MECHANICS. 
diameter of the wheel to be eight inches, 
and the diameter of tlie axis to be one inch ; 
tlien one ounce acting as the power P, will 
balance eight ounces as a weight W ; and 
a, small additional force w'ill cause the wheel 
to turn with its axis, and raise the weight ; 
and for every inch which the weight rises, 
the power will fall eight inches. 
The wheel and axis may be considered as 
a kind'^of perpetual lever, (fig. 8. ) of which 
the fulcrum is the centre of the axis, and 
the long and short arms the diameter of the 
wheel and the diameter of the axis. From 
this it is evident, that the longer the wheel, 
and the smaller the axis, the stronger is the 
power of this machine ; but then the weight 
must rise slower in proportion. A capstan 
is a cylinder of wood, w'ith holes in it, into 
which are put bars, or levers, to torn it 
round ; tliese are like the spokes of a wheel 
without the rim. Sometimes tlie axis is 
turned by a winch fastened to it, whicli, in 
this rrapect, serves for a wlieel, and is more 
powerful, in proportion to the largeness of 
the circle it describes, compared with the 
diameter of the axle. Wlien the parts of 
the axis differ in thickness, and weiglits are 
suspended at the different parts, they may 
be sustained by one and the same power ap- 
plied to the circumference of the wdieel, 
provided the product arising from tlie mul- 
tiplication of tlie power into tlie diameter 
of the wheel, be equal to the sum of tlie 
products arising from the multipUcation of 
the several weights into the diameters of 
those parts of the axis from whicli they are 
suspended. In considering the theory of 
the wheel and axle, we have supposed the 
rope that goes round the axle to have no 
sensible thickness ; but as in practice this 
cannot be the case, if it is a thick rope, or if 
there be several folds of it roufid the axis, 
you must measure to the middle of the 
outside rope to obtain the diameter of the 
axis, for the distance of the weight from the 
centre is increased by the coiling up of the 
rope. 
If teeth are cut in the circumference 
of a wheel, and if they work in the teeth of 
another wheel of the same size as fig. 9. it is 
evident that both the wheels will revolve in 
the same time ; and the weight appended 
to the axle of tlie w heel B, will be raised in 
the same time as if the axle had been fixed 
to the wheel A. But if tlie teeth of the se- 
cond wheel be made to work in teeth made 
in the axle of the, first, as at tig. 10. as every 
part of the circumference of the second 
wheel is applied successively to the circum- 
ference of the axle of tlie first, and as ths 
former is much greater than the latter, it 
is evident that the first wheel must go 
round as many times more tlian the second, 
as the circumference of the second wheel 
exceeds that of the first axle. In order to 
a balance here, the power must be to the 
weight, as the product of the circum- 
ferences, or diameters of the two axles mul- 
tiplied together, is to the circumferences or 
diameters of the two wlieels. This will 
become sufficiently clear-, if itbe considered 
as a compound lever, which was explained 
above. Instead of a combination of two 
wheels, three or four wheels may work in 
each other, or any number ; and by thus in- 
creasing the number of wheels, or by pro- 
portioning the wheels to the axis, any de- 
gree of power may be acquired. To this 
sort of engine belong all cranes for raising 
great weights ; and in this case the wheel 
may have cogs all round it, instead of 
handles ; and a small lanthorn, or trundle, 
may be made to work in the cogs, and be 
turned by a winch ; whicli will make the 
power of the engine to exceed the power of 
the man wdio works it, as much as the num- 
ber of fevolutions of the winch exceeds 
those of tire axle, when multiplied by the 
excess of the length of the winch above the 
length of the semi-diameter of the axle, 
added to the semi-diameter or half thick- 
ness of the rope, by which the weight 
is drawn up. See Crane. 
The construction of the maiu-spring-box 
of the fusee of a watch round which the 
chain is coiled will illustrate the principle 
of the wheel and axis. The box may be 
considered as the wheel, and the fusee the 
axle or pinion to which the chain communi- 
cates the .motion of the box. The power 
resides in the spring wound round an axis 
in the centre of the box, and the weight is 
applied to the lower circumference of the 
fusee. As the force of the spring is greatest 
when newly wound up, and gradually de- 
creases as it unwinds itself, it is necessary 
that the fusee should have different radii, so 
that the chain may act upon the smallest 
part of the fusee when its force is greatest, 
and upon the largest part of the fusee when 
the force i.s least, for the equable motion of 
the watch requires that the inequality in the 
action of the spring should be counteracted 
so as to produce an uniform effect. 
The pulley is a small wheel turning on an 
axis, with a drawing rope passing over it; 
the small wheel is usually called a sheeve, 
and is so fixed in a box, or block, as to be 
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