56 



MECHANICS. 



from the end of the lever, a &, and a wheel attached to 

 the lever, so that this cord may wind upon it as the 

 weight is elevated; then let the power be applied at the 

 otlier end by means of a cord, and a larger wheel be at- 

 tached, so that this cord too may wind upon the larger 

 wheel. These two wheels (fastened together so as to 

 form one), as they are made to revolve on their axis, will 

 now constitute, in a manner, a succession of levers, acting 

 through an indefinite distance according to the length of 

 the cords. The levers here successively acting are of the 

 " first kind," and the axis of the wheel is the fulcrum. 

 This arrangement constitutes in substance the wheel and 

 axle / and its power, like that of the simple lever, depends 

 on the comparative velocity of the weight and the moving 

 force. If, for example, the larger wheel is four times the 

 circumference of the smaller, a force of one hundred applied 

 to the outer cord will raise a weight of four hundred 

 pounds. 



The annexed fiorare exhibits 



Fig. 57. 



one view the power ex- 

 erted through the 

 wheel and axle, where 

 a small weight of C 

 pounds will wind up 

 (or balance) other 

 weights separately, 

 weighing 8, 12, or 21 

 jiounds, as the differ- 

 ence increases between 

 the size of the wheel 

 and of the axle, ac- 

 cording to the rule of 

 virtual velocities already explained. 



The thickness of the rope has not been taken into con- 

 sideration. This is very small when compared with the 

 diameter of the outer wheel, but often considerable when 

 compared with that of the inner. To be strictly accurate, 



and axle^ shoicing the heavier loeightfor 

 less motion. 



