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157
\153
■s^ V
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■^
<* .9
\
r
• I
Compendious System
o p
Natural Philofophy.
With NOTES,
• • "••
I
I MATttEMAtlCAL DEMONSTRATIONS,
A « »
Some Occafional R e m a A k is.
■iSit.
«- -•■»
III Four PARTS.
VOL. I.
- » * • m
mmmmi^mtmmmmmtmmmmmimmiltmmtmmm
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
LONDON,
I Printed f^r Sam. Harding, on the Pavement in
f St. Marlines Lane. 1753.
« / r
$
1 . > r #
^ ■ •
t
. . >
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t^^mm^^md^^mimakmm^mmmmimammmm^mimmmmmmmmm^^^mmmammmm^mmmm^tmmi^
THE
PREFACE.
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
38273Q
ii PREFACE.
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.
9
t
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-
lowed
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
\
P RE FA C E. V
in Bodies^ whereby in fame Qafes they
endeavour to . avoidy or fly from each
other.
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,
it
viii PREPACK
// 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
Pendulums,
\
"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.
•s
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
wbichy
PREFACE, xi
^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
time,
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
xiv PREFACE.
^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
1
PREFACE. XT
• • • «
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-
tbci:.
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,
and
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 ,
s
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
1
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
Tribe,
%
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
"^
PREFACE. xii
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
Propofition*
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
\,.
PREFACE. xxi
Hence an Idea of the different Re-
frangibility of the Rays of Light;
P R O POSITION IX.
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.
Proposition
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.
Hence
PREFACE. xxiu
Henct the Solution of the Phamo-
mena of Bodies deiixading on incliqi-
ed Planes, and the Vibration of Pen-
dulums.
I
r
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.
From
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
PREFACE. XXV
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.
Departure
I>*
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
Bodiest
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,
than
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
likewife
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,
and
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
Part,
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 fubfi.de, 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 :
then
PREFACE. XXXV
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
will
PREFACE. xxxvii
will overpoife it, whatever Dimenfions,
as to their Baies, we fuppofe them to
be o£ .
9
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
forwards^
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,
There
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
below.
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
xl PREFACE
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
one
PREFACE. xli
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.
"V
xliii
THE
CONTENTS.
PART I.
Mechanics.
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«
eUidy
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
Ckap.
contents: ixlY
'CtiAt. Vih OfthiAfpi&fmct\f.'Qhjia$fitn tiraugk
Afedia of different Forms^ • j.%
PllTertation I. OfikeHorhonialMo9H^ 86
OlAf. Vin. Of fb0 Manner whetein Light is refleaiiy<)j
€ii^A>. IX. Of fht R£fte£ii9n sf Light frm plain and
fphertciil Skffaees^ lOo
CtiAP. X, Of fUe Jfypearance of Bodies feen by Light r^
^ fisihd friMfhin and fm . n8 /
<>rAP. XL Vf the different Refrangtbility in the Rays tf
• . ^ Light \ of4he> Colours the dJ/iinii Species of them
/ are difpofed to excite ; and of the Haufe of that Va^-
^''^' riety of Colours which is obfii^aUeih Bodies^ '34
Cm A P. XII. Of the Ratifications in Bodies^ which dif^
pofethem to reflM the Rays of different Colmrsy I4)r
€itAp. XIIL OftheCaufeofCfpacityandTranfparenCy
in Bodies^ * 15^
rlHflert. II. Of the Caufe of Rifraahn of LigU^ 158
'Diflert. III. Of Mierofcopes and Telefcopes^ 169
'Diffeit. IV. Of the Rainhoto^ ' 18^
Qfthe Qbfcura Camera^ and the Migic Lantern^ 9, im
P A R T IV.
Astronomy.
the Introduaiony P^ 3
Chapter I. Of the Bodies which compofe the Solar Syf
tenty and their real Motion^ 1 1
Chap. II. Of the fixed Stars^ 25
£haP^ III. Of fuch of the apparent Motions of the hea^
venly Bodies^ as arifefrom the Motion of the Earth
about its Axis^ 33
Chap. IV. Of the apparent Motion of the Sun arifing
from the EartVs revolving about itp 35
Chap. V. Of the Earth* s annual Parallax^ the Nutation
Xth^ Poksy and tb$ Preceffton of the EquinoSfial
ints^ 5^ -
Chap,
I
1
\
xlvi CONTENTS.
