LESSONS IN PHYSICS. 65 



P X PF = W X WF, in which case P : W :: WF : PF. That is the 

 power and weight will be in equilibrium when they are to each 

 other inversely as the lengths of their respective arms. The 

 greater the difference in the length of the arms, the more 

 effective is the lever in transferring power. If the arms of the 

 lever are equal, the power and weight will be equal, and in 

 case of motion the space moved by each will be equal. If the 

 weight arm is shortened by moving the fulcrum toward the right 

 a given power will overcome a greater resistance and do more 

 work. If the power arm is shortened by moving the fulcrum 

 toward the power, the power becomes less effective for overcom- 

 ing resistance, but more effective for producing motion, as in lift- 

 ing a weight with the hand the power acts through two or three 

 inches, while the weight moves through two or three feet. 



In the case of the compound lever the power and weight will 

 be in equilibrium when the product of the power by the long arms 

 equals the product of the weight by the short arms, as in Fig. 6. 

 P X PF' X P'F = W X WF X W'F'. 



The wheel and axle consists of a wheel and cylinder fitted 

 together so as to turn on the same axis. The power is applied to 

 the circumference of the wheel, and the weight, usually by means of 

 a rope is applied to the circumference 

 of the cylinder or axle. The power acts 

 through the circumference of the wheel 

 while the weight acts through the 

 circumference of the axle. And they 

 will be in equilibrium when P X cir. of 

 the wheel = W X cir. of the axle. An 

 end view of the wheel and axle shown 

 in Fig. 7, shows the wheel and axle to 

 be a lever of the first class and the FIG. 7. 



equation may be P X PF the radius of the wheel =W X WF, the 

 radius of the axle. If power is applied to the axle there is gain 

 in velocity, as in the case of a circular saw. The common wind- 

 lass for drawing water from a well or raising weights is a familiar 

 illustration of this machine. The capstan used in moving build- 



L. S. 5 



