154 BENJ. PIKE'S, JR., DESCRIPTIVE CATALOGUE. 



several circumferences of the wheel. Pulling at the rope, p, 

 to turn the wheel once round, as much cord must be drawn 

 off as winds once about the circumference of the wheel, and 

 the cord to which the weight is suspended will wind once 

 around the axis, and the weight raised through as much 

 space as the circumference of the axis. If the diameter of 

 the wheel be ten inches, and the diameter of the axis be one 

 inch, then one ounce acting as a power, p, will balance ten 

 ounces as a weight, w ; and a small additional weight will 

 cause it to descend, and turn the wheel and its axis, and so 

 raise the weight, w ; and for every inch the weight rises, the 

 power, P, will fall ten inches ; if the diameter of the wheel 

 be five inches, it will balance with two ounces applied as a 

 power, and descend five inches ; or, supposing one ounce to 

 be the power, it will balance a weight of five ounces at the 

 axis ; if the diameter be two inches, or of any other size, the 

 same proportions will be maintained. The wheel and axis 

 may be considered as a lever, whose fulcrum is a line passing 

 through the centre of the wheel and middle of the axis, and 

 whose long and short arms are the radii of the wheel and 

 axis that are parallel to the horizon, and from whose extre- 

 mities the chords hang perpendicularly. Suppose that the 

 power does not act by a rope winding round a wheel, but 

 that it is moved by a man's strength applied immediately to 

 the spokes or handles, i, H, K ; if the man first lay hold of 

 the handle, H, and push it down to K, his hand passes through 

 the space, H K, and the handle will be brought down to K ; 

 he then lays hold of i, and pushes it to H, and so on till he 

 has turned the wheel once round ; and his hand, which is 

 now the power, will describe the whole circumference of a 

 circle, which is to be considered as the circumference of the 

 wheel. A wheel and axis may therefore be considered as a 

 kind of perpetual lever, on whose arms the power and 

 weight always act perpendicularly, though the lever turns 

 round its fulcrum ; and in like manner, when wheels and 

 axis move each other by means of teeth on their circumfer- 

 ence, such a machine may be considered as a perpetual 

 compound lever. 



The Levers. (Fig. 160, next page.) In this arrangement 

 of levers, there is a brass beam or lever, A, having arms of 

 equal length, supported on its fulcrum at the side of the 

 pillar, which pillar is attached to a mahogany base ; in each 