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^
147
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,
THE
Compendious Ststem
O F
Natural Phflofophy.
With NOTES
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*
And
72i« Mechanical Powers*
mmmmmmmi^mmmmmmmm^mmmmmmmmm^mmmmmmmmmmammmmmmmmmmmmmmmimmm-
CAMBRIDQB,
Footed at the UNxyERsiTT;F»if«i'
MDcaoQuy.
\
*^ .>
f
. i
r •
I
, ; » I.
^ 41.
1
^T
» '
•' i
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%
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• . I -• >.
« ." . .'-
• ♦ »
'^
Compendious Systeac
O f
< <
Natural Philofopby.
PART L
. » * • •
The INTRODUCTION.
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
^ The INTRODUCTION.
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.
pofition
.We INTR D U€TJON. 3
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.
Grft
by
tris,
&c.
[ual
on-
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-
fonms
6 The IlfTRODUCTJON.
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.
CHAP.
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>
Extcnfion-
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-
fiblc.
. *. 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, and.tl^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,
How
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
Water:}:.
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
t
• 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 ..'.:...
I
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.
that
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
/
C HA P, III.
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'
furfaces
/
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
Princip.
f Dm* Let there be a Body ^ P, (Fig. 2. J placed any where
withiti
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>.
ing
I
\
itirg; itt<Ual 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*
rate*,
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«
glafs
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.
CHAP. IV.
Of the Lanios of Motion commonly cal-
led Sir Ifaac Newton'x Laws of Na-
ture.
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
upon
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
fo:i
/■
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.
float
' {
I
I
I
.
'-<l
<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.
fen-
^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.
. CHAP. VL
Of the defcent of Bodies on oblique
P lanes y and of Pendulums.
w
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,
lerated
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
I*
^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-
X.
1
J^
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-
duluo).
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^
dulum.
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 $• 7.) ' ii^ ^^^ manner the time B vibrates in, is
that in which a Body would fall through FB, Now the timet
in which Bodies fall through differeBt fpaces are as the iquare
loots of thofe fpaces, that is;^ o^DJ andl FB9 oi of therr baivM
CA^siACBt <- ^* of the lengths of the Pendulums. ^ E* />•
t The Rule fw finding the Center of Ofcilktion.
If theGlobe AB (Fig. 1 1 . J be hung by the llring CD, whole
weight b inconfiderable, the Center of Ofciliatlon is found thus;
ftp-
\
34 Ttndutufns* Pkrt t,
wheftce the length of a Pendulam fe mea-
fur'd, V^hich ill our. Latitude, in a l*endu-
lum thdt.fvt^ings Seconds, i$ }#. 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. $. 4); and as the gravity when
the tinae is given (for the Turn of the velocities produced in any
time will always be as the generating forces) : confoqucntly
when ndthcr is given, they are in a ratio compounded of both ;
the fquares of the times are therefore inverfly . as the gravities-
{Far if in 3 (pumtities a, b, c 5 a i^dshc, thin b : - , i< e: ^ a is
c
gi'ven, as — or as c inn)efj!y,'] But if the fquares of* the times in
' which Bodies fall throx^h given fpacea are iftvertfy^ atf ebe gra-
vities by which thnr are adled upon ; then ^e (^u«ffis erf the
times in which 'PenduhuBs of equal lengths, perform l^dir vibra-
tions, will be alfo in the f^me rfttio, on accour^ of tbe conltMt equii-
Jity between the thne of the vifc^ration of a Pendieiliini, and of the
4lefcent of a Body through eight times its length ($< 12*)
From
\
I
V
i***
^ 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.
CHAP. VIL
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.}
1
I
a
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
QHq,
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
MJq
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
\NKq
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
AH IK
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^
AEq
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
JEq
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
AEa
and dividingbdth fides of the equation by EKy AB^ -^r- . Q^. D.
