1000000031

IV!

P but wben thefe bodies are alJ in a right line. H ere, S

may reprc[ent the {un, K

[he eanh,

and L

[he

moon.

In arder to form

idea ofthe curves defcribed

[ \Va

bodies re\'olviog ahaut their

comlTIon

centre of gravity,

whiltl they tbemeelves with a third bodyare in motion

round the common centre of gravi,y of all lhe three j Jet

ws firl! fuppofe

(Plate

eVl.

fig. t .) to be the fun, and

lhe earth going round him with any moon; and their

moving forces regulated as above. In (his cafe,

whilf~

[he caTlh goes round lhe fun in lhe dotted cirele RTUWX.

óe.

the fun wilJ go round the eirele

ABD,

whofe centre

is lhe commOn centre of gravity between [he fun and

and earth: lhe right

line

f!;J'

reprefeoting lhe

mutual

al·

t raél.ioD

bet\Hen them,

which they

are as

firmly

con–

·s eétcd

[bey wcre fixed a\ lhe

t wO

ends

of an iran bar

Rrong cnoogh lO hold them. SO, when lhe eanh is

,ilt

tbe fun will be al

when lhe earth is al T, the fun

will be at

and wheD the ""th is a'

the fun wiJl ue

G ,

&e.

N ow, le, us ta!:.e in ,he moon

(at the fop of the

fi–

gure,) aDd fuppoCe lhe eanh to have no progrcffive motioo

about lhe fun ; iD which caCe, whiHl: the- moon revolve&

about the eanh in her orbit

'1{125~ I~

"'he eanh \ViII re·

volve io the cirele S

13,

whore centre

is the commOD

centre of gravity of the eartb and mOOD; tbey being

COD–

Ilefled by lhe mutual attraétion betweeo them io lhe (ame

manoer as the earth and fun are.

But the trUdl is, that whiHt the moon revolves about

the earth, the eanh is iD motion about lhe fun; and OOW,

che mooo

wilJ

caufe the earth lO defcribe

irregular curve,

aod not a true cirele, round the fUD; íl being the eommon

centre ofgravity of the eanh aod mooo that wilI theo de–

fcribe the Carne cirele which the earth would have moved

iD,

ir had oot beco attended by

moon. For, fuppo–

fing tbe mOOD to deCcribe a quaner of her progreffive or–

bit abóut the earth io the time that lhe earth DlOves from

it is plain that when lhe earth comes to

the

moon will be found at

in which time, their common

cen're of gravity will have deferibed the dotted are RlT,

Ihe earth the curve

R5.f.

and lhe moon the curve

the lime Ihat the moon defcribes another quarter of

ber orbit, lhe centre of gravity of lhe e3rth and moon

wilJ

dercribe tbe doued are T

lhe earth {he cu rve

f6g,

and the moon the curve

and

on.-And

thus, whiHl lhe moófI goes once round (he canh in her

progreffive orbit, lhei r common centre of gravity dcfcribes

,he regular ponion of. cirele R t T

U 3 V

Vv,

the

eanh the irregul..r curve

RSf6g 7hgi,

and tue moon

the yet more irregular curve

16 /17

u~·

and

ahen, lhe fame kind of tracks o\'er again.

The. centre of gr-avity oP"the eanh and moon is

6000

miles from lhe eanh's centre towards the

0'1000

there·

(ore the cirele S

which the earth defcribes round that

centre of gravity (in every courfe of the moon round her

orbil) is

12000

miles io diameter. Confequently, (he

t:arth is

12000

miles nearer lhe fuo al lbe time of full

moon than al lhe lime of new. [See the earlh atf and

]

To avoid confufion in fo fmall a f.gure, we have fup'

pored lhe moon tO go on1y twice and a half rouod lhe earth,

in the time that the canh gocs once roucd lhe fun: it

being imponible to take in al! the revolutions which lhe

m.lkcs io ayear, and tO givc: a true figure of her path,

unlefs we lhould make the Cemidiamettr of lhe eanh's or–

bit at leall 84 ¡oches ; and then, the proportioual femi –

diameter of lhe mooo's orbit would be oolya quarter of

ao ¡nch.

the moon made any complete number of revolutioDS

abollt Ihe e3rth in the time that the eanh makes one re–

voJution 290ut the {un, [he paths of tbe fun and moon

would return into themrelves at [he end of ever}! year;

aod fo be the fame over agaio : bm thc:y reluro nut into

themfe!ves in leJs than 19 years oearl y; iD which time,

the eanhll13kes aearly

revohuioDS about (he fun) aod

rhe moon

23 S

abaut the earlh.

Ifthe planet A (Plate

ev.

fig.

10.)

be attraéted to–

wards the fuo, with fuch a force as wouJd make ir faH

from A

H, in the time that the projeftilc; irupulfe would

h<lve carried it from A to F, it will defcribe lhe arc

by lhe combincd aBion of thefe forces, jn the Carne

lime!

"that Ihe former would have caufed ir tO faU from A

or the lauer have carried it from A to

f .

But, if the

pr.ojeltile force had been (wice as great. that ¡s, fuch a9

woul!!lr..bave carricd the planet fr9m A

io lhe fame

time that now. by lhe fuppofi lioo, it carries it only from

A to F¡ the fun's attraé1ion mua theo have been four

times as

arong

as formerly, to have kept Ihe planer in

the cirele ATW¡ that 1S, it muCl have been fueh as would

have ea"fed ,he planet to fall (rom

E ,

which is four

times the diClance of A fronl B, in tbe time Ihat the pro–

jeétile force fingly would have carried it rrom A to

whieh is only twice the dillaDce of A from F . Thus, a

double projeétile force will balance a quadruple power of

gravily in the Carne cirele

as appears phin by the 6gure,

and Iball foon be confirmed by an experimento

Plate

eVI.

fig .

The whirling·tahle is

machin.

contrived for lhewing experiments of this na ture. AA is

a arong frame of wood, B a winch or haodJe fixed

the

axis

of the whee!

round which is the cargut flring

whieh alfo goes round the fmall wheels

and

croffing between them and the grear wheet

D . 00

the

upper eod of lhe axis of lhe wheel

above the frame,

is fixed the round board

to which the bearer MSX

may be faHeDed oceafionally, and

~eOloved

when il is not

wanted.

the axis of

d lC

wheel

is 6xed lhe bearer

NTZ: and it is eafy tO fee,

th:H

when the winch

Bis·

turncd, the whcels and b:zrers are PUt inlo a whirling mo,

tion.

Each bearcr has t\Vo w:ires, W,X, and Y,Z, fixed and

{crewed tigh[ into them at the ends by

mUs

on the out–

fideo And

wh~o

theCe nuts are

unrcrew~d.

the \Vires may

be drawn out in order lO change the balls

and V, which

Oide upon lhe \Vires by means of brafs loops fixed into

the balls, \Vhich keep the b,lIs up from louchinE ,h.

\Vood below ,hem.

firong filk line goes.,hrol1gh eacn

ball, aod is fixeJ

it al any length from tbe centre of

the bearer tO its

~nct,

as oecafion requires. by a nut.fcrew

at the ,op of the ball, ,he f.·.an k o( ,he fcrelV going intQ

the centre of (he ball and prcOing the Jine

a~ainl1

lhe un–

der Grle of the hole {har it goes throngh.-Thc line goes

from the ball, and undee a (,11,11 pulley

in the middle

of the bcar.r; then

I1p

lhrou¡¡h a fockct in tb: rOl1na

pl"t>