1000000031

chanics!

3.nd

hold:i uni\'crfal1y true, th:tt \Vh..:n

twO

bodi~s

are fufpc::nded

:lny machír.::;, fo as to aa:

con~

t rary

t O

e:tch othcr :

lhe OIlchine be

pUl

¡me mOlion,

.3nd che

pcrpendicubr aCecm

of ane bod}'

multiplicd

¡mo

weighr, be equJI

10 lhe

papendicular

dCrCcnl of lhe

Othcr

body

multiplied ¡otO its wcighr, [heCe bodies, how

un:!qu:d foc\'er in rheir

w(:ir.IHS,

wiIl balance ane another

01.11

{itl1:ttions: for, 2S lhe

whole areem

of ene is pa·

formecl in lhe (ame time with lhe whole dcreent of lhe

o ther,

tht ir

rerp~{liye

velocities mun be diretl-Iy as

lhe

fpac.es

thcy move through ; and the excefs of weighl in

ane body is compenfatcd

lhe

exccfs of velocity in [he

other.- U pon this

principIe

is' cafy

compute lhe

pO'.ver of any mechaoical engine, whether fimple or com·

pouna; for it is but onl y inquiring ho\V much fwifter

t he power Oloves than the weight does

(i.

how much

f anher in the Carne time, ) :lnd

jufi

fa much is lhe power

i nereafed by lhe help of , he cnsine.

In lhe theory of this fcíe"'e, \Ve f"ppofc all planes

.perfeélly even, al1 bodies perfetll

fmoolh, levcrs

t O

have

.no weigh[, cords tO be extremel}" pli) ble. machines

Jlave no frillion; a nd in nlOrt, a1l im' erfl!él.ion muO: be

f et . Gde until lhe

theor~

be eHablilhed, and then prop";\;.

.allowances are to be made.

The limpie

ma,hil1u.

ufually called

m:challiclllpow:rJ,

.:¡re ,{jx in number, viz. the

I(ver,

lhe

w hceJ and ax/e,

·the

pul/q ,

lhe

il/c!ined plane,

the

wedg:,

Olnd lhe

ftrew.

T hey are ealled meehanical powers, becauf< they help

.us ro raife weights, move heavy bodies, and o\'ercome

reli O:ances, which \Ve could nOl efFeét witbout them.

l .

leiJer

js a bar of iron or wood, one pan of which

b ein!: fupported by a prop, all the other parts turn upon

l hat prop as their centre of motion : Olnd lhe velocity of e–

Yery pan or POiOl is direéHy as its d¡(lance from the prop.

T herefore, when the weight to be raifed at one end is

to the power a:pplicd at the other to rai[e it_ as the di–

n ance of the power from the prop is to the dinance of the

weight from [he prop. the power alld wcight wilI exatlly

.balance o r counterpoire each other: :md as a comOlon

Jever has but very Jittle fr¡étion on its prop, a very tilde

additional powcr wiU be fufficient tO raife the weicht .

There are rour kinds of levers.

l .

T he COOlmon

f ort, where the prop is placed betweeo the weight and the

power ; but much nearer to che weight than to the power.

:;2.

When lhe prop is at one end of the lever, the power

at the olher, Olnd the weight between thcm.

When

the prop is at one end, the weight

the other, and the

power

~pplied

betwecn lhem . 4. The bt:ndcd lever,

which differs only in (orm from the tira ron, but not io

propcrty. T hofe of the urH and fecond kind are of,en

ufed in mechanical engines; but there are fe\'! ¡n(lances

in which the third ron is uCed.

COlllfIJon

ba/a1/u

is a Jever of the 6rCl kind ; but as

.b oth its ends are

tqual d¡nances from its centre ofmo·

tion, they move with equal veloeities; and therefore, as

it gives no mechanical ad..,antace,

cannot properly be

.reckoncd ;tmor.g the mcchanical powers .

A lever of the firn kind is reprcf.nted by lhe bar

BC, (Plate CVI1. ug.

2.)

fupported by lhe prop D.