Alq
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 (Fig.tj.j
.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.
IV- Ttic hcigjit a.Body wMl flfe.to, wfa«ii
thrown perpendicularly upward?* |s sq^I.tp
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. » "
heights
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
have
h
^
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. v.fj^.
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
down.
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
made.
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.
GHAP.
4^ CefUral Forces^' Pdit'li
G H A F; Viu;
9
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
r
)
(
A
I
\
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-
ftratcd.
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.
From
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
motion*.
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^ £, />,
Other
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.
CHAP. IX.
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. > \
Br
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-
ing
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
will
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*
vii;
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-
termine;
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
ftroke.
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
Bodies.
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 '
il
■ 1
J
1
(
t
Qlazp. 10. Mechanical Powers. 53.
CHAP. X-
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
other.
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.
quan-^
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>
mucb
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
Axis,
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
of
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«
III. The PuLLBY.
XIV. A Pulley is an Inftrument compofed
of one or more Wheels moveable on their
Axes.
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*
Power
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,
,1
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*
Crave-
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
i
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
cxprel^
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 "^ '
N
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.
as
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
-£9
«<
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
and
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
', ■ ^^
( I ) ■
AppENDixto Part L
i» * '■■''■ " ifii
CHAP. I.
Of the Vibration of a Pendulum in a
Cycloid.
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.
LEMMA ^.
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^
3
PL : LD : : DM
LD=MN
MT.
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.)
5
7
8
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.
Secondly^
Appendix to Part L
lO
II
LD : DM : : DP : DX
DX=:XB
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
Steps
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,
LEMMA XL
•
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
Diameter.
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
Piopofition
Comparing the firft and
fecond
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 A.X.in with
the laft acquired Velocity^
AB is to AX.
aa
Axiom
Appbnoix to Part I.
Axiom
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.
LEMMA III.
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.
Comparing
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.
LEMMA IV.
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
I
2
3
4
5
6
7
8
9
10
KG=:CI
KI = CG
KI = DF
CG = DF
The Arch CF = AF
The Arch CF c= DG
AF = DG ,
AFD = DGX
FD = GX
CG = GX. Q^E.D,
LEMMA V.
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
CH
I
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.
LEMMA VI.
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.
LEMMA VIL
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
be
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.
Time
ff
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
Ufe.
LEMMA VIII.
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^
Diameter.
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
con^pared
laft
By Part
i7-
L Chap. 5
Comparing the 4th and
5th
2
3
Appendix to Part L 1 1
PROBLEM.
To make a Pendulum vibrate in a given
Cycloid.
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,
that
Comparing the thret
lad Steps
Doubling the Antece-
dents of the laft Step
8
10
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
Diameter.
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).
CHAP.
(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
toDX)
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
Figure
From the lait compared with the
Figure
Comparin^j; th^ lafi with the Fi-
gure
3
4
7
8
AC=2 AE
2 AE = CX
^C = CX
CTP = CX
f AC = CTP
AT=:TP
GA is parallel to TK
GT is parallel to AK
9
10
II
12
3
f4
«S
16
1
GA=TTK,andGT=:AK;
GA = ^ TA
TK = I TA
TK=fTP
TK = KP
The parallel Lines GT
and Pfj are equally dif-
tant from AD
The Arch GA =: the
ArchDH
The Chords GA and DH
are parallel, andG£=
HX. From
Appendix to Part h 13
CHAR II.
0/ the Center of Ofcillation and P?r-#
cuffion.
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
Separate.
The Toint or Center^ of Sufpenfion is the
Point on which the Pendulum hangs.
jti general Rule for finding the Center (f
Ofcillation.
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.
be
KD = PH
GT =3 the Arch AG
AK ;7 the Arch AG
AKD = AGE
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-
flexible
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
III I X PN
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,
confeqttently
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
thing
3
5
IXPNXiCssLxMRXLC
PN:MR::PY:RY
IXPY:I^IC=LXRYXLC
P«PYXPC=RXRYXRQ
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.
rotiild
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
PROBLEM.
