65.] RECTILINEAR MOTION. 35 



63. Power. It has been shown that the time-effect of a force 

 is measured by its impulse (Art. 2), while the space-effect is 

 measured by its work (Arts. 47, 48). In applied mechanics it is 

 of great importance to take time and space into account simul- 

 taneously. The time-rate at which work is performed by a force 

 has therefore received a special name, power. The source from 

 which the force for doing useful work is derived is commonly 

 called the agent ; and it is customary to speak of the power of 

 an agent, this meaning the rate at which the agent is capable 

 of supplying useful work. 



64. The dimensions of power are evidently ML 2 T~ S . The 

 unit of power is the power of an agent that does unit work in 

 unit time. Hence, in absolute measure, it is the power of an 

 agent doing one erg per second in the C.G.S. system, and one 

 foot-poundal per second in the F.P.S. system. As, however, 

 the idea of power is of importance mainly in engineering prac- 

 tice, power is usually measured in gravitation units. In this 

 case, the unit of power is the power of an agent doing one foot- 

 pound per second in the F.P.S. system, and one kilogramme- 

 metre in the metric system. 



A larger unit is frequently found more convenient. For this 

 reason, the name horse-power (H.P.) is given to the power of 

 doing 550 foot-pounds of work per second, or 550x60 = 33,000 

 foot-pounds per minute. 



65. Efficiency of Machines. While the principle of the con- 

 servation of energy was proved in Arts. 57 and 58 only for a. 

 special case, it is known to be of almost universal application to 

 the forces occurring in nature. Thus, in particular in the case 

 of machines it is found to be verified with a degree of approxi- 

 mation corresponding to the precision of the investigation. 



The principle can here be expressed in the form 



W=Wt+W l9 

 if W denote the total work done by the agent driving the 



