58 / 868
M
E
e
H
A
P be placed al
a.y
o( IheCe (ubdioifion., (o as
10
eoun–
terpoifc whu is in (he:
(e,ale, che pounda
a-od odd
OUDee.
thC'rein are:
by
(hu mean.
a.(ccrtained.
T o Ihis kind o( I. ver nlay be , euuced feveral (orts
of infirumenu, fuch as fcifTar:t, pinchcu, (nutrers ; which
I re
made
of twu
leven
adiog
conLrary lO one
another ;
their prup or
ccotre
of motioo beina
the pin
which lu:eps
, hcm logelher.
In common praflice:, tbe looger arm of
Ibis
levergreat·
'y
cxcceds lhe wtight of lhe fhorter;
wllich
gains grcat
advantage, btcaure i, add. (o much ' o ,he po",er.
A
lever or Ihe (econd kind h••_Ihe weight be,ween lhe
'prop and ,he power. In
ti",.
os
well
as
Ihe former,
t he Id ...n"ge g,ineq is as ,he diOance of ,he power (rol1>
Ihe p,op
10
Ihe diClance of ,he weighl (rom lhe prop:
for the rcrptélivc ,,(Iacitice of ,be power and weight are
lQ Ihat proponian; and they
will
balance (aeh otber
\'Ihen ,he intenfi,y of ,he power multiplied by i,. diClance
(rom ,he prop is cqu..1
to
che intcnfi lY of the wcight mul
liplied by itl dill.nce rrom the prop. Thu. , i( AB
(6g.
3 )
be
, 1<\,,,
on whieh the "'eight
W
of 60uDees
hang...
the dj(j,,,,.. of , ineh from lbe prop
G,
and
• poU'cr
P
equal
ca
{he
wdght of one ounee hangs
al
lbe
end
R,
6 inehe. (roO\ ,he prop, by ,he eord CD gOiDg
over Ihe fixed pulley E, ,he pow.. wiJl jun (upport
the \Veigh,: and a fm iJl addi,ion
10
the power wiJl raife
,Ise weighl
I
ineh (or e"ery 6 inehe. Iha, Ihe powe.r
dereend•.
Thi. lerer (hew••he rea(on why IWO men earrying a
b u,den upon a nie\: be''''.en ,hem, bear uneHual (bares
o(
the burden iD ,he in.erre proponion of Iheir diflanees
from
it.
For
al
is weJl koown, lhat the nt arer any of
thcm is
lO
the burdcn, lhe
¡rCaler
Ihare be bcars of
at:
and if he goes dircllly uDder i" he bea.. ,he \Vbole.
So,
ir
one man be
al
G
I
and the other
a to
P,
haviDg
the
pole or lIick
AB
relliDg on Ibei, (houkle.. ; i( ,he bu,deD
or weight
'V
be pl.ced 6ve ,imes a. Dear ,he man
al
G ,
as
il
is
lO
,he man
al
P. the (ormer
will
bcu fivc times
.. much weigbl .. Ihe la"er. T bi. i. likewi(e appJieabte
lo tbe caCe of I\VO horf., o( un«¡ual IIreng,b, ' o be (o
yokcd. as thn each horre may
dr.awa pan
proportionable
10
his IIreng'h : which i. done by dividing ,he beam (o,
,hit ahe
poiOl
of
traélion may
be
as
much
ncaru
ro ,he
/lrong.. borre
th.~
'o ,he weak..,
as
the llreog,h o( ,he
{ormer c:otcecds tbu o( ,he latter.
T o .hi. kind ort«.. may be redoced oor., rudders of
thiPI,
daon
lurniog upon
hinges,
cuttin&
kni"cs
wbich
are 6xed at the poinl of ,he blade, and lbe I,ke.
lf
in ,hi. I..er we (uppo(e ',he pO\V" .nd ,,'eighl
10
ch.ng.pla=, fo ,h...he pO"'er
m'Y
be b<t lVeen ,he
wrighl and ,he prop, it \ViII beco",• • leoer of ,b. ,hird
kind; in \lhich,
chu
(bere: may
be .
baJancc.
betwc.cnrhe
pou'cr .um the
\l.l't:lght.
the
imcnfity
of the
p01L'c.r
muR
c:
cttd the
intrnrity
of the wcight, juO: as much as (he
d
,n.nC'< of ,he ",eighl r,om .he p,op
e~ceed.
,he diCl.nee
o(
,he po"'''
('001
il. Thu.,
1« E
(6g.
4')
be
.he prop
(,he le "
AB.
'Dd '" a \\e.ith, or
I
pound, pl.ccd
3
IImu 1S fa r
rrom
the prop.
a.s
(he
po'...
rr P aas
al
F,
h '
Ihe
curd
e
1':,oiog over Ihe
6xcd palley O;
10
,bis
C2(C.
the
el
OlUn be <c
¡u.tl10
three
p~uods,
in
ordcr ' o (up-
u che
~
ciJ!ht.