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-
tent
'
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 ^
An
^'
.i
n
* < • <
* \ >
s
r»
I
r
II
i
1
A
uOMPENDIOUS 'StSTEM
/
O F
Natural Philofophy.
With NOTES
0)ntaining theMATHEMAxrcAf
Demonstra tions and fbme
occafional R £ m a r £: s.
PART II.
HYDROSTATICS
And
PNEUMATICS;
To which arc added fome DissERTATioWf
relating to thcfe Subjcds.
•***i
C A M B K I t>^G E.
Printed at the Universitv-Pre««^
MDCCXXXV.
• I
i
r, ■..
,' t I
CoMP EN PIOUS System
O F
Natural Philofophv
1
•
'^ . 'M ' * - •^ M
¥
PART It.
Hydrostatics.
t
1
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--
1
• 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
i«pcl
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-
tra<3:ion.
' * • ,
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
Avtrc
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.
fiains
^ "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
Vlll.
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.
pen-
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
-I
\:
I
! 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
fame.
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.
©f
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
tho
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
Place.
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
agAinft
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,
of
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
propox;-
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.
XII
1
p
.;
4
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
Depths.
which
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*
*
I.nr^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\
IIL
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,
as
\
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.
Fluid)
r
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-
caufc
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.
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.
Bafc
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 ,
U'
E *. ym;
•ftu'
•.*■
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 expands.it 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,
that
i
II
ii
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
I
^
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
Miles.
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
Force
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
Diameter.
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.
that
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
Eighty;
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.
r
CHAP. IV.
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.
Rcfift-
^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.
DISSER
DIffeit. I. Of Sound, 47
DISSERTATION I.
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-
grefs.
Thus
I
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
^ifh
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.
bcr
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 obferved.to 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
Trumpet,
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
m
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. ,
however
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
'longer.
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
Umfon
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
furprifing.
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.
fioi
D4SSER-
Difleit. 2. Of Capillary Tubes* 5 7
DISSERTATION II.
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
Philofoph.
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
dowii*
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.
An4
Pwt.II. Hlte.ln.i^.fo,
r-
":,?.
H^rj^.P.y.
^
B
1
D
o^
4?-
i
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.
the
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,
and
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
Icfler
64 Of Capillary Tubts. Part If*
IclTer Part of the Tube would have raifed
it.
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*
and
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
of
•4
i*'
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
DE.
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«
was
H
i
t
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
Column
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
AM
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
Height.
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«
fluids
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
Glafsf.
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. '
DISSER-
Difiert. 3. T^e Origin of Fountains. 73
DISSERTATION III.
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*
to
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. ^ • .
jjttemptcd
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
Surface
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
Truth.
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
the
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
Springs.
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
over-
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
Adion-
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.
VA
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Compendious SysteSt
OF
Natural Philofbphy^,
With >ra,rES.
1
Containing the M ^t^^ » e ma t i b a C
Demonstrations^ andibme$,
occalional REMiWRKSf
■HMMMMl
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^
t;
*
*
» r —
• ♦
♦ I
i
• - * «
T t •- .
■
3piffert4* Of the Sardmetcr, 8 J V^
DISSERTATION IV.
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.
In
* 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
hence
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
once
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
Co-
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
of.
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-
tiom
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.
"In
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
cc
*' con-
I
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
((
eft
i<
(C
4<
4C
CC
CC
CC
cc
cC
cc
cc
cc
cc
>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
4C
C4
i4
C€
Ci
€C
CC
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
Si
u
<i
iC
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,
<c
I
cc
cc
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
^i<
cury
^ 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
'1
CC
fi
Di(reit.4. Of the Bttrwieter. 97
for on the feme Principles with thofe t>f Dr^
Halley.
** !• 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.
\'
c<
8. The
d(
Cft
C€
€C
C(
<c
cc
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
ik&aiS
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
Pa
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,
*wer«
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.
But
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
r
1 06 Of the Barometer. Part II.
at both £nd$3 that none of the Fluid may get
in.
