OF THE MECHANICAL POWERS 



61 



about the axle as the wheel is turned round. Here it is 

 plain that the velocity of the power must be to the ve- 

 locity of the weight, as the circumference of the wheel 

 is to the circumference of the axle : and consequently, 

 the power and weight will balance each other, when the 

 intensity of the power is to the intensity of the weight, 

 as the circumference of the axle is to the circumference 

 of the wheel. Let 

 A B be a wheel, C D 

 its axle, and suppose 

 the circumference of 

 the wheel to be eight 

 times as great as the 

 circumference of the 

 axle ; then, a power 

 P equal to one pound, 

 hanging by the cord 

 /, which goes round 

 the wheel, will bal- 

 ance a weight W of 

 eight pounds, hanging 

 by the rope K, which 



goes round the axle. And as the friction on the pivots or 

 gudgeons of the axle is but small, a small addition to the 

 power will cause it to descend, and raise the weight : but 

 the weight will rise with only an eighth part of the velo- 

 city wherewith the power descends, and consequently, 

 through no more than an eighth part of an equal space. 

 in the same time. If the wheel be pulled round by the 

 handles S, S, the power will be increased in proportion 

 to their length. And by this means, any weight may be 

 raised as high as the operator pleases. 



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 lantern 

 or trundle may be made to work in the cogs, and be 



LECT. 

 HI. 



