ENERGY AND ITS TRANSFORMATIONS. 



21 



partly in doing the useful work of the system, and 

 partly in storing energy ; and the same machine may 

 do work at another instant partly by expending the 

 energy received by it, and partly by expending stored 

 energy previously accumulated. 



Storage or restoration of energy thus always occurs 

 when change of speed takes place. It is evident, since 

 the storage or restoration of energy implies variation 

 of speed, that the condition of uniform speed is that 

 the work done upon the machine shall at each instant 

 be precisely equal to that done by it upon other bodies, 

 The work applied must be equal to that of resistance 

 met at the driving-point. Thus, 



:EPv — ^Rv'-fPdv=fRdv'] . . (i8) 



and the effort at each point in the machine will be 

 equal to the resistance, and will vary inversely as the 

 velocity of the point to which it is applied ; i.e., 



p ^ 



P' = v ('9) 



In the starting of every machine, energy is stored 

 during the whole period of acceleration up to maximum 

 speed, and this energy is restored and expended while 

 the machine is coming to rest again. This latter quan- 

 tity of energy is usually expended in overcoming fric- 

 tion. 



The useful and the lost work of a machine are, to- 

 gether, equal to the total amount of energy expended 

 upon the machine, i.e., to the work done upon it by its 

 "driver." The Useful Work is that which the machine 

 is designed to perform ; the Lost Work is that which is 



