1000000031

Jcept from r01ling down upon it, by a pOIVer equal tO a

.hird pa" of the w.igh. of the cylinder. T herefore, a

weight may be rolled up thi, inclined plane with • third

-pan of the po\Ver \Vhich \Vould be fuflicien. tO dra\V it up

by the fide of an upright \Vall.

th. plane lOas four

, imeo as long a. high, a fourth part of the power would

be fuflicieot; and fo on, in proportioo. Or, ir a pillar

\Va, to be raifed from a Ooor.o the height G F, by means

of the engine ABDC, (\Vhieh \Vould then aa as a halr

wedge, \Vhere the refinanee giv.. way ooly on one Gde)

,he engine and pillar would be io

t qui/ibrio

whel> the

pO\V« applied at G F was to the weight of the pillar

GF to GD ; and if the pOIVer be inereared. fo as to o·

vereome the friétion of the enginoagainr! the Ooorand pil–

lar, the engine will be driven, aod the pillar raifed : and

when theengine has moved its whole length upon the Ooor,

,he pillar will be raifed to the \Vhole height of the engine,

(rom Gto F.

The force wherewith a rolling body defcends upon an

inclioed plane, is to the force of its abfolute gravity, by

",hieh i. would defeend perpendieularly in a free fpaee,

as tbe height of tbe plane is

its length . For, fuppofe

,he plane AB (6g.

9')

to be parallel to the horizon, the

cylinder C \vill keep at ren upon any part of the plane

where it i, laido lf the plane be fo elevatod, Ihal its

perpeodieular height D (fig.

10.)

is equal

half its

leo¡,h AB, the cylinder will roll down upon the plane

"ilb a force equal to hal f its weigh' ; for it would require

pOIVer (aéting on ,he direétion of AB) equal to balfits

",eigh" 10 keep it from rolliog. l f ,he plaoe AS (fig.

1 1.)

elcvatcd, fo as to be perpendicul2r to the hori'ZoD

the

cylinder C will dereend \Vi,h its \Vbole force of gravi.y.

bec¡ufe: the plane contributes Dothing to

fupport or

hindrance:; ;md

thcTcfore,

would re:quire a power equal

to its ",hole weight

keep it from defeending.

L et the eylinder C (fig. I

~. )

be made 10 'uro upon

flender pivou in the frame D . in which there is a hook

l ,

with a line G lied to it : let tbis line go over Ihe fixed

pulley

and have its other end tied tO a hook in the

\Veight

the weigh. of the body

be tOrhe weight

of the eylinder C, added to tha. of its frame D, as the

perpendicular heigbt of the plane L M i, to its length AB,

the weighl will jun fup'pon the e)'linder upou the plane,

aod a fmall loueh of a 60ger will either eaufe it tu afeend

or defeend with equal

e.fe:

theo, if a little addition be

made to the weight

l .

it will defeend, and draw the ey–

linder up the plane. In ,he time that the eylinner mo\'"

from A 10 B,

will rife through the \Vhole height of ,he

plane ML; aod the \Veight \Vill defeeod from

through a fpaee equal to the whole length. of the

pl.ne

AB.

the plane be made tO moY1l upon rolle.. or friétion'

"'heel. , and the eylinder be fupported " pon it ; the fa me

power will draw the plane uoder the eylinder, which be–

fore drew Ihe eylinder up the

pl.ne

, provided the pÍl'ots

the a"es of the fri.é¡ion-wh..

¡,

be fnull. and the wheel.

themfelve, be prett)' large. For, lel Ihe mAehino ABC

(fig. 13.)

(rqual in lenglh and height to ABM, 6g..

12.)

be pro\'idcd \\ hh {our wheels,

whcr~(\f

ttvO

appear

. nd E , and the third under C,

"Inl(!

Ihe founh is hid

í,om fight by the horizon..1 bo>rd /, . L e. the cylinder

A N

e s.

F be laid upon the 10IVer end of th e inc1ined plane CB·,

and the line G be extendeJ from the fra me of the e)'lio–

der, about fix feet paralld 'o the plane CS ; and, in that

direaion. fixed tO a hook in the wall; \Vhieh will fupport

Ihe eylinder, and keep it from rolling off Ihe plane. Let

one end of .he line

be lied

a hook at C in the maehine,

and the other end tO a \Veight

the fame ., drew the

eylinder up the plane before. If this line be PUt over

the fixed pully

the weight

~ill

draw the machine a–

long the horizont.1 plane

L ,

and under the cylinder F:

and wbeo Ihe maehine has been d..wn the IVhole leogtb–

CB, the eylinder will be raifed to

equal to the per–

pendicular height AB above the horiz.ontal pa" at

To .he inclined plaoe may be reduced all hatehets,

ehifels, and other edge·tools whieh are chamfred ooly

OB–

one fideo

The fifth meehanieal pOIVer or engine is the

'Wdg~.

whieh may be eonfidered as I\VO equally inclined planes

DEF and CEF, joined .ogether at tht ir baf.. ,EF: then

DC (Plate CVllI. fig.

l.)

is the whole ,hicknefs of the

wedge at its baek ASCD, where the power is

applied~

EF is the depth or height of the \Ved::e; DF ,he length

of one of its fides, equal to CF the leoglh of the othe<

fide; and OF is its (harp edge, which i, entered into tbe'

wood intended to be fpli. by the force of

hammer or

mallet nriking perpeodieularly on its back. Thus, AS';,

(6g

2.)

is a wedgedriven imolbe cleft CDE of the wood.

FG.

When the \Vood- dóes no. cleave at any diflaoee before'

the \Vedge, thete will beanequilibrium betIVeen Ihe power

impdling the IVedge downward, and the refin.nee of the

\Voool aéting agaion the two fideo of ,he wedge; if the

power be '0 .he refinanee,

half the thieknefs of ,he

\Vedge at its baek is to lbe length of either of il! fides.; .

tbat is, as

A b,

to.Sb

(6g.

2.)

And if the

power be increared, fa as

overcome the

friaion

of the

wedge and the refinanee arifing from the eohelion or niek–

age of the \Vcod, the

wed&.~

\ViII. be drove

in,

aod the

wood fplit afunder,

But, \Vhen the IVood eleaves at any dinance before

the

wedge (as i, generally does) the POWet impelli ng tbe

wedge IVill not be to the teClnanee of the wood,

half

the ,hiekners of tbe wedge i, to tbe length of one of its

fides ; but as half its thieknef, is to.tbe lenglh of ei,her

fide of the cleft , enimated from. the top o, aétiog pa"

the wedge.. For, if \Ve fuppofe the IVedge to be length–

ened down from

10 the bon om of the eleft at E, tbe

fame proportion will hold ; namely. that the power \ViJl

be 10 the refinan«,. as half the thicknef. of the wedge i.

to the length of c:i,her of

its

GJes: or, which amounts

the filme thing. as the whole

thickDcrS

of (he wedge is

the Irngl b of botll its fides.

order

prove

what is

here

advanced

concerning lhe

wedge, lel u; f"ppofe the weJge to be ¿ ivided lengtb–

wife

inlOt\Yo equal parts: il.fld (hen it

wilJ

bccome

two

c..

qually ir.elinecl plan..; oneor whieh, as

abe,

(Plate CVI !.

fig .

14')

may

be mad.

ufe of as a h. lf "'edAe for fepa–

rating the moulding

from lhe

waiDrcot

ABI

is c–

videot,

that

wheft Ihis half. wC'dge has

beco-

driven irs

whoJe

length

bet\V(cn

(he wainCcot aod mOlllding,

¡es

lide

R (

\ViII be al

acd ,he moulding will be f<parate.!