a particular Confutation. Some of the 
Moderns, who held a Tknum^ have account- 
ed for it thus. They imagined, that the Air 
being confined above, as it muft be, if we fup- 
pofe a Tknum^ would, when more than or- 
dinarily rarefied, or (locked with Vapours, 
drive away the neighbouring Air, in order to 
make room for itfelfj and by this Means occa-^ 
iioQ a Wind. Others, obferving a conftant 
and perpetual eafterly Wind to blow at the 
Equator, afcribed its Origin to the diurnal 
Rotation of the Earth, about its Axis from 
Weft to Eafti which they thought would 
cccafion the Air upon its Surface, to feem to 
move ^he contrary Way, being in fome Mea- 
fure left behind. But, whereas there are 
Windsy in iome Places near the Equator^ 

g^ that 

1 1 6 Of the Origin of the Winds. Part II. 

that blow on other Points of the Compafs 
(as we ihail fee hereafter) this Hypotbefix is 
infufficient. Befides, the Air prelling upon 
the Surface of the Eaith by its Gravity, like 
other Bodies ; and having nothing to binder it 
firom moving freely along with it, muft necelTa- 
rily in Time^ acquire an equal Degree of Ve- 
locity, and fo keep Pace:with it, all the Way 

The principal Caufe of the Wind, or, in 
other Words, of the Air's moving-from Place 
to Place, upon the Surface of the Earth, is 
the Atmofphere*s being heated over one Part 
more than over another. For, in this Cafe^ 
the warmer Air being rendered fpecifically 
lighter than the reft, rifes up into the fuperior 
Parts of the Atmofphere, and there diffafes it- 
felf every Way; while the neighbouring infe- 
rior Air rufties in from all Parts at the Bottojii^ 
to reftore the jEquilibrium^ -5 

Upon this Principal it is, that moft of the 
Winds may be accounted for. 

To begin with, thofe which blow under the 

1. Under the Equator y the Wind is always 
obferved to blow from the Eaft Point *^ 


* For the Residei's Eafe (who perhaps is aot fiirniflied 
with the Philofophical Traniadions) I fiiall here infat by ^ay 
dFNote^ from Dr« H^Xfo^'s Account, ib much of the Hii^jK 
Cfae Winds, aa may be peceflaiy for the undcrffamding cbisl^eogw 

|5 ^ 

DifTcTt.^. of th Origin of the Winds. 117 

For, fuppofing the Sun to continne vertical 
over fome one Place, the Air will be moft ra- 
refied there ; and confequently, the neighbour- 

•' The iiniverikl Ocean, hys he, may mofi properly be divided 
** into three Parts, viz, i. The Atlantic and Mtbicfic Seas* 
*' £• The Indian Ocean. ^. The great South, Scz^ or cbe l^acifc 
" Ocean. 

*' I. la the Mantle and Mthiofie Seas, between the Trcficsy 
•*' there is a general eafterly Wind all the Year long, without 
*^ any coiifiderable Variarion ; excepting, that it is fubjedt to be 
*' defleded therei^om, foroe few Points of the Compftfs, towards 
** the North or South, according to the Poiition of the Place. 

** I . Near the Gwtft of Africa^ as foon as you have palled the 
*' Canary Ifles, you are fure to meet a frefb Gale of North- eaft 
*^ Wind, about the Latitude of twenty -eight Degrees North *, 
^' which feldom comes to the Eafl wards of the £aA-noreh-eaft, or 
'^ palTes'^e North«noith-eaft. This Wind accompanies thofe 
^' bound to the Southward, to the Latitude often Degrees North, 
' •*' and about an hundred Leagues from the Guinea Coaft ; where, 
'^ till the fourth Degree of North Latitude, they fall into Calms 
*' and Tornadoes^ or fuddeii Storms. 

^^ z,. Thofe bound to the Caribbe Ifles, find, as they approach 
^ the American Side, that the afoi^laid North-eaft Wind, be« 
^^ comes Aill more and more eafterly, fo as fometimes to be Eaft, 
'^ ibmetimes £aft by South, but yet mod commonly to the North- 
'* ward of the £aft,' a Point or two^ feldom more. *Tis likewite 
/^^ obferved, that the Strength of thefe, does gradually decreafe^ 
'^ as you fail to the Weft ward. 

*' 3. That the Limits of the Trade and variable Winds in 
*' this Ocean, are farther extended on the American Side, than 
^ the African; for, whereas you meet not with this cenain 
*' Wind, till after you have pa&'d the Latitude of twenty-eight 
*' Degrees on this Side ; on the contrary Side it commonly holds 
^ to tbirQr, thirty-oae, or thirty»two Degrees of Latitude ; and this 
** is verinexft likewile to the Southward of the JE^nineBial ; for 
^' near the Cafi tfGe^d Hope^ the Limits of the Tradt Winds are 
/' three or bm tkgttts ncafer the Line, than on the Coaft 
f of ir^^iA . *^ 

Q » f 4. That 



vi% of the Origin of the Winds. Part Ifj 

kig Air will rufli in from every Quarter with 
equal Force. But, as the Sun is continually 
fhifting to the Weftwards, the Part, where the 


^^ 4. That from the Latitude of four Degrees North, to 
*'< the aforeCiid Limits on the South Side of the Equator, the 
*^ Winds are generally and perpetually between the South 
*' and Eaft, and rooft commonly between the South-eafi and 
** Eaft ; obferving always this Rule, th*t on the African Side, 
*' they are more foutherly, on the Br^filiaw mbre eafterly^ £6 a$ 
*' to become almofi due Eaft, the little Defiedion thiey have, be- 
•^ ing flHl to the Southwards. In this P*rt of the Ocean, it 
*^ has bfen my Fortune to pais a full Year, in an Employ- 
*^ ment that ob:iged me to regard more than ordinarily the 
•• Weather ; and I found the Winds conftantly about the 
•* South-eail, the moft ufual Point South-eaft by Eaft : When 
^^ it was eaflerly, it generally blew bard, and was gloomy, 
dark^ and fometimes rainy Weather : If it came to the South- 
wards, it was generally ferene, and a fmall Gale next -to a 
Calm ; but this not very common. But I never faw it to the 



** Weft wards of the South, or Northwards of the Eaft« 

*' 5. That the Seafon of the Year has fome fmall Effed on 
thefe Trade Winds ; for that when the Sun is condderably ca 
Ike Northward of the Bauator^ the South-eaft Winds, efpe- 
cially in the Screight ol this Ocean (if I may fo call ir ) 
** between Brajtiy and the Coaft of Guinea^ do vary a Point or 
*^ two to the Southwards, and the North-eaft become more 
.4c eafterly ; and, on the contrary, when the Sun is towards the 
Tropic of Capricorrtf the South-eafterlp«j^Vinds become more 
eaiierly, and the North-eafterly Winds on this Side the 
♦^ L/w, veer more ;o the Northward, r 

^' (j. That as ti«ere is no general Rule, that admits not of (bme 
*^ Exception, fp there is in this Ocean a Trad of Sea, whereiri 
'^ the ibutherly and South-weft Winds are perpetual, viz> all 
^^ along the Coaft of Gjvinf/f, for above five hundred Leagues to- 
*' gether, firom Sierra Leena^ to the Ifle of St. fbemas : I^r 
the South-e^fi Trade Wind having pais'dthe Irfif^, and approacfi- 
ing the Coaft of Guinea within eighty or an hundred Leagues, 
inclines towards the Shore, and becomes South-ibiith-eafi'; 
and by Degrees, as you come nearer, it veers about tb South, 
^"' 2outh./buch-weft^ and in with ;be Land South^weftj and fome* 


Differ t.' y. Of the Origin of the Winds. 1 1 9* 

Air is moft rarefied, is carried the fame Wayj 
and therefore the Tendency of all the lower Aif 
taken together, is greater that Way, than any 

other* , 

** times Weft-fouth.wcft. Thefe are the Winds, which are o!>* 
^^ ferved on this Coaft when it blows true ; but there are fri^ 
^* quenc Calms, violent fudden GuAs, called Tornadoes^ from all 
^' Points of the Compais, and fometimes unwholfome foggy 
" eafterly Winds, called HermiU, by the Natives, which too 
" often infeft the Navigation of thefe Pans, 

*^ 7. That to the Northwards of the Line, between four and 
*^ ten Degrees of Latitude^ and between the Meridians of Cafe 
" Verde^zad of theeaftermoft Iflands that bear that Name, there is 
a Trad of Sea, wherein it were improper to fey, there is 
any Trade Wind, or yet a variable-, for it feems condemned to 
perpetual CalmSj attended with terrible Thunder and Light* 
ning, and Rains fo frequent, that our Navigators from thence •' , 

*^call this Part of the Sea, the lUins : The little Winds 'that ' 7' 2^ 
** are, being only fome certain Gufts, of very little Conti-'*' 
^^ nuance, and lefs Extent ; fo that fometimes each Hour you . 
" fhall have a different Gale, which dies away into a Calm 
*^ before another fucceeds : And in a Fleet of Ships in Sight of 
*' one another, each {hall have the Wind from a feveral Point of 
^' the Compafs : With thefe weak Breezes, Ships are obliged to 
** make the beft of their Way»to the Southward, through the 
*^ aforefaid fix Degrees ; wherein It is" reported fome have been 
*J detained whole Months for want of Wind. ■ 

*' II. In the Indian Ocean, the Winds afe/^artly general, 
" as in the Mthiopic Ocean ; partly periodical, that *"is, half 
" the Year they blow one Way, and the other half, near upmi 
** the oppofite Points ; and thefe Points and Times of fhifting> 
*' are different in different Parts of this Ocean. 

*^ 1. Between the Latitudes often Degrees and thirty Degrees 
^* South, between Madagafcar and Hollandia nova^ the Cene- 
•* ral Trade- Winds about the South eaft and by Eaft, are found 
*^ to blow all the Year long, to all Intents and Purpofes, 
^' aiter the fame Manner, as in the fame Latitudes in the 
*' Ethiopia Ocean, as it is deicribed in the fourth Itemark 
f* aforegoing, 

2^ Tfiac 

140 Of (he Ori^i^ •f the Winds. Rirt !!• 

ether. Thus the Tendency of the Air to- 
vards the Wpft^ becomes generai, and iu 
Parts impelling erne another, and continuing to 


** X Thit the aforefaid Souch-eaft Winis extend to within two 
•* Decrees o\ the E^matofy during the Months of fMne^ J^J^ 
** and Au^mft^ &c. to J^voember^ at which Time, between the 
•* Smith Latitude of three and ten Degrees, being near the' 
•* hleti4ian of the North End ^i Mada^afcar^ and between two 
*^ and twelve South La^icude, being near Sumatra and yava ; 
•* the contrary Winds from the North- weft, or between the 
•* North and Weft, fet in, and blow for half a Year, vh^ 
^ ifom the Beginning of Detemher till May ^ And this Idoth 
^ foMi is obferved as far as the Moittcca Hies. 

'• 5. That to the Northward of three Degrees South Lati* 
•* tuoe, over the whole Arabian and Indian Sea, and Gttlf of 
** Ben^^ftl^ fron Sumatra to the Coaft of Africa, there is another 
*^ Mofifoon^ blo.ving from OBober to April y upon the North- 
** eaft l^oinrs : Kut in the other half Year, from April to OBtlber^ 
^ upon the oppofire Points of South- weft and Weft-fouth-weft^ 
•* ami that with rarher more Force than the other, accoaipanied 
•* with i^ark, rainy Weather ; whereas the North-eaft blows clear* 
•* 'Tis iixewife to be noted, that the Winds are not fo con- 
** ftant, cither iii Strength or Point, in the Gulf of Bengal^ 
•' as they are iw the Indian Sea, where a cerrain fteady Gale 
** lea roe ever fills. *ris alfo remarkable, that the South- weft 
** Winds hi thcfe Seas, are generally more Ibutherly On the 
*' Afr'fan Side, ami more welterly on the Indian^ 

""• 4. There is a Trait of Sea to the Southwards of the 
** Eqtfitory fub).-d to the fame Changes of the Winds, viz* 
" near the CoaAj between it and the liland MadagaCcat^ 
** or St. Lanrevce^ and from thence Nonhwards, as far as the 
Lir,c \ wherein from April to OBober, there is found a con- 
liar.: frdh South-fouth-weft Wind, which as you go more 
*• noi'ihcrly, becomes ftill more and more wefterly, fo as to fall 
'• in wirh the Weft-fouth-weft Winds, mentioned before in ihofe 
** Months of the Year to be certain to the Northward of the 
'- Bcfuaf^r. What Winds blow in thofe Seas, for the 6ther 
1 <*f Year, I have not yet been able to obtain to ray full Satif- 
(acition s The Accoui;t which has been given me, is only this, 

« That 



Diflert. 5- Of the Origin of the Winds. lai 

move till the next Return of the SUn^ fo much 
of its Motion as was loft by his Abfence, 
is again reftored, and therefore the eafterly 
Wind becomes Perpetual. 


** That the Winds arc much eafierly hereabouts, and as often to 
" the North of the true Eaft, as to the Southward thereof ' 
^^ 5. That to the Eaftward of Sumatra and Malacca^ to 
" the Northwards of the Line-, and along the Coaft of Cam^ 
*^ hoU and Chinay the Manfoons blow North and South ; that is 
** to fay, the North- eaft Winds are much northerly, and the . 
*' South-wed much foutherly. This ConflituticMn reaches to the 
*' £a{hvard of the Philippine Illes, and as far northerly as. 
** ^apan ; the northern Monfion fetting in, in thefe Seas, in . 
^' OStfiber or Sovember ; and the fouthern in May, blowing all 
" the Summer Months. Here it is to be noted, that the Points of . 
** the Compais from whence the Winds come, in thefe Parts of - 
•* the World, are not fo fixed, as thofe lately defcribed ; for the 
" foutherly will frequently pafs a Point or two to the Ea Awards - 
^ of the South, and the northerly as much to the Weftwards 
" of the North, which feems occafioned by the great Quantity o^ 
•^ Land which is interfperfed in thefe Seas. 

^* 6. That in the fame Meridians^ but to the Southwards of the 
*' BqHatffr^ beinguhac Traft lying between Sumatra ^nd Java. 
^ to the Wefi, and New Guinea to the Eaft, the lame northerly 
** and foutherly Monfions are obferved ; but with this DiftVrence, 
" that the Inclination of the northerly is towards the North-weftj 
*^ and of the foutherly towards the South-eaft : But the IPlagdf 
^ Venti are not more conftant here than in the former, viz* va- 
*• riablt five or Bx Points. Befides, the Times of the Change of 
'^ thefe Winds are not the fame, as in the Cbinefe Seas, but about . 
•* a Month, or fix Weeks later. 

" 7. That the contrary Winds do not ihift all at once^ but in 
^ ibme Places the Time of the Chanee is attended with Calms^ 
'^ in others with variable Winds; and it is particularly remark* 
•* able, that the End of the weflerly Monfoim in the Seas of 
** Cbina^ are very fubjed to be tempeftuous. The Violence of 
^ thefe Storms is fuch, that they feem to be of the Nature <iS the 
*' Wefi- India Hurricanes, and render the Navigation of thefe Parti 
2 vcqr unfiife about that Time of the Year. Thefe Tempefis are 

112 Of the Origin of the Winds. Part II. 

Some are inclined to thinks that the ohi- 
tinual ihifting of the Sun to the Weftward, 
iLould produce a wefterly Wind under the 
Equator^ by caufing the Current of Air from 
the Weft to exceed and over-balance that, 

^ by our Seamen, ufiially termed the Bnaking up of the Ido»* 

•^ Illi The third Ocean, called Mare Pacificmm, whofe Er- 
** tent is equal to that of the other two (it being from the Weft 

Coafl of America to the Philipine Iflands, not leCs than an hun« 
died and fifty Degrees of Longitude) is that which is leaft 
*' known to our own, or the neighbouring Nations : That Navi- 
*' gatlon that there is on itj is by the Spaniards ; who go 
^' yearly irom the CoaA of New-Spain to the Manilba's : But 
*^ that but by one beaten Track ; fo that I cannot be fo particular 
•* here, as in the other Twa What the Spanifi Authors fay of 
^' the Winds, they find in their Courfes ; and what is confirmed 
** by the old Accounts of Drake and Candip^ and dnce by 
** Schooten^ who failed the whole Breadth of this Sea, in the 
*^ fouthern Latitude of lateen or fixteen Degrees, is, that there is 
*^ a great Conformity between the Winds of this Sea, and tho& 
'* of the Atlantic and Mthicfic ; that is to (ay, that to the North- 
*' ward of the Equator, the predominant Wind is between 
*' the Eafl and North>eaft ; and to the Southwards thereof, there 
'^ is a conf^ant, f^eady Gale, between the £afl and South-eaft, 
^' and that on both Sides the Line, with fo much Confiancy, that 
they Icaice ever need to attend the Sails : and Strength, that it 
is rare to fail of crofHng this vafi Ocean in ten Weeks 
Time ; which is about an hundred and thirty Miles a Day : 
*' BefideSf 'tis (aid, that Storms and Tempefls are never known 
** in thefe Parts ; wherefore fome have thought it might be as 
^^ fliort a Voyage to ^apan and Cbina^ to go by the Screights of 
** Magellan, as by the Cape oiGood Hope. 

'* The Limits of thefe General Winds, are much the lame 
*' as m the Atlantic Sea, viz. about the thirtieth Degree of Lati<* 
tude on both Sides. Befides, a farther Analogy between the 
Winds of this Ocean, and the JEtbtopic, appears in that, 
•* that upon the Coaft of Peru, they are always touch foutberly, 

^ like as thqr «« ^ad aear the Shores of ^;9Pgv/«« 





DilTert. y. Of the Origin of the Winds, laj 

.which Dppofes it from the Eiaft. For, where- 
as the eaftern Air retains its Heat fome timo 
after the Sun is removed from it^ it muft al- 
ways be rarefied to a greater Degree, and 
alfo to a greater Diftance from the Place to 
which the Sun is vertical^ than the weftern Air 
is; and therefore the weftern Air being more 
ponderous, ftiould be an over-balance for the 
^aftem, and drive its Current before it* 

But it is to be obferved^ that we are not to 
confider the Point to which the Sun is ver- 
tical, but the Point of greateft Rarefaction 
(which upon Account of the Sun s Motion to 
the Weftward, lies always to the Eaft ward) ; 
and then fee, which Side of the Column of 
Air incumbent over that Point, fuftains the 
jreater Preffure from the neighbouring Co- 
fumns* Now, although the Air is rarefied 
even farther to the Eaft of^ this Point, than 
to the Weft, yet ftill, if we fuppofe the Point 
to keep its Place, the Air over it will fuftain 
an equal Degree of Preffure on each Side. 
For, fince no Column can be affigned on the 
weftern Side, but one alfo on the eaftern, 
may be* found under an equal Degree of Rare- 
feftion, and therefore of the fame fpecific Gra- 
vity : And fince Fluidsof equal Heights, and the 
lame fpecific Gravities, (whatever be the 
Breadth of their Columns) prefs equally againft 
equal ObjeiSts, (Chap. x. $. p.) \is very 

evident, that the Column of Air^ over the 

R Point 


t^\ Of the O/i^m of the Winds. Part II. 

Poirt of gicateft Rarefaaion, is preffed equals 
Iv boii* '•*'«ry^; and fo, upon this SuppoCtioii, 
Ciich ^^ )1^d will blow towards that Point with 
equal Force. But, if w^e fuppofe the Point of 
greateft Rarefadion to fliift towards the 
Weft, we fliall find, that this ^Equilibrium 
will by that Means be deftroyed, and the 
Modem of the Air ( upon the whole ) deter- 
mined that Way. For let us confider any 
Portion bf the weftern Air approaching to- 
wards the Point of greateft Rarefaddon, if 
that Point fliifts, in the mean Time, towards the 
Weft, then will that Portion reach the faid 
Point fooner than it other wife would have 
done ; thereby lofing a Part of its Motion, by 
which Means the wefterly Current will be dimi- 
ninifh'd. Again, if, w hile the Eaft Wind blows 
towards the Point of greateft Rarefaction, that 
Point moves on before it, then will the eaftern 
Air have a greater Quantity of Motion, than 
it otherwife would have had ,• that, which 
fliould have been an Impediment to it, being, 
upon this Suppofition, in fome Meafure with- 
drawn; and fo the Eaft Wind will be aug- 
mented. Thus, the Weft Wind having its 
Force leffen'd by the Motion of the Sun, and 
the Eaft one being increafed, the latter at 
length abforbs the former, and drives it before 
it, in its own Direction. 

2. On each Side of the Equator^ to about 
the thirtieth Degree of Latitude^ the }Vind is 



Di!kTt.j. Of tie Origin of the Win Jfl 115 

found to vary from the Eaft Point, fo as to be* 
come North-eaft on the northcarn Side^ and 
South-eaft oa the foothern. 

The Reafon of which is, that, as the e^a^ 
ioreal Parts are hotter than any other, both 
the northern and fouthern Air, ought to have 
a Tendency that Way ; the northern Current 
therefore meeting in its Paffage with the 
eaftern, produces a North-eaft Wind on that 
Side i as the fouthern Current joining with the 
fame, on the other Side the ILquatOTy forms 
a South-eaft Wind there* 

Thefe two Propofitions are to be Ender- 
flood of open Seas, and of Inch Parts of them 
as are diftant from the Land ; for near the 
Shores, where the neighbouring Air is much 
rarefied, by the Refleftion of the Sun s Heat 
from the L.and, it frequently happens other^ 
wife 5 particularly, 

3. On the Guinea Coaft, the Wind alwajrs 
fets in upon the Land, blowing wefterly in- 
ftead of eafterly. This is becaufe the Deferts 
of Jfrica lying near the Equator y and being 
a very landy Soil, refled a great Degree of 
Heat into the Air above them. This therefore 
being rendered lighter, than that which is 
oyer the Sea, the Wind continually rufties ia 
upon the Land to reftore the yEqui/ibrtum. 

4* That Part of the Ocean, which is called 
the Rainsy is attended with perpetual Calms» 

$te .Wiad fcarce blowing fenfiWy ^ith^ on© 

1 16 Of the Orlgm of the Winds. . Part IL 

Way or other. (See its Situation defcribed in 
Note, Page i ip. Remark 7 th). For this Trad 
being placed between the wefterly Wind blow- 
ing from' thence towards the Coaft oi Guinea i 
and the eafterly W ind blowing from the fame 
Place to the Weftward thereof, the Air ftands 
in ALquilibrio between both, and its Gravity is 
fo much diminifhed thereby, that it is not able 
to fupport the Vapour it contains, but lets it 
fall in continual Rain, from whence this Part 
of the Ocean has its Name. 

5. There is a Species of Winds, obfervable 
in fome Places within the Tropics^ called 
by the Sailors Monfoons^ which during fix 
Months of the Year, blow one Way ^ and the 
remaining fix, the contrary. 

The Occafion of them in general is this : 
When the Sun approaches the northern Tropic^ 
there are leveral Countries, as Jrabiay Ter^ 
fia^ India^ &c. which become hotter, and 
refleit more Heat than the Seas beyond the 
Equator y which the Sun has left 5 the Winds 
therefore, inftead of blowing from thence to 
the Parts under the Equator ^ blow the cqn- 
trary Way j and when the Sun leaves thofe 
Countries, and draws near the other Tro- 
pic^ the Winds turn about, and blow on the 
oppofite Point of the Compafs. 

I'he Regularity of thefe Winds making 
them more than ordinarily ufeful in Naviga4 
tion^ they a^-e from tbepce called ^radc, 

Diflerti 5 . Of the Origin of the Winds. 127 

Winds. As to other Circuihftances relating 
to them, and the particular Times and Places 
of the MonfoonSy Sec. fee the Hiftorical Ac- 
count in the foregoing Note ,• all which might 
eafily be folved upon the fame Principle, had 
we aa fa to go upon, and wer^ all the feveral 
Circumftances of Situation, Heat, Cold, ^c. 
fufficiently known \ 

From the Solution of the general Trade 
Winds, we may fee the Reafon, why in the 
Jtlantic Ocean, a little on this Side the 
thirtieth Degree of North Latitude, or there- 
abouts, as was oblerved in the foregoing 
Differtation, there is generally a Weft, or 
South-weft Wind. For, as the inferior Air 
within the Limits of thofe Winds, is conftant- 
ly rufliing. towards the Equator ^ i^om the 
North-eaft Point, or thereabouts, the fuperior 
Air moves the contrary Way i and therefore 
after it has reached thefe Limits, and meets 
with Air, that has little or no Tendency to 

^ Some have thought, that the Regularity of the genertl Traits 
Winds^ is partly owing to the diurnal Motion of the Moon from Baft 
to Weft. For, as the Sun renders the Air fpecifically lighter by 
its Hear, lb does the Moon by attracting it, in the fame Manner, 
as it does the Sea, in railing the Tides. But it is to be obfenred, 
that as the Moon ads with greateft Force upon the fupenpr Parts 
of the Air, and as thofe fuperior Parts are unconfined, and there* 
fore more at Liberty to rufti in, in Order to refiore the JEjuilibn* 
um j it will from hence foUdw, that the rufliine in of the fuperior 
Parts of the Atmofphere will principally contribute towards refio* 
ring the JEquilHrmm ; and M the Mocioa gcodnofid belowa will 
)^ yeiy inconfiderablQi 


128 Of thOri^ht^ the Winds. PartH 

any one Point more than to another, by Reafba 
of the Sun's Diftance, it will determine k to 
Biove in the fame DiraSkion with itfelf* 

In our own Climate we frequently expe- 
lience^ in calm Weather, gentle Breezes blow- 
h% fitmi the Sea to the Land, in the Heat of 
ihe Day; which ^banomenon is very agrees 
able to the Prmciple laid down above: Fw 
the inferior Air over the Land being rarefied 
fcy the Beams 6E the Sun, refleded from its 
Sor&ce, more than that which impends over 
the Water which refleds fewer, the latter \s 
conifetntly moving <mi to the Sh<re, in order 
to reftore the Mquilihriumy when not di» 
(tiiarced by ftronger Winds from another Qnar* 

tier * 

From what has been obferved, nothing \% 
mofe cafy than to fee, why the northern and 
foothem Parts of the Wcx-ld, beyond the Li- 
mits of the Trade Winds, are fubje(fl to fuch 

• Tn CoafimiatJWi of this, we haire an eafj% and rer^ per- 
iibent Experlmenr, rckced by Mr. CUre^ in his MHhn of FlMtdu 
^ Take, jays he, a large Di(h, fill it with cold Water ; iaco» 

* the Middle of tHis put a Water-Plate, filled with warm Water. 
-«* The firfk will jeprefent the Ocean ; and the other an Ifiamf, 
** rarefying the Air above it* Blow cue a Wax Candle, and if 
^ r^e Place be ftill, on applyii^ it luccefllvely to every Side of 
•* the Diih, the fuliginous Particles o^theSnwak, being vifible 
«■ Mid very light, will be feea to move towards the Plate, 
^ and riGnn over it^ point out the Courie oC the Air frooi 
^ Sea t€> Land, Again, if the ambient Water be warmed> and 

* the Plate filled with cold Water, let the finoakiog Wick of tliel 
^ Caodle be held over tlie Plate^ and the cootraiy wiU hap^a* 

Diflcrt,5- Of th Origin of th Winds. 119 

Variety of Winds. For the Air, upon Ac- 
count of its Diftance from the Equat€ry being 
undetermined to move towards any fixed Point;^ 
>s continually ihilting from Place to Place, ia 
Order to re&ore the jEquillbrmmj wherever it is 
deftroyed ; whether by the Heat of the San, 
therifing of Vapours, or Exhalations, the melt- 
ing of Snow upon thei Mountains, and a great 
Variety of other Circumftances, more thaa 
can be eafily enumerated, 

We are told by Hiftorians, of certain Caves 
that emit Wind 5 if fo, it is when the included 
Air is rarefied by Heat, and therefore rufties 
out for want of Room ^ or^ when the Preffuro 
of the external Air, incumbent upon the MoutU 
of the Cave, is diminifhed, and fo permits the 
internal Air to dilate itfeif, and ilfue out* 

For more on this Subjeft, fee Nietiwentyt\ 
Religious Philofopher. Regnault^ Philofo- 
phical Converfations* Clares Motion of Fluids.^ 
Martins Philofophical Grammar. And tho 
Authors referred to in Mr. yohijoris Qu^ftiones 
Phiiofoph. Cap* IV* Qu^ft. i. 2. 

DI S- 

f go Of the Fomuaion and Part It 


Of the Formatim^ and Afcent of Valour Sj 
and their R^folution into Rain^ Snow^ 
and Haih 

THAT Vapours are raifed from off the 
Sur&ce or Water by the Adion of the 
Sun's Heat^ is agreed on by all : But the 
Manner in which this is done, has ever been a 
Controverfy among Philofophers ; neither is it 
at this Time fufficiently explained by any one* 

If we confult a Cartefian upon this Matter, 
he immediately tells us, that, by the A^on 
of the Sun upon the Water, fmall Particles of 
the Water, are formed into hollow Spheres, 
filled with Materia SubtiliSj and by that Means 
becoming lighter than an equal Bulk of Air, 
are eafily buoyed up in it. But, as this Ma-* 
teria Stihtilis Is only a Fidion, the Solution 
is not to be regarded. 

Dr. Nieuwentytj and feveral other Philo- 
fophers, who maintain, that Fire is a parti- 
cular Subftance, diftind from other Matter, 
account for the Formation and Afcrat of Va- 
pours thus : They fay, that the Rays of the 
Sun, or Particles of Fire feparated from them, 
adhering to Part;icles of the Water, make 

Diffett. 6- Jfcent ofVapurs^ kc. 1 ^ i 

up little Bodies^ lighter than an equal Bulk 
of Air i which therefore, by the Laws of Hy- 
droftatics, will afcend in it, till they come to 
an Height where the Air is of the fame fpeci-^ 
fie Gravity with themfelves. And, that Rain 
is produced by the Separation of the Parti cleii 
of the Fire from thofe of thd Water i which 
laft, being then left without Support, can no 
longer be fuftained by the Air, but will fall 
down in Drops of Rain ■^. 

This Opinion is liable to the following Dif- 
ficulties ; FiTft^ Fire has never been yet pro^ 
ved to be a diftin£t Element, or a particular 
Subftance t > and the Change of Weight in 
Bodies in chymical Preparations, heretofore 
thought to arife from the Adhefion of Particles 
of Fire, is found to proceed jfrom the Adhefion 
of Particles of Air §. . 

Secondly-, Should the above-mentioned Sup-» 
pofition be allowed, the fiery Partidles, which 
are joined to the watery ones to buoy them 
up, muft be confiderably large, or elfe a very 
great Number muft fix upon a fingle Particle 
of Water ^ and then a Perfon being on the Top 
of an Hill in a Cloud, would be fenfible of 
the Heat, and find the Rain produced from 
that Vapour, much colder than the Vapour it- 

* See Sieu<wenlyt*s Religious Philofopher, Contempl. 19. 
f See the Authors referred to in Mr. Johnfin^ Quxftiones Phi- 
lofoph. Cap. I. Quseft 30. 
$ By Dr. UaUi<^ in his ugetabh StMics. 

S felf: 

1^1 Of the Formation and Part II, 

felf : whereas the contrary is evident to our 
Senfes j the Tops of Hills, though in the 
Clouds, being much colder than the Rain 
which falls below. 

Betides^ the Manner in which the Particles 
of Water /hould be feparated from thofe of the 
Fire,*fo as to fall in Rain, is not eafily to be 

The moft generally received Opinion is. 
That by the Adion of the Sun, on the Surface 
of the Water, the aqueous Particles become 
formed into Bubbles, filled with a Flatus^ or 
warm Jir^ which renders them fpecifically 
lighter than common Air, and makes them 
rife therein, till they meet with fuch as is of the 
fame fpecific Gravity with themfelves *. But 

Firjiy How comes the Air in the Bubbles to 
be fpecifically lighter than that without, fince 
the Sun's Rays, which aGt upon the Water, are 
equally denfe over all its Surface ? 

Secondly^ If it could be poffible for rarer 
Air to be feparated from the denfer ambient Air, 
to form the Bubbles (as Bubbles of foaped 
Water are blown up by warm Air from the 
Lungs, whilft the ambient Air is colder and 
denfer) what would hinder the external Air 
from reducing that, which is inclofed in the 
Bubbles, immediately to the fame Degree of 

t Pbilofophical Traaik&ioiiS| Ko. i^xi 

Cold^ 'j4fcenuf Fa£Mrsj 8ic. 1^5 

Coldnefs, and fpecific Gravity with itfelf ; 
(Cold being readily communicated through fucb 
thin Shells of Water). By which means, the 
Bubbles would become fpecifically heavier than 
the circumambient Air, and would no longer be 
fupported therein ; but fall down, almoft as 
foon as they were formed ? 

T!hird1y^ If we ihould grant all the reft of 
the Suppofition, yet the following Difficulty 
will ftill remain. If Clouds are made up of 
Bubbles of Water filled with Air, why do not 
thofe Bubbles always expand, when the ambi- 
ent Air is rarefied, and prefles lefs upon them 
than it did before i and why are they not con- 
denfed, when the ambient Air is condenfed by 
the Accumulation of the fuperior Air ? But if 
this Condenfation and Rarefadtion ihould hap- 
pen to them, the Clouds would always conti- 
nue at the fame Height, contrary to Obferva:^ 
tion ; and we fliould never have any Rain. 

The two laft Opinions are more largely ex- 
amined by Dr. T>efaguliers in the Philofo- 
phical Tranfadlions N^. 407. After which he 
endeavours to eftablifli one of his own. 

He obferves, with Sir Ifaac Newton^ that, 
when by Heat or Fermentation the Particles 
of a Body are feparated from their Conta^^ 
their repulfive Force grows ftronger, and the 
Particles exert that Force at greater Diftances; 
fo that* the fame Body iliall be expanded into 
a very large Space^ by becoming fluid j and 




1 g^ Of the Formation and Part IL 

may fometimes take up more than a Million 
of Times the Room it did in a folid and in-r 
comprefllble State, ^' Thus, fays he, if the 
*' Particles of Water are turned into Vapour, 
by repelling each other ftrongly, and repel 
Air more than they repel each other i Ag- 
gregates of ftich Particles, made up of Va- 
pour and Vacuity, may rife in Air of different 
Denfities, according to their own Denfity 
*' depending on their Degree of Heat. " He 
obferv^es farther, that Heat ads more power-' 
fully on Water, than on common Air; for that 
the fame Degree of Heat which rarefies Air 
two Thirds, will rarefy Water near fqurteen 
thoufand Times, changing it into Steam or 
Vapour as it boils it. And in Winter, that 
fmall Degree of Heat, which inRefpeft of our 
Bodies appears cold, will raife a Steam or Va- 
pour from Water, at the fame Time that it 
irondenfes Air. Laftly, he obferves. That th^ 
Denfity and Rarity of this Vapour depends 
chiefly on its Degree of Heat, and but little 
on the PrefTure of the circumambient Air. From 
all which he infers. That the Vapour being 
more rarefied near the Surface of the Earth, 
than the Air is there by the fame Degree o\ 
Heat, muft neceffarily be buoyed up into the 
Atmofphere j and fince it does not expand it* 
felf much, though the PrefTure of the incum-y 
bent Air grows lefs, at length it finds a PlacQ 
where t:he Atmofphere is of the lame fpecific 


Diflert . 6. A/cent of Pa£ourSy &c. 1 5 5 

Gravity with itfelf, and there floats, till by 
ibme Accident or other, it is converted agaia 
into Drops of Water, and falls down in Rain, 

To fhew that Air is not neceffary for the 
"Formation of Steam or Vapour, he gives us 
fhis Experiment. 

'' ABCD {Fig. 37,) is a pretty large Vef- 
" fel of Water, which muft be fet upon the 
" Fire to boil. In this Veflel muft be fufpend- 
" ed the Glafs Bell E, made heavy enough 
^' to fink in Watery but put in, in fuch a Man- 
" ner, that it be filled with Water when up- 
" right, without any Bubbles of Air at its 
*' Crown within, the Crown being all under 
*' Water. As the Water boils, the Bell will 
'' by Degrees be eir^ptied of its Water, being 
** prefled down by the Steam, which riles 
** above the Water in the Bell ; but, as that 
*' Steam has the Appearance of Air, in Order 
" to know whether it be Air or not, take the 
*' Veffel off the Fire,, and draw up the Bell 
•' by a ftring fattened to its Knob at Top, 
** till only the Mouth remains under Water ; 
** then, ^s the Steam condenfes by the cold 
^/ Air on the Outfide of the Bell, the Water 
will rife up into the Bell at F, quite to the 
Top, without any Bubble above it ; which 
fliews, that the Steam, which kept out the 
f^ W^t^r, was not Air. '* 



1^6 Of the Farmatim and Part II 

This Hypothecs, however plaufible it may 
appear, is attended with Difficulties, as well as 
the other. For, 

F/Vy?, If the repulC ve Power of the Particles 
of Water is fufficiently augmented by Heat as 
fuch, (and that by a very fmall Degree of it) 
to make them recede from each other, and be- 
come fpecifically lighter than common Air; 
how comes it to pafs, that all the Particles of 
Water, as foon as, or before it boils, have not 
their repulfive Forces thus augmented, (ince 
they are all under a much greater Degree of 
Heat, than is necelTary to raife Vapour ? 

