1000000031

W ,\ T C: 1 and

K W

935

'lhe whecl D ro ttlrn

:'Iton~

with lhe

Irr.el

:lOU lhe rpring

A kcl'ps the crank

!Jc(\vetll

the teelh

al'

the

ratl.:ht:t-wlh:c1

R .

W c

n.l,,1l

nQw cxpl.tin how tlrnl! is

m..:aful

t'd

hy lIH! 010

tion of lhe pendulum: and how lhe

WI~l'cI

E, upon

Ihe

axis

of which the

minutt.~-h:'lncl

is lix.l:o , makc.:s

bUl

one

pret.:lr~

revolution in

:lO

ho'.}r. Thc vibnuions of

ptollnlum

perronntd in a

{horter

or Jooger

time

proporllon 10 lhe

Icngth of the pendolum itCelf. A pendulum

reet

8-1

}'Te nch liDes in lengt h, milkes 3600 vibrations

an hOUT ;

caeh vibratioa is pcrfwmed in a

recond

of time. and

for

th?l

reafon

call~Jrajt',;ond

p fndultWl .

HUI

apeo–

dulum of 9 inchc:s 2! Freneh lines makes 7'200 vlbratlons

in an hour, or twa vibrations in a

recond

of tlnle, <Iond

c.lled

hdlf'jteoná pmdululn.

Henee, in eonlh "<long a

whecl whole re, olution mul1 be

pcrform~d

given

tiD1~,

the time of the: vibrarions of the pendl.lJum which

regl1l.nes

its mOlian

muO be con(jdered. Suppoling.

lhen,

that tbe

pendulum AB makes

7200

'ribratlons in an hour, Jet us

confider how che whecl E {hall take up an hour in makíng

ODe

rc\·olution. T his entirely depends

{he

numlJer of

ueth io

lhe

whee)s ;¡ríd pinions.

the baJance.wheel con–

fith

t(elh, it

wilt

mm once in lhe time that the pen–

d ulum makes 60 vibrations: for

every turo of

lhe

wheel,

Ihe rame loolh

ététs

once 00 lhe

palctlc

and

once 00 Ihe

paJette

which occafions

t\\lO

feparate vibrations

lhe peo–

duJum

2nd the

whcd

having 30

tttth,

it eccafions l\Vice

;0,

or 60 \'ibrations. Confequl!ndy, this whec:l mufl per–

{,orm

120

revohJtions

an hour; becaufe

Vlbrtuions,

whieh it oeeario"s at every revolution, are contained

J20

times in

7200,

the number of vibrations performed by the

pendulum

'in

hour. Now

order tO determine the

number of teeth for the wheels

E F,

and lheir pioions

~.{,

it mua be rcmarked, tbat one revolurion of

lhe

whecl

mufl

turo lhe pinion

as many times

che

nnmber of

teeth

the pinion is contained

Ihe nU l"Aber of teeth in

lhe wheel. Thus, if lhe wheel

conuins

teelh, and

the pioíoo

6. lhe pioion will rnake twdve revolutions in

t h'!

time that lhe whed makes one; fer c3ch tool h of lhe

whcel drivcs forward a. 100th

lhe pinion, and when the

1ix

teeth of lhe pinion are moved,

complete revolution

is perrol'rned; bUl the wheel

has by that time only ad·

vanced

fix

teelb, and has (ti!!

advance before

i¡s

re–

voIution be complb ted, which will ocearion

more re·

volutions of the pl nlon. For the [ame reafOD, the wheel

ha, ing

teeth, imd the pinion

lite plnion will make

revolutions

~híle

the whcel perfarrus ane. Now,

the

wheel

being lurned by lhe

plOion ~,

makes

revolutians

(or

one

of the whetl

and lhe pinionf makcs ten revo–

JUIions for one of the wed

F ;

coorequently, lhe pinion

perfQrms

times

120

revolutions

the time Ihe

"'!Jeel

performs cnc. BUI lhe wheel

whlch

turn~d

the

pinion

oaar:ons

vibrations in the pcndulum

e:lcn lime ít

UHOS

round: confequently tht: whcel G oc

cafions

times

120

7200

,..ibralions af the pendulum

wJI1Je the wheel

pedorms one revolulion; bu{

7200

the number of vibrations nlade by the pendt!lum in aD

hUlI

a:ld confequeody Ihe whcd

performs bm 'loe revolullon

in ao huur; aud fo of lhe re!"

From

this

rt,,(ooiog,

is cafy tO <li fcover how a dock

may

be m;.de tu go ror any

lenr.th

of time widlout bClng

wflund up:

Hy incn:<tlíng the numuer of Icelh in

Ihe:

wht'. ls. 2,

dilJ1lndhin$!

tlK

numuc:r of teedl in Ihe

p:niuns . 3. Hy

Inct~a(jnp'

lhl.! Itngth of the coro that fuf·

VOL . IlJ. N°.

