238 



Dr. J. Larmor. On the Electrodynamic mid [Jan. 2, 



transformation of the energy of attraction between these poles of the 

 core, into electrokinetic energy of the coil, as the poles close up 

 together. As frictional waste is not essential to this question, we can 

 consider the coil to be a perfect conductor which will store all the 

 energy without loss. We need not postulate that the iron is of 

 constant permeability or devoid of hysteresis. When the distance 

 between the pole-faces is x, let the current in the coil be i. The total 

 energy is 



JwiN + energy of magnetisation ; 



and part of the latter may remain sub-permanent when /, vanishes. 

 The principle of the magnetic circuit gives, as = N, the formula 



1+ X = 47T7W, 



assuming as usual that the lines of magnetic force are conveyed straight 

 across the air-gap between the pole-faces. Thus the electromagnetic 

 energy T, equal to JfitN, is 



and when x is diminished by - 8x, its increment is approximately 



- 2 'm^ +iv w s> (1) 



In this displacement the work expended from the electrodynamic 

 system in mechanical attraction between the poles magnetised to 

 intensity I, equal to k'N//a, is - IS27rI(k, which is 



1--T 2 *S1 & («) 



Comparing (ii) with (i) it appears that in cases for which /x is great, 

 to which alone the principle of the magnetic circuit can be applied, 

 the work of mechanical attraction by which the pole-faces can transfer 

 potential energy to a spring placed between them, by compressing it, is 

 concomitant with equal increase of the electrokinetic energy if the 

 current do not change. As there is no source of energy, the current 

 must therefore vary, and so that the total change of electrokinetic 

 energy given by (i) and (ii) vanishes ; that is, it must diminish by - Sl, 



given by 8t = J^-(l +(1 - -) 2 }S,X', which is practically equivalent to 



I 



This result may be immediately verified by the Lagrangian process. 

 As there is infinitely small resistance, the electric pressure — — in 