Secondly^ Allowing that they may rife off 
from the Surface of the Water, and float in 
the circumambient Air, ' as being lightet than 
it, why do not their repulfive Fortes, a$ 
they rife m) into the Air, and the fuperiricum- 
Vent Prefiure becomes lefs, drive them to 
greater Diftances from each other, and fo caufe 
them to continue lighter than the Air ^bout 
them at all Heights > 

Thirdly^ If the Preffure of the Air abbut 
them, when near the Surface of the Earth, is 
not fufficient to bring them into fo clofe Con* 
tad, as to form Drops of Water there, what 
Force will they find fufficient for it, when they 
are carried aloft into a Region of Air, where 
the Prelfure \s not near fo great ? The Dodor 
hints, that they are formed into Rain, ^^ when 
" by the great Diminution of the fpecific Gra- 

^^ vity 

Dlflert* 6. A/cent of Valours ^ Sec. 1^7 

^^ vity of the Air about a Cloud, it has a 
** great Way to fall, in which Cafe, he lays, 
*^ the Refiftance of the Air^ which increafes 
** as the Square of the Velocity of the de- 
^^ fcending Cloud, caufes the floating Particles 
^' of Water to come within the Power of each 
*' other's Attraction, and form fuch big Drops 
*^ as being fpecifically heavier than any Air> 
** muft f^ll in Rain. '* But as the inferior Air, 
from the Cloud to a confiderable Depth below 
it, cannot be fuppofed to leave it all at once, 
the Vapours muft neceflfarily fall all the Way 
through a refifting Medium ; fo that the little 
Velocity the Cloud can acquire, while it is in 
the Form of Vapour, will never produce a 
Refiftance from the Air greater than the Pref^ 
fure it fuftained below. 

Laftly^ The Experiment brought to make 
Way for thi$ Hypothefis, fliows clearly, that 
Vapour formed without the Afliftance of Air, 
is immediately condenfed into Water again, as 
foon as it is fuffered to cool : Which is widely 
different from what happens to Vapours buoyed 
up into the colder Regions of the Air, and 
floating there, till they fall in Rain.^ 

Thefe are all, or the principal Hypothefes^ 
that have been framed for the Solution of this 
common Thxnomenon : Which as they feem 
inadequate to the Effeds produced, and there- 
fore unfatisfa^ory, I thought it not amifs to 


1 3 8 Of the Formation and Part II 

fugged to the Reader the chief DiflSculties, with 
which I conceive them to be attended. But 
as it is eafier to pull down, than to build up, 
to overturn a weak Hypothejis^ than to raife 
and fupport a ftrong and fumcient one j fo, I 
xnuft own, in this Cafe, I can think of no Way 
of accounting for the Rife of Vapours, accord- 
ing to the received Principles of Philofophy, 
or fay wherein their Nature confifts. Upon 
this Account it is impoflible I fhould giVe a 
Philolbphical Account of their Refolution into 
Rain. It rauft fuffice juft to mention the Caufes, 
which are obferved to produce that Change. 

The firft isy That Part of the Air berieath 
them is carried away by contrary Winds blow- 
ing from the fame Place * j for then the Re- 
mainder being too light to buoy them up, the 
upper ones^ in all Probability, precipitate down 
upon the lower ones, unite with them^ and 
form Drops of Rain t* Another is, great 


* Perhaps it may be thougiit, thac when the Air, which im- 
pends over any Place, is carried away from thence by contrary 
Winds,, the Vapours which float in it ihould be carried away too; 
and fo the few that remain fhould be eafily fupported ; or, if they 
fall, fhould not produce much Rain. 

Now, in Anfwer to this, it muft be conlidered, rhat, as the 
inferior Air is carried away from any Place by contrary Winds, the 
Height of the Atmofphere is diminifhed thereby ; wherefore, in alt 
Probability, the fuperior Air rufhes in by a contrary Current to 
fill up the Vacuity at Top, which bringing in its Contents of Va- 
pour affords a continual Supply for the Rain that falls. 

t A remarkable Inftance we have of this^ in that Part of the 
Mamie Ocean, which the Sailors call die Kaim, (fee Diflert 5 ) 


biflert. 6; ^fient of F^a£ours^ Sec. 1^9 

Quantities of them' being driven by the Winds 
againft the Sides of Mountains, and thereby 

made to coalesce, and fo conftitute Rain "^^ 

' - - . ^ ^ It 

from the fre^ent Rains that fall there : the Occadon of which is, 
that the Attiiorpliere is diminiftied by continual contrary Winds 
blowing froin thence, fo that ic is not able to fuftain the Vapour 

It receives. 

Upon this depends the Differenfce of the Seafons of the Year 

at Malaha¥ znd C$fomandel in the Eaji- Indies, and ac j^amaua 

in the Weft. See Dr. Gordons Difcdiirfe on the Gaufes of the 

Change of Weather, Philofophical Tranfadions, No. 17, ■■ ■ • ^ 

*' The River^ of Indus and Ganges^ fays he, where they enter the 

** Ocean, contain between them a large Cherfonefus , which is di- 

*^ vided in the Middle by a Ridge of Hills, which they call the 

" Gate, which run along from Eaft to Weft, and quite through to 

** Cape Comm. On the one Side isMalahary and on the other, Co- 

" fomandel. On the Malabar Side^ between that Ridge of Mouri- 

** tains and the Sea, it is after their Appellation Summer from Sep- 

** tembef till April \ in which Time it is always a clear Sky, with- 

** out once, or very little Raining. On the otherigidc the Hills, on 

** xXitQoiikoiCoromandel^ it is at the fame Time their Winter, 

" ev«'y Day and Night yielding Abundance of Rain. And from 

'*' April to September it is, on the Af^/tfW Side their Winter, and oa 

^* the other Side their Summer : So that in little more than twenty 

" Leagues Journey in lome Places, as where ihey crofs the Hi Us to 

" St. thomas, on the' one Side of the Hill you afcend with a fair 

** Summer ; on the other you defcend with a ftormy Winter. 

" The like is faid to be at Cape Razalgate in Arabia, And Dr, 

** Tropham relates the lame of Jamaica y intimating that there Is 

•* a Ridge of Hills which runs from Eaft to Weft, through the 

** midft of the liUnd, and that the Plantations on the South Side 

'**'of the Hills have^from Sovemher to April, been a continual 

'^ Summer, whilft thofe on the North Side, have asconflant a 

** Winter, and the c6ntrary from April to November. 

** From thefe ahd fuch like Accounts it feems evident, that a 
'* bare leflening of the Atmofphere*s Gravity will not occafion 
^^ Rain, but that there is alfo needful either a fudden Change of 
'^ Winds, orarRidlge''of Hills to meet the Current of the Air and 
•'* Vapour^, whereby the Particles of the Vapours are driyen toge- 
{f then and ib fiiU down in Drops of Rain. And hence it '^y 

14.0 . Of the Formation and PartH. 

It is generally thought. That if the Vapours 
in their Defcent pafs through a Region crt Air 
fiifficiently cold,, they are there frozen into 


** chat whilft the Wiod blows from the North-eaft, viz. from N»- 
*^ vemher to Apil ({ee the Account of the Moniooos ia the &ce- 
going Difiertation) ** there are continual Rains in the noitherljr 
*' Pbntations of ^msMy and on the Side of Cmonuutdel in 
*^ the Eafi itdieiy becaofie the Winds b«U againfi that Side of 
" the Hills ; and £> there is h\r Weather on the other Side of 
*^ theie HillS) in MaUAof and in the ioutbern Plantations of 3^ 
^. '^ m^icay there being no Winds to drive the Vapoucs togetfaef. 

" But in the (butheriy Monfoons, vi& from Jfril to Hovimhrny 
'^ MalahM9 and the ibutfaerly Planeattons of yamaisn have Floods 
^ of Rain, the Wind beating againft that Side of the Hills, whilft 
'' ifi Ctfom^ndely and the other Side of y^flMf^/fj there is fair and 
** clear Weather. 

'^ This ferves alfo to clear the Singularity fXSeafons in PtfUy bo- 
*^ yond any other Parts of the Earth, and feems to be aligned by ibvjlii 
/^ as the Caufe of ir. P^rirrunbalongfrom the LmSouthwards about 
'* a thoufaad Leagues. It is faid to be divided into three Parrs^ long 
'^ and oarrour, which they call Lanosy Sierras y and Andes ; the 
*' LanaSy or Plains, run along the South>Sea CoaA ; the Sierras ait 
*^ all Hills with fooie Vallies; and the Andes deep and craggy Moun- 
^ tains. The Luinos hzve fome ten Leagues in Breadth, in fome 
'^ Parts leis, and in fome more ; the Sierras contain Ibme twenty 
. ^^ Leagues in Breadth,the^fiifi asmudi^fometimosmore, foroetimf9 
'^ leis ; they run in Length from Nonh to Sooth, and in Breadth 
<' from £aft to Weft. This Part of the World is iaid to have thefe 
*^ remarkable Things : i. AH along the Coafl^ in .the X^irox, it 
'^ blows coatinually with one only Wind, whidi is South and 
^' South-weft, contrary to that which ufually blows under the 
*^ torrid 2U>ne. 2. It never rains, thunders, (bows, or hails ia 
** all this Coaft, or LaneSy though there &Us fi>iiieiimes « imaH 
'^ Dew. ^. Upon the Andes it rains almofi continually, though 
** It be fome times more clear than other.. 4. In the Sierraty 
^' whi<h lie between both £ztream%. it rains firom 4!<^m^ to 
^^ Afniy bnt in the other Seafoos it is.more dear, whidi 15 whea 
*' the Sun is firtheft q£F, and the c^utiaiy when it h nimreft. 
^ Now.theIUaiQaofallXeeiiis to bethta^ The eaftem Bm(e«9, 
rS^TWhich blow conftantly uodcr the LijNh bdag fiopt in thdr 

if Cottd9 

Differt.6. AJcentofVapurs^Bfjc. 141 

Icicles, and form Snow^ But this Opinion feems 
to be falfe i becaufe it frequently fnows when 
the Barometer is high, at which Time the Va- 
pours cannot begin to fall. It is therefore more 
probable, that they are firft frozen into Icicles, 
and by that means fliooting forth into feveral 
Points every Way from the Center (agreeably 
to the Nature of Freezing) lofe their Form j 
and fo becoming fpecifically heavier than Air, 
fall down, and in their Paflage, feveral being 
congealed together, form Fleeces of Snow *. 

Hail . is evidently no other, than Drops of 
Bain congealed into Ice. This happens, when 
in their Paffage through the inferior Air, they 

•* Courfe by the Sierras and Andes ^ and yet the (ame Bree2es be- 
'* Ing to he found in the South-Sea beyond Peru, as appears by 
•* the cafy Voyages from Ptfu to the Phififptnes^ a Current of 
'^ Wind blows from the South on the Plains of Peru, to fupply 
^^ the eaftem Breeze on the South-Seas, and there being but one 
^' confiant Gale on thefe Plains, and no contrary Winds or Hills 
*^ fi>r it to beat upon, this feems to be the Reabn why the Va« 
*' pours are never or very feldom driven into Rafn. And the 
*^ Amies being as high periiaps in many Places as the Vapours 
^ aicend in the bi^ft Degree of the Atmofehere*s Gravity, this 
^' may probably be the Reafouy why the eattern Breete, beating 
^ eonflantly againft thtfe Hills^ occafions Rain upon them at alL 
^* Seafons of the Year. And the sierras being it feems lower 
^^ than the Andesj therefore from Sipfemher to April, when the 
^ Sun is neareft^ and fo the Atmolphere's Gravity lefs, and the 
f* Vapoufs Idwer, they are driven aggiinft the Sierras into Rain. 

The like is to be faid of other CountrieSi They are all, cateris 
paribus, more or leis rainy, as they are more or Ids mountainous. 

J%ypf, wlucb is qtote without Mountains, has feldom or never 
aoy Riin ; but is plentifidly watered by the Me, which yearly 
nifes above its Banks, and overflows the wh^Gountry* 

* See a Sifcoucft oa the Nature of Snow. Philofophical Tran- 

fadioas Ho ya* 

T a meet 

14* Of the Formation and Part II. 

meet with nitrous Particles, which are known 
to contribute greatly to Freezing. Their Mag- 
nitude is owing to a frefli Accefflon of Matter, 
as they pafs along. Hence we fee the Reafon, 
why Hail is fo frequent in Summer, becaufe at 
that Time greater Quantities of Nitre are ex- 
haled from the Earth, and float up and down 
in the Air. 

If the Vapours, after they are exhaled from 
off the Waters, do not rife very high in the 
Atmofphere, but hover near the Surfece of the 
Earth, they then conflitut^ what we call $ 
Tog. And, if they afcend higher, they flill 
appear in the fame Form to thofe, who, being 
upon the Tops or Sides of Mountains, are at 
^^ an equal Height with th§m j though to thofe^ 

who are below, they aj^)ear as Clouds. 

If they fall to the Egrth, without uniting 
into Drops large enough to be called Rain 
they are then laid to fell /n f)e\y. ' ' * 

See ferther on this Subje^, Derhanis PhyT, 
Theolog. Book I. Chap: 3, and Book II. 
Chap. 5. Speaacle de la Nature, Dialog. 2 1 , 
and 23. Nieuwemp Contempl. 19. Clares 
Motion of Fluids. Regnauk, Vol. III. Con- 
verfat. 7. Muffchenbroek Epitoip. Phyi: Ma- 
themat. Par. II. Cap. 24, Melcbior Ver- 
dries Phyfic. Pars fpecial. Cap. V. $. 8. 
And the Authors referred to in Mr. Jobnton's, 
Ru«ftipnQ« PhUofoph. Cap, IV. .qii«ft-7» 

■ '"" "■■■■ Plh 

Diflert. 7. Of the Cattfes of,8cc, 1 4^ 


Of the Caufes of Thunder and Lightnings 
and of the Aurora Borealis. 

THOSE Philofophers, who maintain that 
Vapours are buoyed up into the Air, by 
Particles of Fire adhering to them (as ex- 
plained in the foregoing Differtation) account 
for the ^hanomena of Thunder and Lightning, 
in the following Manner. They fuppofe,, that 
from the Partides of Sulphur, Nitre, and other 
^ombu^ible Matter, which are exhaled from 
the Earth, and carried into the higher Regions 
gf the Atmofphere, together with the afcend- 
ing Vapours, is formed an inflammable Sub- 
ftance ; which, when a fufficient Quantity of 
fiery Particles is feparated from the Vapour by 
the- CoUifion of two Clouds, or otherwife, 
taJles Fire, and flioots out into a Train of 
Light, greater or lefs, according to the Strength 
and Qjiantity of the Materials. 

This Opinion is falfe for the Reafons mentl^^ 
oned in* the foregoing Differtation, which plain- 
ly ihow, that it is impoifible the Vapours 
ihould be attended with &x^ fiery Particles, 
as is here fuppofed^ 

1^4 OftheCaufcsofTbofider PartIL 

Neither have we Occafion to fly to fuch aa 
Jlypotbefis ; for, as Vapours exhaled from the 
Surface of the Water are carried up into the 
Atmofphere ; in like Manner, the Effluvia 
of folia Bodies are continually afcending thi« 
ther : Now we find by Experiment, that there 
are ieveral inflammable Bodies, which being 
mixed together in due Proportion, will kindle 
into Flame by Fermentation alone, * without 
the Help of any fiery Particles t* Whenthere- 


* See the Theory of Feroiefiution explained la the following 

. f Monlieiir Lemery having covered up in the Barth about fifij 
Founds of a Mixture compofed of equal Parts of Sulphur^ and Fi- 
lings of Iron tempered with Water ; after eight or nine Hours 
Time, the Earth whei« it was laid, vomited up Flames. UiSu 
de rAcad. 1700, p. S74« 

From this Experiment we fee the true Canfe of the Flie of 
JEftui aAd Vtfmfius, and other burning Mountains. They fOh 
bably are Mountains of Sulphtr, and fome other Matter proper to 
ferment with it, and take Fire. . From like Cau&s proceeds the 
IJeat of Bath>waters> and otiier hot Springs. 

Mix a iinall Quoitic/ of Gunpowder with O7I of Clov«s^ poar 
^ntly upon this Mixture, two. or three times as much Spint of 
Nirre^ and you will obferve a bright Inflammation Ihddenly ulGng 
from it. A Mixture of the two Fluids alone will take Fire; ttz^ 
Powiier is added only to Augment the laflmnaatian. 

Take two Pounds <of Nitre, or refined Salt-Petre weU dried and 
r!Hluced ro the fineft Powder, with a Pbund of Oyl of common 
Vicriol : Froip this Mixtoie may be drawn by DlfllUatioa a Spirit 
of Nitre capable of inflaming Oyl of Tumndae. Mem. de 
TAcad. 1726, p*97> Sff> Put into a Glais an Ounce <^ this 
S^lait tff Nicra, with an Oaooe *f Oyl of Vitriol ; pour upon it an 
equal Quantity of Oyl of Turpentine, a^ a wry fiiaeFkoie will 
arife fuddenly with a great Explofion* When the Liijuors are 
freih the ESeifl is much greater. If we mix a Dram of the Spirit 
<(N&tr iai4 three of Oyl of Turpentine^ witl^ only oae d^xbs Spirit 


• • ^ • . . , _ 

Differt. 7. md Ughtmng^ &G, 1 4^5 

fore there happens to be a proper Mixture of 
the Effliwia of fach Bodies floating in the Aif^ 
they ferment, kindle, and flalhing like<5jin* 
'powder, occafionthofeExplofions, and Scream's 
of Fire, which we call Thunder and Light- 

As . to the particular Species of Efflmi^^ 

Iwhich compofe this Mixture, that cannot ex*- 

adly be determined ; they are thought to be 

^chiefly fulphureous and nitrous : fulpbureom^ 

-becaufe of the fulphureous Smell which Lights 

ning generally leaves behind it^ and of that 

fultry Heat in fhe Air which is commonly f hp 

JFore-runner of it : nitrtniSy becaufe we donk 

Jknow of any Body fo liable to ja fuddea anfl 

violent Explofionj as Nitre, is * 


* • 

rf Vitrifld, the J4ixtnrc will Uke J?ire immedutely, If the.Cunp 
i^c^iaeticitf >mr3ie wi(h the£akn ofMeccM, a iudden Fl^i^e wiH 
arife, with a Noife like that of the Report of a Gun. 

Tbett aie ewo cekbaiated£xperime«P5 of ihia Kind^ thougb they 
Tie not comeMp.«x*ftly *o J5he prrfent Purpofe, Iwaufe they wift 
-not fuceeed, uiilefe^the togcedieotg be firft heawd, tfae one of At^- 
0mmjitlmmavs^ Jtad ihejolsb^ &LJ^i^s fylmwatfs. The firft i^ 
ft WisBufeaf -Salt of Taiiac .ftttd GoW<iiflrQlved by Jqua JUgia^ 
A fmaU Quaftchy of this, if fmt into.* Br»(s Spoon, and beate^ 
WMh the Pianje.o£jiiCa04k, saufes^ fiidden Noife refemblingibat 
of Thunder ; and goes off ^wiiii great Vipleacf?. The other i$ 9. 
Mixture of three Parts of Nitre, cwpof Sak qf Tartar, and o%e cjf 
Sulphur. Thia Mixdite «ite» fet upon {he.Flfe» and warmed. <;9 
ft certain Degree, is/diffipatad aji tan a fiidd^n with great .Thuor 
4^ng,4U(etheJl4itt^jSK/iir/ttmf. i 

See an Account of Exhalations taking Fire ofthelr own Accord 

in C^ie-Pits. Powers Experimental Philofophy, p. 6z and 181. 

- -* "Dr. Lifter is of Opinion, That the Matter both of Thunder 

and Lightniog. and alio of Earthquakes, la the Effluvia of the 

^ Pyrites, 

1^6 Of the Caujes of Thunder Part II. 

The Efiedls of Thunder and Lightning are 
owing to the fudden and violent Agitation the 
Air is put into thereby, together with the Force 
of the Explofion * ; and not to Thunderbolts 
filing from the Clouds, as fuppofed by the 
Vulgar !• 

Tyrites ; as he does, that the Matter of Vutcafid's is the Pyrites it-^ 
felf. This is a Mineral that emits copious Exhalations, and is ex- 
ceedingly apt to take Fire upon the AdmiiTion of Moifture. See 
the Dodor'b Defence of his Notion in the Philofophical Traniadi- 
ons, No 157. He thinks this may be the Rea(on why England h 
l(y little troubled with Earthquakes, and Italy ^,'zn<^ a!moft all Pla- 
ces round the Mediterranean Sea, fo very much, viz* becaufe the 
Pyrites are rarely found in 'England ; and where they are, they lie 
very thin, in Comparifon of what they do in thole Countries ; as 
the vafi Quantity of Sulphur, emitted from the burning Mountains 
there, feems to ihew. 

^ Lightning is faid to have difTolved Silver, without burning 
the Purfe it was in ; and to have melted the Sword, without 
touching the Scabbard, and the like. The Occafion of this may 
poiGbly be, that the Matter of the Exhalation may be lo fubtle and 
penetrating) that, as we fee it happens with Aqua Fortis, or vola- 
tile Salts J it may pafs through foft Bodies without altering their 
Texture, while it ipends its whole Force on hard ones, in whidi 
it finds the greater Refiflance. 

t Some are inclined to think, that Thunderbolts are artificial, 
and that they were applied by the Ancients to fome Ufe. What 
confirms them, in their Opinion, is, that they are found more fre- 
quently where Sepulchres have been, than in other Places. And, 
0S it was the Cudom of the Ancients to have their Arms buried 
with their Afhes, they think they might be of fome Ufe in War. 
Some are of Opinion, they were ufed in Sacrifices. See Ii/hkbicf 
Terdrieh Phyfic Pars fpecial. Cap. V. J. 9. Wedelittt Exercit. 
Med. PhiloU Cent. IL Dec, I. p. 105. Schmindtittf Profefll 
Marpurg. DUTertat. de Umis Sepulchralibns, 6c Arrois Ltpideis, 
A. 1 7 14. Herman Sttnniftgitts ^epulchret. Weftphal. Mimigard. 
Centil p. if ^ ^0. Hem, Cebarfen Ofllleg. Hiftor* Phy£c. p^ 44,' 

PilTert.y. 0/^i&^ Aurora Borealis. 147 

The Diftdnce the Thunder is from us, may 
nearly be eftimated by the Interval of Time 
between our feeing the Lightning, and hearing 
the Thunder. For, as the Motion of Light is 
fo very quick^ that the Time it takes up, in 
coming to- us' frferti the Cloud, is not percep- 
tible ; and as that of Sound is 4bout a thou- 
farid Feet in a Second ,• allowing a thoufand 
Feet for every Second, that pafTes between our 
feeing the one, and hearing the other 5 we 
have the Diftance of the Cloud, pretty nearly, 
from whence the Thunder comes. 

We fometimes fee Fkflies of Lightning,' 
though the Sky be clear and free from Clouds j 
in this Cafe they proceed from Clouds, that 
lie immediately below our Horizon. 

Of Affinity with the ^hditomena of Light- 
ning are thofe of the Juror a ^orealisy or Nor^ 
them Lights^ which of late Years, have very 
frequently appeared in our Climate *. Thefe 
Lights differ fo much from each other, that to 
give a Defcription of one alone, would not be 

* Phenomena of this Kind are reported to have been very fre- 
quent in Groenland^ Iceland, and Norway y Countries near the 
I'ole. The only ones, chat are upon Record, as having appeared 
3n England^ before that of March the 6th 17 15, are thofe oi jfa-^ 
I7ii4fy the 50th 1560, OB4>beti\it 7th 1564, 24ovember 14th and 
15 th 1574, and a foiall one feep near London on the 9th of 
Amgufi 1708. On November the i6th 1707, a fmall one appeared 
In Ireland* Since that of Marcb the 6ih l7io> they have beenj 
aA4 fliU coBtiaue very eommon* 

U fuffici- 

1 48 Of the Aurora Borealis. Part 11, 

fufficient to acquaint the Reader with all the 
Circumftances wherewith they are attended* 
1 fliall therefore colled together fuch Tbicnih 
mena^ as have been moft generally obferved, 
and reduce them to the ten following Propofi- 
tions, adding in the Notes, by Way of Sped- 
meiiy a full Account of that moft remarkable 
Juror a^ which was feen March the 6th 1 7-f^, 
as it was laid before the Royal Society by Dr. 
Halley^ at their Requeft *• 


* *• On tutfiay the <Jth tXhlarchy in the Year 1716, (the Af- 

^* ternoon having been very ferene and calo)) and fomewhac 

^* warmer than ordinal^) about the Time it began to grow dark 

** (much about feven ot the Clock) not only in London, but in 

*' all Parts of Englandy where the Beginning of this wonderful 

'* Sight was feen ; out of what feemed a dusky Cloud, in the 

** North-eaft Parts of the Horizon, and fcaice ten Degrees high, 

•' the Edges whereof were tinged with a reddifti Yellow, like as if 

** the Moon had been hid behind it, there arofe very long luroi- 

^^ nous Rays, or Streaks perpendicular to the Horizon, fome of 

^* which fecmed nearly to afcend to the Zenith. Prefently after, 

•• that reddifli Cloud was fwiftly propagated along the northern 

*« Horizon into the North-weft, and Itill farther weflerly ; and 

** immediately fent forth its Rays from all Parts, now here, now 

*' there, they obferving no Rule or Order in their rifing. Many 

•* of thofe Rays feeming to concur near the Zenith^ formed there 

*^ a Corona^ or Image, which drew the Attention of all Speda- 

•* tors. Some likened it to that Reprefenration of Glory, where- 

*< with our Painters in Churches furround the Holy Name of God. 

*^ others to thofe radiating StMrs, wherewith the Breafts of 

•* Knights of the Order of the Garter, are adorned. Many com- 

*' pared it to the Cencave of the great CnfeU of St. Panfi 

<* Church, diftinguifhed with Streaks alternately Itghc and ob» 

^< fcure, and having in the Middle a Space lefs bright than the 

*5 reft, refembling the Lanthorn. Whilft others, toexwefs as well 

^' the Motion as Figure thereof, would have it to be like the 

£ Flame Ui aa Qvcn^ reverberated a&d rolling againfi the arched 


DifTert. 7. Of *^^ Aurora Borealis. 149 

The moft general Vhan(mena of an Aurora 
!Borealis are thefe that follow. 

!• In the northern Parts of the Horizon^ 
there is commonly the Appearance of a very 


^ Roof thereof: Some thought it liker to that tremulous Light, 
*' which is caft againft a Ceiling by the Beams of the Sun, re- 
^ fleded from the Surface of the Water in a Bafon, that's a little 
** ihaken. But all agree, that this SpeBrum lafted only a few 
*' Minutes and exhibited itfelf varioufly tinged with Colours, Yel- 
low, Red, and a dusky Greeh : Nor did it keep in the fame 
Place ; for when firft it began, it appeared a little to the 
** Northwards of the Ze.mthy but by Degrees declining towards 
** the South, the long Stru of Light, which arofe from all Parts 
•* of the northern Semicircle of the Harizon, feemed to meet to- 
gether, not much above the Head of Cafiwy or the northern 
Twhy and there foon diiappeared. 
** After the firft Impetus of the afcending Vapour was over, the 
** Corona appeared no more ; but ftill^ without any Order, as to 
'* Time or Place, or Size, luminous KadH^ like the former, con- 
*' tinued to arife perpendicularly, now oftner, and again feU 
** domer ; now. here, now there ; now larger, now ihorter. 
^^ Nor did they proceed as at firft,' out of a Cloud, but oftner 
f^ would emerge at once out of the pure Sky, which was more 
*^ than ordinarv ferene and ftill. Nor were they all of the fame 
'^ Form. Mou of them feemed to end in a Point upwards, like 
«* ered Cones; others like truncate Cones, or Cylinders, fomuch 
<^ refemblin? the long Tails of Comets, that at firft Sight, they 
^ miglic well be taken for fuch. Some of thofe Rays would con- 
^' tinue viiible &r feveral Minutes ; when others, and thofe the 
^* much greater Part, )uft (hewed themfdves, and died away. 
<' Some feemed to have little Motion, and to ftand, as it were^ 
'' fixed among the Scars, whilft others, with a very perceptible 
^^ Tranflation, moved from £»ft to Weft under the Pole, contrary 
'< to the Motion of the Heavens ; by which Means they woul4 
*^ ibmetimes feem to run together, and at other Times to fly one 
*« another. 

^^ After this Sight had continued about an Hour and a hal^ 
^ thofe Beams began to rife much fewer in Number, and not near 
tt, fi> bigb ; and by Degrees, that diffu&d Light^ whii^ had illuf- 

U * " mted 

1 50 Of the Aurora BorcftUs. , Part II. 

black Cloud ; but it is evident that it is no 
real Cloud, becaufe the fmalleft Stars are viy^ 
fible through it. This apparent Cloud is ex- 
tended fometimes farther toward? the Weft, 


** trated the northern Parts of the Hemifphere, feemed to fubfide, 
*^ and fettling on the Horizon, formed the Refemblance of a very 
** bright Crepufiulum, That this was the State of this Thanomenon^ 
^^ in the firlt Hours, is abundantly confirmed by the unanimous 
^* Confent of feveral. For, by the Letters we have received from 
** almofl all the extreme Parts of the Kingdom^ there is found very 
*' little Difference from what appeared at London and Oxford \ uor 
** lels that in the North of England, and in Scotland, the Light 
f^ feeqied fomewhat flronger and brighter. 

*^ Hitherto I have related the Obfervations of others ; as to 
*^ myfelf, I bad no Notice of this Matter, till about nine of the 
^' Clock : I immediately perceived toward the South and South- 
•* weit Quarter, that though the Sky was clear, yet it was tinged 
^* with a Grange Sort of Light ; fo that the fmaller Stars were 
*^ fcarce to be feen, and much as it is when the Moon of four 
*' Days old appears after Twilight. I perceived at the fame Time 
<« a very thjn Vapour to pafs before us, which arofe from the pre- 
•' cife Eaft'Part of the Horizon, afcendlng obliquely, fo as to 
** leave the Zenith about fifteen or twenty Degrees to the North- 
V ward. But the Swiftnefs wherewith it proceeded, was fcarce to 
*' be believed, feeming not inferior to that of Lightning ; and 
5^ exhibitiiig, as it patted on, a Sort of momentaneous Nuheculaj. 
•' which difcover*d itfelf by a very diluted and feint Whitenefe; 
f ' and was no foqner forpfjed, but before the Eye could well take 
'^ ic, it was gone, and left no Signs behind it. Nor was this a 
*' (iDgle Appearance ; but for feveral Minutes, about fix or feven 
^^ Times in a Minute, the fame was again and again repeated ; 
*' thefe Waves oi Vappur regularly fuceeeding one another, and 
f * at Intervals very neatly equal ; all of them in their Afcent pro- 
^^ ducing a liketraniknt Nubecula. 

" By this Particular we were fk^ affiired ; that the VapoiiF we 
*^ faw, became confpicuous by its own proper Light, without the 
*^ Help of the Sun's Beams ; for thele Nubecula did not dKcover 
^ themfelves in any other Part of their Paffage, but only between 
ff Che South-eaft and ^uth, where being oppofxte to the Sun, 

Differt.7* 0/fJ&^ Aurora Borealis. ijr 

than to the Eaft ; fometimes farther towards 
the Eaft, then to the Weft ; and generally takes. 
yp a Qiiarter of the Horizon, more or lefs. 

2. The 

^ they were deepefl immerfed in the Cone of the Earth's Shadow ; 
** nor were they vifible before or after. Whereas the contrary 
^^ niuA have happened, had they borrowed their Light from the 
** Sun. 

*^ On the weftern Side of the northern Horijton, t;/-C. betweea 

^ Weft and North-weft, not niuch paft ten of the Clock, I ob*» 

^* ferved the Reprefentation of a very bright Twilight, contiguous 

** to the Horizon, out of which arofe very long Beams of Light, 

•' ijot exaftly ereh towards the VerteXy but fomething declining 

^^ towards the South; which afcending by a quick and undulating 

••' Motion to a confiderable Height, vanilbed in a little Time ; 

*' whilft others, though at uncertain Intervals, fupplied their 

** Place. But at the fame Time, through all the reft ofthenor- 

*^ thern Horizon, viz* from the North-weft to the true Eaft, 

** there did not appear any Sign of Light to arife from, or join 

^* to, the Horizon ; but what appeared to be an exceeding black 

** and difmal Cloud, ftemed to hang over all that Part of it. Yet 

*^ was it no Cloud, but only the ferene Sky, more than ordinary 

^' pure and limpid, fo that the bright Stars (hone clearly in it^ 

'* and particularly Capuda Cygriiy then very low in the North ; 

*^ the great Blapknefs manifeftly proceeding from the Neighbour* 

^^ hood of the Light, which was collected above it. For the 

^* Light had now put on a Form quite different from all that we 

*' have been defer ibing, and had fafhioned itfelf into the Shape of 

<^ two Lamirt£f or Streaks, lying in ^ Portion parallel to the Hbr/-* 

^* zorty whofe Edges were but ill terminated. They extended them- 

** felves from the North by Eaft to the North-eaft, and were each 

*' about a Degree broad ; the undermoft about eight or n'ne Degrees 

** high, and the other about four or five Degrees over it ; thefe 

^* kept their Places for a long Time, and made the Sky fo light^ 

*' that I belieye a Man might eadly have read an ordinary Print 

** by the Help thereof 

*' Whilft I was viewing this liirpnang Light, anJ expeding 

what was farth^ to come, the northern End of the upper La^ 

mina by degrees bent doWnwards, and at length clof^ with 

** the End of the other that was under It, fo as to (hut up on the 

II l^Qt^ Side an intermediate Sf ace^ w.Ucb fiill continued ooen 

' ' I: to 

'•5* Of the AuroTSiBovedWs. PartIL 

2. The upper Edge of this Cloud (which 
is fometimes within lefs than fix Degrees of 
the Horizon, and fometimes forty or fifty above 


•* to the Baft. Not long after this, in thefaid included Space, I 
** faw a great Number cf fmaH Columns, or whltifh SueakSj to j 
*• appear fuddenly ered to the Horizon, and reaching from the ! 
** one Lamina to the other ; which inftantly dilappearing, were | 
** too quick for the Eye, lo that I could not judge, whether thejr 
•* arofe from the under, or fell from the upper ; by their fuddea 
'^ Alterations, they made fuch an Appearance, as might well 
** enough be taken to refemble the Conflift of Men in Battle. 

^* And much about the fame Time, there began on a (udden to 
•* appear, low under the Pole, and very near due North, three or 
** four lucid Jreaty like Clouds, dlfcovering themlelves in the 
•* pure but very black Sky, by their yellowilS Light. Thefe, as 
*^ they broke out at once, fo after they had continued a few Mi- 
*' nutes, di&ppeired as quick, as if a Curtain had been drawa 
** over them : Nor were they of any determined Figure, but both 
•* in Shape and S 2e might properly be compared to fmall Clouds 
•* illuminated by the full Moon, but brighter. 

*' Not long afcer this, from above the forefaid two Lamina^ 
*• there arofe a very great Pyramidal Figure, like a Spear, (harp 
•* at the Top, whofe Sides were inclined to each other, with an 
** Angle of about four or five Degrees, and which feemcd to reach 
•* up to the Zenitby or beyond it. This was carried with aa 
•• equable, and not very flow Motion, from the North-eafl where 
<* it arofe, into the North- wef^, where it difappeared, flill keep- 
•* ing in a perpendicular Situation, or very near it ; and paffing 
^' fuccefltvely over all the Stars of the little Bear^ did not efface 
•• thefmaller ones in the Tail, which are of the fifch Magnitude; 
y fuch was the extream Rarity, and Perfpicuity of the Matter 
f< whereof it conMed. 

