ELECTROMAGNETS. MAGNETISM OF IRON. 379 



any portion of the cB and 3f curve and the jy-axis. Therefore, 

 ab Vj^nr is the number of ergs of work represented by each unit 

 of area between the cB and &C curve and the j/-axis. 



22. Magnetic hysteresis. The magnetic cycle. The diver- 

 gence of the cB and &C curve for increasing values of df from the 

 cB and cV curve for decreasing values of &C is called magnetic hys- 

 teresis ; or, rather, the tendency of iron to retain a previous mag- 

 netic state which is the cause of this divergence is called magnetic 

 hysteresis. One effect of magnetic hysteresis is that the work 

 regained when iron is demagnetized is less than the work which 

 must be spent to magnetize the iron, as pointed out in Art. 2 1 . 



The magnetization of a given portion of the armature core of a 

 dynamo is repeatedly reversed as the armature rotates, reaching 

 a certain positive value of cB for one position of the armature, an 

 equal negative value of cB for another position of the armature, 

 coming back again to the original positive value of <$, and so on. 

 Such a magnetic double-reversal is called a magnetic cycle, inas- 

 much as the magnetic condition of the iron is precisely the same 

 at the beginning and at the end of the double reversal. 



When a mass of iron is magnetized along the cB and off curve 

 op of Fig. 1 6, and then partially demagnetized along the curve 

 //', a portion of the work done upon the iron during the first 

 stage op is regained during the stage pp 1 ', a portion is lost as 

 heat, and a portion remains in the iron as energy of magnetization. 



When, however, a mass of iron is carried through a magnetic 

 cycle, the algebraic sum of the work spent upon the iron during 

 the cycle, that is to say, all of the work spent upon the iron during 

 the cycle is lost as heat, inasmuch as the magnetic energy in the iron 

 is exactly the same at the beginning and at the end of the cycle. 



Fig. 17 shows the relation between cB and 9C during a com- 

 plete magnetic cycle. The total work spent on the iron is given 

 by the value of the integral 



abV r 



-. x.dy 

 W J 