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
* 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.
fts
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
i
J
w
I-
i.i
^
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,
by
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
dv
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
dv
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 ;
ns
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^ ^
was
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 "^^
That
* 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
X
be — and confequently GE, the Pifference of the Legs EK and
X
KB, will vary ^H-r-. Again, the Variation of the Sur&ce of
ad
the Mercury at B will be the iame with that of the Water in the
fame Place, viz. ■— ; and, iftheTubcis ofthefame Dlametet
da
at D, as at B, the Variation of the Surface at D will alio be the
X
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
da
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
itit
1 1 a Of the Barometer. Part IL
That the Variation in this Barometer may
fce infinite, may be fliewn in the following
Manner.
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
tundJ
tliecommon Method of Reduft ion, *= — • That is, x 1
zm-^ddr^i
« :: 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»
through
y'
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
des
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,
37-
DIS-
1
Differ t. 5. Of the Origin of the Winds. 1 1 5
DISSERTATION V.
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
round*
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
Equator.
1. Under the Equator y the Wind is always
obferved to blow from the Eaft Point *^
For^
* 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-
ing
•' 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
t.
M
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
Air
^^ 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
cc
cc
** 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*
Ci.
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
move
** 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 Afrrc.tn 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
k.4
«(
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.
Some
** 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/««
wUch
«
€€
cc
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
foup4
^..
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
anyi
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
DISSERTATION VI.
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
conceived*
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
lalk,
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^
DifTert.fi. '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
<c
«c
€C
CC
CC
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
gravity
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. '*
Cc
cc
This
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
fug-
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
Qiian-
* 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 )
from
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
Icicles,
** 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^
DISSERTATION VII.
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-
fwe
* See the Theory of Feroiefiution explained la the following
XSiifiertation.
. 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-
ning.
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 *
The
* •
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 *•
I'he
* *• 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
CC
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
black
^ 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,
than
** 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
it)
•* 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-
times
*« 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
Streak
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,
TbU
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.
Imagine
•
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,
titude
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
along.
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 .
alone.
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
Fire.
* 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,
the
I
•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.
be
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.
of
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*
from
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
to
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,'
which
\
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. $.3.
N
1 76 Of Ferrnentatml I^art IL
DISSERTATION Vin.
Of Fermentation4
HAving had Occafion to mention fotne of
the Effefts of Fermentatiori, it may not
be amifs^ before I put an End to thefe Differ^
tations, to add a fhort Account of the Nature
of itj and to fhew how thofe Effefts are pro-
duced by it.
Fermentation is a mutual Commotion of the^
conftituent Particles of Bodies, one among ano-
ther; and arifes from an Inequality in their
Attraiftions of Cohefion. Authors diftinguifti it
into two Kinds ; the one is that which happens
when a Solid is diffolved by a Fluid ,• the other
is^ when two Fluids, being mixed together, fcr*
ment with each other.
Thofe Authors who have treated of the firft
ofthefe, tell us. That to caufe a Fermentation
between a Solid and a Fluid, feveral Circum-
fiances are neceffary. Particularly Dr. friend %
and Ktil t are of Opinion,
I . That the Particles of the Solid muft at-
tract thofe of the Fluid with a greater Force,
than the Particles of the Fluid attract one
another.
*• See his Chemical Leftures.
t S^ hU Letter (0 Dr. CotkbUffi^ Df Legtlt$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
i
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
jnore.
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-^
Wpnf
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.
A
Compendious System
O F
Natural Philofophy.
With NOTES
Containing the
Mathematical DemonstrationSj
and
Some Occafional Remarks.
P A R T. III.
OPTICS.
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.
LONDON:
Printed for Sam. Harding, Bookfeller, on the Pave-
ment in St. Martin' %" Lane.
M.dcc.lii.
![ Price One Shilling and Six Pence ]
I
C o MP EN Dious System
o F
Natural Phitofophy.
I*
P A R T. IIL
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.
That
• 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-
nant
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^
r
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
thems
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.
The
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,
CHAP.
Ghap. ll,TheCaufe ofKeda^iony^c. 9
CHAP. IL
>
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
be
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.