" This' fingle Beam was very remarkable for its Height above 
•* all thofe, that, for a great while before, had preceeded it, or 
•' that followed it. 

•'* It being now pafl eleven of the Clock, and nothing new of- 
•* fering itfelf to our View, but repeated Pbafes of the feme Spec- 
** tacle ; I obferved, that the two Lamina, or Streaks, parallel 
** to the Horizony had now wholly difappeared ; and the whole 
^ Speftacle reduced jtfelf to the RcfemWance of a very bright 

Diflert. 7. Of the Aurora Borealis. 1 5 ^ 

it) is generally terminated with a very ludA 
Arch, from one to four or five Degrees broad, 
whofe Center is below the Horizon. Some- 

*« CrepHfiuJum fetting cm the Northern Horfzofiy To as ta btf 
•* brighteft and higheft under the Pole itfelf; from whence it 
•* fprt;ad both Ways into the North-eaft and North-weft. Un» 
'* der this, in the Middle thereof, there appeared a very black 
•* Space, as it were the Segment of a leffer Circle of the Sphere 
•* cut off by the Horizon, It feemed to the Eye like a dark Cloud, 

** but was not fo ; for by the Telefcope the fmall Stars appeared 
*^ through it more clearly than ufual, confidering how low they 
** were : And upon this as a Bajts, our Lumen Aurorifotme reft- 
^^ ed, which was no other than a Segment of a Ring, or Zone 
*' of the Sphere, intercepted between two parallel leffer CircleSf 
•* cut off likewife by the Horizm ; or the Segment of a very 
•* broad Irisy but of one uniform Colour, viz. a Flame- Colour 
'* inclining to Yellow, the Center thereof being about forty De- 
•' grees below the Horizon, And above this there were feeii 
•* fome Rudiments of a much larger Segment, with an Interval of^ 
** dark Sky between, but this was fo exceeding feint and uncer*^ 
** tain, that I could make no proper Eftimate thereof. 

^^ I attended this fb^nomenon till near three in the Morning, and 
•* the Rifing of the Moon : But for above two Hours together ic 
<< had no Manner of Change in its Appearance, nor Diminution, 
•* nor Increafe of Light ; only fometimes, for very (hort Intervals, 
*« as if new Fewel had been caft on a Fire, the Light feemed to 
<^ undulate and fparkle, not unlike the rifing of a vaporous Smoalc 
** out of a jgreat Blaze when agitated. But one Thing I afliired 
•' myfelf ol, that the Jr/i like Figure did by no means owe lit 
** Origin to the Sun's Beams : For that about three in the Morn* 
*• ing, the Sun being in the Middle between the North and Eaft, 
*' our Aurora had not followed him, but ended in that very Ij'oint 
** where he then «i?as : Whereas in the true North, which the 
•* Sun had long paffed, the Light remained unchanged, and ia 
« -its full Luftre. 

Appearanices of this K'nd have been taken Notice of both by 
Pliny, Seneca, and Arifietle ; the laft of which calls the vibra- 
ting Light near the Zenith, A*Xci ; the more fieady perpendicular 
Streams, £i^o)tQi ; and the Aurora itfelf, from the apparent darkL 
Qoud jud below i^^ 'Xd^f/f^* That Aurora which was obferved 

1^4 O/^i&e Aurora Borealis. PaitIL 

times there are two or more of thefe Arches^ 
one above another. In fome^ the Cloud is not 
terminated by an Arch, but by a long bright 


by MonCeur Gajfendt iti Provenciy on the i ift of $epiemhet^ ia thef 
Year i6ii, was very remarkable, at that Time. 

He cells us. That about the £nd of Twilight in the Evening, 
when the Sky was very clear, and there was no Moon, there ap- 
peared in Che North a Sort of a rifing Mom, which afcending by 
D^rees^ became intermingled with certain Streaksj as it were, 
or Rays perpendicular to the Horizon : And that at the fame Time 
there appeared fome fmall pajftng whltifh Clouds between the 
South and the Place of the Sun's fetting in Winter ; and that in 
the Place where the Sun fets in Summer, a bright Rednefs feemed 
to arife in the Form ofzPpramid^ which moved towards the fetting 
of the Sun at the Equinox ; and which was diAinguifhed into 
three feveral Pyramidsy which in a little Time were confounded 
one with another, and at lad difappeared. When this Rednefs 
ceafed, the northern Whitenefs was rifen forty Degrees and more, 
that is, about the Altitude of the Pole Star, forming itfelf into an 
Arch, and taking up near fixty Degres of the Horizon. After this, 
certain Chevronsy or Columns of Rays^ fome whiter, and foroe a 
little darker, began more plainly to be diftinguiibed, of about 
two Degrees in Breadth, and perpendicularly ponced ; fo that all 
that Part appeared as it were fluted. The whole Circumference 
immediately appeared fcalloped ; and then fome of thofe Columns 
which were in the Middle, and that were the whiteft, began as it 
were to leave their Places with great Impetuofity, and in left than 
a Quarter of a Minute, raided ihemfelves almoft to the Top, put- 
ting on the Form o( Pjramidsy which they would retain four or 
five Minutes. It was about nine of the Clock, when the Arch of 
Whitenefs began to decreafe or fink ; at which Time certain very 
white Streams of Smoke began to ilfue out from the Columns which 
were remaining under the PyramidSy and darting upwards with 
very great Rapidity through the Pytamidsy like Javelins, vaniihed 
immediately when they came to the Tops of them. This Spefta- 
cle la Aed about an Hour ; after which the Whiceneis funk down 
to about fix Degrees of the Hmz,on, Vide Abregi de Gafendl, 
Tom. V. P. 14s, 


Differt. 7". Of the Aurora Borealis. 155 

Streak of Light, lying parallel to the Hori^ 
zon. The Limb of this luminous Arch^ or 
parallel Streak is not always even and regular, 
but finks lower in fome Parts, than in others. 

3. Out of this Arch proceed Streams of 
Light, generally perpendicular to the Hcri-^ 
zon^ but lometimes a little inclined to it. Moft 
of then^ feem to end in a Point, like T^ra-- 
mids or Cones ; and often very much refemble 
the Tails of Comets. Sometimes there is no 
luminous Arch, nor Streak of Light j and then 
the Streams feem to ilTue out from behind the 
dark Cloud, being diftinft from each other at 
their "Bafes. 

4. The upper Ends of the Streams inceflant- 
ly appear and vanifli again, as quick as if a 
Curtain were drawn backwards and forwards 
before them \ which fometimcs caufes fuch a 
feeming trembling in the Air, that you would 

This Vhjtnomenon appeared not only to C/tJjfendi in Provertcey but 
was feen at Places very diftant from thence, as at Tbhfe, Montam" 
hctiy BoufdeauXy OrencbUy Dijon^ Patis^ and Raariy &c ajid at 
moA other Places in Prance^ and th^ neighbouring Councriesj 
that lie to the Northwards of Proveficey unlel^ where it was Inter- 
cepted hy Clouds ; but no where in fuch as lie at any great Dif- 
tance to the Soiithwar<is of it. 

Monfieur Gajfendi is thought to have given the Name of Aurora 
JBorealis to this Ph£nom€non ; but this is obferved by Monfieur 
Mairany to be a Miiiake. See Mr. Mairans Phyfical and Hifip- 
rical Treatife of the Aurora BoreaJUy in the Memoiros de VAcadt" 
mie Koyah des Sciences , Annee 1 7] I* or aa Ab^rait of ic in Phi* 
ioibphtTranika. No, 4^1. 



1^6 Of the Aurora Boreali^. Part IT. 

imagine the upper Part of the Heavens to be, 
as it were, in Convulfions ^. 

5* They fometimes feem to meet in the J35r- 
uitbi or more cbmmonly to the Southward of 
it, about ten Degrees, more or lefs (fometimes 
they deviate a little to the South-eaft of the 
Meridian^ and fometimes to the South- weft); 
and there curling round, in fome Meafure imi- 
tate Flame confined under an Arch ; and be- 
ing frequently tinged with various Orders of 
Colours, exhibit a moft beautiful Appearance, 
refembling a Canopy finely painted t> of about 
ten or twenty Degrees in Breadth* 

In many Juror a Sj there are Streams iffuing 
from thofe Parts of the Heavens, which lie fe- 
veral Degrees to the Southwards of the Cano- 
py 'y and in fome, they appear to arife, though 
very rarely, almoft as large, and numerous 
from the fouthem^ as froln the northern Parts 
of the Horizon. 

6. The Height of the Juror a IBore alls is 
very great ; for that of March the fixth 1 77^ 
was vifible from the Weft Side of Ireland^ to 
the Confines of Ruffia and Poland on the 
Eaft, and perhaps fertherj extending at leaft 
over thirty Degrees of Longitude^ and in La- 

* See their Motions well deferibed in the Account we have of 
^nAufota in the Fhilofeph. TranfaA. No. 595, Art. 2* 

t See the various Colours of the Canopy, as well as thofe of 
an Smora itfelf, accurately deichbed by Plr. Gf^nnwody in Philor 
ibph. Traniaft . Mo. 418^ Art. i, 


Difrert.7' 0/"ti&c Aurora Borealls. 157 

titude from about the fiftieth Degree over al-* 
moft all the North of Europe^ and at all Plea- 
ces, exhibiting nearly at the fame Time, the 
feme Appearances. 

7. Thefe Appearances have always been 
very frequent {as far as the Accounts we have 
of them inform us) in Countries, that lie in, or 
near the frigid Zone^ but very rare in thofe 
of our Latitude j they are now become very * 
frequent with us, but always feem to proceed 
from the North ,• and are as yet unknown to 
the Inhabitants of the more fouthern Parts of 
our Hemifpbere. . Whether they are feen to 
thofe, who inhabit in, or near the other frigid 
Zone^ is to us unknown, 

8. In fome, there are Trains of Light run- 
ning horizontally, fometimes from the Middle 
to the Extremes, and fometimes from one Ex- 
treme to the other. And from thefe Trains 
often arife Streams perpendicular to the Hori-- 
zon^ and accompanying them as they pafs 

9. When all the Streaming is over, the Ju- 
rora Sorealis commonly degenerates into a 
bright Twilight in the North, and there gra- 
dually dies away. 

10. It is prohablei that thek Tbammefra 
often happen in cloudy Nights, though we are 
not fenfible of them j for tis obfervable, that 
m fuch Ni|;ht5> there is frequently more Lights 

X a thani 

158 Of the Aurora Borealis. Part U. 

than what ufually proceeds from the Stars . 

The moft obvious Solution of the Aurora 
!BoreaUsy or at leaft what would appear fo, 
to fuch as have only attended to the Circum- 
ftances of fome particular ones, and which has 
accordingly been affixed by feveral * to their 
Accounts of the Auroras they have feen, is 
that it i^ a thin Nitro-fulphureous Vapour, 
raifed in our Atmofphere confiderably higher 
than the Clouds ; that this Vapour by Fer- 
mentation takes Fire, and the Explofion of 
one Portion of it kindling the next, the Flaflies 
fucceed one another, till the whole Quan- 
tity of Vapour within their Reach, is fet on 

* Profe/Tor Cof^/, at the Eixd of his'Dercription of a Ph^mme^ 
men of this Kind, inferted in the Philofophical Tranladions No. 
565, obferves, that fuppofing a Fund of Vapours or Exhalations at 
a confiJerable Height above us to be diffufed every Way into a 
large and fpacious Plane, parallel to the Horizon^ that Fund of 
mixed Matter by Fermentation will emit Streams ; and that if 
the Wind be ftill, they will afcend perpendicularly upwards; 
otherwife they will be inclined towards that Point of the Horizon 
which is oppodte to that froth which the Wind blows ; and that 
they will appear, by the Rules of Perfpeftive, in the firft Cafe, to 
converge to the Speftator's Zenith, in the other, to fome Point 
not far from it ; and that if this Fund of Vapours bf firuated more 
to the North than the South, it will produce Streams of Light at- 
tended with fuch Circumftance^ as then appeared ; But he does 
not fay, why the Vapours (hould be fituated rather to the North 
than the* South, or proceed to account for all the Pb4somena of 
(he JUfrwa Borealis in general i[<m^ thence« 

Others ' 

Differty. 0/ tib^ Aurora Borealis. 159 

Some have thought, that Vapours rarefied 
exceedingly by fubterraneous Fire^ and tinged 
with fulphureous Steams, might from thence 
be difpofed to fliine in the Night, and rifing 
up to the Top of the Atmofphere, or even be- 
yond its Limits, (as we find the Vapours of 
Gun-powder when heated in Vacuo^ will fliine 
in the Dark^ and afcend to the Top of the 
Receiver, though exhaufted,) might produce 
thofe Undulations in the Air, which conftitute 
this Vhtenomenon. 

But thefe Hypothefes have been rejefted, as 
inluifficient i it having been thought impollible 
to account for all the Circumftances of the 
Juror a by them *. 

* In the Commentaries of the Academy of Sciences it Pefers^ 
Ittrgb, I find a late Solution of the Aurora Borealis from Exhala- 
tions fermenting and taking Fire in the Atmofphere, which th9 
Author Chr. Mater fays, occadon the Appearance of the lucid 
Arch in tlie North, and thinks that the Streams, which feem to 
iflue from thence, are no other than the Light of that Arch rc- 
fleded to us from the under Side of fome thin Cloads, that lie 
above it. As to its appearing in the North rather than in the 
South, he fuppofes that may be owing to the Cold of thofe Regions 
condenfing the Exhalations, and thereby rendering them more 
liable to ferment than they are in the fouthern ; but acknowledges 
itigenuoufly, that he has no Reafon to fuppole this, but its being 
neceflary to his Solution. At the End he tells us^ That it was 
known in ancient Times as well as lately : But omits taking No* 
tice, that it appears much oftner of late Years in our Climate than 
it ufed to do ; and fo avoids accounting for that Particular* ritle 
Commentary Jkadnm. Scientiar* Imperial PitrefoUtan. ToiA. I» 

i6o 0/tibtf Aurora BoreaKs. PartIL 

r Vr.Hal/eytherekrehasKGCOurCetothemag'^ 
%etic Efflucia of the Earth, which he fuppofes 
to perform the fame Kind of Circulation with 
Regard to it, as the Effluvia of any particular 
^errella * do with refpeiit to that, mz^ that 
they enter the Earth near the South Pole, and 
pervading its Pores, pafs out again at the fame 
pittance from the northern : And thinks, they 
may fometimes, by the Concourfe of feveral 
Caufes very rarely coincident, and to us as 
yet unknown, be capable of producing a finall 
Degree of Light, either from the greater Den- 
fity of the Matter, or perhaps from the greater 
Velocity of its Motion ; after the fame Man- 
ner, as we fee the Efflut'ia of EkUric Bodies 
emit Light in the Dark, 

Monfieur de Mairan has given us a PhyC- 
cal and Hiftorical Treatife of the Aurora S(h 
realis^ and endeavours to prove that it is ow- 
ing to the Zodiacal Eighty or the Atmofphere 
of the Sun, fpread on each Side of him along 
the Zodiac in the form of a pyramid. This, 
hefays, is fometimes extended to fuch a Length, 
as to reach beyond the Orbit of our Earth, and 
then mixing itfelf with our Atmofphere, and 
being of an Heterogeneous Nature^ (woduces 

"^ A rouad Magnet^ fo called from the Refemblance it bnrs to 
the -Eartb, 



•Difrert.7. O/fi^^ Aurora Borealis. 161 

the feveral Appearances, Which are obferved 
in the Jurora Borealis \ 

I have juft jnentioned thefe two Sohitions, 
tecaufe they come from two very ingenious 
Philofophers ; though I doubt not but the Rea- 
der will agree with me, that they are much 
too fine fpun to hold, and that they are no 
other than the ingenious Retteries of Perfons 
determined to franie an Hy pothefis at any Kate. 
I queftion not, but we may find Materials for 
the Jurora Sorealisy without going fo far for 
them, as thefe Gentlemen have done ; and in 
particular that we have no Occafion to have 
Recourfe either to the magnetic JEjffiiwi a of 
the Earth, or the Zodiacal Light, the Nature 
of both which we are wholly unacquainted 
with. The Materials employed in the firft So- 
lution (I mean fuch Effluvia as are continually 
exhaled from the Surface and Bowels of the 
Earth) if rightly confidered, will afford a Very 
eafy and natural one, as I ftiall endeavour to 
ihew in the following Manner. 

Firft, We are aflured by Ej^periment, that 
there are fome Steams, (as inflammable fulphu- 
reous ones) which are capable of fo great aDegree 
of Expanfion, that they will render themfelves 
lighter than the Air they float in, though it 

* See hi J Account at large, refened to at the End of Note; 
Page 155. 


I €7 O/^i&e Aurora Borealis. Part II. 

be as rare, as it can be made by Art ; for they 
will rife to the Top of the Receiver, when 
exhaufted \ that is when as much Air, as is 
poflible, is drawn out t : Such Steams there- 
tore or Exhalations, rifing oat of the Earth 
from Mines, Vulcano's, (!;c. muft neceflarily be 
buoyed up towards the Top of the Atmofphere, 
at leaft, till they come to a Region, where the 
Air is as rare and expanded, as it can be made 
by the Jir-Tump^ here below. This Height, 
according to Dr. Hallefs Computation $, 
{which he founds upon the Degree of the Air s 
jElafticity ) is about forty or fifty Miles : but pro- 
.bably it is much greater j for the Air, which 
is higher than Vapours and other Heterogene^ 
ous Matter that is not elaftic, rife to, being 
much purer than any we can make Experi- 
ments upon, may be indued with a much great- 
er Degree of Elafticity, and fo the Atmofphere 
may be confiderably higher, than what he, 
upon that Principle, computes it to be. 

Secondly, Thefe Effluvia being raifed to 
the Top of the Atmofphere, or near it, and 
floating there, will neceflarily be carried to- 
wards the polar Parts thereof, for the follow- 
ing Reafons. i. Becaufe the fuperior Current 

* See Phllofoph. Tranfitft. No, 347 and 360. 

t It is impoffible to extract all the Air out of a Veflel, be6au& 
It is by the Spring of the Air remaining in the Veflel^ that tbe 
Valves of the Pump are opened at eaoh Scroke* 

§ PWlofoph Tranfaa. No, 181. 


t)iffert.7* 0//i&(? Aurora Bdrealls, i6^ 

of the Air, to a great Diftance from the Mqua^ 
tor J is that Way '^. 2. We know from Ex^ 
peritAetit^ that whatever fwims upon a Fluid 
which revolves ^bdut an Jxis^ is thereby car^ 
ried towards that Jxis* This, is exa<5tly the 
Cafe of thefe 'Effiuma^ for they fwim near the 
Top of the Atmofphere which continually re- 
volves .about the^x/j- of the Earth ,• they muft 
therefore neceffarily be carried towards the po- 
lar Parts thereof. 

Thirdly, Thefe Bffiuma being colleded 
together at, or near the Poles, and of an in-^ 
flammable Nature, may eafilv be fuppofed to 
ferment, when they nieet with other heteroge^^ 
1WOUS ones proper to produce fuch an EffeiS, 
and emit Streams of Fire j which Streams will 
naturally rife up into fuch Parts of the Atmof- 
phere as are ftill lighter than that wherein the 
Effiwvia reft, that is, diredly upwards from 
the Center of the Earth* But, according to 
the Rules q^TerfpeUhe^ thofe Streams, though 
they really diverge, as Radii from a Center, 
will appear to a Spectator oft the Surface 01 
the Earth to converge towards a Point: Which 
Point will be diredly over his Head^ if the 
Streams afcend in right Lines from the Center 
of the Earth ; but if they deviate all one Way 
from that Direction, the Point will be oa 

!^ As nqplaiaed in Diflertation V. 

1 64 Of the Aurora Borealis. Part II. 

that Side the Zenith towards which they iff- 
cline * 

To illuftrate this; fuppofe feveral Strings 
hung down from the Ceiling of a Room, and 
a Candle placed upon a Table below them, 
the Shadows of them all will converge towards 
the Point, that is over the Candle. And, if 
they are made to incline, fuppofe all one Way, 
the Point of Convergency will remove from 
over the Candle, towards that Side of the 
Room to which the upper Ends of the Strings 
incline : Confequently if a Perfon had viewed 
them from the Place where the Candle was, 
and referred their Places to the Ceiling, they 
would have feemed to him to have converged 
towards the Point, where their Shadows did-. 

. And if the Streams fpread themfelves as 
they arife, but not too much, they will never- 
thelefs appear tapering towards the upper Ends, 
like Cones or pyramids ; juft as the Sides of 
a long Walk feem to a Perfon that views them 

* This may be made to appear in the fel Wing Manner ; Let 
APB {Fig. }8.) reprefent the Concave of the Heavens, AB the 
Horizotty C the Place of the Speftator, TV a luminous Subftance 
fending fonh the parallel Streams EG, LM, NO, Q^c. Thefe 
Streams will all ieem to converge towards the Point D, if that Poinc 
be taken fuch, that the Line DC drawn from thence to the Speda- 
tor's Eye, be parallel to the Streams. For Infiance, the Stream 
£G will feem to rife from e to g, LM from / to m^ and FH from 
/to b, and fo of the refL And NO will appear wholly in D the 
Place to which the reft feem to convei^e. And ijf the Streams 
are as large, or fomewhat larger at the upper Ends, than at the 
]ow«r» they will flill appear left there, thofe £nds being iartheft 
ftom the Spcftator's Eye* 


Diflcrt-7- 0//i&i? Aurora Borealk 165 

from one End of it, or from a diftant Place, 
to approach each other at that which is fartheft 
from him. 

This being premifed, we may now account 
for the feveral Thanomena of the Aurora 
3ioreaUs before laid down. As, 

1 . The Blacknefs of the Sky, which gene- 
rally appears in the northern Parts of the Ho- 
rizon^ like a dark Cloud, is occafioned by the 
Brightnefs of the luminous Matter of the Ju-* 
TOT a juft above it. That the Sky is clear here, 
is evident (as was obferved before) becaufe 
the fmalleft Stars are feen through it. 

2 . The lucid Arch immediately above, is the 
luminous Matter of the Aurora itfelf, which 
fometimes exhibits the Appearance of a Curve, 
fometimes of a ftrait Line, according to its 
Form and Situation in the Atmofphere, though 
generally that of a Curve : For, by the Rules 
of ^erfpeUh'Cy when a ftrait Line is diftended 
horizontally, and above the Spe(ftator*s Eye, 
it ought to appear bent into a Curve, whofe 
Center is below the Horizon \ Sometimes 
it appears on one Side the North Point, more 

* Thus, when a Perfon flands fronting a Row of Houfes, and 
looks over the Tops of them, if they are all of an equal Height, 
that Houfe which is neareft him, will feem to cut the Heavens ia 
a Point that will be higher than where it is cut by any of the reft ; 
ahd the Points where the Heavens will feem to be cut by the Tops 
oi thpfe, which are oo the Right and Left Hand of the Spedator, 
will de&end lower and lower, as the Houfes are farther off ; fo 
Ihat the Points, taken all together, will reprefeot a Cutve. 

y a than' 

l66 Of the Aurora Borealis. Part IL 

than on the other ; fometimes regular, fome- 
times irregular, as the various Circumftances 
of the Air s Motion at the Top of the Atmof- 
phere, and of the Situation of the flaming Mat- 
ter may be, 

3, The Streams of Light iffuing out of the 
lucid Arch, are Streams of Fire emitted up- 
wards from the Matter of the Juror a^ and 
feem, for the Reafons already laid down, to 
converge towards the Zenith of the Spedtator. 
Why they incline a little fometimes from the 
Perpendicular, will be explained in the fifth 
Remark, where we account for the Situation of 
the Canopy • When no luminous Arch ap- 
pears, it is probable, that it is intercepted by 
the Horizon^ or by the Vapours which float 
in great Quantities therein. 

4, The trembling obferved in the upper Part 
of the Heavens, is owing to the Quicknefs 
wherewith the Flaihes fucceed one another, 
and alfo to the irregular Motions and Agita- 
tions of the f uperior Parts of the Atmofphere* 

5 , So long as the luminous Matter of the 
^Jurora is all of it towards the North of us, 
the Streams cannot feem to meet in a Point at 
the Top, as will appear to any one that confi- 
ders the Figure referred to in the Note (p.i 64), 
but after it has advanced forwards, or become 
kindled over our Heads, then they appear to 
meet, and form the Canopy already defcribed ; 
and when it has paiTed farther ftill, ^bey feem 


Differt7* Of the Amovd^BoxeaWs. 167 

to arife from all Parts j though they are much 
fainter on the fouthern than on the northern 
Side^ fo long as the main Body of the Jurora 
remains on the northen Side of the Canopy, 
which it rarely, if ever, paflfes. The Reafon 
why the Center of the Canopy is generally a 
few Degrees to the South of the Spectator's 
Zenith^:, is becaufe the luminous Streams, 
which ifiue forth from the extreme Parts of 
the Subftance of the Jurora^ will naturally 
diverge a little from the middle ones y and, as 
thofe which appear to us, proceed chiefly from 
the fouthern Side, (that being neareft to usj 
the Point of Convergency will neceflarily be 
placed to the South of our Zenith ^ according 
to what was faid above about the Inclination 
of the Strings hanging from the Ceiling of a 
Room, If the Center of the Canopy is fome- 
times to the Eaftward, and fometimes to the 
Weft ward of the Meridian, that depends upon 
the Motion of that Part of the Air, which is 
above the Subftance of the Juror a^ and through 
which the Streams pafs, as they rife. This 
alfo it is that makes the Streams feem to arife 
fometimes a little obliquely. 

^ According to this Theory, the Center of the Canopy will al« 
Ways be near the Spedator's Zenith, where-ever he is ; which I 
beheve is the Cafe, for I have met with no Account where it if 
otherwife ; and fo every Spedator fees a differenc Canopy, )ufl as 
when feveral Perfons are viewing a Rainbow^ no two Peribns fee 
^ fame Buiabow ac the lame Time. 

e. The 


1 68 0/ fi&<? Aurora Borealis, Part If. 


6. The great Height of the Jurora is owing 
to the exceeding Lightnefs of the Ej^twia^ 
which compofe the Subftance of it (as explain- 
ed above) and the darting of the Streams up- 
wards, into Regions perhaps quite above the 
Atmofphere, occafions it to exhibit at very 
diftant Places the fame Appearances at the 
fame Time. 

7. That the Aurora appears near the Tok'^ 
and never at or near the Equator^ is be- 
caufe of the Tendency the Matter of it has 
towards the Poles, as explained above. And 
that it appears in Places more diftant from 
the ^ok^ than it formerly did, is becaufe the 
Bffltma^ which are now raifed from the 
Earth, are prevented from approaching fo near 
the polar Parts of the Atmofphere, as they 
ufed to do i thofe Parts being already flocked 
with others, which were formerly raifed, and 
are now grown effete by frequent Fermenta^ 
tions and Explofions. 

8. The horizontal Trains of Light are the 
Subftance of the Jtirora juft taking Fire, 
which runs from one Part to another, as in a 
Train of Gunpowder kindled in any one Part ; 
and fends up Streams perpendicularly from 
Places^ where it meets with a greater Quanti- 
ty of Matter than ordinary. 

9. When the Matter of the Aurora is fo far 
fpent, as to emit no more Streams, it appears 
only as a bright fteady Light in the North,' 



Difleit. 7. Of the Aurora Borealis. 1 6^ 

which gradually dies away, for Want of frefli 
FeWel to fupport it. 

I o. As the Vapours, of which Clouds are 
formed, never rife fo high^ as where the Mat- 
ter of the Aurora "Borealis floats ; it is not at 
all inconfiftent with the foregoing Theory, if 
it is fometimes intercepted from our Sight, by 
the Interpofition of Clouds below. 

See farther on this Subjeft, Ariftotel. Meteor. 
Lib. I. Cap. 4, 5. P/mV Hiftor. Natural, 
Cap. 26, 27. Senec^ Quseft. Natural. Lib. I. 
Lycofi. Prodigiorum ac Oftentorum Chronicon, 
paffim. Julius Ohfequens de Prodigiis^ Cap. 
13, 43, 88. Qaj[endi Animadverf. in l^iog. 
Laert. Lib. X. p. 11 57. Cornelius Gemma 
de divinis Nature Charaderifmis, Nicephori 
Hiftor. Ecclefiaft. Lib. XII. Cap. 37. IJid. 
Htfpal. Hiftor. Goth. Tom. I. p. 65. Bibli- 
othec. Orientalis Clementino-Vaticana, TomJ. 
p. 407. Gregor. "Tur. pafllm. Mem. de Lit. 
de rAcad. dQS Infcriptions & belles Lettres, 
Tom. IV* p* 43 !• Mifcellan. ^eroliiu Tom. L 
p. 137. Theatr. Comet. St ant f. Luhienietz^ 
p. 264, 348. Mem. pour fervir a THiftor. de 
France^ Tom. I. p. 168. Mem. de I'Acad. 
Royal, de Sciences, for almoft each Year fince 
1716. Philofoph. Tranf. N^. 305, 310, 320^ 

347^ 348. 349, 35I5 35^3 3<53» 3^5. 3^8^ 375, 
385^395^398, 399*4^2, 41 0,418, 431; and 
the Authors referred to by Mr. Jobnfoiu in his 
Qua?ft. Philofoph. Cap* IV. $.3. 


1 76 Of Ferrnentatml I^art IL 


Of Fermentation4 

HAving had Occafion to mention fotne of 
the Effefts of Fermentatiori, it may not 
be amifs^ before I put an End to thefe Differ^ 
tations, to add a fhort Account of the Nature 
of itj and to fhew how thofe Effefts are pro- 
duced by it. 

Fermentation is a mutual Commotion of the^ 
conftituent Particles of Bodies, one among ano- 
ther; and arifes from an Inequality in their 
Attraiftions of Cohefion. Authors diftinguifti it 
into two Kinds ; the one is that which happens 
when a Solid is diffolved by a Fluid ,• the other 
is^ when two Fluids, being mixed together, fcr* 
ment with each other. 

Thofe Authors who have treated of the firft 
ofthefe, tell us. That to caufe a Fermentation 
between a Solid and a Fluid, feveral Circum- 
fiances are neceffary. Particularly Dr. friend % 
and Ktil t are of Opinion, 

I . That the Particles of the Solid muft at- 
tract thofe of the Fluid with a greater Force, 
than the Particles of the Fluid attract one 

*• See his Chemical Leftures. 

t S^ hU Letter (0 Dr. CotkbUffi^ Df Legtlt$i MraBknis: 

?.• That 

-i^rhitrnPoi^i of the Solid liiuft hot b« 
tfto feiall t6 admit the Psirticles of the Fluid 
ititotl^nii ; ;■ ' 

^; 3* That the Body be 6f fo Iddfe a Contex-* 
tdrej that the Fdrce of Impaa;, With which 
tKd Particles oif the Fluid riifli into its Poresi 
may bd fufficieflt to diluiiite its Partsi 

-•4. Thafc'-the Elaftieity of the Particles tends 
vdry much to "promote, and augment the Feri 
mentation. ; 

r f>r. 3Boerhaa'V6 makes alfo four Conditions 
requifite *. 

I ; Thit th^fc be a due T^o^ortioii betweeh' 
the Size of i^e Particles of the Fluid, and the, 
Pores of the Body to be diflblved* 

• i. That the Figure of the Particles of the 
Fluid have a dieterminate Relation to that of 
the Pores of the Solid. 

.^. That the' Particles of the Fluid be futo 
QOtly folid, : that their Moment, or Force of 
Aftion may not be tckJ weak. 

4.. The lafi Qualification, he mentions, is ^ 
fit Difpofition of the Particles of the Fluid, 
when recdved into the Por^s of the Solid, to 
make fomc ftay^ there, and not immediately 
to pafs through i but to a(ft every Way upon 
the Solid, as they move towards the external' 
Sur&ce thereof. 

z '-'• '>'"^.- ^m 

1 1 1 1 

1 7 3 - Of Fcrmentattm , Part 11 j 

But we have, na Occailon tO' faaiue-Recourfe 
to fo many Suppolitions^- tf th^ .Pai;ty:lBs oFt|ie. 
Solid attrac-t thofe'df the Fluid with a. greater 
Degree of Force tlian either thofe, of -^e Fljiid, 
or thc>^e of tfie ^olid att^aci. one .another. V it 
is luff^cent 5 and there will foUow a ]^iifolii(icia- 
oT the Body,, as nrny clearfy- be d^onftrated 
from the Laws ot pkchamcsy whatever ^e 
other Circumilancesj relating to the Figore or- 
Magnitude ofPores, f^c. may be f* , 

' • Whea 

* ^ - « 

* This miy be thought Aii( impdCbte Snmftr^y ibr the Fm:e 
of Actradlion of Coheficn being as the Surncesi. of the attrfifting . 
Particles, xfrhatcvefSize ot Forittthe* Pamcle§ bt the Solia and' 
Fluid are of, there cannot be'a greater Qdabdit^cfSttrfikcebet^i^ 
ever)' two Particles, one of which is a, Fait^le 6f the Solid, and 
the other a Particle of the Fluid, than there^is^ Between every two .- 
Paftides, which are either both of the SolMi <)^ tfottrof theFJitrd;-^ 
and therefore the Particles of the Solid csof^r^f (taift thofe of Che 
Fluid with greater Force than either thpfi; oF^ the Solid or thoie of 
tfie Fluid attrad one shimhrtr. Bht ir Is t6*l^ ^onhdered, thit we 
aftiLnot ^ well acijuainted'wlth the Na^ur&.oTth^ Attiadlfn cf : 
Cohelion^ as to determine ejr^^l^f in w.l^at Wapna'; and by whac 
Liws it afts. The Experiments made Ufe of for this^Pmpofe^ on- 
l/{hew that fo long as we try them with tliei^me IKiil o^ Bodies, 
the, AttraftioB _is larger Vhefc theCo^taift irfir/. See Part L 
Chap. III. But we have no Method pfdetCTminin^ whether the 
Difftrence of AttraAioW,' Which^ci^^Ax'B6aies exer?^iipbh oi{^' an* 
other^ arises folely frojrtt arDlftetenqe ih thtir'Sh'i^ac^s, or nof. ' 

t ..X)em, Thp^ let /^ fyf^ SPc. (F^ Jp.^ Ve|rdenr f Series of 
the Particles of a I^luid, and /, j, f, ofV. a Series of thofe' of & 
folid Body, contigaoos to* one aftittfef; arid^ let tht jjficlciw 
Lines f/, //, SPc. reprefent the Forces of ^ttraftiiA bccvBTQ^Be: 
the Fluid Particles one among another, and s s, s s, 8v. 
thofe of the folid ones among themlelves : and lee the black 
Lines //, i/, &V, ftjsrels: thifff w^li= rfrPttHWWi' dfc Muid 
And (plid Particles. Now, the latter Forces being by the Sup* 
p^tioA flroDger than ch& former/ the fluid Particd^ wiU recede 


DiiTert. 8. Cf Fermentatiml T7J' 

When a Solid is put into a Fluid, if their 
Particles have the above-mentioned Relation 
to each gther, thofe of the Solid being attra<5l-. 
ed with ^eater Force towards the Fluid,' - 
than they are the contrary Way, they will fall 
off from the Solid, and ,enter in Between the 
Particles of the Fluids and for the like Reafon, 
thofe of the Fluid will open to themfelves a 
Way in between thole or ihe Sojiid, and will 
feperate them from each other. Neither will 
their .refpe(5tive Motions ceafe, unlefs their 

from cacbothWj and fi^er thofe of tive Solid to enter in between 
them ; and for the (ame Reafon, the folid Particles will give Way 
to thdfe pf cbe FJuid. By which ineans, the DiAances reprefented 
iiy the pridced Lines becoming greater^ the Attraftions whtcl\ 
they express, will be diminifhed ; fo that the fluid Particles will 
^nter quite in between t}ie folid ones, and the folid ones between 
the fliud ones ; jand both of them together will conftitute fucha 
Series, as is reprefented in Figftre 40, in the middle Row /, fy s, 
fj Spg, where the folid and fluid Particles lie mixed interchangea' 
Uy one with another in a right Line, Now let it .be fuppofed, 
that this Series is contiggous to one \ybich confifts wholly of Fluid 
above it, as is expreSd in the Figure, and to an6ther below, 
oonfiAing of fq^d P:|rticles only. Beery Iblkl Particle in this 
Series will be^a^ra^ed 4ipwards with ^eater Force, than ic 
is downwards ; and every fluid bne'with greater Force down- 
wards :than it is upwards, as appears by bare Infpedion of 
Uie J^jgurc^ where the black Lines, as in ,the former, ci^refs 
the ffrohger Attrajftions> and the pricked ones the weaker* 
And, if we ftippofe the Kuml>er of Particles in the Solid and in 
Che Fluid to be nearly equals thofe of tt^ Fluid, will not ftop, till 
tjbey haye ^te,|^(fi|d thcou^ the Solid ; for they will always 'flod 
« Series wnolly cohfifting of ibiid Particles before tliem, whil& 
^. wiikh tbey:Ieav« behlrtd, will' be a Mixture of bothj In like 
inanner, the ffjld oi|es will j^a|ulte through the. 4ui4 ones ^ kA 
they will alwayi meet ipith more mid 9nesbeicHie them, tt^aatheu 
kav/r Mind^vidQnthc llpbeie Gif thdr 0^ 

Z a Qlian- 

1 74, 0/ pcrmentatipH. - Part H. 

