100 ADVANCED ELECTRICITY AND MAGNETISM. 



complete magnetic cycle. The total work spent on the iron is 

 given by the value of the integral 



abV C 



I x-dy 



47T J 



extended over the whole cycle ; but the value of J x-dy extended 

 over the whole cycle is the area enclosed by the cB and &C curve. 

 Therefore, the total energy, in ergs, lost in V cubic centimeters 

 of iron per magnetic cycle, is equal to abV/^ir X area enclosed 

 by the <$ and ^C curve. This energy loss is called the hysteresis 

 loss, and it is all converted into heat. The meanings of a and b 

 are explained in Art. 61. 



The hysteresis loss per cycle increases with the range of flux 

 density, and it may be expressed with sufficient accuracy for 

 most practical purposes by the empirical equation: 



W = riV 1 '* (2) 



which is due to Steinmetz. In this equation W is the loss of 

 energy in ergs per cycle, V is the volume of the iron in cubic 

 centimeters, db $ is the range of flux density during the cycle, 

 and 77 is a coefficient which is nearly constant for a given kind 

 of iron or steel. The following table gives the approximate values 

 of 77 for different kinds of iron and steel. 



TABLE. 

 Values of hysteretic coefficient 17. 



Best quality of sheet iron for transformer cores, annealed 0.0015 



Sheet iron for armature cores, annealed 0.003 



Ordinary sheet iron, annealed 0.004 



Soft annealed cast iron 0.008 



Soft machine steel 0.0095 



Cast steel ' 0.12 



Hardened steel 0.25 



PROBLEMS. 



i. The intensity of the magnetic field in the air gap between 

 the pole face and the armature core of a dynamo is 3,500 gausses 

 and the field is at right angles to pole face and armature surface. 



