56 / 868
M
E
e
H
( he difb nce of ::
40000
miles
(rom
the
eUl h's
centre, ¡nd
of
~ 3.}OCO
miles
{fOl11 t11l:
cent re of gravity
oC
lhe
c.lrth
and moon, lo does thl! earth go roum!
,he
(.tOle
centre of
gr.l\'ity r;:very month
¿ l
lhe ddUnce of 6000 miles
flOOl
it
j
lh
tt " .
Irom
H
tO lhe cent r< of lhe e.u-li\.
I
OW ::'5
tbe c.anh is
(in
r!Juan
numbcrs)
Seoo mile:!>
111
diamcter.
it
15
pllio
lholt tU
(id..:
neXt l he m OOn is
ooly
:2000 m iles
{1 0m
the:
comm·,n
cen,lc
of gra",ity of lhe;:
canh am.I
moon ; its cenue
6000
miles d,UaOt
thercfroOl
j
and iu
f.lrth.::{l
{¡de (,om
lhe O1oon 10aoo .
Thcrl!fore
lhe cen–
trirug.tlfurces
of thefe pans
are
as
2 000 , 6 0 00.
and
10000
j
thal ¡s, lhe
centrifugal
force of any
IÍde:
oC
the
c:\rth, when
il 1$
lurned from tbe moon. is
f¡ve
times as
grt :u
:as
when
it
as
lurncd
lowards the moon
And as
Ih< moon', .." .tlion (e" prelt by the nu,"be.
6000)
at
lhe
~arth'5
cenue kccps (he
can h
(ronl
fi ying OUt of this
monthly circ1e, 1t muU
ue
grcO\tcr than
lhe ccntriruga{
force
oC
' he w;ttcrs on the Cicle
" t'XI
hcr; and conCcqucnt–
Jy.
h~r
grc,llcr
degrt c of
attratllon 011
th:tt f¡de is fuffi–
cient
lO
rair~
ltrcm ; UUI as her
attr.tt'bon on lhe oppoCitc
!idc is IcCs
th.lnlhe centrifugal force of {he water there,
lhe exccr, of this
fo rce
i5
fufficicnt 10
raiCe
lhe
water
jufi
a.
high on the oppofite fideo- To prove this ex–
pcrimenl.lly, Iel Ihe bJr
DC
(fig
10 )
wilh il5 fur–
niture be fixcd upon the whirlmg board of the ma-
hine (6g. , ..) by pu!!tiog the pio
P
ioto Ihe ceo"e of
,he board; which pio 1S in lhe centre of gravity of lhe
whole bar with
its
thrce balls
~.f,g.
and moon M.
N ow,
ir
lhe:
whirling board and bar be (urned
no\V
Iy
round by Ihe '\lÍoch, uotil tbe
b. 1I /
hang. over
fhe c('ntre
of
the c:rde, as
In
fig.
I 1.
lhe b.tll
g
will be
I:<pt toward. Ih< muoo by Ihe heal'iefi \Veigh,
p,
(6g" 9')
~nd
the b,,1I
r,
00
aCCOLlnt of
ttS
trcater centnfugal force,
. od Ihe
Idr..
weiglll
r ,
will fly off.s Car tOIhe olbor fide
QS
in
lig.
1.2.
Ano fo,
whilll
the machine 1S kept (Uro·
; n&, lhe balls
r
:md
g
\Viii
hang o\"er the cuds of ,he
d –
lipfis
IJ.~.
So Ih I the « r.triCug_1(orce of the ball e " ill
c xcecd
,h¡:
moon's auraéllon
jurt
as much
as
her au rae·
'tion excecds Ihe centrifugal force of Ihe
hall
g,
whilfi
hcr attraé\ion
juH
bdl¡nccs the centr,
fug.llforce
of
the
b~1I
/t
and mAkes
il
kcep
in
in
circ.l..: . And ht:nce it
i5
cvidcnt th,u Ihe lides mua rife
to
equal Leights at the
(a.metime on oppofi,c
Cid
es of lhe e.\rlh . T his expcri·
rnc:nt,
10
Ihe bcll of my kr.o·" !cdgc , is ent¡rely ne\V.
Fronl the principies lhus dl.tbliflled .
it
is cvident that
lhe can h moycs round Ihe: fu n, and oot Ihe fun round Ihe
~anh :
(ur lhe
centrifug.tll3.w
\l.ill uc:ycr
.lIow
a gre¡ t
body
10
mO'lle roond a fmi\1I one in
al\y
orbit what ver;
cfpcciollly when
\\,le
lind. that if
a
fruall boJy
mo'! s
round
a
~rtat
onc, lhe great ODe mufi alf.l
mo\'c
round the corn o
mon cenue
of
~ra, it)'
belween tht'm
( \\'0.
.'\nd
it
is
wcll
known.
tla t
the q'lantity of
nuucr in
Ih~
foo 15
= l7000
times
as
gr..:at as lhe
qU.lnu t)'
of mJ.ttcr
In
lh..: e-·_nh.
N ow,
as
the Cun's
dil\.m-.:.:
f:o~n
lhe
t ..
nh
is at
h:,!;
~
- 81.000.000
of miles.
ii
\\'C di,;de th.H
Jl!hnce
by
? 'l7000,
\/ole
0, ..11
}¡ we. onl)'
;Si
fo..
lhe
n·lol'.Jer of nules
Ih1.t
the. ctntre
of
I!rolvity b t\Yeco
,he
fUD
;md
c::lrth
is
d tlhnl from the fo n's centre
J\n,l
<lS
lhe fun's
f.·:ni,Jia–
meter
is
T
of
a d.:grec,
Wh:Cll.