Quantities be very unequal,. till they gre dift- 
fufed uniformly onei among another, as we 
may very eafily conceive ^ for till then, there 
will alv^/'ays be fome Particles attrafted with a 
greater Degree of Force one Way than they 
are another. 

And if more of the Solid be added to this 
Fluid, the Particles of the Fluid will alfo en- 
ter into that Solid, till each is furrounded on 
all Sides with folid Particles, as far jas its at- 
traftive Force reaches. After which the Fluid 
is faid to be faturated-^ and will diflblve nQ 

Again, if more of the Fluid be poured upon 
that Solid, the folid Particles will diffufe 
themfelves farther into the Fluid, till each of 
them is encompafled with Particles of the 
Fluid, as far as its attradtiye Force extends ; 
and then they will fpread themfelves no farther* 

But in either Cafe, if another Solid^ or 
Fluids the attractive Force of whofe Particles 
differ from thofe of the former, be added, a 
frelh Fermentation will begin^ provided the 
attrai^tive Forces between the Particles of the 
jformer Mixture, and of thofe which are now 
addedj ha vipfuch Relation tQ each other, as 
is neceffary to produce it; 
^ 'Upon this Principle it fhpul4 feem, that a 
Fluid fhowld always be capable of diffolving 
liiore-thannan equal Quantity of a Solid -and 
i^^fi $oUd iljQqlcl be; qap^U^. of .^i^triog ia , 

Differr., ^* Of Rrmenrmtf»l r 7^^ 

and diffuling itfelf through more than an equal 
Quantity of Fluids The Reafon why it is fre-* 
quently not fo, is^ becauTe it commonly happens^' 
tibat the Fhiid and the Solid are not of equal 
fpecifie Gravities, When the Solid is heavieft^' 
fo many of its Particles will not aicend and 
enter into the Fluid, as would otherwife hava 
done i and on the contrary, when the Fluid i$ 
heavieft, the Weight of its Particles thrill be an 
Impediment to their riling into, and diiTolving 
the Solid. 

We have no Occafion to diftinguifli Fer- 
mentation into two Kinds, with regard to its 
Caufes; for, according to the foregoing Theory, 
whenever two Fluids, or a Solid and a Fluid, 
are put together, if the Particles of the one 
attract thofe of the other, with greater Force 
than either thofe of the one, or thofe 'of the 
other attraiSi: themfelves, a Fermentation will 
equally enfue, the Caufe being the fame in 
both Cafes. 

When two Fluids, or a Solid and a Fluid,' 
ferment with each other, if the Agitation and 
intefiine Motion of their Particles be very great, 
or continues a long Time,' and if the Subilance 
of them be of the inflammable Kind, they will, 
by continually rubbing one againft another, be 
fuificiently heated to take Fire, and burft out 
jinto Flame ; as was laid of the feveral Com- 
TOfitions fneiipipqed in the foregoing DifTerta-^ 

Xlfi Of' FermemMtiS, '■' Part I J,- 

• See riie Authors, who- bm nrpiained ao(I 
defended the old Solution, referred to by Mi^ 
Jobujim in his Qjiscftiones Philofoph. Cap. ill.' 
CJMft. 5, <,7. 

I'he BnJcftbc Seconi'Pan. 


Compendious System 

O F 

Natural Philofophy. 


Containing the 

Mathematical DemonstrationSj 


Some Occafional Remarks. 

P A R T. III. 

To which is annexed a Dissertation on the 
SubjeA of the Horizontal Moon. 

The Third Edition. 

By J. R OWNING, M. A. 

Reftor of Anderby in Lincolnshire, and late 
Fellow of Magdalen College in Cambridge. 


Printed for Sam. Harding, Bookfeller, on the Pave- 
ment in St. Martin' %" Lane. 

![ Price One Shilling and Six Pence ] 


C o MP EN Dious System 

o F 

Natural Phitofophy. 



O p T I c a. 

C H A P. L 

Of the Nature and Tropagation gf Light. 

IN treating of the Nature of Fluids, I have 
explained fuch Phanomena as refult from 
fmall Particles of Matter collected toge- 
ther, and aded upon according to the. 
Laws of Mecbanifm ; the Order of my Defign 
now brit^s me to ihew hoW according to the 
lame Laws fuch Pbanomenay as refult from 
the Emiflion of infinitely fmall Particles from 
luminous Bodies; are produced ; which Pba^ 
nomena^ being the Means, whereby the Images 
of external Objeds are reprefented to our 
Minds, by the Intervention of our Organs (jf 

A Sight, 

4 Of the Nature and Part III. 

Sight J are for that Realbn called Opticaly and 
the Doftrine, \y which they arc explained> 
the Science of Optics ♦. 

Every vifible Body emits or reflects incon- 
ceivably fiaiall Particles of Matter from each 
Point of its. Surfaces •which ifbe frppi it con- 
tinually, (oot unlike Sparks from a Coal) in 
ftrait Liines and in all Dire£tions* Thefe Par- 
ticles entering the Eye, and ilrikiag upoa the 
Retina (a Nerve expanded on the back Part 
of the Eye tardceive their Impulfes) excite in 
our Minds the Idea of Light. And as they 
differ in SubftaUce^ Denfityi Velocity, or 
Magnitude -f-, they produce in us the Ideas of 
dMerenr€olours ; as will be explained in its 
proper Place. 


• Optfts is generally diyided info twa Pu'ts, ntix, Diopirics^ 
under which is comprehended every Thing that relates to the 
Appcara«ce$Qf Bo4itt feen tlttongh tfanfpm&tSubftanCcI ; Md 
Cafof tries ^ or What relates to the feeioe of Bodies by reSefWd 
Light. To theft w€ may «dd a third, which properly comes wl- 
dfir Mitbef of Ihe forxner SiDiadiDfis, and that is,, tie J^oBrim 
gfCclvuru which explains every Thing that relates to tlw? Caufc& 
of the Divetiity of Cdlours obfervable in natural Bodies. 

f It is more probaUiC, thn they difo eithev m Mftgnimde* 
or Denfity, thajo ia Velocity or Subftance« JPoc, if the Difiex- 
ehce of Colours ^rife from the different Velocity of the Rays of 
Islght, then theC«>loursof Obje£U ivould appeaFchftnged t04» 
Eye plated binder Wattfr ,or within any Meihm difleriB4( fronv th« 
Air in Dcnfity : For when a Ray of Light paires4>ut of a Mtdi^ 
ufn into another of different Denfity, it undergoes an Alteration 
in its Velpcity, t& will be e^cplaincd botsaftet. Ani to fiippofe^ 
them to differ in SubiUnce, is contrary to thait Unifonmty of 
ThingSj^ which is obfervable in the Univcrfe i as wdl tm repug- 

Chapel, Pr9p0gatidn of lA^t. j 

That the Particles^ which cpoftlbite Lights 
are exooedingly fmaU} afmevs from henoe> 
viz. that if ^ HoIq be maae through a Piece 
of Paper with a Needle, Rays of Light irom 
«very Objedt on U19 £u:ther Side of i^ are ca- 
pable of p^Eng through it at once without the 
leaft Confufion ; for any one of thofe Obje&s 
may as clearly be ieen through it as if no Rays 
pafled through it frooi any .of the reit Fun. 
ther, if a Candle is lighted^ ,aod there be no 
Obftacte in the Way to qt^rudt the Progrefs 
of its Rays, it wUl fill all the Soace within 
two Miles of i^ eyery Way with luminous 
Particles, before it has loft the leaft ienfible 
Part of its Subftance thereby. 

That thefe Particles proc^ firont every 
point of the Surfape of a vifible Body, add in 
all Direftions^ is ckar from, hence, m»^ be^ 


nant to that JLmgnuitj m the 'primogeneal Parts of Mattery 
which from the Experiments hitherto made, is thought to exift 
tvery where. Whereat, if we fuppofe them ta AiSet either m 
Magnitude or Denfity»nothing is more eafy than to fee how thofif 
of the fame Kind (hotdd, however refraflect, produce the fiime 
Colours; and alio how thofe which produce different Colours, 
flionld fufier diftcrent Degrees of Refraftion in paiBng thmagh 
the fame Medium. As to the llrft, it is felf-«iridcnt» becaufe 
Refraction cannot alt^r their Magnitudes or Deniities ; as to the 
fecond, it is probable, that the more intenfe and ftronger Co* 
lours, the Rays of which fufFer the leaft Refraction, are produ- 
ced By the Urger, or more denfe Particles of Light : For, that 
fiich Partida mbald be le(s refracted than others, is quite con^ 
Ibnaat to the tawsof AftraCtionof Cohefion, which, as it a& 
in Proportton to the Surfaces of Bodies only, moft neceflanly 
$Sk€t the larger, or the tOBftt denfe Particles, lefs than it does 
the reft ; becade fuchJiave larger Momenta or Forces ifi Pro* 
portiaa to their Surfaces, than others have. 

A 2 caufc 

6 Of tie Nature and Part III. 

caufe where-ever a Spectator is placed with 
Regard to the Body, every Point of that Part 
of the Surface which is turned towards him^ 
is viiible to him. That they proceed firotn the 
Body in right Lines, we are aflured, becaufe 
juft fo many and no more will be intercepted 
in their Paflage to any Place, by an interpo/ed 
Objed, as that Objed: ought to intercept, fup- 
pofingthem to come in fuch Lines. 

T^ht Velocity, with which they proceed 
from the Surface of the vifible Body is no leis 
iiirprizing, than their Minutcnefs : The Me- 
thod wherebyPhiloibphers efHmate theirSwift- 
jiefs, is by Obfervations made on the Eclipies of 
yupiter^s Satellites, which Edipfes to lis ap- 
pear about feven Minutes iboner than they 
ought to do by Calculation, when the Earth 
is placed between the Sun and him 3 that is, 
when we are neareft him, and as much later, 
when the Sun is between him and us, at which 
Time we are ^heft from him ; from whence 
it is concluded, that they require about fevcn 
Minutes to pafs over a Space equal to the Dif- 
tance between the Sun and us> which is about 
eighty one Millions of Miles *• 

♦ This affords us anotber Proof of the furprizing Finenefs of 
the Particles of Light ; for the above-mentioiied VelociC3r of the 
Rays is confiderably more than a Million of Times greater than 
that of a Canon Ball. Were they not therefore iiconceivabl/ 
fmally the Eye would be rather wounded than delighted with 


chap. L Prbpagation of Light. 7 

A Stream of thefe Particles iflbing fro mthc 
Suifice of a vifible Body in one and the fanae 
Piredlion, is called a Ra^ of Light, 
• As Rays proceed from a vifible Body in all 
Directions, they neceffarily become thinner 
and thinner, continually fpreading themfelves, 
as they pafs along, into a larger Space, and 
that in Proportion to the Squares of their Dif- 
tances from the Body * 5 that is,* at the Dit 
tance of two Spaces, they are four Times thin- 
ner, than they are at one ; at the Diflance of 
three Spaces, nine Times thinner, and fo. on : . 
the Reafon of which is, becaufe they fpread 
themfelves in a twofold Manner, viz. upwards 
and downwards, as well as Side- Ways. 

them ; and the tender Flowers of Plants would he fb far fronn 
being cheriihed by them, that they would be torn in Ficce^ 
and not able to Hand before them. 

* ThisPropofition is demonftrated mathematically thus; let 
us conceive two concentric Surfaces ABD^ and £FG (Fig, i.) 
and in tlvefe, two fimilar Portions £LFI» and AHBK ; let the 
R^ys C£ and CF, with the reft proceeding from the Center C, 
fall upon the I'ortion ELFI and cover it ; it is evident from In- 
fpeftioQ of the Figure, that the fame Rays at the Diilance CH 
will cover the Portion AHBK only ; now thefe kays being the 
fame in Number at each Place, will be thinner in the former, 
than they are in the latter, in Proportion as that is larger than 
this ; but thefe Spaces being fimilar Portions of the Surfaces of 
Spheres, bear the fame Proportion to each other, that ttic Sur- 
faces themfelves do, that i?, they are to each other as the 
Squares of their Radii CL, CH 5 the Rays therefore are more 
diffufed, or thinner in Proportion to the Squares of the fame 
Rtidiii^ or «f their Diftances from the luminous Point C. 
^ E; D. 


S Of the Nature^ &c. Part III. 

The Particles of Light are ful]jea: to the 
Laws of Attra^oQ ^ Cohefion like other 
fmall Bodies, for if % Ray of Lighj; be made 
jBo pofs by th$ Edge of a Knife, it will be di- 
verted from its natural Covrfe, an^ be infled^ 
ed towards the Edge of the Knife. The like 
Infledion faiippens to a Ray when it enters ob<» 
liquefy intp a denfer or rarer Subftance than 
^at in which it wias before, ia whiph Cafe it 
is faid to be refra0ed\[ the Laws of which 
Refra^ion are the ^ubjed of the loUowing 
Chapter *4 . 

* The Cartifi99 Notion of Light, was not, that it is propa* 
^ated from luminoos Bodies by the Emiffioo of fmall Particles, 
tut that it was comtnttnicaitd to the Organ of Sight- by their 
^flure upon the MaUria fuhtilu^ with which they fuppofed the 
Vniverfe to be full. Bat according to this Hyfothefe, it could 
never be dark ;, becanfe when a Fluid fuftains any Preflitrey if 
t&at Fluid fills all the Space it takes up, abfolutely^ without 
leaving any Pores, which is the Cafe of the fuppofed Matiria 
Jaitilis ; then that Preflure muft necefiarily be communicated 
i^iaiiy and infimtmmoHfy to twery Part : And therefore, whe- 
ther the Sun were above or below the Horizon, the YrtSnm 
commonicated, and confequently the Light, would be the 
i&me. And farther, as the Prefiure would be inftantaneoo?, fo 
would the Light, whi^h is contrary to what is celle£led» as Wf 
^bkited above^ from the Edipfes of Jufitep^^ Satellites, 


Ghap. ll,TheCaufe ofKeda^iony^c. 9 



Of the Gaufe of Rcfradion, and the 
Law by which it is. performed, 

WHatever Subftance a Ray of Light 
pafTes througb, or if it pafs through a 
Space void of all SubilancCi it is faid by Phi« 
lofophers to pafs through a Medium \ and 
therefore if it pafles out^ of any Subftance, as 
Air or Glafs, into a Facuumy or the contrary, it 
is faid to pafs out of one Medium into another. 
All Bodies being <;ndued with an attia&ive 
Force, which is extended to fome Diftance 
beyond their Surfaces 3 when a Ray of Light 
paileiout of a rarer into a denfer Medium (if 
this latter has a greater attradlive Force than 
the former, as is commonly the Cafe ♦, and: 
what we (hall hereafter always fuppofe^ unfefe. 
it be mentioned to the contrary) the Ray juft 
before its Entrance, will begin to be attra<^ed 
towards the denfer Medium^ and this Attrac- 
tion will continue to adt upon it, till fome 
Time after it has entered the Medium^ as wc 
fhall (hew by and by j and therefore if a Ray 
ap[M:oaches a denfer Medium in a Dire<3ioa 
perpendicular to its Surface, its Velocity will 

• In oily and ir.flammablc Bodies it happens otherwife; for 
they arc obfcrved to attract more ftrongly than others of greater 


lo T%e C^/^^Refra£tion>^f.PartIIL 

be continually accelerated during its Pai&ge 
through the Space in which that Attradion 
exerts itfelf ; and therefore, after it has pafled 
that Space, it will move on, till it arrives at 
the oppofite Side of the Medium^ with a greater 
Degree of Velocity than it bad before it en- 
tered. So that in this Cafe its Velocity only 
will be altered. Whereas, if a Ray enters a 
denfcr Medium obliquely, it will not only 
have its Velocity augmented thereby, but its 
Diredtion will become lefs oblique to the Sur- 
face. Juft as when a Stone is thrown down- 
wards obliquely from a Precipice^ it ^Is to 
the Surface of the Ground in a Diredtion 
nearer to a perpendicular one, than that with 
which it was thrown from the Hand. From 
hence we fay a Ray of Light in paffing out of 
a rarer into a denfer Medium^ is refra^ed to^ 
wards the Perpendicular ; that is, fuppofing 
a Line drawn perpendicularly to the Surface 
of the Medium^ through the Point where the 
Ray enters, and extended both Ways, the 
Ray in paffing through the Surface is refrafted 
or bent towards the perpendicular Line ; or, 
which is the fame Thing, the Line which it 
defcribes by its Motion after it has paflcd 
through the Surface, makes a Icfs Angle with 
the Perpendicular, than the Line it defcribed 
before. All which may be illuftrated in the 
following Manner. 


Cli^p. 2. the Caufe ^Refi:a^ioh,#^. 1 1 

lidt us fiippofe firft, that the Ray pafles a ^^rttvimto the denfer Medium K 
BCD, (Ff^i 2.) and that the attra&ive Force 
of each Particle in the Mediuni is extended 
from jits refpe£tive Center to a Diftance equal 
to that which i& between the Lines AB and 
EF^ or.AB and GH| .aiid let KL be the Path 
defcribed by a Ray of Light in its Progrefs 
towanls the dtn&xMeMunL This Ray when 
it arrives at L will enter the attraftive Forces 
of. i^ofe Particles which lie in AB the Su^ fece ) 
of jthe .denfer Medium^ and will therefore ceafe 
to proceed any Idnger in the right Line KLM» : 
but will be diverted from its Courfe by being . 
attraAed towards the Line AB> and will be« 
gin to defcribe th&Curv^ LN, pafling through 
theiSuiface AJB.ih fome new Direftion as OQ^ 
thereby making a iefs Angle with a Line as 
PR drawn perpiindicularly through thePomt 
N, than it would have^done^ had it proceeded 
Jn its firft Dirediott KLM* 

Farther^ whereas We have fuppofed the 
attradive. Fbrce. .of each Particle to be ex- 
tended through a Space equal to the Diftance 
b^ween AB and EF» it is evident^ the Ray 
after it has entered the Sur&ce^ will Hill be 
attraded downwards,: till it has arrived at 
the Line £F; ^dt till that Time, there will: 
not be fo many Particles above it which will: 
attradfcit upwards, as below^ th^t will at-* 
tvzsk it downwards. $o that after it has en-» 

;B . tercd. 

1 2 j^ Gi2^«^Refi:adiob,^f.Fact lit 

tared the Surface at N» in the Dire&kn OQ , 
it will QOt proceed in that DiveAbn^ but will 
continue to defbibe a Oirve^ as N3> after 
which it will proceed Arait on towards the 
oppofite Side of the Medium, being attraAed 
equally every Way $ and therefere will at laft 
proceed in die Diredion XSTD flaU nearer the 
Perpendicular PR than before* 

Now if we fuppofe die Space ABYZ not to 
be a Vacuumy but a oarer Medium than die 
other, the Cafe, will fliU be the £une; but 
die Ray will not be fo much cefitodied fiomits 
refitilineal Courfej becaufe the Attraftion of die 
Particles of the upper Mtdium. being in a ooru 
trary Diredbn to that of the* Attmftbn of 
thoie in the lower one, the Adndioa of the 
denfer Medium will in iome Meafure be de« 
ftroyed by that of the rarer* 
: On the oontrary^ when a Ray pafles out 
of a denfer into a racer MeSum, if its Direc- 
tion be perpendicular to. the Surface of the 
Medium, it 'wiH only lo& fomewhat of its 
Velocity, in paffing through the Space of At* 
tra^on of that Medium (ifaat is, the Space 
wherein it is attraded mpre* one Way dian it 
is^ another.) If its Dire&ion be oblique^ it 
will continually r^ede from the Perpmdico- 
lar during its Faflage, and by diat Means hav^ 
its Obliquity encrcafed^ jiift osia Stone dirown 
up obliquely froni;i the Surfiu:e of the Earth 
inefeafea its Obliquity all the time it ri&s. 
l^hus, fuppofing the Ray^TS pafling oiit of the 


CliJip.2.7&Gi»g^«f Re 1:3 

dtti&r Medkim ABCD iQto the rarer ABYZ, 
^en it aurrii^isat S it wiU begin to beattradt- 
ed !(lownw»rdi> ahd &> wiU de&ribe the Curve 
SNLbtaad tl»)i procted iniheiight LineLK, 
making a laifjer Angld with thie.Beq)en(|icukr 
ISR^ than the Line TSX in which it proceeded 
during its Paflage through the other Medium. 

The Space thrbugh wWch the Attraaion o( 
Coheiion of the Particles of Matter is extend- 
ed is fo very foiali, that ihconiidering the 
Progrefs of a kay of Light out of one -mJ?^- 
Mm into another^, the • Curvature it defcribes 
ifi;p«^ng through the Space of ;Ajttra(ftion is 
generally negleiaed i . and :it5 P^ J§ fuppofcd 
toljbbent^ or ki iheufiial Terim^ the Ray 4s 
fupptifed to be rcff^aed only in the Point 
wkese it enters t|ie denier Medium. 

Now the Line,' which a R»y defd-ibes be- 
fore it enters a denier or a racer Medium is 
caii*dthe Incident; Ray % that whifch it de^ 
fcribes after it. has enterecl, is the 'MefraSi^d 

The Angle ciotnprfehended bet^cSii the ItJ- 
cideefc Kay and the Perpendiculai, is the y&H 
"gk of Incidence j and that between the reffa€&- 

ed Ray and the Fcrpendlcularr is the jdngle 

Tiere is a <^ertairt( and immutable Law dr 
Kule, t>y whieh Refradion is always perforn>» 
ed; and ibat is* this :, Whatever Inclination a 
tUy of Light has to the Surface df any Medi'^ 

' -* ' B 2 um 

urn befomit enters it, the Degree of Kefra&ioa 
will always be fuch, that the Prc^ttion be^ 
tween the Sine oi the Angle of its Incidence^ 
a^d that of the Angle of its Refiftdion^ will 
always be the £une. in that Medium ^; 


* Immit. If from a Point as M {Fig'. 4.) taken any ji^here 

without the Circle PNQ, a Line as MP be drawn pafling throu^ 
"* L the Center of the Cirde.and terminated in the Circamference 
at P, the Hrodqa of MC^miiltipliecl j?7 MP isequalto the Dif- 
ference between the Squares of ML an^ BL. 

J>eMonfiration of iht Lemm(i. Call MQ, 4 ; and the Radius of 
the Circfo LQjor LP, h 1 then WtU theJbiaineter QP be^ ex- 
preffible by thy and the whole Lija« MP, by 42«^2^ s'theHmiil* 
" tiplying MQby MP, that is, a by a^zbi we have for thrf ro- 
• du6lof this, Ma*\»2ab. Now the Square of the LiiieKILy 
which is expre^le by 44-^> hw^ia^^^^^fk, and .tSej^t^tie 
of PL is bb ; but the Difference bet>vee9 thefe Squares^ o/nt:. 
■ aa+^ab^bb and bb is evidently aa^^'^ j and therefore- tBe 
Produd of MQjsnktplyediiy MP is equal to the Difoeooe be- 
tween the Squares of ML and PL. . ^ £. />• 

Demanftration of-lhe P'ropoJitiorL, When a Ray of Light pafl^ 

« through the Space of Attraction of any Medium^ it is evident 

.tl(at ks Motion wiH befubjefl to the like Laws vin|h^tbit of 

troje£ii!es^ provi<^e'd we fuppofe it to be aded upon wit^ an 

-^cqual Dq^ree oTFofce during its whol^ PaiTage throtigh that 

Space, as is commonly fuppofed to be the Cafe in Proje^ 

vhatjpver Height tl^ey are thrown from the Earth. .We; will 

therefore put a Cafe as nearly parallel as may be to that which 

-wasdemonOi^tedof*^^^^^^^'in the fevcnth Chapter of the 

. &rft Part ; ai&d iuppole firil, that the Force of Attra^on of tJ|e 

denfiei' Medium is at all Diftances the fame as far as it re^tches, 

-and that the Ray proceeds out oC a denier into a rarer Medium ; 

in which Cafe it will be actrafled back towai:ds the denfer td^^ 

dium, daring its Pafiage through the Space of A.ttradion, in 

)ike Manner as a Projectile thrown upwards is while it tifes from 

•the Earth. Let then ABCD (¥ig, 4.) reprefent.the denfer Me- 

4ium> and ABEFth^ Space of Attraction; and let GH be a 

Ray about t6 enter the Force of Attra^ion at H,. and let GH 

*1)e produced tp M. Now it is evident, that in this Suppofttion, 

tixe Ray when at H, is in th^^ame Circumftances with a Pro- 

:. : TbiUoftrat&.this, Let us fuppofe AfiCD 

!(f%v30 i(b rfeprefent a rarer, and AB£P a 

4n^ i^dhiffi i let GH bp a Ray of Light 

v: J J • • , pafling 

ije&ih about tobe jthrown upwards from H towards M, it will 
' thefefore defcribdaf PorcioA of a Farnbola as HI ; to wbich the 

Line HM w^U J>sa Tangent at H ; and the Line IK, in which 

it would proceed;afier it has pafied the Space of Attradion, a 
..Tangent to it at I> for after having left the attractive Force a( 
:I,.itgoet Aratt.on ipitslaft DireSion. Let the Perpendicu- 
. lauf IR be drawn iheeting GH produced in M> and let Si be 
• teoduoedto L.i ' On the Center L with the Radius LI, d«« 
. i0:ibe tlie Cirde PNQ, let faU the Perpendicular LO ^ipon MR» 

and joittthi^, Points Land N. Now it is demonftrated in the 
. Cafe of FrojeCiiles^ that the P^raoutir of the Point H is equal 

to "Tjr*. ^^ therefore the Par'amter multiplied by MI is 

cqoa] to HM^. And it is there farther demonlb^ted, that the 
^d Parameter is equal to four times the Height which a Bodf 
.irioft fall from, to acquire the \t\ocity the Projectile has at 

'-H ; this Parameter tl^refore is a Quantity not at all depending 
on the Dire&ion of the Projectile, but on its Velocity only;, 
nndcoikieqiiently in theprefentSuppofitionit is a given Quan* 

'«ity» the Ray GH being fuppofed to have the fame Velocity. 

•whatever is its Inclination to the Surface AB. Now the Tan* 
gent KI being produced to L, will by the Pr(>perty of the As- 

'raholM^ bifeCt the other Tangent HM, wherefore the Line LO 
being parallel toHR, MR wiH alio be bife^d hi O ; and add- 
.ing the equal Lines Ol and ON to each Part, MN,w!n be equal 
to IR ; but the Line IR is alfo a Line independent of the Incli- 
nation of the Ray GH, its Length being determined by the 
Bnsadth of the Space of AttraAion ABEF only, and therefore 
MN is a given Quantity. Now, whereas MI, when multf*. 
plied by the Parameter of the Point H, which before was (hewn 
to be a given line, is equal to the Sqnare of HM, therefore the 
'^mie Line MI when multiplied by any other given Line {nn%^ 
MN) ifit is not equal to, willneverthdefs l^aragiven ft-o- 
poitioR to the Sqnftre of HM : But itnce MI multiplied by MN 
.bears a ftiven Proportion (v/«. a Proportion that does not depend 
on the^uicliaation of the Ray GH) to the Square of MH, its 
equal, <i;ii^. theProdua-of MQ^multipliedby MP (37. £1. 3) 
gr what is equal to this, the Difference between the Squares of 


1 6 73«(?tf/^fl/'Rc6:aftiod,AI?c.PartIII. 

paffing through the firiland entttingtbe iibeond 
at H^ ^nd let |II be the refr^dRfry ; dien 
fupppfing the PerpendkularPllclnivitethrottgh 
thie Feint H, on the Center H, and with any 

ML and PL (by the foregDtng Lmmt^ or, rnlutk is the&op 
Thing, of ML and Lf, (beatufe PL and LI are JUJii of the 
fame Circle) does fo too. Now the Square of ML bean alfo^ 
given Proportion to the Sqliam of MH (ML llcing equal to half 
MH) confeaoendy there is a given Pr^pdrtion bc^waen the 
Sqnaivof MLud the Diffierence of thcSqnaresof MLand U ; 
and therefore there is a certun Pranortiott between the Lines 
themfelves, wz. between ML and Lh But in every Triangle 
tJie Sides are proportionable to the Sines tf ditivbppofiee Anglei, 
therefore in theTriangle MLI>the $ine of the Aft^ LMI hafc a 
given Proportion to the Sine^ of the Angle LIM, or of its Coai- 
plement to two right ones MIK (for they have the fajneSihe :) 
But LMI bemg an Anglemade by i^e incident lUy GH pt&- 
dttced, with the Perpend JGubi: KM, is^hp Angkoflacidaiety 
and MIK. being made by^the refra£Ud Ray IK^ and the iaine 
Perpendicular, is the Angle of Refradion^ therefore in this 
Caie there is a confiant Ratio between the. Sine of the Angle of 
Incidence, and that of the Angle of Re£»^iQB« 

We have here foppofed that the Force of Attradion is jptery 
where oniforiB, batif itbcotberwife, ptovided>ic bethefane 
every where at the iame Diftances from ^he Surface AB* the 
Proportion between tlie foreinentioned Si^MS will fiiil be A given 
one.. JPor, let iis imagine the Space of .A):tva{tioA divided into 
parallel Planes, and the Attra^on to be ^t fmf^t ihrou^ Uie 
whole Breadth of each Plane though difiasent ia dif^n^ent maa, 
the Sine of the Angle of Incidence out of each wil, by what 
has been demonftnitcd above, be to th^>Sin0 of the Aagjb 
of Refra£Uon into the next in a giyien R^Hh S aiid theiefore, 
fince the Sine of the Angle of Refra^^ion odt of one will be 
the Sine of the Ang^e of Incidence into the next, it is evident 
that the Sine of the Angle of Incident inio the iiril wiUbein 
a given Rmti§ to the Sin^ <>f the Angle of Refftftioo ont of 
the laft. Now let oa fiippofe the Thklaada of thefe Planes di- 
minifhed im infinitwmy and their Number. ipf^orlioBaUy in- 
crea&d, the Law of Refradion will ftiU oondviie the fane.; 
and theicfore whether the AttraAion befmiforttkor not, dicre 
will be a conftant Rati^ between the Sine OJF tie 
dence and of Refradio;i« ^E.D,. 


Cb$p.2. jC5tf ^«^ ofReB:a!Sdon0c. 1 7 

Radius defcribe the Circle APBR, and from 
G and I where the inddont and refracted Rays 
cut the Circle, let &I1 the Lines GK and IL 
perpeodicukirly' upon the Line PR, the former 
of thefe will be the Sinadf the Angle of Inci- 
dence, the latter of Refradtion. Now if in 
this Cafe, the Ray GH is fo rcfradted at H, 
that GK is doiible or treble, &c. of IL," then 
whatever other Inclination the Ray GH n^ighfc 
havfe had, the Sine of its Angle of Incidence 
Would have been double, or treble, &t. to 
that of ite Aiglfc of Refradlion. For Inftance, 
had the Ray pafled in the Line MH before 
Refradion> it Would have pafled in fome Line, 
^ HN afterwards, fo fituated that MO fhbuld 
have been double or treble, &c. of NQ. 

When a Ray paflcs out of a Vacuum into 
Air, the Sine of the Angle of Incidence is 
feiind to be to that of Refradion, as 1 000 j6 

to lOOOOO. 

When it paiTcs' out of Air into Water^ as 
about 4 to 3^. 
•When out of Air into Glafs, as about 17 

to II. 

Wheijr pttt of Air into a IMamon4, as about 
jf to 2, 



0/ the RefraSiion of Light in pajftng 
thro plain and fpberical SmfsLces. 

AS Rays of Light are capable o( having 
their Progrefs altered by Refra^lion or 
Reflediion, it is poffibk they inay acquire va-* 
rious Inclinations and Dire<9:ions difierent fronx^ 
thofe which they had at their Emifiion from 
the Surfaces of vifible Bodies. 

When they recede from each other as they 
pafs alongy they are iaid to diverge i and the 
Fbint they proceed from> is called the Radi-^ 
ant Point. 

When they proceed towards any Point ap- 
proaching nearer together in their Progrefs^ 
they are then faid to converge ; and the Point 
towards which they tend, is cdled the Focus. 

This Focus may be either real or hnagina-^ 
ryy it is faid to be real> when the Rays a^- 
^ly proceed to it ; but if they are intercepted 
in their Progrefs, or turned another Way be- 
fore they reach it, it is called their imaginary 

Sometimes it happens, that Rays are fo re- 
fraded or reflededf, that they proceed after- 
wards, as from fome Point, which is not their 
true Radiant, then alfo that Point is called 
Aeir imaginary Focus. 


Ci^ap. 3. 77)e Caufe efKttta^ioriy^c. 1 9 

.When they proceed in parallel Lines, they 
are then called parallel Rays 5 and both their 
Focus and radiant Point is fuppofed to be at 
an infinite Diftance. 

When Rays pafs out of one Medium into 
another, they fufier various Alterations in their 
iMotion. All which are exprefled in the eigh* 
teen following Propofitions, 

I. When parallel Rays fall obliquely on a 
plain Surface of a Medium of different Denfi* 
ty, they are parallel alfo after Refradlion, For 
having all the fame Inclination to the Surface^ 
they fuffer an equal Degree of Refradion. 

II. When diverging Rays pafs out of a rarer 
into a dcn{QT Medium through a plain Surface^ 
they are made thereby to diverge lefs. 

For being all refradled towards their respec- 
tive Perpendiculars, (but thofe the moft that 
are the moft oblique to the Surface,) they are 
brought nearer to a Parallelifm among them- 
ieives ; that is, they are made to diverge lefs 
than before. 

See this and the following Cafes exprejfed more 
determinatelyy and demonftrated in the Note 
below ♦. 

IIL When 

■ ■ ,• . 

* I. When Rays vpafs out of one Medium into another of 
different Denfity through a iplain Sarface ; if they diverge, 
the focal Diftance will be to that of the radiant Point ; if they 
converge, it will be to that of the imaginary Focus of the inci^ 

C den( 

20 Tie Cau/^ofRcfra^ionJ^cPsiTt III 

III* When they proceed out of a denfcr m« 
to a rarer MeJium, the contrary happens ; ibr 
then being refradled from their reTpe^ive Per- 
pendiculars^ and thofe the moft that are the 
ijioft oblique^ they are made to diverge more. 

IV. So 

dent Rays, as the Sine of the Angte ot Incidence is to that of 

the Angjie of Refraidion. 