Let
Cli^p. 2. the Caufe ^Refi:a^ioh,#^. 1 1
lidt us fiippofe firft, that the Ray pafles
aut.cf 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
denier
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
iffRefraBioti,
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 ^;
To
* 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^iki.to
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
HM
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
Ml
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 $ine of the Aft^ LMI hafc a
given Proportion to the Sine^ of the Angle LIM, or of its Coai-
plement to two right ones MIK (for they have the fajneSihe :)
But LMI bemg an Anglemade by i^e incident lUy GH pt&-
dttced, with the Perpend JGubi: KM, is^hp Angkoflacidaiety
and MIK. being made by^the refra£Ud Ray IK^ and the iaine
Perpendicular, is the Angle of Refradion^ therefore in this
Caie there is a confiant Ratio between the. Sine of the Angle of
Incidence, and that of the Angle of Re£»^iQB«
We have here foppofed that the Force of Attradion is jptery
where oniforiB, batif itbcotberwife, ptovided>ic bethefane
every where at the iame Diftances from ^he Surface AB* the
Proportion between tlie foreinentioned Si^MS will fiiil be A given
one.. JPor, let iis imagine the Space of .A):tva{tioA divided into
parallel Planes, and the Attra^on to be ^t fmf^t ihrou^ Uie
whole Breadth of each Plane though difiasent ia dif^n^ent maa,
the Sine of the Angle of Incidence out of each wil, by what
has been demonftnitcd above, be to th^>Sin0 of the Aagjb
of Refra£Uon into the next in a giyien R^Hh S aiid theiefore,
fince the Sine of the Angle of Refra^^ion odt of one will be
the Sine of the Ang^e of Incidence into the next, it is evident
that the Sine of the Angle of Incident inio the iiril wiUbein
a given Rmti§ to the Sin^ <>f the Angle of Refftftioo ont of
the laft. Now let oa fiippofe the Thklaada of thefe Planes di-
minifhed im infinitwmy and their Number. ipf^orlioBaUy in-
crea&d, the Law of Refradion will ftiU oondviie the fane.;
and theicfore whether the AttraAion befmiforttkor not, dicre
will be a conftant Rati^ between the Sine OJF tie
dence and of Refradio;i« ^E.D,.
Radius
Cb$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,
CHAP.
CHAP. III.
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
Focus.
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.
When
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 ;
ufqm
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
leis.
For
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.
^E.D.
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.
TWs
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*
.All
^ 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^
r
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
EF
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-
nUh.
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
is
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»
IK,
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.
Now
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
tU
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,
and
ihe AngU oflneidence s which Sine the Line FB.tf/ 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
pro-
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-
tion.
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.
Dim*
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
have
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.
Am.
Cfeap.3, 7k Re/r/t0m ^Mghtj^f <r.s I
cpijycrjwig Rl»ys AS, CIX SF {Fig. 7,) pa^
the
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.
Cafi
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-
tivc
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
4
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!
Surface.
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
Surface.
• • • <*
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,
which
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.
For
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
4he
•* 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
Sphere.
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^
<«
(<
u
4*
it
** 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
Kefraftion.
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
lefs.
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
convex
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
them.
XII. If
XII. Jf they diverge^efoce RefiraAion^ them
for the fame Jleafon^ ^Gf oie raade^to ^verge
wove.
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<*
ter
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-
face.
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
I
r
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.
CHAP. IV-
0/*Lenfes, and tbt Manner m wbid
Rays are affeSled in faj}ing through
them,
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,
The
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,
If
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-
fite
1
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
If
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
Re.
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 *.
When
* 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.
