MACHINES WITH VARIABLE CURRENT. 737 



For a given velocity this energy is a maximum when R = Lw, which 

 gives 



The resistance corresponding to the maximum energy and the 

 value of this maximum are proportional to the velocity. The mean 

 square of the intensity, and the retardation relative to the maximum, 

 have constant values half those which they would have if the velocity 

 were infinite.* 



If the total resistance R is made up of two parts, the one a 

 which comprises the machine and the connections, the other x 

 corresponding to a useful work u, and having no self-induction, we 

 have 



U = ^L 



a + x 

 x 0^2 i 



It will be seen that at constant velocity the useful work is a 

 maximum when the value of x is equal to the apparent resistance 

 of the electromotor; the corresponding values of the useful work 

 and of the efficiency are then 



U. = ^ 



The machines with alternating currents have the remarkable 

 property that the relative efficiency for the maximum useful work 



* JOUBERT. Ann. de V Ecole Normale [2], Vol. x., p. 131. 1881. 

 VOL. II. B B B 



