700 INDUSTRIAL APPLICATIONS. 



which corresponds to the heat disengaged in the resistance R of 

 the machine alone. We have then 



U = El -RI 2 = I [//</>(!) -IR], 

 and the maximum of useful work corresponds to the condition 



or 



The current I which gives the maximum useful work is no 

 longer in general half the current I , which the machine would 

 produce if short circuited. 



The efficiency for the maximum work is 



IR i 



2 



This efficiency is equal to 0*50 if the function </>(!) is a constant; 

 it is lower or higher than 0^50 according as the derivative </>'(!) is 

 positive or negative. 



Let us imagine two machines traversed by the same current I, 

 one of which serves as electromotor and the other as motor, the 

 former absorbing the work !<(!), and the second producing the 

 useful work n^l^l). The expression for the efficiency is 



~ *(!) ' 



it is simply equal to the ratio of the velocities when the function 

 </>(!) is the same in the two machines. 



1257. VARIOUS TYPES OF MACHINES. All the properties of a 

 machine with a strictly uniform current are then defined by the 

 function <(!), and the form of this function might serve to classify 

 various types of machines. We shall observe that the product !<(!) 

 represents the work absorbed by the machine during a period. 



i st. We shall apply the term tlectrodynamic to those machines 

 in which the inductor and the induced body consist simply of 

 wires, and traversed by the same current. The work W 1 is then 

 proportional to the square of the intensity of the current, and we 

 may write 



or <>! = !. 