I.et 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=
Idr
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
where
^v«
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 $ine of the Angle of tnci*
deace btan the faae Proportion* to the Srne of tihe Ahgid
•f Refradion, that the Sine of the Angle off Refra^ioil
Ajes' teethe Slue of the Angle of Incidence, when they pai^
OfSC of' a nirisr into ef denier. This being obferved, by thei
aforeiaid Propofition^ ive ihall have the Rmtia tioihpottnded of /^
tbi focal Diftance, to ■ ■ ■ * ■■ / > the imaginary Focus ofthi
\dr
kttidtm Raff^ aildo f ; ■« ■ i . « >* — /•f^, the Dijtance iet«wuii
i<f— K!tf*-*Rr
tii imaginary Focus oMdtbe Ontor^ toy^^r'Si the Diftana hetween
tie CcnUr and the Foeut^ as R to 1« Which Equation, if we reductf
\dr \dr
the mixed Qgantites . , ■ , ^ — /, and r , „." -^ /
^/: into improper PmdBons, willfbuid thus:
^' iJLXflAr
*aHd ^% * ' ft ' I
LA^W/4.R^/+R>'/4-I^/--R^//— Rr/ .
U lU Kr
And, compounding tbefe Ratio^s^ we have
U ij '^ ' U — yji
i r* . o " . ' : : R : 1. And, throwmg out
the two equal Denominators W— R^— Rr and W-*R^-— Rr^
and multiply isg Extreams together and Means together, we have
lUr^^lUtyJ^lKdty^lRrty^ Uda-ll^sy—lRrsy=l?jhy^
ItUty^ KRd/y + KKrty + lRdrS'^l?Jts^+ RR^/j -+• RRr^ i
Which Equation, being reduced, giv«sj= ^J^^^^ h^'
P Thia
52 Of Lenfes, ftPr. Part III
is refracted one Way ingoing out of the fecotnd,
as much as it was the other in entering the firft;
and therefore proceeds afterwards not in the iamd
Diredion^butinonethat is parallel to that which
it had before. Thus if the Ray AB {Fig. 27.)
enters the denfer Af^^/ix^^CDEF terminated by
the parallel Sur&ces CD and £F, it is refraded
at B towards the Perpendicular BI, proceeding
to a Point as G, where it is as much refraded
from the Perpendicular GK in going out, and
proceeds in the Direction GH« not the fame,
but parallel to the former ABL.
m
This Theorem may be applied to all Cafes whatever^ even to '
plain Surfaces mutatis mtUattdit ; v. g. the RoMus of a concave
Surface being negative (as lying the contrary Way) witli Refpeft
to that of a convex, and the Raiiu$ 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.
m
CHAP,
I
Chap. V. Of the Eye. 5 j
C H A P. V;
Of the EjQ,
r
^^^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
18
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
Chapter,
CHAP,
$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
Rajrs
^}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 *.
To
■ . • ■ ■ "
♦ On this depends the Struflure of the Ohfcura Camera^
wkkh ii a Contrivance to exhibit the Reprefentation of fuch
Objefts
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«
croik
id
•a.
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-
longs.
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
Mind.
• 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 ^.
The
* 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.
Form
I
t
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 *. .
V
»
• 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.
And
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^ aa.is 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.
Cud
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
con-
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
•J
1
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 *♦
When-
♦ 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*
gain.
€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
Diver^i'
I
f
^ 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. ♦
[pro-
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
eanfufcd*
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
fbisPart.
per
U-
• ^
X
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
Per-
I
' 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
thereby,
ceed
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
to
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
of
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
CD,
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.
been
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
double.
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
fame
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
DISSERTATION L
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
Matter.
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-
ter
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
narrow.
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
It
cc
cc
cc
cc
ic
cc
cc
cc
cc
cc
u
C€
4€
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.)
in--
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\
Other
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 bywhich.it 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%>. gives.ua 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*
I
i
cc
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
$un. Moon, and Stars to be farther from us
when in the Horizon than in the Meridian ;
bccaufc we have nothing elfe we can refer
their Places to, but that.
Now, poflibly, the Caufe why we think the
Heavens of that Form may after all be only
this, viz. That, as the Rays which come from
the upper Parts of that imaginary Surface, the
Sky,
^6 /Of the Hotizontal Moon^Partlll^
filcy, t>afs through a )dk Portion of the Atmo^
^bere than fuchas come from the horizontal
Parts of it, the Sky appears tb^v&iaocJtdijiinB''
fy^ and generally, more itn^i^/ intho&.Part$
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-'