;u ro
h1 eu
.1
,I¡lhnce
",$
thl t
of the fun.
nlUn
b:
ro !
c.CsdHn 3S
I
~oo
mih.s,
ir
11".
be illd
ti
by
35 7. lhe q"cli.c¡ will be lo6S';.
A
N
1
e
s,
43
which OICWS th:u lhe common C\!ntre of cravity js
withio
lhe
body of
lhe
fun . and 1S only lhe loG8.,. part of
bis
felH1di3melcr from his centre toward his fudue:.
AII
globul...r
bodics~
whofc pan s
c.tnyt<:ld . and \\hich
do nOI tum on their 3XCS, mun be perfea fpheres, be...
caufe
311
pJ.n s of thci r furfaces are equall y
attr~tlcd
lO ...
ward their centres. But all fuch globcs which do turo
on their
axes~
will be
obl.Hefpheroids; that is, their
furf3ces
\Viii
be higher. or ranher from che
c~ntre,
io.
\he eql1:u orial {h an
in
thc polar regions. For.
as
the
e–
qualortal pans move quickcrt. they mun llave the grear–
en
centrifug:ll force ; and will therefore rccede
fanhe(~
from the: axis of motion. T hus,
if
twO circular hoops
AI:I
. od
CD ,
(Plate
CVII. 6g.
l .) m. de IhiD .od Be""
ible, and cro!ling one anolher al rigl'ot angles, be lurned
round lheir
axis
EF
by me:ans of the winch
111,
the whe:cl
11,
and pinion
o,
and the axis be loofe in the pole or in–
lerCeaíon e, lhe middle paru
A,B,e,D
will Cwell out fo
as tO firike ag. infl Ihe (id.. of Ihe frame
al
F and G,
ir
the
pole~,
in únking
·10
lhe pin
E, b(
nOI flopt
by
it (roal
fiokiog farlher:
Co
1041
Ihe \Vhole wil! ' ppe.r of an ov.1
6-
go re~
lhe: equatorial diameler being confider...bly longer lhan
the polar. T hal our eanh
is
of this
figure~
is
dt lUon–
firable from ¡ (tu..) meafur(ment ?f (ome degrees on
its
furface. which are found
tO
be
lon~el
in lhe frigid
zon~s
than in lhe tOrrid : and the difference is (ound to be
fuch as prove lhe eauh's equ;u oTlal diarncler lo be
35
miles longer tluo its axis .-Since lhen, lhe eanh
is
high ...
er at lhe equalor than at lhe
pole:s~
lhe fea, ·which Jike
0111
othcr 8uids naturally runs downward (or towards the
pl ace5 which clre ne:aren Ihe earth's ce:otre) \Vould
run
towarcls the polar regions. and leave the (quatorial parts
d ry. if the
centrjfuga~
{orce of fhe w:oIter, which carried
it
lO
thof~
pans, and fo raifcd them, did not de(ain and
kecp it from ruoniDg back .gain loward. Ibe poles
oE
!he
earth.
0/ ,he M uhan;cal
PD'tUU',
I'T
\Ve conriJer lodies
in
motion, and compare theDl
tOAclhrr. we may do this
eilh~r
with refpeét lO the
quan.
I¡ties of m: tter
\h~y conta;n~
or the vclocities wilh' which
lhey
al~
mot"c:d
T he
heavi~r
any body
¡S,
lhe greater
is the po\\'cr requircd
eith~r
tOmove it or .tO flop
ltS
mo–
lion : ól:od at!,ain,
lhe
f",i(ler
h
mO\Tes, the greatcr is
its
force,
So
lhat
the ·\Vhol~
1JJonlr nlmn
or qoantilY offorcc
of a
mo\'in~
body
is
lhe rerule
of
its quantity of mauee
muh ipl:ed by lhe velocity with which it is
move-d.
And
when
th~
produéls ¡rilins. (ro",
the
nluhiplication of
tbe
p.lrdcular qu..ntitics of IUJtter in any
1\"0
bOlhn by lheir
rcfpc:éhve \' I:)cities arl! I!q ual, the
n!oll},ml a
or eotire
forces are ro
100.
Thu. , Cuppo(e
1
booy, which we {hall
call A,
lO
wei~h
';0
pounds, 3nd to rnove al lhe rate of
two mil s in
él
m:nutc
j
and another body, which
\Ve
(hall
ctlJ
S ,
lO \'oCigh onl)" rour poun¿s, and
10
move
20
miles
in a
nur-u·e ; the entire forces "'¡Ih
\1,
hich the(e l WO
b.Jdi~s
wodd Hnke
againfi
any
obOacle v:ould be cqua.!
lO
t aeh
otha. and lhc:rdorc it \\'ould require ( qua) powers
tn flop them.
For
40
muhiplit"d by
2
glves
80,
the force
of thc hoJy A and 20 muhiplied by 4 givc. 80. Ihe
force of Ih. b<>ly
1:1.
V uo Ihis caCy princi 1: dCP:Dds !he whole of me–
d lolOics :