Energy of Magnetized Iron. 181 



In order to find the points Q, Q' appropriate to the ellipsoid 

 (50 : 1) from P, P', we have merely to measure PQ, P'Q' 

 equal to EM. We thus obtain the curve AQEQ'FC, on 

 which the points of zero magnetization are the same as on 

 the original curve *. We see that a much stronger field is 

 now required to produce the higher degrees of magnetization, 

 and that there is less hysteresis — the magnetic state is more 

 nearly a definite function of the external field. A similar 

 construction might be used reversely to pass from observed 

 results relative to ellipsoids of moderate elongation to the 

 curve appropriate to ellipsoids of infinite elongation, on which 

 alone we can base our views of the real character of magnetic 

 media. 



Prof. Ewing has traced by experiment the influence of 

 various degrees of elongation on the magnetism of cylindrical 

 rods. Results of this kind are exhibited in his fig. 3, but 

 they are not strictly comparable with those obtained above, 

 not only because the latter relate to ellipsoids, but also on 

 account of the different character of the magnetic operations 

 represented. His curves begin at a condition of zero field 

 and zero magnetization. 



The work expended in producing a small change of mag- 

 netization of the ellipsoid, acted upon by a uniform field, is 

 fe'dS simply per unit of volume. This we may see, perhaps 

 most easily, by supposing the iron to be replaced by an electric 

 current of equal magnetic moment. The element of work 

 done then depends upon the coefficient of mutual induction 

 M of the two circuits, and M may be regarded as the number 

 of lines of force due to the original current which pass through 

 the fictitious circuit. The whole work is thus 



= $$d3+ iN3 2 , 



if we reckon from the condition of zero magnetization. 

 The first part is that already considered, and shown to be 

 almost entirely wasted ; the second, which in most cases of 

 open magnetic circuits is much the larger, is completely 

 recovered when the iron is demagnetized. 



Thus in fig. 2, since QQ / = PP / , the areas of the two curves 

 are the same, which indicates that the same amount of work 

 is dissipated in a complete cycle. But the work absorbed 

 during one part and restored during the remainder of the 



* Dr. Hopkinson (loc. cit. p. 465) has already applied this method to 

 the determination of the particular point F, indicative of the residual 

 magnetism in the ellipsoid, when the external force is withdrawn. 



