1000000031

e s.

portion of lhe lengtlí of the wedge'. fide to the thickoef.

of its

b.ck,

and wheo they are (o adjuned, the wed¡:e

will be in

<quilibr;o

Wilh the rdiftance of the cylindcr••

The

wedg~

is a very great mechanicaJ powcr. (jnce not

oDly wood but even rack. can be fplit by it; which would

be impollible

effetl by lhe le.«; wheel and axle, or

pulley: fOr the force of lhe blow, or Clroke, Ihake. ,he

coheriog pam, and ,hereby make. them feparate lhe more

ellGly.

Tlie !ixth and Jan mechanical power is lhe

ftr<'IJJ:

which canno,

prop~rly

be called a GDlple machine. bec,u(e

Ir is never ufed

wilhout

the

applicatioD.of

a lever orwinch

to .affifl io turaing

it:

and

theD

becomes a compound

cogioe of • véry·gre'. t force eitber in pre!ling tbe

P''''

bodies dore together. or in r.iGng gre'l weights,

may

be conceived to be made by cutting • piece of paper ABC

(6g,

)' ioto the form of

indined pl. ne or h. lf \gedge.

and lhoo

co~ling

it rDuod

cylioder AB (fig.

6.)

A nd

bere

is-cvident,

that

tbe winch E mufl

the cylin.

der once round

I:i~fore

the weight or refiCl.nce

cán

moved fro"m one fpiral winding to another. as from

therefore, as much as the circumference of a órcJé

de(cribed by the handle of lhe winch is greate< than ,he

i.'Ieroal or· diClahce be,ween lhe (

pir.ls

. (o much i; tbe

fOrce of tlie ferew: T liu., f"ppofiog the dinanee bet\veen

the fpirals 'to be

balf

ao ¡oth. arid lbe leogth of Ihe wineh

to be Iwelve inehes; the eirde deferibed by Ihe haodle of

lbe 'wíncb where the power aas will be

iDehes Dearly,

<fr·aliout

h alfinehes, and eODfequeDtly

152

times as

great as the dillaDce between the fpirals: aDd therefore,

power at the handle, whofe iDteDr.lyis equal to DO nlore

Ihan a GDgle pouDd. will balaDee

52 pounds aaing a–

taiDft the fere",; aDd as mueh additioD.1force.

i. fuf–

Beient to overcome tbe friélion, wil(raife lhe

152

pourrds ;

aíld the velodlY of the po",.. will be to ,he veloei,y al"

Ibe weigbt. a.

'52

l .

H eoce it appean, that Ihe

longer the winch be made. and the Dearer tbe fpirals are

lb one ano,her, fa, much the grearer

the force of lhe

fcrew.

A m.ehine' fOI" lhewlOg ,he force or power oF Lbe ferew

may be' contrived in Ihe following manner. Le! Ihe wheel

(6g,

7.)

have. ferelV

on its axis, working in Ihe

t""h of the wheel

whieh fuppofe to be 48 in number.

I'r

is plain, th.. for every time the wheel C and ferew

are turned round by the winch

Ihe wbeel

will be

moved one roolh

the fcrew; aDd therefore, in 48 re–

volu,ions of Ihe winch, the whe'e1

will be turned once

round. Tlien, if the circumference of a ci rde defcribed

J;y the handle of the winch be eq\Jal to the cireumferenee

óf a groove

mund the

~/heel

the veloeity of the bandle

will be 48 ,imes

gre..

Ihe veloeilY of .ny given poi

in the groove. Conrequeotly; if a line G ' (above number

48) go.. tound ,he groove '. and has a weight df 48

pOunds hung

it helow Ihe pedenal EF, a po\Ver ,,<¡ual

'o one pound at ,he haddle wiJl balance .nd fuppo n Ihe

weight. To prove this

experiment,

tet

the circum·

ferences of ,he grooves of ,he \Vheels C and

be equ.1 tO

one another; and then ifa weighl H of one pound be fuf–

penóed by a line going round the graove of lhe whcel C,

il will balance a weigllt of 48 pOllndo hangiog by the line

VOL.

lll, N° 7"

