MECHANIC POWERS. 37 



The velocity of the power, therefore, will be to 

 that of the weight, as, the circumference of the 

 wheel to that of the axis. 



That the power and the weight may be in equi- 

 librio, therefore, the power must be to the weight 

 as the circumference of the wheel to that of the 

 axis. 



It is proved by geometry, that the circumfer- 

 ences of different circles bear the same proportion 

 to each other as their respective diameters do ; 

 consequently the power is to the weight, as the 

 diameter also of the axis to that of the wheel. 



Thus, suppose the diameter of the wheel to be 

 eight inches, and the diameter of the axis to be 

 one inch ; then one ounce acting as the power P 

 will balance eight ounces as a weight W ; and a 

 small additional force will 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, of which the fulcrum is the 

 centre axis, and the long and short arms the dia- 

 meter of the wheel and the diameter of the axis. 

 See Plate 2. fig. 2. 



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, with holes in 

 it, into which are put bars, or levers, to turn it 

 round ; these are like the spokes of a wheel with- 

 out the rim. 



Sometimes the axis is turned by a winch fas- 

 tened to it, which, in this respect, serves for a 



d 3 



