1000000031

1\·1 E

, heir ,eodeoci<s ' o fly off (rom ,he eirele. ,hey de(eribe) ,ime.; aod ,here(orc, ,he (qulre. o( ,he

peri~d.

o( V

are in Jireét proponian la their qunntÍties of maner mul· and

ar~

one ,,"other as lhe cubcs of (hc.r

d,n.mees

tiplied

iOlO

thcir rcfpctlive

\'clocillC3,

or ioto their di- from

and

'UI,

which are

lhe

centres

thc:ir r

Ipt!~hve

llanees (rom che centres of lhcir refpeéti\'c cireles. Far, cireles. t\nd

lhe: wc:ight in lhe tO\Ve O be

rut.r

oun·

{uppofing

which weighs 6ounces, to be

( \Vo

¡oches from ces, cqual

tO lhe

fquareof

2. lhe

dlH~nce

of V

frvJll lhe

¡es

centre

of motian

'tIJ ,

lhe

wcight multiplicd

lhe

dí-

centre

and

lhe

\Vcight in

the

h)w<r

P be.

10 (Junces,

ll. oee is 12 ; aod (uppoGng V, whieh weighs ooly ooe oe. r1y <q"al ,o ,he (qudre of 3t, ,he diltaocc ot' U fronl

ounee,

in:hcs

diChnt

(rom its

Centre

010-

'U';

\ViII be found,

upon lurnlng lhe

m-.cI\

lne

tiy the

tioo

t ;

(he weight r ounee O1uhiplied

(he dittanee

wineh, that ,he balls

"nd

wllI raife Iheir rl".{petllvc::

¡nches is

12.

Aod as (hey revolve in equdl times, their weights al very ncarly lhe Came inrt.+.nt of lime. \Vhich

veloCitic:s are as their dinances from the centre. namely, confirms chal famous propofition of

K &'l.. i. R,

vi%.

'T hat

the fquares of the

p~riodical

dmes of lhe planclS round

If theCe two balls be fi xed at equal diCbnces from lheir che Cun are in proponíon to the

cu~es

of lhelr dltt.lnces

refpel'tive centres of motion, lhey will O1o\'e Wilh equd from him ; and that the fun's attraétiun is inver{c1 y

a.s

velocities; aod if (he lowcr

has 6 times as much weight the equare of lhe diHance (rom iu centre: thal ¡s, at

put ioto it as lhe lower P hu, lhe baUs will raire their

wice lhe diftancc, liis attra!hon is rour times Jee,

and.

weight

lhe f...me momento

T his O\ews. thal the ball thrice rhe dlfiance. oíne times leC,

at four times lhe

di ~

U ,

b~ing

fix limes as heavy as lbe ball

has fix times n.lnCe, fixlten

lim~s

)¡:fs ; and fo on, to lhe remoteft part

mueh eeotrifug,1 (orce, i.... de(eribing ao equal eirele of ,he (yflem.

\Vi,h ao equal v<loei,y.

T,ke off ,he ea'gu, flri og

from ,he

great

wheel

If bodie. of equal weigh"

rev~

io equal eirele.

and ,he (m.1I wheel

and le, ,he Itriog

reo"in

Wilh unequal velocicies , theircl:!ntrifugal forces a e as (he

~pon

rhe wheels

and G. T ake away aleo Ihe be"rer

fquares of ,he veloei,i... T o ljilll'e ,hi. law by 'o e,,-., MX (rom ,he whidiog·board

aod iollead ,hereof

perimeo" 1« ,wo balls

and

of equal weigh" be pUl ,he maehioe

(6g.

4.)

upon i" 6xiog ,hi, m' -

6xed on tbeir cords at equal dilhnces from lheir re.fpec. chine tO the centre

01'

the board by the pin,

and

ti,

l ive ceotres of motion

and

x :

and then let the calgUt in fuch a maoner, thal the end

may rife above

[he

Hriog

be pu, rouod ,he \Vheel

(who(e eireumfereoee

bo.rd

'o an angle of

degree. . l o ,he upper

is ooly oae half of the circumrerence of the wheel H or (¡de of 'Ihls machine there are twO glafs tubes

:\nd

G )

.od over <he polley

'o keep i, ,igh, ; and le, (our

e1o(e Oop'

bo,h eods; .od eaeh ,ube i. abou, ,h ree

times as much weight be put in the tower P as in the tower quan ers ful l of Wlter. In tbe tube

is a liltle quick.

