Energy of Magnetized Iron . 177 



consider, first, a ring electro-magnet with an iron core, of 

 length I and section a. If n be the number of windings, the 

 whole inductive electromotive force is ncr . d23, and the element 

 of work is ncrC . d^d, C being the current at the moment in 

 question. But 



I § == AirnG ; 



so that the element of work is, per unit of volume of iron, 

 If we express 23 in terms of © and 3, we have 



of which the latter part is specially due to the iron. In 

 practice the former part is small, and the distinction between 



^§d23 and $d$ 



may often be disregarded. 



But it is by no means a matter of indifference whether we 

 take 23 d& or § <#B. The difference between the two modes of 

 reckoning may be exemplified in the case of iron already 

 nearly " saturated," and exposed to an increasing force. 

 Here J23 d& is large, while j§ d$$ is small ; so that the latter 

 corresponds better with the changes which we suppose to be 

 taking place in the iron, as well as to the circumstances of 

 ordinary practice. 



Let us now consider a little more closely the cycle of fig. 1. 

 From A to B, § is negative, while d$3 is positive ; so that 

 along AB the inductive electromotive force is in aid of the 

 current, and work is received from the iron of amount repre- 

 sented by the area ABM. From B to J), £> is positive as well 

 as d%$, and work represented by BDNB may be supposed to 

 be put into the iron. From D to E, work, represented by 

 NED, is received from the iron, and from E to A work, repre- 

 sented by AME, is expended. From this we see that not only 

 is work, represented by the area ABCDEA, dissipated in the 

 complete cycle, but that at no part of the cycle is there more 

 than an insignificant fraction of work recovered. The case is 

 not one of a storing of energy recoverable with a small rela- 

 tive loss, but rather one of almost continuous dissipation. 



And here the question is forced upon us, whether it is true, 

 as is usually supposed, that the strong residual magnetism at 



Phil Mag. S. 5. Yol. 22. No. 135. August 1886. N 



