1000000031

•

M E

.to

from (he

\V3tnrcot.

N ow, from what has beco al ·

rcady

proved

of (he inclincd plane.

appears, that

have

ao equilibrium between(he powcr imptdling thehalf.wedge

80d the refiltanee of the mouldiDg. the forme r mull be to

Ih!

I",Her as

oc..

that

¡'.

as (he thickners of tbe

baek whieh reeei..s ,he Uro"e is 'o the length of the fide

asainfl which lhe

moulding aas.

Therefore, fince the

power upon lhe

half wcdge

is to

the

re(iflance

againll its

fide, as (he h31fback

lhe wholeGde

oc,

is plain,

th.. the power upon the \Vhole wedge (where ,he wbole

baek i. double the half baek) mull be to ,he refillance •

gainll both in fid eo... ,he ,hieknef. of ,he wbole baek

¡s to the length of bOlh the lides. fuppDfing the wedge

at the borton> of the cleft; or as the ,hieknefs of tbe whole

baek to ,he Itngth of bo,h fi des of the cleft. when the

wood fpl i" at

anydillane~

before the wedge. For, \Vhen

'thoe wedge is driven quite ioto Ihe \Vood, and the wood

{plits at ever fo fm.!I a

dilla~e

before i" edge. the top

of the wcdge lhen becomes

aéting..fart, becaufe the

wood does no' ,oueh

any where e1fe. JlIo¡d fi nee the bot-

10m of the cleft ",un be eoofidered as tha, pArt where the

whole

Uickage or refi(lance is accumul.ted,

plaio.

{rom ,he oaturo of th 1 ver. th" the farther the p",er'

:41{ls from ihe:: rclirlancc, the greatcr is the advantage.

Sorne wrtters have advanced, that the power of the

wec.lge is to the refiflance to

overcome, as tbe tbick–

flef. of ,be baek of ,he wedge i. 'o Ihe leog,h only of one

.of its fides; whieh feems very Ilrange': foro if we fup.–

.pofe AD (Plate CVIlI. hg 3.) 'o be a (\rong ioflex,ble.

,bar of wood or iron h"t into the grouod a' CS. and D

and

E 'o be two bloeks of marble Iying 00 the ground 00 0ppo,–

file fides of the bar. i, is evideot ,ha! ,he block D may be

feparateel from the bar to the diaanee

equal 'o

ab.

.driving the indined plaoe or half wedge

abo

dowo bell'leeo

them; and 'he block E may be feparaled to ao

equal.di–

/laoee on the other fideo iD like maoner, by tbe half wedge

•do.

BUI the pow« impelling eaeh half \Vedge will be 'o

'the refillanee of the block againll ilS fideo as the thieknef.

of that half wedge is to the leog,h of ilS .ltiog fide o There–

fore the pow.. to drive both ,be half wedges i. tO both

,he refiílanee•• as both the half b.eks is to the leogth of

both the alting fides. or as halflhe ,hiellnefs <if the whole

baek i. 10 the length of eilher fideo And. if the bar be

takeo away. the bloeks pu, clofe ,ogether. aod the tlVO

h alfwedges joined to m. ke one; i, will require as mud,

foree tOdrivc

down between the blocks. as

equal to

the fUDl of the feparate powers altiog upon tbe half wedges

when the bar

was

between them.

To eonhrm this by an experimento let Iwocylinders. as

AB (fig. 4') and CD. be drawn to\V.rds one another by

Jine. running over fixed pulley•• 20d a weighl of 40 ouoees

hanging at the liDes belonging to eaeh eylinder: and le, a

wedge of 40 ouoe<5 weight. having ilS baek jull as ,hiek

a. dth« 01 its fides is long. be put between the eylinder••

.vhieh will theo altagainn eaeh fide wilh arefillaoee equal

400unJes . whilfl: its

own

weight cDdeftvours to .briog

it down and feparate them. And here. the po\\'er of Ihe

\Vedg.·s gravity impelling i, downward. will be 10 the re–

r.1l. nee of uoth the eybnders againn the wedge. as the

tni,knd. of Ihe

wed~e

is 10 the length of bOlh its fieles;

{Df

Ihe,e wil! Ihtn be an equiJib,iu/Il belween the \Veigh,

e s.

of ,he \Vedgo and the , efillaoee of the oylindero againtí

i~.