G; and a fmall addition la the weight

will caure' it;t"

defeend, .nd (o raue up Ihe o,her "eigh"

If the line G, inftead of going round lhe graove

e oC'

tbe whed

goes rouDd i...,de

1 ;

the power of the ma–

chin"e \ViII be as much increafed, as the circnmrerence

the Rroove

exceeds lhe circlJmfereoce of rhe

axle :

WhlCh,

fu ppoGng it to be' ux times, llien one pound

H will ba·

laDee 6 limes 48. or 288 pounds hung tOthe Iioe on Ihe

akIe-: and hence the powc:.r or advantage of this machine

",iJl be as

i88

tG l. Th'.t' is lo ,lay, a nian, who by' hi.

oatural'ft reng'h could lift an hundred weiglit. will ' be ablé

to raife 288' hUDdred. or

14......

toO weight by·'his en–

gioe.

But t,he 'followiog enginé 'is lliJl more powerful,

a'e–

eount of ilS haviDg the additioo offour pulleys: and in it

we niay look ripon

.11'

the meehanieal powers eombined to–

gether, even'

\'fié

take jn the baláncc.

For

as the' a'xi'–

(6g,

8,)

of the llar AB il in i.. middl' át C, it iSo

plain ,hat ir equal w'eigh" are furpendcd upon any t\VD pio!/'

equidi!!ant· from the axis

Ihey will eouorerpoi(e eaeh;

otJ:¡er,-;-It becomes a lever by: l1anging a fmill weighl

upon th'e pin

ti;

ahd a weight ,as much heavier úpon ei!,

ther of the pin's

ó,

dJ~'

'or'/, as is in proporlioo'lo

tbe

pins being f" muen nearer the axis. The' whetl' ahd ' axle'

is evident; fo is Ihe ferew' E, wliich takd io ,the in-'

dined plane. aod with i, tlie half wedge. Par! of' a eórd'

goes round th'e axl•• ,he reft under the ·Iow'er pulley,.

K.m.

over the upper }>ulleys L.n, aod IbeD it is tied to'

a hook at 1I/'in -the 'Iower or moveable block, on whieh'

h aogs the weigh,

'V.

lo ,his machine, if tlie \Vheel ;Fha.

teeth. it wilr

be ,uroed once round in lhiny revolu,ions of tHe bar AB;

whieh is 6Xl

lhe .xis

of the ferew

if Lbe lenglh

of th. bar is equal to twiee Lbe'diamerer of the "heel,

the pin,

aDd'n at the ends of Lbe bar will'move

times

as fan as the teelh oflhe wheel do: .nd eonfequeorly,

one ounee at P will balance

OUDCes hung UpOD

,oo,h

iD the horizonral diame,er of ,he wheel. Then. if

th e diameter of the wheel

times as great a. the

diamerer of Ihe axle G, Ihe wheel ",iJl have

,i'mes the

veloeity of Ihe .xle; and thei'efore one ouoce

tbe

end

Ihe lever AC \VilI balance lO ,imes

6000

ounees hung to the rope H whieh &oes round llÍe axle,

L aClly. if four pulleyo be added, Ihey will make Ihe' ve-

10eilY of Ihe 10\Ver block

and weight

four times

lefs than the' veloeity of Ihe axle : ahd this bcing the lall:

power in the machine, which is (our times as great as

,h.. gained by the axle, it makes Ihe whole power Df the

machine 4 times 600, ar 2400.

So'

that a

mao

who

éould lift one hundred 'weigh' in his arms. by his natural

II reng,h; would be abl. to raife

2400

hundred weighl by

this engine.-But

is here as' in all other

mechanical

cafe~;

for Ihe lime Ion is allV.y.. as much as ,he powe"

gaincd. bec::lufe the vtlocity with which the power moves

will

cver

exceed the veJocity with \Io,liieh the weight rifes,

as much as the intenfity of (he \\eight exceeds (he intcn–

!i,y of t\le power.

The triélion of ,he fcrew ilfelf is very eonfiderable '

and ,here are few compound

cngines,

but

what,

upon ac:

eount of lhe fritlion of the pan. osainCl on. anolher,

will