MECHANICS. 



fbr every inch which the weight rises the 

 power will increase eight inches. 



The wheel and axis may be considered 

 as a kind of perpetual lever, (fig 1 . 8.) of" 

 which the fulcrum is the centre of the 

 axis, and the long and short arms the di- 

 ameter 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 cy- 

 linder of wood, with holes in it, into 

 which are put bars, or levers, to turn it 

 round ; these av-e like the spokes of a 

 wheel without the rim. Sometimes the 

 axis is turned by a winch fastened 

 to it, which, in this respect, serves for 

 a wheel, and is more powerful, in pro- 

 portion to the largeness of the circle it 

 describes, compared with the diameter 

 of the axle. When the parts of the axis 

 differ in thickness, and weights are sus- 

 pended at the different parts, they may 

 be sustained by one and the same power 

 applied to the circumference of the 

 wheel, provided the product arising from 

 the multiplication of the power into the 

 diameter of the wheel, be equal to the 

 sum of the products arising from the 

 multiplication of the several weights into 

 the diameters of those parts of the axis 

 from which they are suspended. In con- 

 sidering the theory of the wheel and 

 axle, we have supposed the rope that 

 goes round the axis 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 round 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 cnt 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 the wheel B, will 

 be raised in the same time as if the axle 

 had been fixed to the wheel A. But if 

 the teeth of the second wheel be made 

 to work in teeth made in the axle of the 

 first, as at fig. 10. as every part oi the cir- 

 cumference of the second wheel is ap- 

 plied successively to the circumference 

 of the axle of the first, and as the former 

 is much greater than the latter, it is evi- 

 dent, that the first wheel must go round 

 as many times more than 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 

 multiplied together, is to the circumfe- 

 rences or diameters of the two wheels. 

 This will become sufficiently clear, if it 

 be 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 increasing the 

 number of wheels, or by proportioning 

 the wheels to the axis, any degree of pow- 

 er may be acquired. To this sort of en- 

 gine belong all cranes for raising great 

 weights ; and in this case the wheel may 

 have cogs ail 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 ; which will make the power 

 of the engine to exceed the power of the 

 man who works it, as much as t3ie num- 

 ber of revolutions of the winch exceeds 

 those of the 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 

 thickness of the rope, by which the 

 weight is drawn up. See CRANK. 



The construction of the main-spring- 

 box of the fusee of a watch, round which 

 the chain is coiled, will illustrate the prin- 

 ciple of the wheel and axis. The box 

 may be considered as the wheel, and the 

 fusee the axle or pinion, to which the 

 chain communicates 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 low- 

 er circumference of the fusee. As the 

 force of the spring is greatest when 

 newlv wound up, a?id gradually decreases 

 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 its force is 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 moveable round a pin passing 

 through its centre. Pullies are of two 

 kinds'; fixed, which do not move out of 

 their places ; and moveable, which rise 

 and fall with the weight. 



When a pulley is fixed, as Plate II 

 Mechanics, fig-. 11. two equal weights 