Then 'uro ,he IVioeh

aod the b.1I

will revolve fil ver, whieh oaturally

(. 11.

down ' o ,he end

io ,he wa–

twice as f3fi as Ihe ball

in a cirele of lhe rame diameler. ter, becaufe tt is heavler lhan iu bulk of water ; aod on

becau(e ,hey are equidifl,ot (rom ,he ceo'res of,he cird.. ,he tube

i•• (m.1I eork whieh no... upoo ,he ,op of ,he

in which they revoh'e

and lhe weights in the towers water at

t ,

becaufe

is Iighrer; and

is {mal! eoough

will

bOlh rife at the rame ¡nnant

which (hews, that a tOha...e Jiberty

rife or fall in ,he lube. W hile the

dV'Jble velocity iD lhe

fa me

cirele will exatlly balance a board

wnh {his machine upon it continues al ren, ,he

quadruple power of anraaion in the centre of the cirele. quickfilver lies al the bOllom of Ihe tabe

and lhe cork

For lhe weighlS in the towers may be conlidered as the floan

Ihe water

nc~r

the

10p

of {he tube

/J.

Hu"

IIp.

:attr¡¡flive forces io the centres, aaiog upoo the revoh'ing on turning the winch, and puuing the machinc in mo·

bJlIs : which, movian in equal circles, is the

f.me

thíng tion, the contents of e-ach

\I,Iill Oyoff towards the

i( ,hey bo,h moved iD ooe aod the (ame cirde.

uppermofl end. (wbieh are (. "hefl from ,he eeotre of

7. 1

r bodiesof equ31 wcights revolve in unequalcirc1es,

morion)

,he heavíefi- with the grcaten force. T hcrerorc.

io (ueh a m.ooer ,ha, ,he fquare. of ,he time. of ,heir ,he quiekfilver in ,he ,ube

will fly

off

qui'e

.he cnd¡;

going round are

the: cubes of Iheír diflances from lhe and occupy jls bulk of fpace there, exeluding lhe water

centres of Ihe cirelc-:o chey dc:fcribc ; their centrifugal from thal pl ..ce, becaufe

Ít

is lighter th,;m qUlckfi1ver ;

forces are invcrCely as lhe fquares of their diflance-s from but the water in the (ube

fiying off tO iu highcr cnd

thofe centres . For, the catgUt Itring remaining as in the will exclude Ihe eork from lhat pl<

t.ce,

an c3ure the cork

Iafl experimeo" le, ,he diClao« or ,he b..

1I V

(rom ,he ' o de(eend ,owards the lowermoflend o( ,he ,ube, where

centre

be made equaJ tO two of the crors divlfioos on it

\Viii

remain upon the lowefi cnd of tbe w:uer near

i" beater, and ,he difhoee of ,he b.1I

(rom lb. een-

for ,he heavier body having ,he greater «ntrifug.1

tre

'UJ

b: ,hree aod

fix.tl p.rt;

,he

b.lI.

'hen,(.I... (orce, will ,herefore potree. ,he upp<rmof! part uf ,he

beiog of equal wdghu, and

making tWO revoJudons tube

and lhe lighter body

will

keep be.twcen lhe heavil:!r

turning the: winch in the time {hal

makes one: fo and ,he lo\Vermofi pan.

that ir we fuppoft lhe b.+.1I

rtvolve in one moment,

T his demonrlrates the abrurdity or the Cauefian doc·

lhe ball

wil!

revolve in IWO Olomenu, the fquílres of trine of the. plancts moviog round tlu: fun in vortexes :

which are

one

and rour: for the fqutlre of

is only r, aDd [or,

the plaoct be more denCe: or hea\'y Ihan the bulk

the fquarc: of

is"

thereroH:1he fqu3re orthe: period or of the VOrte",

will

rly

ufF therein, fanher and

r ..

rahcr

revolution of the ball

cont~ned

4 times in the equare {rom the fun

Il!fs

deoee:, il will come clown

rhe

of ,he b.1I

Bu, ,he diflaoee of

2 .

,he cubo of lowefl pa" of ,he vortex,

,he (un: 30d ,he whole vor·

",hieh is 8; .od ,he diflance o( U i. 3'}, ,he eube of

teX

it(elf ",ufl be (urrounded wit" (ome'hiog I,ke • grea,

wüieh

very oeul,

wüich

is contain:d (our ..a1I, otb"wi(e i, v/ould

o!T, pla,.ts od a11 ,og<ther.

Bu,