1000000031

put into mation, is to conúnue moving

a flraight lioe,

ahhcugh by the force thac moves thc Oiog i, be made to

revolvc: in

acilde.

The change of motion produced is in proportioa

the

force impretr<:d: for (he efFc!éls of

nalura) caures

are al..

ways pl'Oponionatc la

the

torce

power of lhofe

cauCes.

By the:<: laws it is eaCy to prove tIlat a body will de·

fcribe the diagooal of a Cquare or parallelogr>m, by twO

forces conjoined, in the filme time

Ih<tl

would

de(cribe

. ither of ,he udes by ooe force lingly. Thus, CuppoCe

, be body A (6g . 7.) to repreCent a /hip at Cea; aod that

ir is drove

(he wind. in the.right Jine AB, with fuch

a force as would carry ir

uOlformly

from A to B in a

minute: rhen,

ruppor~

a fiream or currenr of water run–

Ding iD

rhe direélion AD, witb

fueh

a force as

would

carry the /hip ,hrough ao equal fpace from A to D io a

111inute.

rheCe

(wa

forces, aél:ing together at right

angles to each o,her, the /hip will d<fcribe ,he line AEC

in a minute: which Jine

(becaufe the forces are equaJ

and perpendicular 'o each o,her,) willJ be the diagooal

of an exaa fquare . To con6rm thi. law by ao expe·

timent, let ,here be a wooden fquare ABCD (6g. 8. )

fo cootrived, as tb have the part BEFC made to draw

ou' or pu/h ioto ,he Cquare at pleafure. To this pan let

the pulley H be joined,

as 'o turo freely

ao axis,

which will be at H wheo the piece is pulhed in, aod a'

",beo it is drawo out. To this part le, tbe ends of a

nraight wire

be tixed, fa as to move along ",ith lt,

un–

der the pulley: and let the ball G be made to Oíde ea(¡ly

,be wire. A thread", is 6xed to ,his ball , aod goes

over tbe pulley 'o

by this ,hread ,he ball may be

drawo up

the wire, parallel 'o tbe lide AD, \Vheo ,he

partoBEFC is pu/h<d as far as it will go in,o the Cquare.

But, if ,his pan be drawo out, it will carry the ball a–

loog with it, parállel tO the bottom of the Cquare DC.

By ,his means, the ball G may ei,ber be drawn pepeodi–

cularly upward

pulling the ,hread

or moved hori–

fontolly along by pulling out ,he pa" BEFC, io equal

times, and throllgh equal {paces; eaeh

~ower

aéling

rquahlyand feparately upon it. But if, wheo the ball

is at G . ,he upper end of the ,hread be tied to the pin

in the corner A

tbe 6xed fquare, 3nd ,he· mo..able

pan BEFG be

~rawn

ou', the ball wiJI then be .aed upoo

by both ,he powers tOge,her: for il \ViII be elrawn up b}

the thread tOwards ,he top of ,he fquare, and at the fame

time earricd

with

its wire

towards the right hznd

Be,

moving all ,he while in the diagonal line L; and \ViII be

found at

when the fliding part is drawn out as far as it

"asbcfore, whichtheo will have caured thethread to draw

Up the bal! 'o ,he top of ,he iolide of ,he fquare, jufl as

bigh as it

W3.S

before, wbeo drawn up ungly by the

thread withoul moving the nidinC parto

,he .aing forces are equal, but a' oblique aogles to

tach o,her,

will ,he fieles of Ihe parallelogrom be: and

the diagonal run ,hrough by ,he moving body wil! be

longer or lhorter, according

the oHiquity is greater or

fmaUer. Thus, if ,wo equa! forces aa conjoindy upon

VOL . IIl.

N°.

70.

,he body A, (fig 9) ooe having a tendeney td move it

th roufh ,he fpace

in the fame time tholt lhe other ha,

a tendency to move

th rough an eqtlal fpace

AD;

w:ll

defcribe tbe diagonal

AGC

iD the fame time that dthc:r

of the (ingle forces would have c;¡ufed it

defcnbe euher

of ,he fides . If ooe of ,he forces be greater thao the

other, ,hen one ude of ,he paralJelogram will be

mueh longer. than the other. For if ooe force uogly

would carry ,he body through ,Ile fpace AE, in ,he Carne

time that the other would have carded the {pAce AD, the

joint aliion of both

will

carry it

the filme time through

the fpaee AHF, which i. the diagon:1 of ,he oblique pa–

rallelogram ADEF.

If both forces aa upoo the body in fueh a m.nner, as

' o mOTe i, uoiformly, the diagonal deCeribed will be a

Clraight line; but if one of [he forces aéls in fuch a

manner as to make

(he

body move fafler and fafier as

goes forward, theo rhe line dt:fcribed

will

curve.

And ,his is ,he cafe of all bodies which are projeaed iD

reailioe.l diretlioos, and at the fame time aéled upon by

tbe power of gravity, which has a eoollan' teodeDcy to

accelerate their motioos

[he direélion

whereio

aéh~

La'WJ ofthe Planetary motionJ.

Ft<OM ,b. uniform projeaile motÍoo of bodies in flraight

liDes,

and

the univerfal power of

gravity

or attraétion,

a–

riC.. ,he curvilineal motion of aH ,he heavenly bodies. If

the body A (fig.

10.)

projeaed .Ioog ,he flraight lioe

AFH

apeo {pace, where it meeU with

refillance,

aod is not drawn alid. by any power, it will go on for

(ver witlr

lhe

fame velocity, and in (he fame direélion.

But if,

the Carne moment the projeélile force is given

at A, tbe body S begios to amaa it \Vi,h a force duly

adjufl-ed·, and perpendicular to

motion at

wiU

then be drawn from ,he flraight line AFH, and foreed to

revolve about

¡nthe circle

ATW;

in tbe Carne manner.

and by the fame law, thar a pebble is moved round io a

fling . And if, wheo the body is io aoy pan of its orbit

(as fuppofe a' K) a fmaller body as L, withio the fphere

of am.tlion of ,he body K, be projeaed in the right Jin.

LM,

with a force duly adjufled. and perpendicul;;r 'o ,he

line of attraaioo LK; then, the fmal! body L will revolve

abour the large body K in Ihe orbi, NO, aod accompany

it iD its whole courfe (ound ,he ye' larger body S. But

theo, the hody K wiH no longer mo.. io ,he cirele ATW;

for that eirele will now be defcribed hy ,he common ceo–

tre of. gravity betweeD K aod L . Nay, eveo ,he grea,

body S wil! oot keep in the centre; for it

\Vil

l be the

camman

centre of gravitybetweeo

all

the tbree bodies

S, K

and

that will remaio immoveable there. So,

fuppoCe S and K eonottled by a

~re

P ,har has no weighr,

aod K and L conoeaed by a wlre

that has no \Veighe,

the commoo centre of gravi,y of alJ theCe three bodies will

be a poin, in the wire P near S: whidl poin, being fupport –

ed, the bodies will be

alllO

tqui/ibrio

as the)' move

rouod

it. Though indeed,

flri~tly

fpeakioc. ,he Cbmmoo cen–

tre of gravi'y of all ,he three bodies

will

oot be in tbe wire

T~ mak~

tl1e p:-oicélile

force

a jufl balance to Ihe

gravitating

po,,"e:-, ro

as to

keep thc p1:tnet moving

circJe '

n.,uft

gt"c

fueh a

"eludty

as !he rlanet \Veultl acr;ci:e

&ravity wh:o it had

fulkn

throtl¡;h h,lf Ibe fcmidiametcr of

ti"t

ctrcle.