J ts

principal u(e is tO Joofen large nones in the gro\lnd,

<lr raift great wdghts tO fmall heights, in order lO have

ropes pue under them for r.lilinfl thcm hi gher by other

machin(:s. The pans A!3 aud

tiC,

on dilferen t lides of

the prop

are cal1t:d rhe;¡,rms of rhe lever: the cnd A of

the {horta <trm A B bcing appplied to the weibht ¡ntend–

10 lh:!

rai(ed , or to the refilld.nce lO be overcome : and

the pO\'.'c!r applied

the end

of lhe Jonger arm

BC.

I n

nukin!~

e x perimeras \Vith this mdchioe, lhe (horter

arm AB mu ll be as much thicker

th.tn

[he longer arm

as will be fufficienl lObalance it

the: prop. T his

fuppoft::o, jet

repr~fent

a power whofe ¡ntcnGey is e ·

q ua!

one ounce, and W a weigh t whofe ioteofity

equal

10 , 2

ounces. Then, ¡rlhe power be

1 2

times

[ar

{rom the prop as the weight is, the}' \ViII exat11y Counter–

poiCe ; and a Cmal! ad,1ilion

the power

will caufe it

tO dcfccnd, and raife [he

wei~ht

W; and ¡he \'elocity

w¡th '" hich che.p·ower defcends \ViII be to che velocity

w¡th which lhe weight rifes, as

thal is, direétly

as their dillances from the prop; and

conf~quendy,

the fpaces through which thty move . H cnce it 1S

pld.in•

thal a mao who by his natural Hrcngth , wi,hout the help

of any machine, could (upourt aD huodred weiglH, \ViII

by the help of this lever be enabled to fupport twelve

hundred .• I f (he weight be lers, or the power greater,

lhe prop m4y be placed fo mueh the farther from the

wcight; and then it can be raifed to a proportionabJy

grearer heighl

F or uoiverfally, ir the imenlity of the

\Veight muhiplied ioto jts dlltdnce from the prop

equal to the inten(ity of the power mulriplicd into

:Wtance from the prop. lhe power aod wcight

will

ex–

atlly

balanc~

each olher; and a JittJe addition to the

power will ra¡.fe the weigh t. Thus, iD lhe pte{cnt in–

n ance, the \Veight W is

ounees, and its dill.tDce from

the prop is

¡nch ; and

muhiplied by

12;

the

power

is equal tO

ouore, and its di(lance from the

prop is

¡nches, which multipJicd by one

again :

and therefore there is an equil,brium between them . So.

a power equal tO

ounces be applied at the d¡(lance

of 6 ioeh.s from the prop, .il wiJl juH balance the

weigll t \V; for 6 múltiplied uy

1 2,

as before. And

a power equal tO

ounees placed at 4 inches dillaDce

from the prop would do

t.he

(ame ; for

times 4 is

•

a nd fo on, in pioponion.

The

jla/~ra.

or R oman

jJu l;'ard,

is a Je\""er of this

k ;nd, contrived for 6nding the weights of dlfferent bo–

dies by one fingle weight pl.eed al dilF<rent.diHanees from

the·prop or centre. of motion

F or. if a (caJe hangs

at A, the extremlty of the nlorter '3rOl AB

:md is of

fuch a weight as \\ ill exaéUy counterpoiCe the longer arm

Be;

if this arm be divided ioto as many eq tlal pan s as

it \ViII contain, e::tcb cqual

AS, the (ingle weight

(whieh we may fuppofe

pound) wiJl ferve for

weighiog any thiDg as heavy as ilfdf, or as many times

heavier as (here are divifions in the arm

BC,

or any

'luilnti ;:y between its Own weigh t and that quantity. As

for e".mple, if P be

pound ,

amI

pl.ced 3t . he Grn di–

vifioo

in che arm

BC_

iI \ViII baldnl'e

pound in the

fcale'H A: ir il be: n 'moved to the fecond Ji"j(ion at

2 .

\ViII balance

pounds in the fcale

if to the tRird,

;; pounds; and fo

tO the end of the .rm BC.

eaeh

of {heft: integral di,,¡fians be fubdividcd into as many c.

qual ,pans as a pouDd contaiDS ounees, and lhe weight