. This Propofition aclmits of four OJhi4 

Cafi 9. OfdivcrgingRayspaffingoatofaiarer into a den- 
ier meiittm* 

Amrt Let X {Tig. to.) r^rt&nta rum, xnd Z tdoAr 
JMnAmv, fepatated froia«ach other b^ thn pUm Surface AB ; 
Tuppofe C!B and CD to be two diveigmg Rays proceeding From 
the Point C, the one perlsetidiailar lo the Sorftce» the othnir 
iMqnes thitmgh B draw the Fef^cRdtcuk? PJC. The Ray 
CD being perpendicular to theSurfaCt will proceed on in the 
Vight Line 0Q> but the other Mingtm it obWely at &, «nd 
there entring a deafer MiMm^ wiflMfer a Jtdtaajoatofvnads 
the Percendicolar £K. Let thfen EG be the refraded Ray, 
and proauce it back till it interfeds DC {)r(Odaced ali)^ in f ; 
this will be the local {Vkt. OntheOoneetr fi ^ui witik tht Ra- 
dios EF* defcribethearole AFfiQ|^ aad produoa EC loH; 
draw HI the Sine of the Angle of incidence and GC that fi 
Refraftion \ equal ti)i3ils is I^ t>f -CM» whidi let Ibe^wa. 
Now Sr wel^p|)A thn FMnts. D and $ cootig^iotif, or neM^ 
fo, then will the Line HE be almoft coincident wkh FD, wA 
therefore FD will be to CD as HE to C£ ; hot HE !s to CR 
as tit ID CM, bhmnft ^e Trianf^ HIEandCMB iiviimi- 
tar 4 that h^ t]|e focal Diteice of the Ray CE is to theDiOoiice 
of the Radiant Point, as the Sine of the Angle df Incidence 
IS to that of the Angle of Refraction. ^ E. D, 

Obf« I. Whereas the Ratio o/lE to ME, 9r which is the fame 
Tling, that §/ nD te CD hears the exaa Pr^fertiws of HI /• 
CM. and hecasffe this^ {being the ^iao of the Sine of the Angle 
tf tncidence to that of the Mngle of HefiraBidn) is e^t^s the 
fitmi^ the Line In is in all btciinatims of the key C^ «f the 
fame Difianeefrm CM ; tonfifnently hoA CE ieen -Mncideni 
with CD, the fbint H hadfal&nttfon n ; ^md heceiufe ^Cirde 
pajffs through both H and F, F wonld alfo have falltH ttfon n ; 


IV. So when conver|;ing Rays pafs. out of 
a rarer into a denfer Medium^ through a plain 
Sur£ice, they are made thereby to converge 


wipdn <vBicb Account the Focus of thi Saj CE tvoM have been 
there. Bui the Ray CE being oblifue to tbe Surface DB, tbt 
Point H h 4/ fome Dtfiance from n j and tberffire tbe Point 
Jf it mcejfarifyjo too^ndtbe morofihf bow mucb tbegr^^tr tbat 
Difiance it : frotm vfbence it it clear, tbat no tnuo flajt fiouning 
from tbt radtoMt Point C and falling wtb diferent Obliqmti^ 
mt tbe Snrfaco BD» tvill aftfr JHeftaBion tbere. proceed at from 
ttb/ame Point J tbepefyrejlri&hffeahing^ tbere is no one Point 
in tie Line D frodHcod, tbat can more froptrly be called tbe For 
ems ef Raye fiovaingfrom C, tban another ; for thofe <wbicb en^ 
tor tbe reftaSiag Surface near D» 'will after Refra&ion fro' 
gotd, tetbgeiienob/ervedi from tbe Parts about n^ ^ofe wbicb 
tmter near £, wll/ow at from tbe Pmett about P ; tbofit nubich 
4iii4r aiont T, as from fomo Points in tbe Line DF produced, 
4fiC. Atd it is farther to beob/emfed» that when tbe Angle DCS be^- 
40taes large^ the Line nF increafos aface ; nvherefvre tbofe Rays 
nsfbiehfailnearTj proceed tf^tr Refra&ion^ as from a more 
diffilfrd Sfgce^ than fbofe vAicbfM at tbe famADytance fyom 
Htcb other near the Point D* ifpn fffbicb Jccoun( it is ufml 
tvith Optical JVriters to fuppofe tbe Diftance betiveen the Points 
nobort the Rays ekter tbe flain Surface of a refra&ing Medi ' 
um» to be inconfiderable with Regard to tbe Diftanct of tbe rtSf 
dUtntPoint^tief diverge % ♦r tt that oftbeir imaginary Foc^sjf 
they cpKfUtrge : and nnleft tbert be fimt particular Rt^^fon to the 
4ontrjary% they tonfider tbemt 4/ entrif^ tbe refraSing Medium 
in 4t EdreSion as nearly perpendicular to itsSurfaus as may be. 

Offit t. Of diverging Rays proceeding out of a denftr into 
A rarer Medium, 

Dem. Let X be the denfer, Z the rarer Medium^ PD and 
F£ two diverging Rays proceeding from the Point F | and fiip- 
pofing the Perpendicular PK drawn as before, FP will be the 
Sine of the Angle of Incidence of the oblique Ray Pk, which 
in this Cafe beil^g ireffaCted fron) the Perpendicular, will pafs 
on in fome Line as ER, which being produced back to the Civ- 
camfercnee of tbe Circle mil cut the Ray FD fomewhere^ fup-> 

C ? poie 

2 2 7i&« Caufe o/Reflraaion, ftPc. Partlll. 

For being all refracted towards their refpcc- 
tive Perpendiculars, and thofe the moft that 
are the mofl oblique, they themfelves are 
brought nearer to a Parallelifm, and fo con- 
verge lefe^ 

V. On 

vofe in C, this therefore will be the imaginary Focoi of the 
refrafted Ray £R ; draw RS the Sine of the Angle of Refrac^ 
tion, to which HI will be equal : but here alio FP or its equal 
CM, is to HI, as EC to EH, or (if the Point D and E be con. 
jidered as contiguous) as DC to DP ; that is, the Sine of the 
Angle of Incidence is to the Sine of the Angle of Refraction, 
as the focal Diftance to that of the radiant Point. ^ £. />. 

Cafi 3. Of converging Rays paffing out a denfer Mediam 
into a rarer. 

Dim. Let Z be the denfer, X the rarer Midtam, and GE 
the incident Ray; this will be refra&ed from the Perpendicular 
into a Line as EH ; then all Things remaining as before, G£, 
or its equal FP, or CM will be the Sine of the Angle of Ind- 
dcnce, and HI that of Refraflion : but thefe Lines, as before, 
are to each other, as DC to DP s that is, the focal Diftance 
is to the Diftance of the imaginary Focus, as the Sine of the 
Angle of Incidence to that of the Angle of Refradion. 

Cafe 4. Of converging Rays pafling out of a rarer into a 
denfer Medium, 

Dem, Let Z be the rarer, X the denfer Medium^ and RE 
the incident Ray ; this will be refraAed towards the Perpendi- 
cular into a Line, as EF ; C will be the imaginary Focus, and 
F the real one, HI which is equal to RS, the Sine of the An- 
gle of Incidence, and FP that of the Angle of Refradion: 
but thefe are to each other, as DP to DC ; and therefore the 
focal Diftance is to that of the imaginary Focus, as the Sine of 
the Angle of Incidence is to that of the Angle of Refradion. 

II. When parallel Rays fall upon a fpherical Surface of difte- 
rent Denfity, the focal Diftance will be to the Diftance of the 
Ctnter of Convexity, as the Sine of the Angle of Incidence is 
to the Difference between that Sine and the Sine of the Angle 
0f Refsaflion. 


Chap. 3* 7%eCaufeofReh3i€tiony^c. 2$ 

V. On the contrary, when they proceed 
out of a denfer into a rarer Medium^ they arc 
refradted the contrary Way/ and fo made to 
converge more* 


^ This Propoiition admits of four Cafes.' 

Cafe I . Of parallel Rays paffing out of a rarer into a den- 
fer Medium through a convex Surface of the denfer. 

Dem. Let AB {Fig» 1 1.) reprefent a convex Surface, C its 

Center of Convexity ; HA and DB two parallel Rays, paffing 

out of the rarer Medium X into the denfer Z, the one perpen* 

dicular to the refracting Surface, the other oblique : draw CB, 

this being a Radius, will be perpendicular to the Surface at the 

Point B ; and the oblique Ray DB being in this Cafe refraded 

towards the Perpendicular, will proceed in fome Line, as BF, 

meeting the other Ray in F, which will therefore be the Focal 

Point : produce CB to N, then will DBN, or its equal BCA 

be the Angle of Incidence, and FBC that of Rcfradion. Now^ 

^whereas any Angle has the fame Sine iviih its Complement to t*wa 

right ones, the Angle FCB being the Complement of AQ^^ which 

is equal to the Angle of Incidence, may here be taken for that 

Angle ; and thererore, as the Sides of a triangle ha<ve the fame 

Relation to each other ^ that the Sines of their oppoftte Angles have^ 

FB being ofpojite to this Angle ^ and FC being oppofite to the An^ 

gle of Refra^ion, they may here be confidered as the Sines of 

the Angles of Incidence and of Refradlion ; and for the fame 

Reafon CB may be confidered as the Sine of the Angle CFB^ 

v^hich Angle being together with the Angle FBC, ejual to the 

' external one ACE (32. £/. i.) is itfelf equal to the Difierence 

between thofe two laft Angles ; and therefore the Line FB is 

CO CB as the Sine of the Angle of Incidence is to the Sine of 

an Angle which is equal to the Difference between the Angle 

of Incidence and of Refraction: Now, becaufe in very fmall 

Angles as thefe are, for nvefuppofe in this Cafe alfo 'the Diftance 

AB to 'vantjh, the Reafon of which ivill befiewn by and by, their 

Sine^ bear nearly the fame Proportion to each other that they 

therofelves do, the Diftance FB will be to CB as the Sine of the 

Angle of Incidence is tp the Difference between that Sine and 

the Sine of the Angle of RefraClion j but becaufe BA 'vanifhes^ 

FB and FA are equal, and therefore FA is to CA in that Prtf. 

portion, ^ '£, A 

OK. z^ 


24 ThCau/eo/KefrsiCkiony^.Partlll^ 

All which may be illuftrated in ^he folknr- 
ing Manner, i. Let AB, CD, (Fig. 5.) b9 
two parallel Rays falling on the plain Surhcc 


Obf. 2. // appiort /hm thi fvrepnng Demonjtration, that ibi 
fitml Diftanif ofth§ OUiqut Ray DB, isfwh^ thai the Une BF 
JbmUhtu MUne CBqrCAmt ihSilfe tf $U Jmgh •f hci- 
4M€rt9tb€ Sha tfam JhgU^ ^hieh JbgU i$ tfml to tbt Dife* 
rtMce bitnjoiin tbt Jngk rflnctd^nci ^md RifroBim i $birtf$r$fi 
kMg 4f ibf Jtigies BCA, «{C^ «r# /msll, fi Img tbs Urn BF t> 
ftttty mMcb tftbt/me l^gtb, b€<a^fl/mali Jmgks h^fot n$arif 
ibtfimi Rdatim to ntcb Qtbfr tbmttbiir Siaa bimt. Butwobfw 
tb§ Point B u rmtf9i4 ft» firm A, fi ib^ tbt S^tj^ DB nttrs 
$bo Smfaee, /ttfpofi tJhnt O. tbt ^ngUt BCAt Uc. buommg 
iatp, tbt'^int of tbt Attgh tf Md^nct btgm ft bt^ 4 cmjidt* 
rsbfy l$fi Proper twt to tbt Sine tf op Jtgb mfbi<b it Sfwl to the 
DiJirtMCt befwttti tbt 4ttglt tf MAiUt 4ml Rltfrm^iom tbma 
b^t^mMdtbfrt/trttbt LitttW btgins $t btmrm tmhUfiPr^" 
tiomtotCi Vfbtrt/ort ttt Ungibdetr^tifit mpttict : [/#Mr mMtb 
jLtoMMi tbofi Rays vtbicb tmttr tbt Smfott ^btt^ O, nal tnfy 
wuttmttU'ertbtCtnttrofCtn'0fttitythmtbof9niri^btHUr tU A> 
bnt^rt tolk^td into a nmrt diffttfed Spti€t, from hnct it ii» 
tbat tbt Point wbtrt tbofi onfy *wbicb tnter ntttr A> ^rt. <9lUSi' 
td. is rtthntdtbe true Focus \ 4nd tbt D'/lnnct AB in all XV- 
"monftrationt rotating to tbt Foci tf faraljel l^n^t tmtring afjbt^ 
tical Surf act *whetbtr conHftx or eontavt^ is fnff^ed to ra- 

Cajt I. Of parallel Rays paffiag out of a dtnfer into a raifr 
Medium through a ooncavc Surface of the denfer. 

Ptm. Let X be the deufer^ Z the rarer Medium, AB (hp 
Sur&ceby which they are feparated, C the Center of Couvexi* 
ty, and HA and DBtwo parallel Rays, ai before. Throi^ 
B the Point where the oblique Ray DB, enters the rarer Af#- 
^'wndraw the Perpendicular CN ; and let the Ray PB, being 
in this Cafe rcfradcd from the Perpendicular^ proceed in the 
Dire&ion BM i produce BM back to H ; this will .be the ima- 
ginary Focus, and DBN, or its equal ACB wiU be the Angle 
of Incidence, and CBM, or its equal HBN (for they are veni^ 
ca)) that of Rqfraaion i produce DB to L and draw BF fuch, 
that the Angle LBP may be equal to DBH : then becaufe NBO 
and DBH together are equal to NBH the Angle of Refrac- 
tion, therefore BCA which is equal to the firA, ^d LQF which 


Chap. 3 . TheCaufe ()/'Refra(aion,^c.^5 

EF of a Medium of a different Denfity : Now 
becaiife thfey both make equal Angles of Inci-^ 
dence with their rdpe<ftive Perpenaicolars GH» 


IS t^aaX to the feoond, are together equal to the Angle of Re* 
frafUoo ; but LBP i% equal to BFA (as being alternate to it) con- 
feqnentl/ BPA and BCA together are equal to the Andeof fte- 
/b&ion ; and therefore fince One of them, <x;re. BCA is equal 
to the Angle of Incidenee, the Other is the Difference betmen 
that Apgle* and the Angle of RefrafkiOd. No^ PB the Sine of 
the Angle PCB, or which is the fame Thing, oflts Cbmplement 
to two right ones BCA, the Angle of Incidence, is to CB the 
Sine of the Angle BFC, as FB to CB« that is as HB to CB ; for 
the Angles DBH and LBF being equal, the Lines BP and BH 
are fo too ; but the Diftante BA vanifhing, HB is to CB,as HA 
to CA : that is, the Sine of the Angle of Incidence is to the 
Sine of an Angle which is the Difference between the Angle of 
Incidence and Kcftaaion, or becaufe the Angleif are ftnall, to 
the Difference between the Sine of the Angle of Incidence and 
that of Refra£Uon, as the Dlllance of the Focus fit>m the Sur* 
face is to that of the Center from the fame* Si^E,^, 

Cafe 3. Of parallel Rays paHlng out of a rarer into'a denier 
Medium through a concave Surface. 

Dtm, Let X be the denfer Medium having the concave Surface 
AB, and let LB and FA be the incident Rays. Now whereas, 
vvhen DB was the incident Ray, and palTed out of a rarer into a 
denCer Mtiiumi as m Cafe the firfl, it was refraded into thd*Line 
K^, this Ray LB having the fame Inclination to the Perpendi- 
^ular» will alfb fulfer the fame Degree of Refraction, and wih 
therefore pafs on afterwards in the Line. FB produced, *o. g. to* 
wards ?. So that, whereas in that Cafe the Point P was the 
real Focus of the incident Ray DB, the fame Point will in this 
be the imaginary Focus of the incident Ray LB : But it was 
tberb demonilrated, that the Diltance FA is to CA, as the Sine 
of the Angle of Incidence is to the Difference between that and 
^e Sine of the Angle of Refradion, therefore the focal Di«- 
Itiince of the refra£ied Ray BP is to the Diftance of the Center 
of Convexity in that Proportion. ^E,D. 

Cafi 4. Of Parallel Rays paiHng out of a denfer into a rarer 
Medium through a convex Surface of the denfer. 

Dem, Let Z be the denfer Medium^ having the convex Sur- 
face AB, andlet LB aQd FA be the incident Rays, as befbce. 


26 rhe ReframonofU^tj^cVzit 111. 

IK, before Refiradtion^ they will make equal 
Angles of Refraction with them afterwards^ 
and fo proceed on in the parallel Lines BL 

No^ whereas when DB was the ihctdent Ray |>a(CngOttt of a den- 
fer into a rarer Medium, it was refradled into BM, as in Cafe the 
fecondy having a Point as H in the Line MB produced for its 
imaginary Focus ; therefore LB« for the like Reafon as was gi- 
ven in the lail Cafe, will in this be refraded into BH, having 
the fame Point H for its real Focus. So that here alfo the Fo- 
cal Diflance will be to that of the Center of Convexity^ as the 
Sine of the Angle of Incidence is to the Difierence between chat 
and the Sine of the Angle of Refradion. ^ E. D. 

III. When diverging or converging Rays enter into a MUU 
SORT of different Denfity through a fpherical Surface, the Ratio 
compounded of that which the focal Diftance bears to ihic Di- 
fiance of the Radiant Point (or of the imaginary Focus of th« 
incident Rays, if they converge ;) and of that, which the Di- 
ftance between the fame radiant Point (or imaginary Focus) and 
the' Center, bears to the Diftance between the Center and the 
.Focus, is equal to the Ratio^ which the Sine of the Angle of 
Incidence bears to the Sine of the Angle of Refradlion. 

This Propofition admits of fixteen Cafes, 

Cafk I. OfdivergingRayspaiCngoutof ararer intoa denfer 
Medium^ through a convex Surface of the denfer, with fuch a de- 
gree of Divergency, that they (hall converge after Refradion. 

Dtm. LetBD(Fi]^. 12.) reprefent a fpherical Surface, Cits 
Center of convexity, and let there be two diverging Rays AB 
and AD, proceeding from the radiant Point A, the one per* 
pendicular to the Surface, the other oblique. Though the 
Center C produce the perpendicular Ray AD to F, and draw 
the Radius CB and produce it to K, and let BF be the refra&d 
Ray ; then will F be the focal Point ; produce AB to H, and 
through the Point F draw the Line FG parallel to CB. AB 
being the incident Ray, and CIC perpendicular to the Surface 
at the Point B, the Angle ABK, or which is equal to it, he* 
€aufeofthe parallel Lines CB ami FG, FGH is the Angle 
of Incidence. Now nvhereas the Complement of any Angle 
to two right ones has tht fame Sine with the Angle itjtlf 
the Sine of the Angle FGB, that leing the Complement of 
FGH to two right onts, may be tonfidered at the Sine of 


iy*tf. i. Let the diverging tistys AB, A1, 
Al?, (B]g>. 6.) pafe out of a tiittt iftto a den- 
fir AUfdhm, ffoodgh tbe ]^lain Sur^ GH, 


ihe AngU oflneidence s which Sine the Line the Sides of a 
TrkmgJe hfve fh9fdm koUHti f emth ctber^ th»t ibe Si/in of 
fMr ^tt^ft't Att^Ut hemj, may be taken for. Afxin^ theAn^ 
EBC irtae Angle of Refeuftioii, en: its equa}, heeaufe uftefnette 
#r //, BFG, to which BQ ^'«# «» «^^^ Side, may be looked 
npoirasthe Sine. Bttt FB i»to BG in a Rath compooAded of FB 
to 6 A, and of BA to BG^ for thg Ratkr /Wiw; tnjoo ^emtithi 
biar to ouif othor, ig comfoMded of the Rado, ^Uch the Jirjt 
bomrt t$ a^ other, mndoftbe Ratio luhieh thmt offher beat's to the 
focdmL Now FB is to BA, Jhfpofing Bl> to i/MttJ^, at FD v& 
DA ; and BA is to BG, ie^ai^ ofthefntedlet Linei CBavdFG,' 
at AC td CF. THae is; the Ratio compounded of F]>, the foe J$ 
Diftaaeer to DA^ tho UiJ^ce of the radiant FoiOt, alid df AC, 
the Diftamce betnveen the radiant Point andthf Gettfer, to Ct, tbi 
IHfianco hmioeott thtCifhfor and tho Focus, is e^l to that 
which the Sine of th^ Angle of Incidenet beats to the Sii^e ol^ 
^ Aikgle of Refraaiort. ^ E, D, 

Obf. 3. Whereas the focal Diftauce oftht ollique Ray AB h 
Jkdt, Jtburtheo^ouitdMtio 6f FSto BA afitd of AC to CF 
Jt4tt bo the fintt, whatever be the Bijtaneo btfmeen B and D^ 
i0 Ts amtdrnfi ihatfince AC is aJways of the fimm Lutgth, thit 
mofi^tBeUi^Ah /engthens, the more FB mnfi tengthiti too, 09^ 
M FC muftjhorten ; htt it oHiArs bf Infiefaitm of th4 Ftgi^e^- 
tteet //BF kngthens, CF ^ti do Jo too, and in d greats Fr4^ 
^hmmitk tef^^ to iti &wn Length than BP <ni/l, thihfoHf 
tkt ItmHhening of W *udli eondnce ththinv tofUiikrds frefir^ing 
tkr EfStiilty of the Proportion : but as AB len^fhous, Maud 
&m^boeh fbortett^ 'wbicb is the oufy foffltto WaytoberO/f 
fbiPnpOrthamihfbeeOHtinuedthtfastte, jM it is alfo afpa^ 
r^sthttf the farther B mo>oes front D to^OfdtO, tin f4fh^ 
Miien^tbenSf emd thertfbre the farther the Rays onttr frott^ 
P^ ibon^rof to the refraSing Surface i$ tbt Flaee when thf 
mtet,\ bttttikSfuee they dretolhUed in, it tSe^ wUre AW^eA e 
Mud thmfki^g iU this Csift, as weil as thofi tahn Notico of hi 
the twoforegoiitgOb/hrtvations, different Rst^, iiu^b flnk'htg^ 
ffiSdo t^t pnii Foht, fMl emftitttte' Sfftrm Pd€tas*s 1 (hd 
ttom^fejk eftftdal at thofiwbieb tfntft mf$f nfitff mar tbi 

Jb FoM 

\ " 

28 TieRefraBiono/Ughty&c.VsLTtllt 

dnd let the Rajr AB be perpendicular to that 
Surface ; the relft being refradlcd towards their 
refpcftive Perpendiculars EK, FM, and thofe 
the moft that fall the farthefl frorti B, they will 


Point D. And fence the feme u obfamMU ef converging as njoeU 
as of din)ergtng Rays^ none except tbo/e nvbicb enter wery near 
that Point, are u/ually taken into Confederation ; upon nviicb Aor- 
eount it is^ that the Diftanee DB, in determining the focal Di- 
feancet of diverging or converging Rays entering a convex or con- 
cave Sufface, is fuppofed to 'TZXtSoi. 

, Thofe who would fee a Method of determining the preciie 
Point which the Ray AB, whether it be parallel, converging, 
or diverging to the Ray AF, converge to or diverges from after 
Refradtion at B or any other given Point in the Surface DO, 
may find it in the Appendix to Mo/ineux's Optics, which for 
the Sake of thofe who have not that Book;, I Ihali fubjoin at 
the End of this Note. 

Cafe 2. Of converging Rays paffing out of 'a rarer into a den* 
ier Medinm through a ioncave Surface of the denfer with fuch a 
Degree of Convergency, that they fiiall diverge after Refrac- 

Dem, Let the incident Rays be HB and FD pacing out of a 
rarer into a denfer Medium through the concave Surface BD, 
and tending tov^ards the Point A, from whence the divergiog 
Rays flowed in the other Cafe ; then the oblique Ray HB hav* 
ingitsAn^le of Incidence HBC equal to ABK the Angle of 
Incidence in the former Cafe, will be refraded into the Line 
BL fuch, that its refraded Angle KBL will be equal to FBC 
the Angle of Refradion in the former Cafe ; that is, it will pro- 
ceed after Refra^ion in the Line FB produced, having the tame 
focal Diftanee FD with the diverging Rays AB, AD, in the other 
Cafe. But, by what has been uready demon(bat6d, the Ra* 
tio compounded of VD^ the focal Diftanee^ to DA, in this Cafe, 
the Diftanee of the imaginary Focus of the incident Rays, and of 
Ac, the Diftanee between the fame imaginary Focus and the CeU' 
ter, to CF, the Diftanee between the Center and the Focus, is 
equal to that which the Sine of the Angle of Incidence bean 
to the Sine of the Angle of Refradion. ^E.D. 
' Cafi 3. Of diverging Rays paffingout of a rarer into a den- 
fer Af^^SrvM through a convex Surface of the denfer, with fath 
a Degree of Divergency as to continue diverging. 


proceed in the Dircdions EN and FO, diverg- 
ing in a lefs DeCTec from ^the Ray AP, than 
they did before Refraftion. 3. Had they pro- 
' ' ' ' ' ceeded 

Dem. Let A6, AD {Fig. 13.) ^^ the diverging Rays, and let 
their Divergency be (0 great, that the refradled Rav BL (hall a1f9 
diverge from the other ; produce LB back to F which will be the 
focal Point ; draw the Radius CB and produce it to K, produce 
BA likewife towards G, and draw FG parallel to BC. Then will 
ABK be theAngle of Incidence, whofe Sine BFniay be taken for^ 
as being oppofite to the Angle BGF, which is the Complement 
of the other to two right ones. And LBC is the Angle of Re- 
fradlion, or its equal KBF,or which is equal to this, BFG» as be^ 
ing alternate ; therefore BG the oppofite Side to this may be ta- 
ken for the Sine of the Angle of RefradUon, But BF is to BG, 
for the like Reafbn as was given in Cafe the firft, in a Rat 19 
compounded of BF to BA, and of BA to BG. Now BF is to 
BA, (DB vanifhing) as DF to DA, and becaufe of the parallel 
Lines FG and BC, the Triangles CBA and AGF are fimilar, 
therefore BA is to AG as CA to AF, confequently BA is tQ 
BA together with AG, that is, to BG, as CA is to CA together 
with AF, that is, CF. Therefore the Ratio compounded of Df 
the focal Didance ro DA the Difiance of the radiant Point» 
and of CA the Diflance between the radiant Point aod the 
Center, to CF the Diftance between the Center and the Focus, 
is equal to that which the Sine of the Angle of Incidence bears 
to the Sine of the Angle of RefradUon. ^E-D. 

Cafe 4, Of converging Rayspaflipg out o? a rarer into a^den- 
fer Medium through a concave Surface of the denfer in fuch 
. Manner that they (hall continue converging. 

Dem. Let HB and CD be the incident Rays pafTing out of the 
l^rer into the denfer Medium through the concave Surface B D, 
and tending towards A the fame Point from whence the diverg- 
ing Rays flowed in the laft Cafe. Then becaufe the Ray HB 
has the fame inclination to the Perpendicular CK that AB had 
before, it will fuffer the fame Degree of Refradion, and pafs 
on in the Line LB produced, having its Focus F at the fame 
Dilbuce from the refradting Surface as that of the diverging 
Ray AB in the other Cafe. Therefore, ^c. ^ E. D, 

Cafe c . Of diverging Rays paifing out of a denfer into a car ec 
Medium through a concave Surface of the denfer. 

P « Dertk 

JO Th Rff ration ofUi^tfifp.Vm II J. 

ceeded oiuof a ^xs^tx joto a rjur^r Mediupff 
tbey would have been ceiraded ^om thieir Ber^ 
pendicularfi EK, FM^ and thoie tiiemoil irbkh 
were the moft oblique, and therefore would 


Dm. Let AB, AD {Tig. 14O bedic incident lUys f^fiff^ 
out of^idenferintoanrcr Jlf/4£iK0v throoejti t^ conc«v/c $»- 
face BD, whofe Ceoter is C ; and let BL be the redded Ra/^ 
which produce back to P, and draw JFGf^amllel to CB. Hene 
ABK is the Angle of Incidence, to which its alternate one fQfi 
jbcing equal, FB the oppofue Side may be confidexc^ as the 
iSine of it The Angle of Refradion i^ LBC or FBK» of wiudi 
BFG being the Complement to right onos, B^G the 4}|ppQfiCf 
Side may be looked upon as its Sine, ^qt BF is to BG, in tke 
compound Ratig of BF to BA a^d of BA to 4Q for the Bealbi| 
j^ven above. Now (BD vaniihing) BF is to BA at OF tp DA^ 
and BA is to BG as CA to CF. That is^ the RatU con* 
pounded of the focal Diilance •to .the Difi^ce of tfaje radiant 
Point, ^c. ^ E. D. 

Cafe 6. Of converging Rays pailing oat of ^ denfer into ;| 
rarer Medium through a convex Surface of the denfer. 

Dim, Let HB, CD, be the incident Rays temding to.w;ard| 
the Foint A which was the Radiant ui the la& Cafe. Then, 
for the Reaion already given, the oblique Ray will ifSipT fach 
a Degree of Refraflion, as to have its Focus f fX the fame Di- 
Cance from the Surface, as t^e diverging Ray^ I^, AD had 
in that Cafe. Therefore, fe'r . ^ £, D. 

When the Mediums tikTO^gh which Rays pais,and die rtGnA- 
iiig#rfaces are foch, that Rays flowing from A [Fig. 12.} are 
coUeded in F, then Rays flowing from F through the (ame Me* 
fiums the coD^ary Way, will be collcded in A. Forwhen Rays 
pafs oat of one Mtiium into another, the Sine of the Angle of 
Incidence bears the fame Proportion to the Sine of the Angle of 
Kefra6Uon, as the Sine of the Angle of Refxa^on does to the 
Sine of the Angle of Incidence, men th/ey pais the contiaiy 
Way. This if applicable to each of the fix following Cafes 
compared refpedively with the fix foregoing ; therdbre they 
yuybeconfideredatttie Coni^erieof them; ior i^ may ^ 
iemonflrated independently of them, at followt. 

Cafe 7. Of divergii^ Rays paffiqg oat of ^ i^enier \tm a 
iirer iUa&M through a convex SoiMip of th^ dp^ fii as j^ 
converge afterwards. 


Cfeap.3, 7k Re/r/t0m ^Mghtj^f <r.s I 

cpijycrjwig Rl»ys AS, CIX SF {Fig. 7,) pa^ 


P/w., Let AA AP (Pi:. 1 5 ) ** ^vo div^ ij^ing Rays j^ti^g 
trough the convex Svuf^ce Bi) i^ito a^-^rpr Miiinm. Let ^ b^ 
the Center of Convexity, and BF .ttc f;cjrrafted JRay. P/^CJ^ 
^ prodRce it to JJ .and draw FQ p^aflel to it ifxsf^iv^ AB j?ro- 
dgced in G. T)ien wil) ABC Jbe tke Ai^gle of I^idei^ce^ of 
which F9 i>cuag oppofite to its ^te^^u^e and fis^T^ A^g^^ FQ6, 
maj^ be confidered astheSji^e. The'Afigleof JRLefra^iofi i$ )?^, 
of which GB being oppofite to itsCoxnpxen\epc tQ t>yp ^ifJbtPQCf 
(SFB^ nay be ^a^a for the Sij^e- Now F^ is to iSQ« m ^ £41- 
' /<« ^compounded of FB to BA, and of JBA jto BG. B]i|t (pD 
vai)i(l]iiQ^ FB i? t.Q B A as FD to DA, and b^caufe of th^ jpa^all^ 
Lines Cf and FQ, B A is to BG a^ C A to CF. Theietor/^ tln^ 
loc^ Diftance, l^c. ^ B. D. 

CafifB. Of coQvergiog Rays pafling out of a^enfer lata n 
rarer Medium through % concave Surface of the 4en(er )fo as tp 
diverge afterwards. 

pm. Let Gfi and Pp be the incidenjt Rays tes^diiig iQw^rda 
A, and produce pB tp L. Then as AB in the laft Cafe ^^ 
r<efra^e4 into BF, GB wil} jn thi$ be re^£^ into ^L, fofr 
the Reaibns already givjcn, having F for its focal Point. There* 
for.% ^c. ^ £. D, 

Qa/e 9. Of diverging Rays pafling out of a denfet intp a rarer 
MeMum through a convex Surface of the denier, in fucfa Maa« 
ner as to continue divervng. 

Dtm. Let AB, AD (Fig, 16.) be two ]Rays pai&ng out of % 
denfer into a ^rer Midium^ through the ^convex Svirfaos D9. 
tvhofe Center of Cpnvexity is C. Draw CB, produce it {0 Kt and 
let BL be the refra£):ed Ray, produce BL back to F, ai^l draw 
FG parallel to CB meeting BA produced in G. Then wilj AIJC 
be the Angieoflncidejice, of which FB being ppppfite to ka 
alternate and equal Angle FGB^ may be confi^red a,s the Skie* 
The refra^ed An^le i$ LBK, or its equa} CBF> of whid» 9Q 
being oppofite to its (^omple^nent to two right ones BFG, 19 €h« 
Sine. liow BF is to BG in the compound Ratio of BF to BA 
andpfBAto BG: but BF is to B A as DF to DA $ andb^cai^s 
of the jp^ajlel Lines CB and FG, the Triangles B^CA, AiQP 
are fimiJar, therefore BA is to AQ as CA to AF, and cppft* 
^\icntly BA is to BG as CA to CF. Therefore, i^c. ^. £. D. 


3 2 72^ Re/raBsonof Lights &^c. Part Uh 

tlie plain Surface GH, and let^hcRay AB be 
perpendicular to that Surface/then the mother 
Rays being refiradrd towa'ds their refpec- 


Cafi 10. Of converging Rays paffii^ out of a denfcr into a 
TSJer Medium tbtPtt^t-»<pntave Surface of the denfer, in fach 
Manner as te'continuc converging. 

Dm, hit HB, MD be the incident Rays tending towards the 
fbint A. ' Then will the oblique Ray HB for the Reafons al- 
ready given be refrafted into BF. Therefore, fcfr . ^ E. D. 

Cmfe 1 1 . Of diverging Rays paffing out of a rarer into a dea- 
ler Mtdiwn through a concave Surface of the denfer. 

Pern. Let AB, AD [Fig, 17.) be the incident Rays pailing out 
of a rarer into a denfer M/iftW,through the concave Surface BD» 
whofe Center of Convexity is C, and fuppofing the Line CB 
drawn and produced to K, the refraQed Ray BL drawn and pro^ 
doced back to F, and alfo FG drawn parallel to CB, ABC will 
be the Angle of Incidence, of which FB being oppoiite to it^ 
Complement to two right ones BGF, is the Sine. The Angle 
of Refraaion will be LBK or its equal F6C, of which BG be- 
ing oppofite to its equal and alternate one BFG, is the Sine, 
Now FB is to BG in the compound Ratio of FB to BA and of 
BA t> BG. But (Bio vaniftiing) FB is to BA as FD to DA,and 
becaufe of the parallel Lines FG and CB, BA is to BG as CA 
to CF. Therefore, (^e. ^ JJ. Z>. 

Ca/e 12. Of converging Rays pafling out of a rarer into a 
denfer Medium through a convex Surface of the denfer. 

Dm, Let HB, MD be the incident Rays tending towards A 
the radiant Point in the lad Cafe ; then, as was explained above, 
BF will be the refrcftcd Ray, Therefore, ^c. ^E, D. 

Cafe 1 3. Of Rays palling out of a rarer into a denfer Medium 
from a Point between the Center of Convexity and the Surface^ 

Dm, Let AB, AD {Fig, x8.) be two Rays paffing out of a 
rarer into a denfer Medium from the Point A, which let be po- 
iked between C the Center of Convexity and the refradling Sur« 
face BD ; through B draw CK, and let BL be the re^aAed 
Ray ; produce BL back to P and draw FG parallel to BC 
Then will ABC be the Angle of Incidence, of which BF being 
oppofite to its Complement to two right ones BGF, is the Sine.' 
LBK will be the Angle of Refradion, or its equal FBC, of 
which PQ bdn^ oppofite to its alternate and equal one BFG, 

• is 


Chap. 3; ToiRrfraBionofhi^ty^c. 3 3 

tive Perpendioilars DK, FM, and £F for 
Inftance more than CD, they will proceed 
in the Diredtions^ DN, FN converging in a 
leis Degree towards the Ray AN, than they 

IS .the Sine. But, as before. BF isto.BG in a compound Ila- 
iioof BF to BA ahd of BA to BG ;. and (BD vaniOiing) BF is. 
to B A as DF to DA, and becaufe Uic Lines CB and FG are pa- 
rallel, BA is to BG as CA to CF. Therefore, tfTr . ^. E D. 

Cafe 1(4. Of Rays paffing out of a rarer into a denfer Medium 
towards a Point between the Center of Convexity and the! 

Dem, Let the incident Rays be MD, HB, tending towards 
A from whence the other proceeded in the la^ Cafe. Then as 
in that Cafe the refra^ed Ray BL being produced back paiTed 
through F, iii this the te^^fted Ray itfelf, for the like Rea- 
ions as were given in the foregoing Cafes,will pafs through that 
l^oint. Therefor^, ^c, ^ E. D. 

Cafe 1 5. Of Rays paffing out of a denfer into a rarer Me£um 
from a Point between the Center of Convexity and the Surface. 

Dent. Let AB, AD (Fig, 19.) be two diverging Rays pafling 
out of a denfer into a rarer Medium through the refra^Ing Siir- 
face BD, whofe Center of Convexity is C, a Point beyond that ' 
from whence the Rays flow. Through B draw CK, and let BL 
be the refradled Ray, produce it back to F, and draw FG pa- 
rallel to BC meeting BA produced in G. ABC will be the An- 
gle of Incidence, of which BF being oppoiite to its alternate 
and equU Angle BGF, is the Sine. The Angle of Refra^Ion , 
is.LBKor its equal FBC, of which BG being oppofice to its 
Complement to two right ones BFG, is the Sine. But BF is 
to BG in the compound Ratio of BF to BA and of B A to BG ; 
a)id {^^ vanilhing) BF is to BA as DF to DA, and becaufe of 
the parallel Lines CB and GF, the Triangles AFG and ABC 
are fimilar. BA therefore is to AG as CA to AF, confequently 
^A is to BA and AG together, that is, to BG, as CA is to CA 
and AF together, that is, to CF i and therefore the focal Di- 
Hance, i^c. ^ E. D. 

