234 Br. J. Larmor. On the Electrodynamic and [Jan. 2, 



from the form of the curve of hysteresis for retentive iron in 

 high fields that the fraction that is directly available at the actual 

 temperature must always be small, and he supports the inference by 

 considerations of the nature of the above analogy ; in the absence of 

 hysteresis there would be no such direct availability. He derives the 

 practical result that a complete magnetic circuit is deleterious for 

 induction coils in which length of spark is the desideratum, the increased 

 total induction attained inside the ring-core being more then neutra- 

 lised by the diminished promptness of magnetic reversal. 



In fact, if the core, laminated so as to have merely negligible con- 

 ductivity, is surrounded by a perfectly conducting coil or sheath, and 

 its permanent magnetism is removed at constant rate - dl/dt by an 

 ideal process applied to it, the intensity of induction in the core 

 will diminish at the rate - iirdl/dt ; and this defect of induction 

 must be made good by the influence of the current thereby induced in 

 the sheath, as otherwise there would be a finite electromotive power in 

 it, which is impossible on account of its perfect conductivity. This 

 restored induction is of the form H' + 47rl', where I' is the magnetism 

 induced by the force H' due to the induced current ; thus 



| ( H' + 4.r )+4 4 . o, 



and the actual total rate of fall of magnetisation is diminished to 



— _ which is only the fraction hr ^^LAiJ- of the constrained loss 

 dt dt * 4 dt 1 dt 



of retained magnetism dl/dt. In this most favourable case the action of 

 the coil or sheath thus delays the time-rate of loss of permanent 

 magnetism in the core in the ratio (47tk') _1 , where k is the effective 

 permeability for small additional force under the actual circumstances ; 

 that is, the delay in reversal more than compensates the gain in in- 

 duction. » 



5. There remains another question, when viscous and other hyste- 

 retic effects are practically absent so that the changes of magnetisation 

 exactly keep step with those of the currents, and the degree of 

 availability of residual magnetic energy thus does not arise ; — whether 

 the energy of the magnetisation comes from the store of heat of the 

 material and is thus concomitant with a cooling effect when no heat is 

 supplied, or whether it is in part intrinsic inalienable energy of the 

 individual molecules merely temporarily classed as magnetic. So far as 

 it may lie the latter, it must for each element of volume depend on the 

 state of that element alone, like the part (iii) of § 2. It has already 

 been seen that no part of (ii) or (iii) can be supplied from the electro- 

 dynamic field. This points to the intrinsic energy of paramagnetism, 

 except an unknown fraction of the local part (iii), which depends 

 only on the state of polarisation of the element of the medium, being 