V L. IIJ.
-o. {l.
N
1
e
s.
45
T o Ihi. (ort of lever are generally referred lhe bone.
of a manOs arm: for
when
\lit!
lirt
il
weight
by
,he hand .
the murcie' that exc.rts
ltS
force
lO
raife
thar
weight,
.¡,
6xed to che
bODe
about
cne tcnlh pUl
as {ar
bclow
th.e
clbow
a.
,he haod is. And lhe e1bow being ,he
eenlr~
round which lhe
low~r
PJrt of Ihe arm turns, lhe
murcie
mufi thereforc cxert
a.
force teo times
a.s
great as the wci¡:ht
that is n iCed .
A. ,his kind of lever is a di(.
dv.nuge tO .he moviog
power.
it
¡,
nc.ver u(cd
bUI
in cafes of
occdTity;
fuch as
,ha' ofal.dder, whicb, being Gxed at one end ,
is
by ,he
Clrcngth of a man'a arros rcared againfi a wall
i
anei in
d ock \Vork, where all ,be wheel. may be reckoned leven
of tbis kind, becaufe the powcr that moV'cs cveu whecJ.
except
tllC
lirn, ae.s
~pOD
it
near
the
centre of motion
by
mcans of a {mall pinioD, and
,he
refinance
a'
ha.s
toovec–
come
alh ag'ainfi
the tecth round
ir, circumrercnce.
The (ou"h kind of lever
rlifF.rsoOlhing from
,b~
lirll. bUl in beiog bended for ,he (ake of con\'eDienee.
ACB (6g.
S.)
i. a lever of Ihi. (on, beoded
al
e,
which is it, prop. or centre of motion. P
i.s
a powcr
adiog upon ,be longer arm AC al
F,
by mean. of .he
cord D E goiog ooer Ihe pulley G; and W i. a weiglrt
or reGllance .é1ing upoo lhe end B of .he
(bo"er
arlU
BC. l f the powe, be
10
Ihe weight a. BC i. ' o CF,
Ihey are in
(qui/i6rio.
Thu., (uppo(e
W
' o be
S
pounds
ac!ling at tbe JiHaoce of one
rOOl
from the centre of mo–
lion' C, and
P
' o be
I
pound aaiog
al
F,
6ve fCCl from
tbe ceotre C, ,he powe, aod weighl will jun balance
..eh o,ber. A harnmer drawing a naif is a levcr o( ,bis
(ort.
2 .
The (econd mechanieal power is lbe
whu/ and
11,,/t,
in
wbich
the power is appJicd
10
the
circornfcreftce ofthe
wbeel, and the weighl i. rai(ed by a ropé wbich coils
a–
boot
the
axle
as (he
wheel
is
turned round. Here it
is
plain, lbat ,he veJoeity of Ihe power mull be lO ,he velo–
city of tbe
wcight, as
the circumference of
che
wheel
is
to ,he cireumfe«nce o( ,he axle: and eoo(ec¡ueotly, ,he
power and wcigbt wiJl baJance
e.ehothcr, when
the
iD–
teofi,y of ,he power is lo ,he inlCor.,y o( ,he weigbl
03
tbe circurufcrcn(:c of tbe
axle is
to
che
circum(ercnce
of
Ibe ",heel.
Le<
AB (fig
6.)
be a wbeeJ, CD its ule
and fuppofc
lbe
circumferencc
of
the whec.l to
be
8
tim~
as
gre.atas
the
circumfereDce
of
the axJc
i
then a power P
equal tO , pound haDgiog by lhe cord 1, which goc. round
,he wh<eI, will
b~l.oce
a weigli,
W
of
8
pound. h.nging
by Ihe ropeK ..h,eh go<, rouod ,he axle. And as ,he frie–
tion on the
pivolSor
gudgcons or the
axle
is
but rmalJ,
a
{mall .ddilion
10
,he power will c.ore il 'o de(<<nd. aod
rai(e lhe w.ight: bo, Ihe weigh, w,1I rife ",i,h
only
aD
cigbth pan
o(
the
veloc.ity whercwith the power derccod,.
aDd
confequently
tbrQugh
no more
Ihan
an eighlh pan
of an <qu.J
(p.ce, in tbe (ame ,ime.
Jf
lhe ",hecl
be
pulled round by lb< handles
S,S,
,he power ",ill be
,ocre~<d
in proporrion
10
,heir leng,h . And by .hi.
meaDS. any weight mar be
raile,I
as high as ,he opcrator
plta(.,.
T o .hi. (O" of engioe belong .11 crones (or nifiDg
grC2t '\Ifcights: and
In
this are. the whee.J may bave cogs
. JI
arouod
It
rnn..d or h.ndl.., and a (mall lantcm o,
truodle may be
ru.delO work iD tbe cog', aod be ,uroed
1
t
~