Cafe 16. Of Rays pafling out of a denfer into a rarer Af/- 
dium towatds a Point between the Center oi Convexity and the 


• • • <* 

Demi : 

• ' 

54 ^ Uefra^iMcfU^j^el^ztt IIT. 
did before. 5. LaAIy, fa^ iht frfl! i^Sttm 

iccn the deftftr, thejr «^dii!rf fetve bee* «* 
ihiaiMi the othcA: my, ah(f ^leMftkfe hkt& 
Catitt^i more. 

VI. When 

Dmh. tee fit, MD be th« Ititt^ettt lUys, ha^ng fof Adk' 
ijlhaginaiy ^oca$ the Pofot A which wai the lUditot in ^ ]i# 
^e,and let C the Center df Convexity of the izhk^g Surfiurd 
be ^fited beydnd thit ^oiht. Thefi will tIB, ftr tlte terffiltf 
dready given, be reffaAed ittfo BF, hivii^ did jArint P for its 
ttA Pocos wKieh was tlie imaginaiy ofld or dediveiiJbig Rayi 
ABy AD in the former Ode. Therefore as before the Raiif 
<jDfnpotifided of that which the focal l>ifbiiee bears ft> the^ tX« 
Jhnce of die imnginas^ Focus of the incident Rays, and of that 
f^hich the Diftance b^ween the fame iniagiilaty Focus and the' 
Center, bears to the Diftance between the Center «Ad the Po* 
ctis, is equal to the Rath which the Sine of the Angle of In. 
ddenoe bean to the Sine of the Anj^ cf Fteff ^ftion. ^ S. t). 

The firft Tertn in the foregoing PropOrtiOd (4riV. that in Pfo- 
pibfitiDn the 3d of this Note) being alwa]^s an unknown QgaA- 
dty, thofe who are not well verfed in the tfk of fuch FrOpo- 
fitiOllSy may think it tmpoffible to iilvelligate the focal Diftance 
of fliy refraAing Surface by it: I fhall thef^ore exemplify it 
in the following Inftance, by which the Manner of doing it in 
all others will clearly be onderftood, <v, g. Let it be requiitd 
16 determine the focal Diftance of diverging Rays paiBn^ oat 
of Air into Glafs through a convex Surface, and let the iX-^ 
Cance of the radiant Point be' 20, and the Radius of Convexi- 
ty be c : Now becaufe we muft make Ufe of the focal Di- 
Ibuce before we know it, let that be exprefled by fome Sym^ 
faol or Charader as ^ : Then, becaufe by the aforefaid Propb- 
fitioa the Ratio compounded of that which the focal Diftatfce 
bears to the Diftance of the radiant Point (thsit is in this Suppv- 
fition^ of X to 20); and of the Rath which theDiftamceof the 
finie radiant Point from the Cehter beafs to the Diftance betweeil 
iht Center and the Focus (in tfats Cafe, of 25 to jt — ^5) ts e^p^ 
to the Rat2Q which the Sine of the Angle ofineidence bears ttf 
the Sine of the Angle of Refra^Hon (that is, of (7 to 11), ibo 
ffiall have in th^ fnftaiice befote u»; the foUowiiig Proportk>n,<6^ 
# : 20 p 

> : : 17 : II, and compoondrng them into one, 


chap. 3. The RefraBion o/Liglity&^c. 3 5 

VL When Rays proceed out of a rarer into 
a denfer Mediumy through a convex Surfacc^ 
of the denfer, if they are paralkll before Re- 
fraftion, they become converging afterwards. 


which is done by mutliplying the two firft Parts together, we 
have 25;^: 20;r— 100 : : 17 : ii, and multiplying the extream 
Terms and middle Terms together, 340*— 1700=27 5 jf, which 
Equation after due Redaftion gives *= » Jf <» . 

In fome Cafes which might have been put, the Quantity 65 
would have been negative, and then the Quotient arifmg from 
1700 divided by that, would have been fo too ; that is a? the 
focal Diftance would have been Negative, in which Cafe the 
Focus muft have been taken on the contrary Side the Surface to 
that on which it was fuppofed to fall in ftating the Problem ; 
that is, it muft have been taken on the fame Side with the ra- 
diant Point, for in calling the Diftance between the Center and 
the Focus X — 5 it was fuppofed the Focus would fall on the fame 
Side with the Center or on that which is oppofite to the radiant 
Point, becaufe otherwife that Diftance muft have been expreifed 
by ;f4*5» ^ ^^y ^"^^ "*^y ^^^ ^y Infpeftion of the 1 3th or 14th 
Figure, in which the Focus of diverging Rays entring a convex 
Surface, is fuppofed to fall on the fame. Side with the radiant 

Point. ^ 

In like Manner as this Problem was performed a general 
Theorem may be raifed to folve it in all Cafes whatfoever, by 
ufing Charadlers inftead of Figures ; as every one who is not 
unacquainted with algebraic Operations very well knows. 

See this done, and applied to the Paflageof Rays through the 
Surface of Lenfes in the fecond Note to the following Chapter. 

A Method of determining the Point which a Ray, entring a 
fpherical Surface at any given Kftance from the Vertex of it, 
converges to or diverges from after Refra6kion at the (ame. 
From the Appendix to Molineux*/ Dioptrics. 

«* Prop, To find the Ftff«i of any Parcel of Rays diverging 
4€ frem, or converging to a given Point in the Jxis of 2i fpherical 
** Lens [Surface] and inclined thereto under the fame Angle; 
** the Ratio of the Sines in Refradkion being known. 

" Let GL (Fig. 20.) be the Lens, P any Point in its Surface, 

" V the Pole [Vertex] thereof, C the Center of the Sphere 

" whereof it is a Segment, O the Objcdt or Point in the Axis to 

' - £ <i or 

3^ ThRefroBsmrflS^ait^cJ^ 

For in this CaCe^ the Fecpeodicul^s gt die 
Poitus where the Rays enter the Sar^ice, .are 
all drawn ifirom the Center »cf Gonve»ty on 


•* or from which the Rays do proceed, OP a given Ray ; and 
<' kt the i^iff of jlefraaion be as r to / ; make CR to CO a» 
" / to r for the Immerfion of a Ray, or as r to / for the £iner« 
*< ilon, (that is, as the Sines of the Angles in the Medium which 
*^ the Ray enters, to their coriefponding Sines in the Medium 
** out of which it comes) and laying CR from C towards O^ 
*^ the Point R (hall be the fame fpr all the Rays of the Point O. 
** Then draw the Radius PC (if Need be) continued, and with 
^' the Center R and Dillance OP fweep a Touch of an Arch in- 
** terfedUng PC in Qj the Line QR being drawn (ball be pa-* 
'* rallel to the refra^d Ray, and ?¥ being made parallel 
*' thereto, ihall interfed the Axis in the Point F, which is the 
*' Focus fought. Or make it as CQj CP : : CR : CF, and CF 
" ihall be the Diftance of the Focus from the Center of the 
Dm, Let fall the Perpendiculars PXon the Axis, CY on the 

fiven Ray, and CZ on the refracted Ray. By the Condradion 
F and QR are parallel, whence.the Triangles QRC and PPC 
are fimilar, and CR to QR, as CF to PF, that ib CR to OP as 
CF to PF. Now CF: PF : : CZ : PX oh ftmilia Triang. 
whence CR : OP : ; CZ :PX, and CR : CZ : : OP : PX. Again, 
CR is to CO as the Sines of Refraction by ConAruAion, tha^ 



** is,a8Jtor,orrtO/; and as CR to CZ, fo (COis?) L or 

s r s J 

*♦ — CR to 7or 7CZ, and fo is PO to PX : But as PO to PX, 

<• foCOtoCY. i?rjfaCY=:-^ar*-CZ,thatisCYtDCZisa« 

•' the Sines of Refraaion, but CY is the Sine of the Angle of 
« Incidence, and CZ of the refrafted Angle. grEo ^tuAat 

** Propojiiio, ^ * •' 

" Hitherto we have confidcred only oHifuf Je^^i j it now re. 
•* mams to add fomething concerning Rays faralleJ to the Jxfsr 
•« In this Cafe the Point O muft be confidered as infinitely di. 
*' ftant, and confequently OP, QC, and CR are aU jn&iite j 
*' and OP and QC arejn this Cafe to be accoqnted as alway* 
!:[ e^ual, {finge they difer but by a fart of tht M^i^ius of the 

;• Sphem 

die otHer Side; and th^-efone, as the Rays 
are refraftfed toWatds thdfc Petpendicularsi 
they are neceffarily refrafted towards eacK 
other; and thettby madfe ta converge. 

VII: If they cnt^ diverging, then for the 
fcme^Reafon, they are made to diverge lefs^ 

« SphJurc GPVL, whieh'isnrfl'artof eithet of them) where- 
*> fore-the Ratio oi CRto OP will be' always the fame, viz^ 
•^ as i to r for immerging Rays, and as r to j for thofc that 
•« emerge. And by this Proportion CP is to PF in the fame? 
** Raiio: It remains therefore to fhew on th&BafeCP how to find 
«* alj the Triangles CPF,wherein GP is to PF in the Ratio given 
•« by the bcgreex3f Refraftion: This Problem has been very 
'< fully confidered by the celebrated Dr. ^^///i in his late 
*' Trcatife^of A]gebrajp.2f 8, to which I refer^; but I muft here 
** repjpat the Conltruftion thereof. See Ftg. 21 and 22. 

^j^Let QPV>Lbe a If>y/, VCor^PC the Radius of its Sphere/ 
** and'lft ifrbe reqidTed^toAAd all the Points f, /;' fufch, as Cf 
** may be to ]^in the given Ratio of s tor for immerging Rays,- 
*• eras r to ifer the emerging. Divide CVinK, and continue* 
•• CV toFi that CK may betoVK, aodCP toVP in the? 
** propofed Ratio. Then divide KF equally in the- Point a^. 
•« and with that Center fweep the Circle FKF ; this Qrcle be- 
" ing drawn gives 'reddily aU the Kirr of the parallel . RaysOP, 
" OF. For having continued CP till it int^rfea the Ctircle in 
** F,' PF ihall be always eaual to V/the Diftance of 'the Focus 
*< of^ach-refpeftite* Parcel of Rays OPfrom the Vertexor Pole 
«« o^theiLfwr. 

. •* To demonftrate this, draw the pricked Line VF, and by 
•* whit^is delivered by Dr. Wdltis in the above-cited Place, VF 
'*' and CE w^'be always in the fame propofed Ratio* Again*, 
« Vybeing made equal to PF> CF and Cy will be likcwife^ 
" equal, asare CP, VC ; and the Angles PC/; VCF being ad 
" 'verticem are alfo equal : -Wherefore ^^will be equal toVF, 
•* and cOnfequently C/'to ly in the fa^ie Ratio as CF to VF, 
** whence, and by what foregoes, the Points-/, /, are the fe- 
ver al refpeftive F<7fi of the feveral Parcels of Rays, OP, 
QS^r ^ E. D. 

If any one would fee how this is to be applied in all other In*- 
fiances, he may confult thN^ Place. 

£ a to 

3 8 7J5^ RefraBion ©/Light,^^ .Part IIL 

to be parallel, . or to converge, acccNrding to 
the Degree of Divergency they have before 
they enter. 

For if they diverge very much, their being 
bent tovirards their refpedlive Perpendiculars in 
pafling through the Surface^ may only dimini(h 
their Divergency ; whereas, if they diverge in 
a fmall Degree it may make them parallel, or 
even to converge. What Degree of Divergency 
or Convergcncy before Refradlion in this and 
the following Cafes, is neceflary to make Rays 
become parallel, will be (hewn at Se<aion the 
17th of this Chapter. 

VIII. If they converge in fuch Manner as 
to tend dircftly towards the Center of Con- 
vexity before they enter the Surface, they fall 
in with their refpedlive Perpendiculars, and fo 
pafs on to the Center without fuffering any 

IX, If they converge lefs than their Perpen- 
diculars, that is, if they tend to a Point be- 
yond the Center of Convexity, they are made 
by Refradion to converge mo^^e j and if they 
converge more than their Perpendiculars, that 
is, if they tend towards a Point between the 
Center and the Surface, then by being refrac- 
ted towards them, they are made to converge 

This and the three foregoing Propofitions 
may be illuftrated in the following Manner. 
I. Let AB, CD {Fig. 8.) be two parallel 
Raysentrmg a denfer Medium through the 


Chap..^. thi^effaBion ofUghty^csg 

convex Sur^ce DB,whofe Center of Con vcxi- 
ty; is E J an4.1ct one of thefc, i^/>. AB be per-^ 
pendicular to the Surface. Tbis will paib on 
through thci Center without fuifering any Re- 
fi-adion^ but the other being oblique to the 
Surface, : .will be refraded towards the Perpen- 
4icular £D, and will therefore be made to pro^ 
q^pd in fon^ie l^ine, as DG, converging towards 
the other Ray, and meeting it in G, which 
Point for that Reafon is called the Fficvs. 2. 
Had the Ray CD diverged from the other, fiip- 
pofein the Line AD, itw:ould, by being re- 
frained towards , its Perpendicular ED, .have 
been madp either to diverge . lefs, be parallel, 
or to converge. 3. Let the.Line ED be pro- 
duced to F,. ind if the Ray had converged, fo 
a,s to have defcribed the Line FD, it ^ would 
then have been coincident with its Perpendicu- 
lar, and have fuffered no Refradrion at alh 4« 
If it had proceeded from any Point between C • 
and _F, as from H, or which is the feme : 
Thing, towards any Point beyond E in the 
Line BE produced, it would have been made 
to converge more, by being refradtcd towards 
the Perpendicular DB, which converges more 
than it; and had it proceeded from fomc 
Point, as I, on the other Side F, that is, to- 
wards any Point between B and E, it would 
then have converged more than its Perpendi- 
cular, and fo, being refrafted towards it, would 
have been made to have converged lefs. 

X. When 

IS:. When R^^proceedoa^ of sdfenfer into 
» rarer Midiumj througd^ a concave Sor&oe of 
die dtafer^ the contraty happens in each Cal^. 
Bor bcingnowreftaSed from their re(pe£dve 
Berpendicukrs, as* they' were^ before towar ds^ 
tben)^ If they^ are parallel htihi^ RfefradioB| 
the^ diverge ^rvntrd^; if they diverge) thd^ 
Ifivergency is increafed ; if they^ converge m 
the- Dk'e&ion of -their Perpa^fdiculars^, they fui^ 
fer no Refra&ioti ; if they converge lefs thaib 
theip refpedSve i^pendiculars,- they are maife 
to converge ftill' ief^, to be parallel) or to di^ 
verge ;- if they* converge' more, their Convem^ 
g(sncyi8 increased. All which may clearly be- 
feen by the Figure, without any* farther lUu A 
tration, imagining the Rays AD, CD, &t. 
bent tfce contrary Way in their RefradioflStO' 
what they were in the fomier Cafes^ 

XL When Rays proceed out of a rarer into^ 
a^ienfer Medium i through a c6ncave Surfice* 
of the denfer, if they are parallel before Re- 
fka^ion, they are rnade to diverge. 

For in this Cafej the Perpendiculars at the 
Points where the Rkys enter the Surface, being 
drawn from a Point on that Side of the Surface 
from which the Rays tend, if we concave 
themtopafs through the Surface, they will 
be fo many diverging Lines on the other Side,' 
and therefore the Rays after they have" pafled 
through the fame Points, muil necef&rily be 
rendered diverging in being refrafted towards 

XII. If 

XII. Jf they diverge^efoce RefiraAion^ them 
for the fame Jleafon^ ^Gf oie raade^to ^verge 

XIII. UaleTs they proceed dire^ly fromthe 
Center, in which Cafe ithey^fall in with their 
Perpendiculars^ and luffcr no Jleira6);ion : or 
from fome Point between the Center. of Co?i»- 
vexity and the Surface, 'for then they diveiige 
more than their re^e&ive Perpendicukrs, ^nd 
therefcMre being by Re&a<^on brought towards 
them, they become lefs diverging. 

XIV. If they converge^ then being relra<3:e4 
towards their Perpendiculars, they are either 
made lefs -converging, parallel, or diverging, 
according to the Degree they converged in be^ 
fore Refraftion. 

To illufk^te this, and the ttliree ibretgoifiig 
Cafes. I. Let AB, CD {Fig. g.) be two pa- 
rallel Rays entring the concave anddenfer Afe^ 
dium%y the Center of whofe Convexity i$ 
£, and the Perpendicular to the refracting Siiir*r 
face at the Pohit D, is £F ; die Ray AB if we 
fuppofe it perpendicular to the Sufface at B 
will proceed on dire^Hy to G i but the oblique 
one CD being refraiSbed towards the Perpen^ 
dicular DF, will recede from the other Kssf 
AG in fome Line as DH. 2. If the Ray CD 
had proceeded from A diverging in the Direc-^ 
Irion AD it would have been bent nearer to the 
Perpendicular, and therefore have diverged 
more. 3. But if it had diverged fr<^ the Cen<* 


42 73&tf RefraSlionofU^ty^c. Part III. 

tcr E> it would have fallen in with the Per- 
pendicular EF, and not have been refratfted at 
all : and had it proceeded from I, a Point on 
the other Side the Center E, it would by being 
rcfradled towards the Perpendicular DF have 
proceeded in fome Line nearer it than it other- 
wife would have done, and fo would diverge 
!cfs than before Refra^ion. 4. If it had con- 
verged in the Line LD> it would have been 
rendered lefs converging, parallel, or diverging, 
according to the Degree of Con vergency, which 
it had before it entered into the refradting Sur- 

XV, If the fame Rays proceed out of a den- 
•fcr into a rarer Medium through a convex Sur- 
face of the denfer, the contrary happens in 
each Suppofition : The parallel are made to 
converge; thofe which diverge lefs than their 
refpedtive Perpendiculars, that is, thole which 
proceed from a Point beyond the Center, are 
made lefs diverging, parallel, or converging, 
according to the Degree in which they diverge 
before Refraftion ; thofe which diverge more 
than their refpedtive Perpendiculars, that is, 
thofe which proceed from a Point between 
the Center and- the refrafting Surface, arc 
made to diverge ftill more. And thofe which 
converge,are made to converge more. All which 
may eafily be ieen by confidering the Situation 
of the Rays AD, CD, ' &€. with Refped to 
the Perpendicular EF • and therefore • requires 
no farther Illuflratioa. 

XVI. When 



XVI. When diverging Rays arc by Refrac- 
tion made to converge, the nearer their radiant 
Point is to. therefra&ing Surface, the farther 
is their Focus from it on the other Side^ and 
vice versa. 

For the nearer the Radiant Point is to the 
refrading Surface, the nmorc the Rays which 
fall upon the fame Points of it, diverge before 
Refraction, upon which Account they con- 
verge the lefs afterwards. 

XVII- When the radiant Point is at that 
Diftance from^.the Surface, at which parallel 
Rays coming through it from the other Side 
would by Refra<3:ion be colleded, then Rays 
flowing from that Point become parallel on the 
other Side, and are laid to have their Focus at 
an infinite Difltance. For the Power of Re- 
fraction in the Medium is the fame, whether 
theRay pafles one Way or the other. For 
Inftance, if the parallel Rays AB, CD' {Fig, 8.) 
in pailing through the refracting Surface BD 
are brought to a Focus in G, then Rays flow- 
ing from G as a radiant Point will afterwards 
proceed in the parallel Lines BA and DG. 
^nd the Point G, where the parallel Rays AB 
and CD meet after Refradion, is called the 
Focus of parallel Rays. 

XVIII. When Rays proceed from a Point 
nearer the refradting Surface than the Focus, of 
parallel Rays, they continue to diverge after 
Rcfradtion, and their Focus is then an imagi- 

F nary 

44 Of lefafcs, ^c. Part III. 

nary one> and iituated on the £mie Side the 
Surface with the Radiaot. 

For in this Cafe^ their Divergency being 
greater then that whidb they woald have, if 
they had proceeded from the Focus of parallel 
Riys^ they cannot be brought to a Parallelifm 
^ith one another, much lefs be made to con^ 
verge, and therefore they continue to diverge^ 
though In a lefs Degree than before they pa^ 
fed through the refradirigSurfeqe; upon Which 
Aetxjant, they proceed after Refrattion, as if 
they came from fome Point farther diftant froto 
$he rcfra<aing Surfecc than their Radiant. 


0/*Lenfes, and tbt Manner m wbid 
Rays are affeSled in faj}ing through 

ALem^ is a Medium terminated on one 
Side by a fphcrical Surfece, on the other 
by a Surface cither plain or fphcrical. And of 
thefe there are five Sorts. The firft, as A, 
{Fig. 23.) is plain on one Side and convex on 
the other ; the fecond, B, convex on both 
Sides } the third, plain on one Side and wn- 
cave on the other, asC; the fourth, C), con- 
cave on both Sides 5 the fifth, convex oa one 
Side and concave on the other, as E, which 
is by fome called a Menifius, 


C3iap. 4* Of Lenfes, ^(^ 45 

The Axis of a X?isrx i|g a Line paffiqg per- 
pendicularly throqgh both its Surfaces : TnuS) 
the Line FG is an Axis common to all the five. 

Lenfis are diflinguifhed into two general 
KindSy convex and concave ; the iirA and fe- 
cond Let^es are confidered, as convex; the 
third and fourth, as concave : the laft, if its 
Convexity is greater than its Concavity, is 
looked upon, as convex ; if on the contrary, it 
as coqfidered as concave. 

A Lens is always fuppoied to confiil of a 
Medium denfer than the circumambient one^ 
onlefs where the contrary is expreff^d. 

Wheq parallel Rays fall upon the Sur&cp 
of a convex Lens^ they are refra&ed towards 
<ach other in paffing through it, and thereby 
collected to a Ftwus on the other Sidp. 

To explain this, let us trace the Progrefs if 
a Ray as AB {Fig. ^4.) through the convcic 
Lens CDEH, whofc Axis is IK. Let L be 
the Center of the firft Convexity CDE, and M 
that of the other CHE ; and let the Ray AB 
be parallel to the Axis ; through B draw the 
Line LN which will be perpendicular to the 
Surface CDE at that Point- The Ray AB in 
cntring the denfer Subftance of the Lens will 
be re&adted towards the Perpendicular, and 
therefore proceed after it fa^s entered the Sur- 
j&ce at B in fome piredion inclined towards 
the Axis, as BP. Through M the Center of" 
Cojuvexity of this Surface and the Point P draw 

F 2 the 

46 Of Lcnfcs, ^c. Part III. 

the Line MR, which paffing through the Cen- 
ter will be perpendicular to the Surface at P, 
and the Ray now entring a rarer Medium will 
be refracted from the Perpendicular into fomc 
Diredlion as PF, In like Manner, and for the 
lame Reafons, the parallel Ray ST on the 
other Side the Axis, and alfo all the interme- 
diate ones asXZ, 0*r. will meet it in the fame 
Point, unlefs the Rays AB and ST enter the 
Surface of the Lem at too great a Diftance from 
the Axis IF, the Reafon of which has already 
been fully explained *. 

The Point F where the parallel Rays AB, 
SF, ^c. are fuppofed to be coUeded by paf- 
fing through the Lem CE, is called the Focus 
of parallel Rctfs of that Lens. 

. If the Rays converge before they enter the 
Lens, they are then collected at a Point nearer 
to the Lens than the Focus of parallel Rays. 
If they diverge before they enter the Lens ythty 
are then colledled in a Point beyond F; unlefs 
they proceed from a Point on the other Side at 
the fame Diftance with the Focus of parallel 
Rays, in which Cafe they are rendered paral- 
lel. If they proceed from a Point nearer than 
that, they diverge afterwards, but in alefs De- 
gree than before they enter the Lens. 

If the Lens is plain on one Side and convex 
on the other, the Rays are refradcd the fame 
Way, but in a lefs Degree. 

• Sec Ohfervation 3, in the foregoing Note, 


chap. 4. Of Lenfes, ^c. 47 

- If the Rays AB, ST, be fuppofed to pro- 
ceed from a radiant Point on one Side of the 
luens^ and be refrafted into a Focusy as at F, 
on the other ; then Rays proceeding from that 
focal Point, F, as from a Radiant, and foppofed 
to pafs through the Lem the contrary Way, 
will becollefted in that Point which was the 
Radiant in the other Cafe : and the nearer the 
'Radiant Point is to the Lem^ the farther is the 
Focm from it on the other Side, and vice versa. 
If the Rays AB, CD, EF, &c. {Fig. 2^.) 
be parallel to each other, but oblique to GH the 
Axis of the Lens IK, or if the diverging Rays 
CB, CF, proceed as from fome Point C which 
is not fituated in the Axis of the Lens^ they 
will be collefted into fome Point as L, not 
dirc<ftly oppofite to the Radiant C, but nearly 
fo : for the Ray CD which paffes through M 
the Middle of the Lens and falls upon the Sur- 
face of it with fome Obliquity, will itfelf ful^- 
fer a Refradtion at D and N ; but then it will 
be rcfrafted the contrary Way in one Place to 
what it is in the other, and thefe Refractions 
will be equal in Degree if the Lens has an equal 
Convexity on each Side, as we may cafily per- 
ceive if we imagine ND to be a Ray {^mng 
out of the Lens both at N and D, for it is evi- 
dent the Line ND has an equal Inclinationto 
each Surface at both its Extremities. Upon 
which Account the Difference between the Si- 
tuation of the Point L and one diredly oppo- 


48 Of Lenfcs, ^e. Part III. 

&xt to C, is fa fqialt, that it is generally neg- 
k<Sed \ and the Focus is fuppofed to be in that 
I^ine, which a Hayi that would pafs through 
the middle Point of the Lem^ were it to fuffer 
po Rc£*a&ion^ would proceed in. 

AH which \% fufi^cieotly clear, from what 
b^ been (aid coocerning the Laws of Refrac- 
tion explained in the foregoing Chapter. 

When parallel Rays fall qpon g^ concave 
Lms^ they are refracted froni e^ch other in 
pailing through it^ and thereby n)ade to di- 
vcrgp9 proceeding as from an iiaagtnary Focm 
on the firft Side of the Lens. 

Ii) order to comprehend this, let ABCD 
iJFig* 26 .) reprefent a^ concave Lem^ EO its 
Axis, GH the Radius of the firft Conipavity,IK 
that of the fecond ; produce HQ to L, and let 
MG be a Ray of Light eptring the Lens at the 
Point G, This Ray being refraiSed towards 
1^9 PerpcndicuW GL, will paf? pn to foroc 
FoinC ais K in the other Surface more dift^nt 
from the Axis than G, and being there refraflt- 
ihI from the Perpeadicular |K> will be diverted 
farther flill fronpithe Axis, and proceed in the 
X>ir^<5lion KN as frofn fome Point, O, on thp 
firft Sjckof the h^ns* In like Manner othej: 
Rays as PQ^ parallel to the former, will prQ- 
<mi after Refraidioo ^t both Surfaces as frpi^ 
the feme Point O ^ which upon that Acoovin|: 
will he the imaginary Fofjw of parallel I^ys of 


Chap* 4. Of Lenfes, &<:. 49 

If the Rays diverge before they enter thi 
Ltni^ their ihiiaginary 'BQcm\% then nean^ thd 
{jm\ than that of the parallel Hays. If ihey 
converge bcforie they enter the LeM proceed** 
ing tovrards fisme diftant Point in the PiX\% as 
E, they are then rendered left converging : if 
they converge to a Pbinf At the fame DiCkiioi 
from thei>» withthejF^riy^ of parallel ilay^ 
tbey then go out parallel j if to a Point at a 
lefs Diftance they remain converging, but in a 
Sefs Degree than before they entered the Lem^ 

When the Rays enter the Ltm diverging^ 
the nearer their radiant Point is to it, thfe 
nearer alfo is their imaginary Focui after Re*- 
fraflioq^ and vice verfd. 

If the Lens is plain on one Side and concave 
.on the other, the Rays fuffer a like Re^^radion 
in each Cafe, but in a lefs Degree. 

The Truth of what has been iaid concerning 
the Paflage of Rays through a concave Lens^ 
IS eafily to be deduced from the Laws oi Re- 
fradion delivered in the foregoing Chapter. 

But the Method of determining the exa^ 
focal Diftances of Lenfes is to be had .from the 
Propofitions laid down and demonftrated in tht 
Note in the foregoing Chapter, Thus, the 
Progrefs of the Rays after their Refradion at 
the firft Surface where they enter, a Lem^ is 
had by one of thofe which determines the fo- 
cal Diftance of Rays entring a denfer Medium 
Qi fuch Form : And their Progrefs after their 


50 Of Lcttfcs, ^c. Part IIL 

Refradiion at the other Surface where they go 
out, is had by computing what Progrefs Rays, 
moving in the Diredion they are found to have 
after their Entrance at the firft Surface^ will 
acquire by being refracted at the other ; which 
is to be efiedted by one which determiixa the 
focal Diftance of Rays paifing out of a denier 
Medium of like Form with that of the hem *. 


* Or a general Theorem may be made after the following 
Manner, to determine the Progrefs of Rays after Refra£tioa at 
both Sides of the Lin$y whatever be the Matter of \ty or the 
Form wherein it is made. 

Thus fuppofe GH [Tig. 28.) to be a |^ven Lins^ and E a Pbint 
in its Axis from whence the diverging Rays £L, &fr. fall upon 
the Lensy AL,the Radius of the i^rft Convexity, and CK that of 
the fecond ; let LK/*be the Dire^on of the diverging Ray £L 
after its Refraftion at the firfl Surface^and KP its Dire^on after 
Refradion at both. Then will / be the Focus of the Rays after 
their firft Refradion^'and F the Point they will meet in after both. BD be the Thickneis of thei>»i,and let the Proportion which 
the Sine of the Angle of Incidence bears to the Sine of the Ang^e 
of Refraaion be exprefTed by the Ratio of I to R. Call £B, di 
BD,/j AB, r; CD, ii B/.;rj DF, jp : Now, to find/ their 
Focus after RefraAion at L where they enter the firfi Surface of 
the If)»/, comes under the third Propofition in the foreroentioned 
Note : According to which the Ratio compounded c^x^tbt focal 
Diftance fought^ to d, the Dijlance of tie radiant Point ; and of 
d'ipT^ ihi Difiance htivcen the fame Point and the Center, ,t0 
«.»r, the Difiance between the Center and the Focus, is as I to R ; 
compounding thefe two Ratios therefore (that is multiplying them 
together) we have dx^rx : dx-^dr : : 1 : R j which Proportion 
being converted into an Equation, and duly reduced, gives x= 

Thus having found the Difiance B/*, and confequently the Point 

/ to which the Rays converge from L,we muft proceed to find F, 

that to which the/ will converge after having pa/led through K 



ChajJ. 4. Of Lcnfcs, ^c. 5 1 

Wliea a Rarf pafles through £i Medium tef-« 
tnaoated by two plain and parallel Surfaces, it 

I • is 

wbeiae they faffer s fecofld Rdfra^ion : Tlii> comes tinder thq^ 
iamcf Propofition ; but, if we would ufe the^ fame Letters as be- 
kftty t9 estprefs the Proportion whkh the Sine of the Angled of 
locidence bears to tl^t of th« An^^ of Aefo€liofi^ they muH 
DC pat one for the ether 9 becaafe. when Rays pafs out«f a 
cfeAier into a xzttt MiJkum, the $ine of the Angle of tnci* 
deace btan the faae Proportion* to the Srne of tihe Ahgid 
•f Refradion, that the Sine of the Angle off Refra^ioil 
Ajes' teethe Slue of the Angle of Incidence, when they pai^ 
OfSC of' a nirisr into ef denier. This being obferved, by thei 
aforeiaid Propofition^ ive ihall have the Rmtia tioihpottnded of /^ 

tbi focal Diftance, to ■ ■ ■ * ■■ / > the imaginary Focus ofthi 

kttidtm Raff^ aildo f ; ■« ■ i . « >* — /•f^, the Dijtance iet«wuii 

i<f— K!tf*-*Rr 

tii imaginary Focus oMdtbe Ontor^ toy^^r'Si the Diftana hetween 

tie CcnUr and the Foeut^ as R to 1« Which Equation, if we reductf 

\dr \dr 

the mixed Qgantites . , ■ , ^ — /, and r , „." -^ / 

^/: into improper PmdBons, willfbuid thus: 

^' iJLXflAr 

*aHd ^% * ' ft ' I 

LA^W/4.R^/+R>'/4-I^/--R^//— Rr/ . 

U lU Kr 

And, compounding tbefe Ratio^s^ we have 

U ij '^ ' U — yji 

i r* . o " . ' : : R : 1. And, throwmg out 

the two equal Denominators W— R^— Rr and W-*R^-— Rr^ 
and multiply isg Extreams together and Means together, we have 
lUr^^lUtyJ^lKdty^lRrty^ Uda-ll^sy—lRrsy=l?jhy^ 
ItUty^ KRd/y + KKrty + lRdrS'^l?Jts^+ RR^/j -+• RRr^ i 

Which Equation, being reduced, giv«sj= ^J^^^^ h^' 

P Thia 

52 Of Lenfes, ftPr. Part III 

is refracted one Way ingoing out of the fecotnd, 
as much as it was the other in entering the firft; 
and therefore proceeds afterwards not in the iamd 
Diredion^butinonethat is parallel to that which 
it had before. Thus if the Ray AB {Fig. 27.) 
enters the denfer Af^^/ix^^CDEF terminated by 
the parallel Sur&ces CD and £F, it is refraded 
at B towards the Perpendicular BI, proceeding 
to a Point as G, where it is as much refraded 
from the Perpendicular GK in going out, and 
proceeds in the Direction GH« not the fame, 
but parallel to the former ABL. 


This Theorem may be applied to all Cafes whatever^ even to ' 
plain Surfaces mutatis mtUattdit ; v. g. the RoMus of a concave 
Surface being negative (as lying the contrary Way) witli Refpeft 
to that of a convex, and the Raiiu$ of a plain Surface beins an - 
infinite Line i if we n'ould apply this Theorem to a concave bur-- 
face, we muft change all the Sines of tbofe Members wherein 
the Symbol exprei!ing the Radius of that Surface occurs ; and, 
ifto a plain Surface, all the Members which involve the Ra^^ 
dius muft be coniidered as infinite Quantities ; that is, all, ex- 
cept them, muil be ftruckout of the Equation as nothing. So, 
likewife if we would have it extend to other Rays oefides 
diverging ones, the Point where converging Rays would meet 
lyhig on the contrary Side to that from whence the diverging 
ones were fuppofe^ to flow, its Diftanee muft be -made nega- 
tive ; and, thcDillance where parallel Rays meet being infinite, 
it is only changing the Sines of all thofe Members in which d 
is found, if the Rays are fuppofed converging^ or making thofe 
IVfcnibers infinite,, in Cafe the Rays are luppofed parallel ; 
which ys done by ftriking out all the reft, as bearing no Fro* 
portion to them. 

See the Method of reducing this Equation to fewer Terms, 
where it is alfo illuftrated with divers Inilanoes, in Dr. Bronjon^% 
Appendix to Grtgcrf^ Optics, or in Dr. Hallef^ Method of 
finding the principal Focus of Optic Glares univerfally, Phi« 
lofoph. Tranfadt No. 205. 




Chap. V. Of the Eye. 5 j 

C H A P. V; 
Of the EjQ, 


^^^W ^HE Form of the Eye is fuch as is repre-. 

I ♦ fented in Figure 29, and would be a 
|)ctfe<^ Sphere, were not the fore Part A A 
ibmewhat more protuberant than thie reft. 

The Defcription of it, fo far as is neceflary 
to explain the Nature of Vifion, is as follows: 

It is inclofed in three diftindt Coats or Tegu- 
ments ; the outermoft of which, viz. aa^ is 
called^ Tufiiea 'Sclerotica 5 the next, cc^ Cbih 
tcid^y or Uvea ; the third and innermoft, dd^ 
derives itis Narhe from that of its Difcoverer, 
^d 'is called Tunica Ruyfcbiana. 
••Tbefe Goats are contiguous to each other 
ewity ^hcre, except on the fore Part of the 

Uyti ; 

*^ That Portion of the Sclerotica which lies 
between A and A is more protuberant than 
^e F^ft^ is tranfparent, and has the Name of 
H^nita Cornea. 

