102 TREATISE ON ALTERNATING CURRENTS. 



The rate at which energy is lost in the elementary path is, 

 therefore, given by 



_ 

 ' 2 x 10 16 1 J 



C 3 



2 



- 2b x 10 16 

 since 



a : b = x : y 



The rate at which energy is lost in the whole stamping is, there 

 fore, given by integrating from y = o, to y = ~b, and is 



where V = dbL is the volume of the stamping. 



The rate at which energy is lost per cubic centimetre is, 

 therefore 



i 2 ^ 2 cosV 

 8 x 10* 6 WattS 



and the average rate per second at which energy is lost per cubic 

 centimetre is given by 



*-&*/:" 



where T is the periodic time 



16 x 10 18 



4 x 10 16 



where n is the frequency of the flux. If ~b is expressed in 

 mils., this becomes 



^(bnBf x 10- 16 ...... (30) 



This value is, however, probably too large, and the value (-T/3-) 



will be more approximate, since the eddy currents will not 

 generally take symmetrical paths as is here assumed, owing to 

 the iron not being quite homogeneous. 