~9.

pend, the weight ; . n'l lallly, by aoding

the number of

wh;:c:ls and pinlOlls,

BIII,

in proportlol1 as lhe time is

aUf,menrcd, if lhe wtlght COIHlnues the f.. me, the force

wll1ch

commuOIcates tO lhe Jan wheel

GH will

dimi ..

nilhed.

only remílins

lak.e notice of

the

number of teeth

in the whecls whlch turn lhe hour and minute hands.

T he

wheel

per(orms one revoJution

an hour; lhe

wheel

NN,

wlllch IS wtllt!d by lhe aXIs of the whee!

muH Ilk\'wlfe nt:tke ooly one revolution in lhe"

ram~

time

and the miAUte-h,lOd

hxed tO Ihe barreI of this whecl.

The w!leel

has

leeth, and a(ts upon lhe whecl

which h:.s hk.ewife 30 leelh, and lhe fame diarncter; con –

fequcntly lhe wheel O ukes one hour tOa reveJulion: now

tht: wheeJ

cariles lhe pinion

which has

fi x

lCClh, and

which &léis upon Ihe wherl

'1q

of 7'2 t(elh; confequentJy

the pinion

m:\kes

revolutions while (he:" whceI

'11

makes

one, and of courCe lhe wheel

takes

hours to ODe re–

voJulion; and upon the barrel of this wheel lhe h'Our_haod

is fixed .

We (ha))

conclude

with

remarkiog, that

~1I

that

has been raid here concerning the revolutions of lhe wheeJs,

Ce.

is equally applicable to w¡¡eh" as to c!o<k,.

O( Ih.

/I1"hanifm

V(A:"CH.

ATeH

welJ as clocks, are compofed of wheeJs

aod pinions, and a reg'lilater

direét lhe quick nefs or flownefs

of lhe whed s, ar.d of a fpring which cOO1municates mOlion

tO tbe wkole machine.

But

the reguJator and fpring of

walch are vafiJy inferior-to

lbe

weight and pendulum of

dock, neither of which can be employed in wiHches.

place of a pendulum, thercforedwe are obliged lO ufe a ba–

lance

(6g. 4.)

regul.HC

lhe motion of a watch

and of

;} fprmg (fig .

6.)

which fe n'es in phce of a wtlght,

give.

motion

lhe wheels and bal;¡nce,

T he wheels of

walch, like lhofe of a cloek, are placed

in a

(l ame:

formcu or two piAfes and fou r pillars,

Flg.3.

reprefenls lhe ¡nfide ofa watch, afler the píate (Iig .

S.)

taken off.

dh!

Garrel which conlaios lhe fpring

(6g.

6.) the chain is rolled about the barrel, with ooe end

01'

{jxed

10 the b<trrel

and

the

other

lhe furee

When

w~lch

wound up,

the chain whlch was UpOD the

barrel winds

about

lhe

(ufee!, and by this means the fpring is

Hretched

for lhe interior (!od of Ihe fpring is fixed

hOCJk te ,he immoveabJe axis. abotlt which the barrcJ revolves;

lhe ex'lerior end of the fpring IS fixed to the ¡nfide of the

barrel, which turns upoo an axi,.

is lhererore edfy t

percc.ive how lbe fpring eXlends itftJf, and how its e1&llbci.

ty forces the barre l

tu ro round, and confequeotly obJiges

the chain wlllch is upon the fuf(!e

unfold and turo lhe

fufee; lhe motion of the furee

cOfDOlu nicated tO Ihe

whtcl

ce ;

lhen, by rnt'ans oC rhe te't th, to the pinion

whlch carr ies the wheel

D ;

then

the pinion

""hich carries dl'e wheel

chen

the pinion

which

carries Ihe

wheel F;

Ihen

lhe pioion

upon whlch is lhe;:

u.tlance.wheel

wbofe rlVOt rUlIs in

Ihe

pieces

caJled

po.

u nce, and B Cilllt'd

Ihe

followcr, which are fixed on

tbe

pJ.ue

fiJ! .

TllIs plate, ofwhichonlya part Í$ reprclt"tlted. isappli–

thal of

(liS 3 )

luch

I~H\nntr.

that the p:V01S

the

whcdscntt:r into hvJes madc in Ihe plale (Iig.

3.)

T llUS

thc IR}–

prdrt:d fOI ce of lhe l'pring is

communí~alt'd

the

whee!t ;

<{mi

,he piníon

IJcil'\g

~hcn

c{lnneéted tO Iht: whe, I F,

obligt:s íl

10 l urn

(fig 7 ) "!""hís whed al'ls upon Iht: p..lt:ttes

Oflhev\!rge 1

7,(I;u

4.)theaxl:, v!" whichcalflts tht:b:,¡);¡nce

3 Z

HH.