" That Portion of the Choroides which is fitua- 
ted between b and b ij called the Iris^ and is' 
that which by it$ Colour denominates an Eye 
blacky grey, '&c. In the Middle of this there 
16 a round Hole as/^/, called the Pupil. 

The /m confifti of two Kinds of mufcular 
Fibres > the firft Xi^ extended from its Ejctrc- 
w- G z mity 

54 Of tU Eye Pkit III. 

mity like the Radii of a Circle, and point to* 
wards the Middt^ of the Pupil as towards a 
Center : the other are circular ones and fur<r 
round the Pupil, having the Middle of it for 
their common Centor* Tbeie are connected 
to the former where they crofs them : and 
therefore when thefc ooiUJaft, the JPupil is di- 
mmifhed ; when the other, it ii inUrged. 

Within the Cavity of the £y^, and not &r 
behind the Pupil, there is a foft tmnfpacent 
Subftance CC, not unlike a double copFez 
Zfnsj one of whofe Surfaces a$ S, is more coq« 
vex than the other. This is called the Cryf^ 
talline Humour ^ and is fufpeoded within th^ 
Eye by certain Ligaments, as C/, C/, called 
Ligamenta Ciliaria^ or froctffui Gliwt^i 
thefe are convex towards the Pupil, as expreff* 
ed in the Figure, and concave on the other; 
Side, and are mufcular, and therefore capable 
of CQntra<3:|on and Dilatation. The Qoavex 
Sides of thefe Ligaments are lined with a very, 
black Subftance, as is alfo that Side of the /r/| 
which is next them. 

The Tunica Ruyfcbiana leaves the Cberm^ 
4es at /, and, pailing behind the UgMimtA 
Ciliaria and the CryftaUinfe Humour^ is con-!> 
tiguous to them, and joins the Cboroidet again 
at /, on the other Side the PupiL 

3y means of the ibrementiqued Parts^ tb« 
Cavity of the Eye is divided into two Portion^} 
the one of which VV 1% filled with- a Fluid 

ncvly of |lw lame Dcnfitjr with Watqr, 90A 


Chapes- Pf thU^yt,, 55 

is therefac called Humor Aqueus ; the other 
TT contains a. Fluid whofe Confiftency is 
greater than that of the fohner, and is called 
Humor Vitr^us : And both thefe Humours are 
rarer than the Subftance of the Cryftalline. 

At the back Part of each Eye, but not di- 
teBtly oppofitc to the Pupil, there^ enttr$ a 
Nerve a$ NN^^ which is called the Optic 
Nenx. ' 

The Fibres of tiiiis Nerve, after thdr En^ 
trance into the Eye at N, fpread themfelves 
over the itanermoft Coat of it as far as the Uga^ 
menta GliariOf and form a very thin Mem-^ 
farane, called Tunica Retina. 

The innernioft Coat of the Eye is every 
where covered (except that Part of it whidl 
is contiguous to the back Part of the Cry ftal* 
line Humour) with a very black Subi^nce, 
not unlike that v^ith which the back Part ck 
thfi Iris and fore Part of the Ligamenta Citi^ 
aria were obferved to^be covered. This is to 
hinder any Light from being refledted from 
thofe Parts to the Retina 5 for that would 
render the images of Objeds indiftindt ; as we 
fliall fee when we have explained the Naturi^' 
of Vificai, which is the Subject of the next 


$6 Of the Nature of Mon. Part ih: 

C 3 A P. VI. 
Of the Nature of Vifion. 

SUch is the Subftancc and Form of the Hu- 
inours of the Eye, when lodged in their 
proper Receptacles, that Rays of Light in|)ai^ 
fing through them are affed:ed in the like Man- 
ner as in paifing through a convex /i^^xri, as'we' 
(hall fee immediately : and therefbre,to under- 
iland.thc Nature of Vifion^ which depends on 
the Paflage of Rays flowing from th&feveral 
Points of a diftant Obje<a through thofe Hu- 
mours, little more is required than to know 
how the fame Rays would be afFeftcd, were 
they fuppofed to pafs through a convex X^m.* 
Which may eafily be done by applying to this 
Cafe what has been delivered in the fourth- 
Chapter concerning the Manner in which 
Rays flowing from a fingle Point are afifedted 
in paiSng through Lenfes of that Kind, 
. We have already fcen, in the abovemention- 
ed Chapter, that Rays flowing from a fingk 
radiant Point, and afterwards falling on a con- 
vex Lens^ are coUeded to a Focus in fomc* 
Point oppofite, or nearly fo, to the radiant. 
Let us now fuppofe an Objed placed before 
a LenSy but farther from it than the focal Dif- 
^nce of its parallel Rays; and let it fend forth 


^}PP-^- Of: th^' Nature of ^\{\KTCi. 57 

R^s^ from each jiPoint of its Surface in every 
E^iie^ibn, as ^frpro? fo many radiant Points; 
Soncx^ of the Rays which flow ff om each Point 
o£ that Sjurface of the Objeft which is turned 
towar4s the Lem will neceflarily fall upon it, 
arid, paffing through it^ will be coUedted in fa 
many diflinS focal Points on the oppofite Side, , 
as there aire diilind radiant Points' in the Surface 
ic Objedtfrom whence they came. Now,, 
tc radiant Points are contiguous to each 
other in the Surface of the ObjeS on one Side 
of the LenSy the focal Points will alfo be con- 
tiguous on the other ; and as each focal Point 
is oppofite to its refpedtive radiant, their Places, 
will have the fame Relation to each other, thai 
thofe of the radiant have • and, confequcntly: 
thefe Points, taken together, will be a true Re- 
preientation and perfedl Image of that Objc<9: ;,- 
for each Point will exhibit the feme CoIouj:. 
that its corrcfpondent Point in the Objedt is of: 
But,becaufe each Point in the Reprefentation is 
oppofite to its refpedtive one in the Objedt, 
the Image will be inverted. The Truth of 
this may eafily be experienced, if we. hold a' 
clean white Paper facing the Lem in the Place, 
where the focal Points are, and take Care to 
prevent all other Light from falling upon the . 
Paper, except that which pafies through the 
Lim *. 


■ . • ■ ■ " 

♦ On this depends the Struflure of the Ohfcura Camera^ 
wkkh ii a Contrivance to exhibit the Reprefentation of fuch 


ij S Of tie Nature of Vifoft. Paf t lit 

. To iHuftrate this, IctPQR (%. 30.) rc- 
prefent an Obgeft placed before the Lem AB^ 
and fending forth Rajs from each Point m its 
Sofiace; and let q be -the focal IMancc of 
Rays proceeding from Q^ and paffing tfarougb 
the faid Lens. Then will all the Rays that 
proceed from the Point Q^bctwecn the Lines 
QA and QB, be collected in y ; in f ike Man- 
ner all that flow from P, between the Lines 
PA and PB, will meet in the oppofkc Point 
f i and fo many as proceed from R, and pais 
through the Lensy will be colle<3:ed in r ; and 
all the Rays^ that flow fium the remaining 
Points^ between P and R and fall npon the 
Lensy will be coHcdted in as many Points be- 
tween p and r j and, if the Rays are received 
there upon a while Surface, there will bef 
cxhibked an Image of the Objeft PR, but 
inverted ; becaufe the Rays PL/ and RLr 

Objefts as snybe feenfixnn a Winiow^ ii{)eii ibme j^a 
white Surface held before the. Window withm the Rooiiu Ik 
order to do this, a common Spedlacle* Glafs or Burning, Gh& 
(both which are convex Lenfes) muft be fixed- in an Role ifi the 
WindowOlutcer ; Ibr then» if no Lighttbe fnftsred to entet into 
the Room, but what pafles through the Hole;, and' a Sheet of 
White Paper beheld oppofite to the Hole at that DiHance where 
tbe*Ray» proceeding from the Objeds abroad, and paffing 
through the Glafsy are colleded into their, reibedlive fWfVwe- 
iball have the Images of all the ObjeAs which lie before the 
Hole- rcprefented.upott. the Paper, inverted'; bttr in s much 
more lively and exa^ Manner that can be done by the j^iunli. 
and not only the Objefb and their refpedive Situations, but, 
what is peculiar to this Sort of Paintings their Motions will 
94fo be exprefied« 




Chap. 6. Of the Nature of ViCion. 59' 

crofs each other at L in paffing through the . 
Lens *. 

Thofc Rays which flow from the fame' 
Point of an Objedt, when confidered together, * 
are called a Cone or Pencil of Rays. Thus the* 
Rays QA, QL, &c. conftitute a Pencil flow- 
ing from theroint Q ; fo thd Rays PA, PL^ 
&c. a Pencil from the Point P; and the mid- 
dle Ray of each Pencil, as PL, QL, &c. is 
called the Axis of that Pencil, to which it be- 

Now in like Manner as the feveral Pencils 
of Rays flowing from the difliinfl: Points in the 
Surface of an Obj«£t placed before a Lens^ arc 
coUedted in fo many Points at a certain Dif- 
fancd on the other Side of the Lens^ and form 
an Image there when received upon a white 
Paper i fo Pencils proceeding from an Objedt 
placed before the Eye at a proper Difl:ancc 
from it, and being refrafted in paffing through 
the Humours of it, arc collefted into their 
refpeftive Foci upon the Retina^, where they' 
form a Reprefentation of that Objeft j and by 
their Impulfes upon the tender Nerves of the 
Retina^ an Idea of the Objed is excited in the 

• A burning Glafs is no other than a Piece of Glafs ground 
into the Form of a convex ^^i : for if the Rays of the Sun are 
permitted to pafs through fuch an one, !hey will burn very 
ftrongly in the Place where they are collefted into their refpec- 
tive Foci ; upon ysrhich Account it is, that the Point where Rays 
in {;enenil are colledted^ is called their Focus^ that is, their. 
Plac^ of BwTHngrf • 1 

- H The 

6o Of the Nature ef Vifiom Part III. 

The Progrcfs of the Rays through the Hu- 
iftours of the Eye, are cxprcffcd in the 31ft 
Figure : where ¥Gt is the Eye, FG the ^ir- 
niea Cornea^ /^the PupUt A A the aqueous 
Humour, HH the chrilblline, and V V the vi- 
treous. And RS reprefents an Q\^^ placed 
before it, emitting Pencils of Rays from its (e* 
veral Points R, S, T, (Sc The Rays which 
conftitute the Pencil GTF,in entring the aq[ue** 
ous Humour, pafs out of a rarer into a denfer 
Medium through a convex Surface, in which 
Cafe diverging Rays are made to diverge lefs^to 
become parallel or to converge (Chap. 3»Prop. 
7.); in entring the cbriftalline they dothe like; 
and in paffing out of that, rfiey proceed out of 
a denfcr into a rarer Mediumy throurii a con- 
vex Surface of the denfcr, which alfo has the 
fame Effcdt (Chap. 3. Prop. 15.) By whidi 
Means they are made to converge, as defcribed 
in the Figure, and to meet together in a !Facui 
at /, a Point in the Retina. ^ In like Manner 
the Rays flowing fronx R, and coi^ituting the 
Pencil GRF, will proceed as defcribcd in the 
Figure, and after Kefradion meet in rj and 
the Rays proceeding from S will be CoUe&ed 
in J, &c. by which Means an Image of the Ob- 
ject will be formed in rts upon the Retina^ but 
becaufe the Pencils crofs eada other m pafling 
through the Pupil, it will \k inverted ^. 


* O^thfs weliave experimexital Proof : Fori^wc «ae»w»y tlui 
back iPirt of ain E/e, and apply, a Paper there^ we toll Jk% tUe 

' -^'^ Images 

chap/ 6. Of the Nature cfYi£<m. 6i 

The lef&tbe IMfl^Qce between the O^tOt and 
the Eye is, the more the Kays which come 
from the Object, are faiij to diverge, and ^ conr 
fra : Not that the Situation of the; Eye m^^kes 
any Alteration in Ae Progrefs of thofc Rays, 
but that, when the Eye is placed nearer mc 
Ofcjcd, h Fccdtves into its Pupil Rays which 
^ycrgc in a greater Degree than thofe which 
it can receive when placed farther off. *Thm 
^owing^Hluftratipn \vili make this clear : I/^ 

AB* {J^* 32.) reprefenf an Objcd qjiitting 
itays from fcach ^^:|i^t of its Snrfece^ and let 
Cd^ €lr, f^e. exprefs thofc which flow ffom 
-the Pom*G: let^be a Pupilof an Eye placed 
-at ihc.DiflianccCM froniitj 'tis plain tb^ Pu- 
pil wiH receive hrto jt the diyer^ng Rays Cr, 
€/ ; whereas the Rays Coy Ct will' divtsrge 
the moft oifatty th^t can enter the f^me Pupu, 
when|4aced at the Diftance G^j but t|ieic 
diverge lefs dkn the fomjer, the Angle 0^ 
being incl^ded iij the Angle rCjr. 

.liBUgeiof »it0»tal«Okjt{|^plaMl tkem^n, at actofHttf^ is m 

on the Paper, except that wl^^ich paflps tljrough the Hyi&Qurs 
oC-thtBye'. ^' ' ..'/•'-» 

9PMf[ Wii9« Jiire «iid« it.Msim ofgreai: DMcrIqc m ie^ 

teiTpiije tl« Poiot wierc.the^w of thoPeociU wliiclkcivcr the 
Ere, CK>(§ e^ch 6ther ; ferjie placing it jn the Centef ot the 5y.e, 
Mbrim.ttiei)&nq^of tKechnftattii^Uomoar, other* ia tb^ 
of the Tunica Cornea : Bat as the Rays of each Pencil fill the 
Pupil, or ^s tjic P,Mgil,itfclf js.a^coromon Bafe to each Pcijcilf it 
U inconcf^iyahlc JiQW thQ JpeU of thofo Pencils ftiould crofs c^fh 
other in any o^er Place than the Center of the Papil. ' Scf 
Figure 31, Or any other where* feveral Pencils are reprefented, 
as paffipg through the Aipil of an Eye. 

H 2 Vifion 

.62 Qfthf Nature 0/ Vifion. Part III. 

Vifion is diftinguiihed into bright and ob^ 
fcure J diJlinSl and confufed. 

It is faid to be bright ^ when a fufficient Num- 
ber of Rays enter the Pupil at the fame Time ; 
vbfcure^ when too few. It is diJlinSi^ when 
each Pencil of Rays is collected into a Focus ex- 
actly upon the Retina 3 confufed^ when they 
meet before they come at it, or when they 
.would pafs it before they meet ; for in either 
-of thele laft Cafes, the Rays flowing from dif- 
ferent Points of the Objed^ will fall upon the 
Jame Part of the Retina^ wluch muft necei&- 
lily render the Image confufed and indiftind. 
. Now that Objcds may appear with a due 
Brightnefsy whether more or fewer Rays pro- 
ceed iirom them, we have a Power of contrad- 
ing, or dilating the Pupil by means ofthe muf- 
cular Fibres ofthe h-is (as explained in the 
foregoing Chapter), in order to take in more 
or fewer Rays as Occaiion requires. But this 
Power has its Limits. * 

And that the Rays may be coliedled into 
Points exadiy upon the Retina^ that is, that 
Objeds may appear dijiin£iy whether t^ey be 
nearer or farther off, that is, whether the Rays 
proceeding from them diverge more or lefs,wc 
have a Power of contrading or relaxing the 
Ugamenta Ciliaria^ and thereby altering the 

• • • 

' ♦ In fome Animals, this Pdwer Is much greater than in 
others ; particularly in fuch as ailB obliged to make UTe of their 
Eyes by Night, as Well as. by Day, as in Cats, 16fc. 




t^hap. 6. Of the Nature of V\£i6n. 6^ 

Fonnofthe chriftalline Hu^Bour, and \^ith 
that the> focal Diftancc of the Rays. Thus, 
.when the Objcd: we view is far off, and the 
Rays fall uponthe Pupil with a very fmall Dch 
• gree of Divergency, we con trad the Ligamen-- 
1 ta Ciltaria^ winch being concave towards the 
vitreous Humour, do thereby comprefs it more 
than otherwife they would do ; by this means 
it is made to'prefs harder upon the back Side 
of the chtiftalline Humour, which is thereby 
irendered flatter ; and fo the; Rays proceed far- 
ther before diey meet in a Focus than other- 
wife they would have done. Add to this, that 
•we- dilate the Pupils of our Eyes (unlefs in 
Cafes where the Light is foftr ong that it offends 
the Eye) and thereby admit Rays into d^em, 
that are more diverging.thanthofe which would 
otheswife enter. And when the Rays come 
from an Objedl that is, very near, and there- 
ibre diverge too much to be coUedled into their 
Tcfpedive i%a upon the Retina^ by relaxing 
jthe Ligamenta Ciliaria we give the Chriftal* 
line a more convex Form, by which means the 
Hays are made to fuffer a proportionably greater 
l)egree of Refradion in pafGng through it *. . 



• Some Philofophcrs are of Opinion, that we do this by a 
Power of altering the Form of the Eye ; and others, by remov- 
ing the Chriltalline forwards or backwards as Occafton requires ; 
but neither of thefe Opinions is probable ; for the Coats of the 
Eye are too hard, efpeciaUy in fome Animals, for the £rll ; and 
as to moving the Chriftalline out of its Place, the Cavities of 
the Eye feem to be too' well filled with the other Humours to 
admit of fuch Removal. 


64 0f*he^atur4€fVifi&[i. Part III* 

And WiklfS tbifi, tw OQDtradiiig tho Pupia of 
.our Eyes, we eiraude tlie num divcfigisig 
Rty^ and admit only ftidi aa gre morecafiiy 
^nfrai^d ime their refpo£)ire Fm* *. But 
Vtfief^ 16 not dUlkift a( att jDiftaaoas, % 
our Boww of oontRuftiag and ];efaxing tbs 
Ugamenta&iariakzlh tiMKkUxkrllbtd mA^ 
in certain Limits. 

The near^ an Objed is plaocjd ta ^m Eyi^ 
the greatep is the Iniage ofat iifoa tho JSMtm. 
Becauie the Peacik flowing fi^om the extccne 
^rtsof the OlMe& whennear^ make a lacfdr 
Angle with eadn other in the Ptapilwbere th«|r 
^rdis, than the fknoe Pencils do when the Ob^ 
jed is placed farther off. Thus AR {Bg.$ ^Jj 
«he Iniaee of the Ob|ea CD, fa^ Gxqecds £F 
that of*the feme Ofc^od; G{f» plaeed at a greater 
JDiftance from the Eye^ etideat fimn bi^ 
fpedion of the Figure. 

In thoi^ Eyes where the Tunica Cor/k^a k 
very protuberant and convex, the Raji^ of 
Light fufier a very confiderahle ^Refira^on at 
their Entrance intOitbca(|a60u&Hufiiaiir, and 
are therefore collected to a Focm before th^ 
fall upon the Retina^ unlefstheOhjoft bepku 
ced very near, fo that the Rays which enter 
the Eye, may have a confiderable Degree qf 
pivergenqy. People that have ilich Eyes, aif$ 

* Accordicglx it ia obftrvftUe, tliat if we make a Qaall HqI| 
with Che Point of a NeecUc tkrouah a Piect of Paper, aaAaKpty 
that Hole cbfe to the £yc» makiog Ufiv of it» as it weae» jjotteaj 
of a Pupil» we (hall be able to fee an Qbjed 4iftiQ^Jf .thrqagli 
^> though the Objedt' be placed within half an Inch of the Eye. 


Chap* t.Ofih Nature d/ Vifi^ti; 6^ 

jQi^d to b« purbiind. NoW the nearer iti Obt- 
jcd is placed to !hc Eye, the greyer -. h the 
Image of it therebi as exjplaiojdtd above % . tfatfe 
Peo^e th^fore cin fee mUch iihaikr Objeid:^ 
than dthtrs^ as feeing much c^tm^r. ones^wkh 
thd fame Dii^ia<£tile(s« AiAd their Si^bt cdn-- 
tintttfs g6od longdr ihaa that bf other PMple, 
becAiife the TumcM Gornm a£ their E3rei» •a^ 
they gf 6W Old, becomes, plainir^ for WaDt <$f 
that. RedtindansJy of Humours with which 
tjicy Were fiUetJ before. 

On the cofitraryt old Meh having the Cir-* 
nea of their Efe$ top fkt fm want of a ftiffid*^ 
ent Q|ianfity of the aqtieou$ Humour to (Hi 
theni out^ if the Rays diverge tdo much bdbra 
they enter the Eye, they, canfeot be brought 
tti a Focus before they reach the Rstma^ oil 
whiK^ A<tcount thofe Pbdpk cannot fee dU 
{k\\iOiVfy unlefa the Ot^eCt be iituated at a 
gteatd: Diflacrci from the Eye, than is reqoired 
for thofe whofe Eyes are of a due Form. 

8ifice thig lo^es of the Objeds we look at 
afi inserted ill the Eye, it may be thoi;qght thd 
Objefks themfi^ ves ought to appear fo > but ifc 
iKHift be (^onfideted> that there it n4> maeur&t 
Conocdion bc!twben theJ^inottrMind) m^ 
the. Image upon the Retina y w6 fifyd by Ex*^ 
ptlticiiQt, thit when foch an Lha is extited in 
our Mind, fuch an Objeft (lands before us in 
filch a Pofition asid of ftich k Potitt ; whenever 
therefore the Itk^ IJe& Is excited agiin, we 


66 Of the Nature of Vi{\6n. Part III. 

conclude there is a like Caufe of it. For it is 
found by Obfervation, that People who have 
been born blind, and have afterwards received 
their Sight, have had no Inform^ion from 
their Eyes at firfl, concerning the particular Si- 
tuation or Form of Bodies ; but have been ob-> 
ligedto fUy till Experience has taught them 
whatFigures and Situation of Bodies correfpond 
to fuch and fuch Senfations in the Mind ^. 

In like Manner it is from Experience that 
an Objed appears fingle, though there be an 
Inuige of it in eachlEye ; for after we find, 
that its Place, acccu-ding to the Reprefentation 
of it in each Eye, is the fame, we neceflariiy 
conceive it to be but one. The Manner how 
we come to find this, feems to be as follows : 
There is one Part of the Retina upon which 
when the Image fells, the Objed appears 
brighter and more diflind:, than when it falk 
upon any other, . as is evident, becaufe we al- 
ways fee one Part of an Objeft with greater 
DiftinAnefs than any of the refl. This Point 
I fhall hereafter call the Point of diftinSi Vi- 
Jion. This naturally leads us to turn our Eyes 
fo, that the Objed may be fituated diredly 
oppoiite to this Point. And this Adion di 
ours is that which has given Rife to thofe ima- 
ginary Lines, which are fuppofed to .pafs di- 

. • Sec Mr. Chiffilden's Obfeirations on a yoang Qendeman 
coached by him at the Age of 13 Years. Philofoph. Tnmfadl^ 
No. 402. * . 

" • redly 



Chap. 6. Of the Nature 6/ Vi^on. 67 

rcftly through the Eye and to terminate in the 
Objedl we view, and are commonly called the 
optic Axes. We therefore turn our Eyes fo that 
the Obje&may appear in thofe Lines. There-* 
fore,iince thefe Lines concur at theObje£l,wheii 
we indeavour to view it with Difiincftnefs, each 
Eye affords us an Idea of the Objedt in the 
fame Place^ from whence it neceilarily appears 
but one *♦ 


♦ Thcfc arc other Meth6ds bf accoilnting f6r thefe two laft 
ThMHomena^ ibme of which, perhaps, the Reader may think 
snore plaufible ; for the Connedion between the Image on the 
Ittiinm and the Idea in the Mind being purely metaph^cal, w^ 
can never hope to arrive at Certainty in this Matter. 

^ Some are of Opinion, that we judge thofe Rays which painty 
the uppermoll Part of the Image in the Eye to proceed from the' 
lowermoftPart of theObje£l, becaufe they ftrike opoti the Re- 
tina^ as coming from that Part ; and that we condudefrom hence 
that the Objed'is ere6l, though the Image be inverted ; as if the 
Diredion, wherewith the Rays ftrike the Retina^ informed the 
Mind which Way they came.This Solution fervessdfo to explicate 
the Pbanomifipn of ieeing but one Object with both Eyes i for 
as the Mind is informed, by the DireSion with which the Rays 
ftrike the Retina^ of the Place from whence they come ; there- 
fore when it appears that they enter each Eye a$ from the fame . 
Place, the Objedt neceffarily feexUs to be but one ; becaufe we ' 
can't fuppofe two to exift in the fame Place at the fame Time. 

* Some have been io abfard as to embrace an Opinion, the firft 
Author of which was Gajfendus, that we fee one and the fame 
Point of an Objed only with one Eye at a Time, {otiante alio,' 
as they exprefsit) while the other does nothing. Vid. Gajfmdi 
Epiftol. de Magnitud. Solis ; or Tacquet. Optic. Lib.1. Prop. 2. 
Some imagining that the optU Nerves confift of a Bundle of 
fmall ones wrapped up in one common Tegument, are of Opi« 
nion, that fuch as lie upon the Retina at equal Didances from 
the Point ofdiRinSt Vifion, and on the fame Side of it in each 
Eye, are connedted tpgcthcr in one, before they terminate in the 
Brain ; and fo, whether one or both are affe^ed, only one Id^u 

1 is 

68 Of the Nature ofVi&oD. Ite III, 

Whenever the Eyes are fo fitnated widi re« 
{pe& to an Obje£l» that the fame Part of the 
RetiM in each Eye is afFedsed by the Ri^ 
that flow from it» which is are waattobesdT- 
feded when two Objeds are j^aoed beftre 
the Eyes, the Mind, receiviiig no Ii^brmatioii 
from without, but by the ImpaUes of the 
Rays upon the Refinay judgfss that there ate 
two Objefts. Thus, let A, B {Fig. 34.) repre- 
feat two Eyes whofe optic Axes are directed to 
the Point C, and let E be anObjed on one 
Side the Point C; and F an GbjcSt on the other. 
Now, Objeds thus fituated muft appear fqxt- 
rate 5 othcrwifc, every time we viewed an ub- 
]eCt we muft imagine all the different Points 
in its Surface to be but one, which is con<^ 
trary to Experience. In this Caf<^ the Point 
d in each Eye will be affefted l^ the Rays 
which flow from thoie Objedk^ but fo ic 
will, if a finglc Objcft be placed at D| and 
therefore, for the Rcafbn given above, an Ob* 
jcd in that Situation (hall appear as i^c two 
feparate ones E and F, diat is, double. A-^ 

ir excked in the Mind. GfrsnH^an/cotArm^ this Opinion^ 67 rf- 
ferting that, in all Animtlf wnich lo^ at the (kme ObjdEt with 
both Eyes, the q^tic Nertes^concur, befbre the}r enter rhrBnitf ; 
and that, in fach as look at one Objed with one Eye, and as 
a difoent one with the other, they are ffepante all' the W$y. 

Others, with Briggius (fee his Optbahnog, ChM». tx.)'do 
not contend, that the forementioned correfjponding Parts cif the 
ofiic Nerves are conneted before thef terminate m the Brain i 
but that they are of an eqaal Tenfion, and therefbitexelte the 
fiimc Senlatia»in the Mind* 


€Akzp. 6. 0/ tie /VaHtri tf/Vi&m. 69 

gain, Itt diere be an Obje£k placed wkfaoot the 
€pticjixi5^ as at G, Rays flowingfrom thfiwili 
^ed the iame Part in each Eye^ as if there 
were two diftind Objeds, viz. one at £» and 
d)e other at H s this therefore will alfo ap- 
pear double. Farther, as the Objeds D and 
G are fituated in this Figure, if both are at- 
tended to at the fame Tioie (the o^tic Axes 
being ilill direded to the ftme Point C) they 
will appear as three, being iituated oppofite 
to the three Points F, E, and H. And what has 
been faid of the Appearance of the Objeds 
D and G, as they arc fituated in this Figure, 
may be applied to their Appearance as they 
are placed in the next, where they are repre- 
fented as being beyond the Line HF^ So that 
wherever an Objed is placed, provided it be 
nearer to the Eyes than the Point where the 
optic Axes concur, or farther from them, it 
appears double. 

There is (xie Part of the JUtina of each Eye, 
upon which when the Image falls, the Objedt 
cannot be feen at all with tbat Eye ; the Proof 
of dbis we have from the following Experiment. 
Fix two Obje&s upon a Wall, of fuch fiigneis 
that each may hide a fquare Inch of it, or 
thereabouts, and at the Diftance of about a 
Foot or two from each other, and go back from 
the Wall about three times that D^ance ; then 
(hutting the left Eye, look at the left 0\ifi& 
with tlK right one, and while the right Eye is 
in that Pofition, the right Objed will not be 

I 2 feen. 

70 Of the Nature of VSmi. Part III, 

feen. So,i£ in that Station we look at the right 
Objca with only the left Eye, the left Objca 
will difappear. The Reafon of this is ftippofed 
to be, that the Image'of that Objed which 
difappears falls upon the Blood-veflels of the 
optic Nerve, from which no Seniation is con* 
vcycd to the Brain. 

The Angle comprehended between the Rays 
which flow from the extreme Parts of the Ob- 
jeA) ,and crofs in the Pupil, is called the optic 

*Tis by means of this Angle that we are able 
to form fome Judgment of the Magnitude of 
an Objeft ; becaufe,the larger this is, the larger 
is the Image upon the Retina^ that is, a greater 
Portion of it is affcdcd by the Rays which flow 
from that Objed:. But this is not fufficient 
alone, becaufe different Objeds at different 
Diftances from the Eye, may fubtcnd equal 
Angles at the Pupil. We ought therefore to 
know alfo the Diftance of the Objed. 

This, if the Objefl: be very near, we are 
able to form a tolerable Judgment of, by tht 
Degree of Divergency, wherein the Rays 
which flow from the fame Point of the Objcd 
enter the Eye 5 becaufe we find it neceflaryto 
adapt the Eye accordingly, in order to bring 
them to a F«:«x upon the Retina. 

But, u hen the Objcft is at a greater Diftancfc 
from us, a confiderable Variation in the Di- 
ftance of it makes but a very fmall one in the 



^ Chap. 6. Of the Nature of Virion, ii 

Divergency of thofe Rays, and therefore this 
Rule of judging ceafestobe ofUfe. The only 
Expedient then is the Angle comprehended 
between the optic Axes at the Objed to which 
they are diredted, or, which is the fame Thing, 
the Pofition of the Eyes with refpedl to each 
other when they view the Object *. But in 
' very large Diftances this Pofition varies fo lit- 
tle, that it is alfo of no Ufe^ in which Cale, 
we make the beft Judgment we can from the 
Brightnefs, Diftinftnefs, and apparent Magni- 
tude of the Objedt, and likewife from its Situati- 
" on with refpeft toothers which are interpofed-f. 
When we are unable to judge rightly con- 
cerning the Diftance of an Objed, we conceive 
it greater, the farther we imagine it to be from 
us. znA vice versa I becaufe it requires a lar- 
ger Objeft to exhibit the fame Image upoh 
the Retina y when it is fituated at a great Dif- 
tance, than when near. Thus we imagine the 
Sun and Moon to be farther off, when they 
are in the Horizon^ than when they are near 
the Meridian^ and accordingly think them 

♦ That the Pofition of the ottic Jxes is a Means whereby we 
judge of Diftances, is evident from hence, viz. that they who 
have loll the Sight of one £ye» find it much more difficult to 
eftimate the Di&inces of Objedts, than they did^ when they 
kad the Ufe of both. 

•I" Wc have a remarkable Inftance of the Error of our Judg- 
ment concerning the Diftances of very remote Bodies, in that 
we look upon the Sun, Moon, and Stars to be all at the fame 
Diftance, wheteas fome Of them are a thoufand Times farther 
irpm «s than othcn. ♦ 


72 Oftht Appear mee Part III. 

proportionably larger in one Situation than in 
the otbfr, though Uiey are found to exhibit the 
£)me Iniage upon the ^tina in both Cafes *• 

We are never able to fee very diftant Objefls 
with DiiUn£tnefs^ this is not folely owing to 
ChePupirsnot receiving into it afufficientNum^ 
l)er (^Rays fcx that Purpofe, or becaufe they 
are not collected into foci upon the Rrtina^ 
but becaufe the Obied being very far off, the 
Ray? which flow from Points of the Objed 
that are contiguous fall too near each other 
upon the Retina to excite diflin^): Senfations in 
Wie Mind, fo that the Idea of the Whole is 


CHAP. vn. 


€f the Appearance of Objeds fern 

through Media of different Forms, 


•THHat what we £hall fay upon the Subjeft 
1 of this Chapter may more readily be un* 
'dcrftood, we fhall premife the five following 
Particulars, which are all coroprifed in the 
£>regoing Chapter^ or fdlow immediately from 
what has been there laid down, viz. 

I. That, as each Point of an Objed, when 
iriewed by the naked Eye, appears in its pro^ 

^ Se« tte PifinrtfttioA oq the hrk^hU Moon, annexed to 




• ^ 


Chappy- 0/Objcas,^r. ^3 

per Pkce, and as that Place is always to be 
found in die Line in which the Axis of a Pen- 
cil of Rays flowmg frofti it enters the Eye, we 
from hence acquire an Habit of judging the 
Point to be fitctated in that Line ; and, becatife 
die Mind is tinacquainted with what Refirac^ 
tions the Rays fuflcf before they enter the Eye. 
therefore, in Cafes where they are divertea 
ftoBi their natural Courfe by paffing through 
any Medium^ it judges the Point to be in th&t 
Lme produced back in which the Axis of af 
Pencil of Rays flowing firom it is fituated the 
Inftant they enter the Eye, and not in that it 
was in before Rcfradlion. We ftiall therdTore 
in what follows, fuppofe the apparent Place 
of an ObjeA, when feen through a refrafting 
Medium to be fotnewhere in that Line produc- 
ed back in which the Axis of a Pencil of Ray» 
flowing from it proceeds after they have paflect 
through the Medium. 

2. That we are able to judge, though im- 
pcrfcfkly, of the Diftance of an Objefl: by the 
Degree of Divergency, wherein the Rays flow- 
ing from the fame Pomt of the Objedt enter the 
Puptlofthc Eye, in Cafes where that Diver- 
gency is confiderable ; but becaufe in what fol- 
lows, it Will be necciTary to fuppofe an Obj'cft, 
when feen through a Medium whereby its ap- 
parent Diftance is altered, to appear in fbmcr 
determmate Situation ; in thofe Cafes whettf 
ll^e Divergency 9f the Rays at dieif Enttanc;? 

74 Of the Appearance Part III, 

into the Eye is confiderable, we will fuppofe 
the Objedt to appear where thofe Lines which 
they deicribe in eotring, if produced back, would 
crois each other ; though it muft not be a£ert-« 
cdthat this is the prepife Diftance \ becaufe the 
Brightoefs^ DiftinAnefs, and apparent Magni* 
tude of the Objed, on which its apparent Dif^ 
lance in fome Meafure depends, will alfo fufier 
an Alteration by the Refra^on of the Rays in 
palling through that Medium* 

3. That we eftimate the Magmtude of an 
Objeft by that of the optic Angle. 

4, That, Vifion is the brighter^ the greater 
the Number of Rays is which enter the PdpiL 
And, :> 

. 5. That,in fome Cafes, the apparent Bright^ 
ne/Sj DiJlinBneJs^ and Magnitude of an Ob- 
ject are the only Means whereby our Judgment 
is determined in eilimating the Diflance of it 

Prop. L An Objedl placed within a Medium 
terminated by a plain Surface on that Side 
which is next the Eye, if the Medium be den- 
fer than that in which the Eye is (as we (hall 
always fuppofe it to be, unlefs where the con- 
trary is cxprefled) appears nearer to the Sur* 
face of the Medium than it is. 

Thus, if A be a Point of an Objed placed 
within the Medium BCDE (Fig. 36), and A^, 
Ar be two Rays proceeding from thence, thefe 
Rays pafling out of a denfer into a rarer A&- 
4ium^ will be rcfrafted from their reipedive 



' Chap* 7* of Obje As ^ tic. 75 

Perpendiculars bd^ ce^ aftd will enter the Eye 
at H, foppofe in the Dire<flions bf^ cg^ let then 
f hefe Lines be produced back till they meet in 
F 5 this will be the apparent Place of the Point 
A ; and bccaufe the refrafted Rays bf^ eg will 
diverge niore t3han the incident ones A^, Ac 
(Ghap. III. Pi'op. 3.), it win be nearer to the 
Points b and c^ than the Point A 5 and as th6 
feme is true of each Poinj ia the Objed, the 
Whole will appear to an Eye at H, nearer to 
the Surface BC than it is ♦. 