~nd

will remaio at ,¡ny

hei~ht

belwecn them; requiring

JuH as much power

pulh

upward as to pull il down.

ward.-If another wedge:: of cqual weight .and depth

with

this. and ooly half

thlck,

put bcnveen the! cylinders

it \ViII requi re twicc as Oluch weighl to

hung al Ihe end;

the Jines which draw lhem together, lO keep lhe wedge

from going

clown

between them. Th at

¡s, a

wedge of

40011nees. whofe baek is only equal 'o half the leogth of

ooe

Íls

fides, will require 80 ounces lO each cyl'nder.

to keep

in ao equilibrium betweeo them: and t\Vice 80

160, equal

four

times

40'

So that che power will

alw.ys

'o Ihe refirt aoee. as the thieknefs of the baek of

the wedge is 10 theleoglh (not of its one fideobUI) ofboth

its fides.

The beft way. thollgh perhaps not ,he nea,eíl. for m.–

king

wedge with

its

appurtenances forfuch experimeDls,

i. as fu!lows . L et

I KL~I

(6g. 4') aod LMNO be two

¡¡a, pieees of wood, eaeh abolll 6fteeo ioehes loog aod

three or four io bre.dtb. joined ,ogelher by • hinge a'

LM; and 1« P be a gra<luated areh of brafs. 00 whieh

<he

faid pieces of wood may be opcned ro . ny angle DO' ",o,:e

than

deerees, and then 6xt

the given angle by

means

of the two

ICrew~

aod

Then. IKNO will reprefent

the baek of Ihe wedge. LM i" Iharp edge whieh enle..

Ihe wood. aod the oUllides of the pieees IKLM aDd

LMNO tbe two fides of ,he wedge agaioll whieh tbe wood

alts in cleaving. By means of ,he faid areh. the wedge

may be opeoed fo as tO adjull the thiekDefs of its back

io any proponioo to the leDg,h of eilher of its fide•• but

DO' 'o exeeed thal length: aod any weigh,. as

may he

huog 'o the wedge upon the hook M. whieh weight. to–

gerher with ,he weighl of the wedge itfelf. may be eooli–

dered as the impelling power; whieh is all ,he fame iD ex–

periment. wh«her it be

I.id

upon ,he baek of ,he wedge

'o pulh it dowo. or hung 'o its edge ' o pull it dowo•

-Le< AB aDd CD be two wooden eylinders. eaeh abont

'wo ioehes thiek. where ,hey toueh the outfides of the

wedge; and le, Iheir ends be made like ,wo rouod fla'

pla,e•• ' o keep

Ih~

wedge from Ilipping off endwife be–

,weco ,hem. L e, a fmall eord wi,h a loop on ooe end

of it go Dver a pivot io Ihe eod of eaeh eylioder. and the

eords S and T belongiog ,'o the cylinder AB go over ,he

fixt pulleys W and X. aod be fallened al theirother eod.

' o the bar

'Ulx.

on whieh aoy wtight. as Z. may be hUDg a'

ple.fure. In like manoer. le, theeords

and R belong–

iog to the eylinder BC go over the 6xt pUlleys

and V

'o ,he bar

,1(1.

on whieh a weight Yeqll.1 to Z may be

hung. Thefe weights. by ¿r.wiog th. cylillders ,owards

one another•. may be eonfidered as Ihe refillanee 01 tbe

wood alting equally a¡:aioll oppofile fides of the \Vedgo. ;

Ihe cyliDders .themlelves beiog fufpended oear and pa–

rallello eaeh other. by ,hei, pi,'ots in loops 00 the lin••

E .F .G .H; wbich line.s may be 6"ed tO hooks io ,he ciel–

iog of the room. T he longer thefe line. are. the better ;

aod they Ihould never be lefs Ihan four fee, each. The

further airo ,he pJllley. V,r .V'and W .X are from the

eo}–

'linders,

the

lTUf r

\ViU

the experiments be; and they

illay

tUrD

upon pins lixed into the \Vd l!.

lo thi. maehine. the weights Y aod.Z. and the weigh,

may be varied al plealin e, fo as 10 be adjufied in pro–

portion