Prop. II. 

* From hence it is» that when pne End of a fink Stick it 
pat under Water, and the Stick is held in an oblique Podtion, 
It appears bent at the Surface of the Water ; vix, becaufe ea^h 
Point that is under V/ater appears nearer the Surface, and con* 
fequently higher than it is. 

From hence likewife it is, that an Obje£l: at the Bottom of a 
VeiFel may be feen when the VefTel is filled with Water, though 
it be fo placed with RefpeA to thb Eye, that it cannot be feea 
When the VeiFel is empty. To explain this i let ABCI) {Fig. 37.) 
itprefent a Veflel, and let £ be an Obje^ lying at the Bottom of 
it. This Objed, when the Veflel is empQr, will not be feen by an 
Eye at F, becaufe HB the upper Part of the Veffel will obftrua 
the Ray EH ; but wHen it is filled with Water to the Height 
GH, the Ray EK being refradked at the Surface of the 
Water into the Line KF, the Eye at F (hall fee the ObjeA by 
Means of that. \ 

In like Manner, an ObjeA fituated in the Horizon appears 
above its true Eace, upon Account of the Refradlion of the 
Rays whicji proceed from it in their PaiFage through the J/mo^ 
/fben of the Earth. For firfl, if the Obje£l be fituated beyond 
the Limits of the Atnujphere^ its Rays in entering it will be re- 
fia&d towards the Perpendicular, that is, towards a Line 
drawn from the Point where they enter, to the Center of the 
£arth which is the Center of the Atmofphtre^ and as they paft 
on they will be continually refradted the fame Way, becaufe 
they are all along entering a denfer Part, the Center of whofe 
Convexity is ftill the fame Point ; upon which Account th^ Line 
they dcfcribe will be a Curve bending downwards ; and there* 

K fore 

76 Of the Appearance Part III 

Prop. II. An Obje£t feen through a Medium 
terminated by plain and parallel Surfaces, ap- 
pears nearer^ brighter y and larger^ than with 
the naked Eye. 

For Inftance, let AB {Fig. 38.) be the Ob- 
jea, CDEF the Medium, and GH the Pupil 
of an Eye, which is here drawn large to pre- 
ventConfufion in the Figure. And ift let RK, 
RL be two Rays proceeding from the Point R, 
and entering the dehfer Medium at K and L i 
thefe Rays will here by Refiradtion be made to 

diverge lefs (Chap. III. Prop. 2.) and to pro- 
fore none of the Rays that come from th^tOlijed can enter an 
Eye upon the Surface of the Earthy excrot what enter the At^ 
mo/there higher than they need to do^ if they could come in a 
rignt Line from the Objed ; confequendy the Objed muft ap- 
pear above its proper Place. Secondly, if the Objefi be placed 
within the Atmofphert^ the Cafe is ftill thd fame ; for the Rays 
which flow from it muft continually enter a denfer Me£um whole 
Center is below the Eye, and therefore being refraded towards 
the Center, that is, downwards as before, thofe which enter the 
Eye muft neceffarily proceed as from fome Point above the Ob- 
jc6l, wherefore the Obje£l will appear above its proper Place. 

From hence it is^ that the Sun, Moon, and Stars appear a- 
bove thr Horixon, when they are juft below it, and higher than 
they ought to do, when they are above it : Likewife difiant 
Hills, 1 rees, i^c, feem to be higher than they are. 

Farther, the lower thefe Obje£U are in xht Horizon ^xht greater 
is the Obliquity with which the Rays which flow from them, 
enter the Atmofphert^ or pa6 from the rarer into the denfer 
Parts of it, and therefore they appear to be the more elevated \ 

by Refraction ; upon which Acconnt the lower Parts of them 
are apparently more elevated than the other^ This makes their 
upper and under Parts feem nearer together than they ought to 
do, as is evident in the Sun and Moon, which alppearof an oval 
Form when they arc in the Horizon, their horixonta/ Diameten 
appearing of the fame Length they would do if the Rays fuf- 
fered no RefraCtion^ while their ^vertical ones are Ihortened 


Chap. 7. f)f Objeds, '^c. 77 

ceed afterwards, fuppofe in the Lines K^, L^ ; 
at a and b where they pafs out of the denfer 
Medium^ they will be as much refra<5led the 
ccMitrary Way, proceeding in the Lines ac, bd^ 
parallel to their firft Direftions (fee Chap. 
iV.) ; produce thefe Lines back till they 
meet in e, this will be the apparent Plaf e of 
the Point R, and it is evident from the Figure 
that it muft be nearer the Eye than that Point j 
and becaufe the fame is true of all other Pen- 
cils flowing from the Objedt AB, the Whole 
will be fecn in the Situation fg^ nearer to the 
Eye than the Line AB. 2d, As the Rays RK, 
RL would not have entered the Eye; but have 
paffed by it in the Direftions Kr, L/, had they 
not been refrafted in paffing through the Afc- 
diumj the Objed: appears brighter. 3d, The 
Rays Ai&^ B/, will be refraded at b and / in- 
to the lefs converging Lines M, //, and at the 
other Surface into ^M, /M parallel to Kb 
and B/ produced (fee Chap. 4.), fo that the 
Extremities of the Objed will appear in the 
Lines M^, M/ produced, viz. iny'and'^, and 
under as large an Angle/M^, as the Angle A 
jB under which an Eye at q would have (ttn 
it, had there been no Medium interpofed to 
refrad the Rays; and therefore it appears larger 
to the Eye at GH, being feen through the 
interpofed Medium^ than otherwife it would 
have done. But it is here to be obferved, that 
the nearer the Point e appears to the Eye oa 

K 2 Ac- 

7 8 Of the Afpearanci Pait III. 

iVccouBl of the Reftadion of the R«y$ RK« 
RL« thp (hotter U the Image /^^ becaufb it is 
terminated by the Lines %fij and M^, upcm 
which Account the Obj?^ js made to appear 
lefs ; and therefore thp appari^nt M;ign|tuae of 
an Obje^ is npt much augmented by being 
feen through a Medium of^ this Form. 

Farther, it is apparent from the Figure^that 
the EfFcdl of a Medium of this Form depends 
wholly upon its Thickniefs ; for the Di^ance 
between the Lines Rr and ec^ and confequentn 
ly the Piilance between the Points e and R de* 
pends uppn the Length of the Lipe Ka: Again^ 
the Diftance between the Lines AM and /M, 
depends on the Length of the Line bk\ but both 
Ktf ^nd bk depend on the Diftance between the 
Surfaces CE and DF, and therefore the Efied: 
of this Medium depends upon its Thickuefs* 

Prop. IIL An Ohjeft feen through a convex 
LenSy appears larger^ brigbter^ and Tmre di^ 
Jlanty than with the naked Eye. 

To illuftrate this, let AB {Fig. 39.) be the 
Objcd, CD the Lens, and EF the Eye. u 
From A and B the Extremities of the Objcdk 
draw the right Lines AYr, BXr croffing each 
other in the Pppil of the Eye j the Angle ArB 
comprehended between thefe Lines, is the 
Angle under which the Object would be feen 
with the naked Eye, But by the Interpofi* 
tion of a Lem of this Form, whofe Property 
it is to render converging Rays more fo (fee 
^hap. IVO the Rays AY and BX will be made 


Chap. 7. of Objcdfi, ^c. 79 

to crofs each other before they reach the Pupih 
Thfre the Eye atE, will not perceive the 
Sxtremities of the Object by means of thefi; 
Rays (for they will pafs it without entering), 
butby fpme others which muft&H without the 
Points Y and X, or between them 5 but if they 
fall between them^ they will be made to con-» 
cur fooncr than they themfelves would have 
done, and therefore if the Extremities of the 
Objed); could not be feen by them, it will much 
lefs be feen by thefe. It remains therefore, 
that the Rays which will enter the Eye from 
the Points A and 6 after Refra<5tion^ muft fall 
upon the Len% without the Points Y and X ; 
let then the Rays AO and BP be fuch. Thefe 
after Refra&ion entering the Eye at r, the Ex- 
tremities of the Objeia will be feen in the Lines 
rQ^rT produced, and under the optic Angle 
QrT which is larger than ArB, and therefore 
the apparent Magnitude of the ObjeSi will be 
increafed. 2. Let GHI be a Pencil of Rays 
flowing from the Point G j as it is the Property 
pf this Lem to render diverging Rays lefs di- 
verging, parallel or converging (fee Ghap* 
IV.) it is evident, that fome of thofe Rays 
which would proceed on to M and N and mifs 
the Eye, were they to fufFer no Refradtion in 
pailing through the Lens^ will now enter it \ 
by which means the Object will appear bright^ 
er. 3 . As to the apparent Diftance of the Ob* 
je^, that will vary acc(^diing to the Situation 


Bo Of the Appearance Part \1\. 

of it with rcfpcft to the Focus of parallel Rays 
of the Lem. i . Then, let us fuppofe the Ob- 
ject placed fo much nearer the Lens than its 
Focus of parallel Rays, that the refradled Rays 
JCE and LF though rendered lefs diverging 
by paffing through it, may yet have \ confide- 
rable Degree of Divergency, fo that we may 
be able to form a Judgment of the Diftance of 
the Objedl thereby. In this Cafe, the Objedl 
ought to appear where EK, FL produced back 
concur, which, becaufe they diverge lefs than 
the Rays GH, GI, will be beyond G, that is, 
at a greater Diftance from the Lens than the 
Objeft is. But becaufe both the Brightnefs and 
Magnitude of the Objed will at the fame Time 
be augmented. Prejudice will not permit us to 
judge it quite fo faroflPas the Point where thofc 
Lines meet, but fomewliere between that 
Point and its proper Place. 2. Let the Objeft 
be placed in the Focus of parallel Rays^, then 
will the Rays KE and LF become parallel 
( fee Chap. IV. ) and though in this Cafe 
the Objcft would appear at an immenfe Di- 
ftance, if that Diftance were to be judged of by 
the Direction of the Rays KE and LF, yet 
upon Account of the Brightnefs and Magnitude 
of it, we fhall not think it much Jartber from 
us, than if it were feen by the naked Eye. 3. 
If the Objcfl: be fituated beyond the Focus of 
parallel Rays, as in AB {Fig. 40.) the Rays 
flowing from thence and falling upon the Lens 


Chap. 7. ^/Objeds, ^c. 8t 

CD, will be colleded into their refpedive Foci 
at a and 6^ and the intermediate Points m^ n^ 
&c. and will there form an Image of the Ob- 
je<a AB i and after croiBng each other in the 
feveral Points of it, as expreffed in the Figure, 
will pafs on diverging as from a real 0Qe<5t. 
Now if an Eye be fituated at c, where Ac, 
Bcy Rays proceeding from the extreme Points 
of the Objedt, make not a much larger Angle 
A^B, than they would do if there were no Lem 
iliterpofed ; and the Rays belonging to the 
fame Pencil do not converge fo much as thofe 
the Eye would receive, if it were placed nearer 
to a or iy the Obje£t upon thefe Accounts 
appearing very little larger or brighter than 
with the naked Eye, is feen nearly in its pro-* 
per Place ; but if the Eye recedes a little Way 
towards ai^ the Objcd: then appearing both 
brighter and larger, feems to approach the 
Lem * : which is an evident Proof of what has 

• That theObjcft fliould feem to )ipproach the Lms in this 
Cafe, was a Difficulty that exceedingly puzzled the learned 
BarroWfZnd which he pronounces infuperable, and not to be ac* 
counted for by any Theory we have of Vifion. Molintux al(b 
leaves it to the Solution of others, as that which will be inex- 
plicable, till a more intimate Knowledge of the viiive Faculty, * 
as he expreflfes it, be obtained by Mortals. 

They imagined, that feeing an Objedl appears farther off^ 
the Ufs the Rays diverge which fall upon the Eye ; if they 
fhould proceed farallel to each other, it ought to appear exceed- 
ingly remotey and if they (hould coffuerge, it fhould then appear 
more Sftant ftill: The Reafon of this was, becaufe they look- 
ed upon the apparent Place of an Objedl, as owing only to the 
Direction of the Rays whatever it was^ and not at ail to its ap-» 
parent Magnitude or Splendour. 


82 Of the Appearance Paf t lit 

been fo often aflerted, wz. that we judge of 
the Diftance of an Objedjb in fome Meafure by 
ks Brightness and Magnitude * ; for the Rays 
converge the mof e the farther the Eye recedes 
from the hem % and therefore if we judged of 
the Diftance of the Objed by the IXre€tionr of 
ihc Rays which flow from k, we ought inr this 
Cafe to conceive it at a greater Oiffance, thtn 
whei? the Rays were parallel^, or diverged at 
thei# Entrance into the Eye. 

Prop. IV. If aff Objcdt be placed ferther 
from- a convex Lem^ than' its Fora^ of p^aRel 
Rays, and the Eye be fituated ferthtir frota k 
on the other Sicfe, than the Place where the 
Rays of the feveral' Pencils are collc<9ted into 
their refpefitive Foci^ the Objcft appears^ tn^ 
wrted\ and penduhm in the Air^ belwccni the 
Eye and the Lens. 

To explain this, let AB {Fig. 40.)^ repW- 
fcnt the Objefl?, CD the Lens^ and let die 
Rays of the Pencil ACD be colledcd in tf, and 
thofc of BCD in b^ forming there arf inverted 
Image of the Objed AB, and let the Eye be 
placed in F : It is apparent from the Figure, 
that fome of the refra&ed Ray« which pafs 
through each Point of the Image^ will enter 

* Perhaps it may proceed frosa our judgiog.of eke Diftance 
of an Objed in fonie Meaiure by its Magnitude, that that 
t>eception of Sight Isommonly obferved by Travellers ma/ 
arife i *vi»* that upon the iiril appearing of a Building larger 
than ufualy as a Cathedra/ Charch» or the like, it genlerallf 
^emi nearer to them^ than they after waifds find it to be. 

Chap. 7. 'Of Objeas,^f. 83 

the Eye as from a real Obje<a in that Place, 
and therefore the Objcdl AB will appear there, 
as the Proportion aflerts. . But we are fo little 
accuftomed to fee Objeds in this Manner, that 
it is very difficult to perceive the Image with 
one Eye ; but if both Eyes are fituated in fuch 
a Manner, that Rays flovjririg from each Point 
of the Image may enter both, as at G and H, 
and we dired our optic Axes to the Image, 'tis 
eafy to be perceived. 

If the Eye be fituated in a or h^ or very near 
them on either Side, the Objecft appears exceed- 
ingly confiifed, mz. if at d^ the Rays which 
proceed from the fame Point of theObjeft con- 
verge fo very much, and if at ^, they diverge 
fo much, that they cannot be coUedled together 
opon the Retina ; but fall upon it as if they 
were the Axes of fo many diftind Pencils com- 
ing through every Point of the Lem 5 where- 
fore little more than one fingle Point of the 
Objeft is feen at a Time, and that appears all* 
oyer the Lem ; from whence nothing but 
Confufion arifcs. 

. If theX^«^ be fo large that both Eyes may 
be applied to it, as in i& and^, the Objeft will 
appear double ; for 'tis evident fi-om the Figure j 
that the Rays which enter the Eye at h from 
either Extremity of the Objedt A or B, do not 
proceed as from the fame Point with that from 
whence thofe which enter the other at k fcem 
to flow } the Mind therefore is here deceived, 

L and 

84 Of the App«firame Part HI 

and looks upon the Objed ^ ^tutted in two 
different Places, and therelbrc judges it to be 

Prop. V. An Ol^eQ feen through a concave 
I^iM appears nearer ^ fmaikty and kis bright^ 
than with the linked Eye. 

Thus, let AB {JFi^. 41.) b^ the Objed, CD 
the PupU oi zfi Eye, ancJ EF the Lens; Now, 
as it is th« Property of a Lem oi this F«o^ 
to render diverging Rays more fo, and converg«T 
ing ones left fo^ the diverging Rays GH, Gl, 
proceeding from the Point G, will be made to 
diverge more, and fo to enter the Eye as from 
fome nearer Pointy: J and the Rays AH, Bit 
which converge, will be Jtnade to converge Icls, 
and to enter the Eye as frdru the Poiniss a and 
b ; wherefore the Objedt will appear in the ^ 
tuation agby lefs and nearer thati without the 
Lens. Farther, as the Riys whkh proceed 
fi-om G, are rendered more diverging, fame of 
them will be made to pafs by the Pupil of the 
Eye, which otherwife would have entered it, 
and therefore each Point of the Obje^ will ap-* 
|)ear lefs bright *• 

Prop. VI, 

* From what has been obfervjSid about the Properties of CQfi<> 
vex and concave Lenfesy we may fee the keafon why the for- 
mer Sort are nvide Ufe of by old Peapk to help tfadr Sight ; 
and the latter by thoie who are purblitMU Old TeQfk^ a& wai 
obferve4 before, having the Tunica Cornea of their Eyes too 
JUty require that the ObjeA be placed at a greater Diftance 
from them^ than other People whofe Eyes are of a joft Fonp, 
that the Rays which en(er the Pupils of their Eyes from the 


Chap. J. Of Objcas/^r^ 85 

Prop. VL An ObjeA fccn through a polygon 
mus Gh.% that is, fuch as is tferitiiiiated by 
feveral plain Surfeces, is multiplied thereby. 

For Inftance, let A {Figi 4a.) be an Ob- 
jedfc^ and BC a polygonous Glafs terminated by 
the plain Surfaces BD, DE, &c. and let the 
Sitiiadoo of the Eye P be fach^ that the Ray$ 
ABbeiAg refraded in paffing through the 01a&, 
Iday enter it in the Dkedion BF, and the Rays 
AC in the Direfiion GF, Then will the Eye 
by means of the former, fee the Objedt in G» 
•fid by the ktter in H ; and bj means of the 
Rays AI^ the Object will appe&r alfo in its 
l&'Ojper Situation A^ 

Thus much for the Principles of Di$pfficii 
todtheSoIutioa offome ckifvioMs Pb^enomena 
Whidh tend to confirm the £Mne : Thofe which 
yet remain to be accounted for, ihall, acootd- 
kig to the Method we have hitherto obferved^ 
be treated of in the Differtations of this Part. 

fiune Pokt of the OhjeSt, may not diverge too mach. Now 
a convex Lens makes thofe Rays diverge leCs, as they would 
. naturally do if the Obje£^ was placed f;iirther off. Again, 
dioie who are purbiind^ having the Tunica Cornea too protu- 
berant, require foch a Lin9^ as may render thoib.Rays more di<* 
verging, left they flioutd be colleded into their Yefpedive Foci 
before they M upon the Ritina ; and therefore £#/k/?/ of th« 
concave Sort are of Ufe to them. 

h z D I S» 

86 Of the. HorizQQUl Moon. Part IIL 


Of the Horizontal Moon. 

THE Pbantmenm of iho* borizmtat 
Moon is this : When the Moon is 
juft above the Surface of the Earth, 
either immediately after (he is rifeo, or jaft 
before fhe fet«y (he appears four or five Times 
;reater in Diameter, than virhen (he is in 
ter Meridian Altitude : And yet her appa* 
rent Diameter, if taken by an Inftrumen^ is 
found to fubtend the fame Angle in either Si- 
tuation *. 

The Moon's apparent Diameter being found 
to fubtend the fame Angle, whether ihe be in 
the Horizon or Meridi^, it is evident the 
Image of her preceded upon the Retina of an 
Eye, is of the fame Dimenfions in either Cafe ; 
and therefore that (he (hould appear of a dif- 
ferent Magnitude in one Situation from what 

* What is fald here of the Moon^s Diameter, as taken by an 
Infirument, muSt be underftood of her horizMtal Diameter, and 
not of her *vertkal one, for the Length of this is dimini(hed by 
Kefraaion (as explained Chap. VII. Note the firft) and» 
therefore, if it be taken by an Inftrument, it will not be fojund 
to fubtend the fame Angle in the Horizon as in the Meridian : 
But nocwithdanding this, it appears longer to the naked Eye 
when in the former, than in the latter Situation^ as well as 
the horizontal Diameter, 

DiiTert. i. O/'/ifi^ Horizontal Mobn. 8j 

ihe does in the other, has always been Matter 
of great Speculation among the Connoijeurs 
both in Optics and jljlronomy. Des Cartes 
was of Opinion, that we think the Moon 
larger when (he is in the Horizon, than when 
fhe is in the Meridian, becaufe in the former, 
Cafe by comparing her Diftance with that of 
interpofedObjeds, we imagine it greater than 
when (he is elevated : And that as we judge 
her Diftance greater in that Situation, we of 
Courfe think her Diameter longer, becaufe it 
fubtends the fame Angle' in either Cafe. But 
more of this by and by, when we come to 
the Explication Dr. Wallis has given of this 

G^W//i was of Opinion, that becaufe the 
Moon appears lefs bright when in the Horizon 
than in the Meridian, we view her in the for- 
mer Situation with a larger Pupil, than we do 
in the latter ; and from thence he concludes, 
that the Image of her upon the Retina muft be 
larger. But this is contrary to the Laws of 
Optics ; for if the refra<ftive Power of the Hu- 
mours of the Eye collefts the Rays of the fe- 
veral Pencils into their refpeiftive Foci upon . 
the Retina (and there is no Reafon to fuppofe 
the contrary in this Cafe) the Breadth of the ' 
Pupil makes no Alteration in the Magnitude 
of the Image j becaufe the Situation of thofe 
Foci is determined by the ^es of the feveral 
Pencils^ which crofling each other in the Cen- 

88 Of the Hotizontal Moon. FiartllL 

ter of the Pupil (as was ihewn Chap. VI« pag. 
6i. in the Note) pais on to the £uxie Points 
of the Retina^ whether the Pupil be broad or 

MoUneax in the Philofophica! Tranfadions 
No. 187. tells us of a certain French Ahbi^ 
that revived the forementioned SuMofition of 
GaJJfendus^ and adding two others of his owo^ 
cndeavoiu^ to account for this Pbanomemn. 
His Suppofitions were thefe, viz.- *' That this 
'* contrading and enlarging the PujhI (fop* 
ofed by Gaffendus) caufeth a difierent 
hape in the Eye ; an open Pupil making 
^' the Cryflalline flatter, and the Eye longer^ 
*^ and the narrower Pupil fliortening the "EjCf 
and nuking the Cryftalline HuRK>ur more 
convex. The firft attends our looking at 
Obje<3s that are remote, or which we think 
fo, the latter accompanies the viewing Ob- 
y^Gt^ nigh at Hand. Like wife an open Fu-^ 
pil and flat Cryflalline attends Ob^eds ei 
a more fedate Light, wfailft Object of more 
forcible Rays require a greater Convexity, 
and narrower Pupil. From thefe Pofltions, 
'^ continues MalineuXy the ^^A/ endeavoured 
to give an Account of our Tbanomemnj as 
foUovrs. When the Moon is high the Ho* \ 
rizon, by Comparifbn with intcrpofed Ob« 
je€ts, we are apt to imagine her much far^ 
^ ther from us than when more elevated, and 
*' therefore we order our Eyes as for viewing 

** an 






Difiert. i. 0/^i^ Horizontal Moon. 8 9 

^' an Objed farther irom as ; that is, we fome^ 
^ thing enlarge the PupiU &nd thereby make 
^^ the Cryftailine flatter $ moreover the Du& 
^' kifhnefs of the Moon in that Pofture does 
not fb much ftrain the Sight ; and conie^ 
quently the Pupil will be more large, and 
^^ the Cryftailine more flat ; " hence a larger 
** Image fhall be pro^eded on the Fund of the 
w<< Eye, and, therefore, the Moon ihall appear 
^* larger. Thefe two foremenrioncd Accident^, 
** viz. the Moon's imaginary Diilance and 
^^ X^uikifhnefs gradually vanidiiDg as fhe rifegr, 
^ a different Species is herdby introduced in 
^* die Eye, arid confeqoently (he feems gradu- 
'* ally lefs and leis, till again fhe approaches 
^* nigh the Hotizon/* 

As to what is taken for granted in this So- 
lotion concerning a Change in the Cryftailine 
Humour and Form of the Eye, upon viewing 
an Objedt in a /lujky or faint Light, that feem's 
to be very ill grounded. We know of ho fuch 
Cohned:ion between the Mufcles of the Jns 
and thofe of the Ligamenta Oiliaria^ as h 
neceifary to produce this EfFe£t. And the 
Coats of the Eye are not fo pliable, as cafily 
to admit of an Alteration in their Fwm ♦. 
Could the Author have made good his other 

Suppoiition, viz. That by Comparijbn with 


* See what has been obferved concerning the Power we have 
of making an Alteration in the E/e, in order to fee Mftinffljm 
(Chap. VI. pag. 62.) 


90 Of the HonzoTital Moan. Part lit. 

interpofed Oi/eBs we are apt to imagine ber 
muA farther frtm us, tkan when more ek^ 
vated, he need not have had Recourfe to any 
other ; this alone would have been fuffident ; 
but bic Labor efi. This alone, I fay, would 
have been fufiicient ; for if by comparing her 
Diftance with that of interpofed Objeds, we 
imagine it greater when (he is in the Horizon, 
than when Ihe is in the Meridian ; as (he inb- 
tends an equal Angle in both Cafes, we muft 
in Confequence thereof (agreeably to Dei 
Cartes's Notion above-mentioned) imagine 
her to be bigger in the former Situation than 
in the latter ; becaufe a diftant Objed cannot 
fubtend the fame Angle at the Eye that one 
which is nearer does, unlefs it be proportion- 
ably larger *. 

. The famous Hobbs endeavoured at a Solu- 
tion of this Pb^enomenony but it is hardly 
worth mentioning : The Figure he has drawn 
Co explain his Solution by, feems to have 
been the Occafion of his Error. He draws a 
Circle to reprefent that blue Sur&ce common- 
ly called the Sky, in which the heavenly Bo- 
dies feem to be fixed, and concentric to this, 
a leiler, to reprefent the Surface of the Earth, 
but vailly too big in Proportion ; fo that a 
Spectator upon the Surface, of this Earth, is 
confiderably nearer to the upper Part of the 

• Sec Chap. VI. pag. ji\ 


DK&Tt I. 0/the Horizontal Moon. 91 , 

ether Circle than to the Sides of it : Where- 
fore an Objed that fubtends the fame Angle at 
different Heights muft neceffarily hide a great- 
er Portion of that Ark when^ it is in the Hori- 
zon, than when it is in the Meridian j bccaufe 
that Ark is farther behind the Objcft in the 
former than in the latter Situation ; from 
whence he concludes that the Moon muft ap- 
pear bigger in that Situation than in the Me* 
ridian. Had he drawn his Circles in any tole- 
rable Proportion to that which he dcfigned 
them to reprefent, he would eafily have fcen 
his Miftake* 

A few Years ago Mr. De Veil publifhed a 
Trtatife upon the Subjcft of the horizontal 
Moon^ wnich he dedicate^ to the Ladies of 
Ntfrtbampton. If I remember right, his Solu- 
tion of if^sR m the fallowing Manner : 1. 
When an Objedt is placed beyond the Focus of 
parallel Rays of a convex Lens^ the farther 
the Eye (fituated on the other Side the Lens) 
recedes from it towards the Fcfcus of flie Rays 
which flow from that Object, the larger that 
Objeft appears. 2. Rays of Light flowing 
from the Moon, and paffing thro' the Atmo-- 
Jpbere of the Earthy are colleftcd into a Focus 
on the other Side of it. 3. When the Moon 
is in the Horizon, we are nearer to this Focus 
by almofll a Semiiameier of the Earth, than 
when (he Is in the Meridian : And therefore, 
the Moon ought to appear larger when in the 
former than in^the latter Situation. 

M The 

92 Of the Horizontal Mooh.T 

The PcopofitioDsiii this Solution are all true, 
but the Se^nd is not applicable in thf prefent 
Cafe ; for unlefs we confider theRefra<^ion that 
Rays of Light which flow from the MooQ,gnd 
pafs through the Atmofphere of the Earth, 
fuffcr in their Emerfion, that is, while they 
pafs through the latter half of ; it, as well as 
that which they fuffer in their Immerfion, or 
while they pafs through the former half, we 
ihall find that they will not be colleded into 
their reipedtive Foci on the other Side the 
Earth, as this Gentleman imagines : Which if 
it can be (hewn, his Solution falls to the Ground 
of Courfe j for the RefmAion which the Rays 
fuffer in their Em^riion is not to be , taken into 
Coniideration, becaufe they reach the Eye of 
g Spectator upon the Earth as ibon as they 
have paflfcd through the .firft . half of * the At- 
mofphere, when the A^oon ;is in Jt^is Horizon ; 
and before they have paiTed through that half, 
when iht is in his Meridian. 

Let us then imagine two Rays flowing from 
one and the fame Point of the Surface of the 


Moon, it being neceiflary in order to conftitute 
a Focus that fuch Rays jliould after Refraftion 
meet in a Point 5 the Meeting of fuch as flow 
from different Points in the fame Surfiice is not 
iufficient ; if it were, we might then have Foci 
where we pleafed, and that as well without 
refra(3:ing or refledling Surfaces as with them. 
And let the firft of thfofetwo Rays fall perpendi- 
cularly upon the ij^^tmofphere of the Earthed 

{/ be 

be 'fuppfidldlb pft& tbroi:^ the Center of it 1 
and. let the other after Refradion pa& by thQ 
Surface! aflthc-^Earth; Now, the Moon's P^- 
rallaxy thsatda, the Angle under whiditheSe^ 
mkliameterbfethe Earth 'is^feen from the Moon, 
being about rOkOe Degree^ it is evident that thefe 
Rays ixKifcl^, <. before their Incidence upon thtf 
Earth'5 Atoaofphere, diverge the one frcwi. the 
other . by i&ch?afl. Angle.' -; But it appears, froni 
Sir IfaatiN€ficivn'$ Tabie df Rcfraftioiis pub- , 
iifced by'Dr!. Halleyi inthe PhilofophicalTraof- 
gjiSionSj N0.3 6(8, that^ iwhen any bi the hes%'Qn-p 
ly.Bodtfca-^gyeaPS ih the I^orkon, the Rays by 
^hkhit iftifetfn, are refraded but by in Angle 
ci thic£y-tbr.ijetMinujtea anc} .forty^five Seconds; 
and therefo^thfi; Rayi which we haver fiirppofed 
after Ris^ficafficHi t4.[^:by the Surface of the 
Earth will be refradled only by fucH ah An- 
gle ; 1 which i&llifl^g cohiiderably fhoit of one 
Dc^reeV-the Jingle diverged fronti, 
the^perpendrtiiiar one before Refradion V it w^Hi 
beJfo &^;frQm:being made to^converge towards 
it there1^9.:that it will Aill be in a Slate of 
Divcrgericjr fcdmj it. And ihcrcfcre Rays ^6 w- 
ing from^fttieMoon apdfej^£l;ed only, in their 
Immerfiofii into thie Atoio^^ere of the Earth, 
will .not he:OoUe£ted kita their refpcftive Foci 
on the:oth» Side : Which was to be ;fhewn. 
; iDr^ff^aiiis'm the PhilofopbicalTranfadtions, 
Na ^w%>. a^obrtioip qi the horiasontal 
Moon (or rather an Explication of what Des 
Chrles had gfven bcfofe) vfrhich is as foUpwsj; 
. '1 ^» M 2 He 

94 0//iS« Horizontal Moon* Part Hi 

He afoibes tliis Phammemm to the Deception 
of the Iii^ginatiQn> and accountB for that De« 
ception in the following Manner. Heobfervesr 
Firft, that the Imaginktioti d^ not eftimate 
the Greatnefs of an Ofa^d ieen» bjr the oftit 
Ai^le only, bat by this cooipflored with the 
fiippofed Diftance« So that if two Things are 
leen under the fame or eqaal A^^es^ and if» 
upon any Account whatevcr,,we apptebend one 
of tfaefe to be £iitber irotti us t]:»n the other^ 
that which we appreiietdi to be &cth^ fi-om 
aiSy will -to the Ism^fnatbn appear gres^er^ 
Sdcondly» That one great Advantage fos efti* 
mating the apparent Diflance of aay Things 
18 froaa the Variety o£ inlernfiediate^ Qb^ds 
betweca the Eye and the .Thing feen ^ foi 
then the Iihagination inuft allow Room for all 
thofe Things. . . - 

^< Now, fays he, when^tbe Sun ^ or Moon 
is r^ar the Horizoh/tbc Plrofpb(f)r ^e Jbave of 
Hill^iand Vallies, Plains antt^ Woo^s, ^c. 
cepr^fent^o our ioiaginactioh a great Di* 
ftan€e> capable of receiving ail th^; Xk^H 
it happens that thefe interpofed Objeds are 
not adually feen> yet, having . been accu^ 
'{lomed to kt. th€m,r the Memory &i^eils to 
us a View as large as is the vifibie Horizon. : 
<^ But when the Sun 'or Moon is in an hig^ 
er Pofiftion^ we fee nothing between us and 
thenr (unle&, peifhaps, fome Cloudis) and 

. * For tl^ Sun appean Urger in the Borixon, as well as th^^ 
Moon. " • 

** thCEC* 



Diflbt. • 1 . 0/iie Horizontal Moon. 95 

'^ therefcn. nothing ithat can prdent to oat 
^' Imagtrntioii fb greata.Diftance as the other 

k. ibut therefore, Jt^fflugh both be fwn im« 

dertkeifanie Angle,, they, do not appear (ta 
^^ the Imagination) of the fame Bignefs, be^ 
^^ caufe. Bot fanfied at the &me Diftance : Bat 
^^ thatiKar the HodboDis judged bigger (be<f^ 
'* caiafe iiip^ofed iatther off ) than dhec£une> 
•* wfaeniat a greater Altitude/^ .1 

If I migJadLhQ alio wed .t;D citentbn any iHung 
ef my ^own, after the& great Geniu^s. have 
given tfaetr Opinions upon this I^tter^it!ihouki 
be thisy'^ visi. That I hoise ofiten thought^, . that 
he wbo't^uld give oj ilational A€x:oiuit^ ^hy 
the Sun or Mcob: appear^ farther from os in thie 
Horizon than in the Meridian (forthatisail 
thatis i^e^ttifite, towards a Sdlntion of the ho^ 
rijiK)intal^oon,,: as has been already obferved) 
ihouid firfl ihow why that apparent aatire 
Surface we call the Sky » does not ieem to be 
an entire c6ncSLVC Hemifpbere^ but only a Por- 
tion of fuch an one: For our judging the Jlca^ 
vens to be na more than fuch a Portion, is un« 
doubtcdly the Caufe why we judge both the 
$un. Moon, and Stars to be farther from us 
when in the Horizon than in the Meridian ; 
bccaufc we have nothing elfe we can refer 
their Places to, but that. 

Now, poflibly, the Caufe why we think the 
Heavens of that Form may after all be only 
this, viz. That, as the Rays which come from 
the upper Parts of that imaginary Surface, the 


^6 /Of the Hotizontal Moon^Partlll^ 

filcy, t>afs through a )dk Portion of the Atmo^ 
^bere than fuchas come from the horizontal 
Parts of it, the Sky appears tb^v&iaocJtdijiinB'' 
fy^ and generally, more itn^i^/ intho&.Part$ 
than, in Bie latter; mA> therefore,' fince we 
daily ob&rve that didfe ObjeOs whkh^ appear 
moftidfftinB 2Xt'^^^ tucti '^zssm nearefi 
lto\us,c atid.alib a^ ^rigJk Objeds, when we 
have nothing but Hare imagination' to deter- 
puhedis in effimatmg^ the Diftahce of them, 
Bppiar. nearer to us tlian the iame Objedb 
whonilel^ fb *, we think the upper J^uts of 
tiBkt.S\if nearer ut than the lower. : Where- 
1f(Av^ ^nce:w^ieferidLtheheavehly Bodies to 
this iSunfeoe, we iieceflarily imagine them far-* 
iheri £rbm us, and confequentty larger, and 
$i& ontoib diftant from each other *f , when 
oartfite'Horizon, tfaaii when th^ are arrived 
tt their meridian^ Altitude. . . 

Vl f,. 

• •' .♦ *■ 

• ^ 8e^ wlut Jim bfeo £ud ^oncm^ tke Brig^tiidf of m 

Obj^^beinga Means. 'whereby it appears ne$u«r as, undec 
Tixip.'j. of ihe 7th Chtptet.' t * 
• . f; The uppa^^t Aomooul Ptftaiice of two $(«» ftom one 
^noche;- is obferved to be {r^atcr^yvi^eo they aie in the tibrixoD^ 
than in the Meridian. " ' 

' . - - OCT 201921-'