Theory of Electromagnetic Action. 449 



line of the channel great in comparison with r the radius of 

 the channel, since L 2 depends on log R/r. 



(3) Considering now the case of two shells, we have the 

 same expressions for dTand dW as in (11); but the equations 

 (10) become, since now 1^ = 0, E 1 = 0, 



Liyi^i + M ?/i*/2 + yifadM =o, | 



L 2 y 2 dy 2 + My 2 dy { + y^dK = 0. J * 

 Thus substituting in (11) we find 



dT=-y 1 y 2 dM, (14) 



wnicj 



r hich is equal and opposite to the work done by the elec- 

 tromagnetic forces in moving the system. Here, it is to be 

 observed, the electrokinetic energy is diminished through the 

 action of the electromotive forces by just double the amount 

 by which the electromagnetic forces increase it. 



The performance of a finite amount of work by electro- 

 magnetic forces in overcoming external forces, or in giving 

 the magnets kinetic energy, and the diminution of the elec- 

 trokinetic energy by an equal amount, are quite consistent 

 with only a slight alteration of y 1} i/ 2 , and therefore of the 

 magnetic moments of the magnets. Indeed,, the alteration 

 in the magnetic moments of the magnets actually produced is 

 opposite in sign to that which would be caused by dy l9 dy 2 , 

 and is due no doubt to magnetization produced by a turning 

 round of magnetic molecules in the body. But in an ideal 

 case, in which the molecules could undergo no such altera- 

 tion of position, it is only necessary to suppose that L l5 L 2 

 are each great in comparison with M to enable the effect of 

 dy x , dy 2 on the magnetic moments to be small, a supposition 

 which is very possibly in accordance with fact. 



There does not seem to me, therefore, to be any insuperable 

 physical difficulty in the way of the application of the general 

 dynamical equations to magnets as well as to circuits carrying 

 currents. Of course our ignorance of the current strength, 

 &c, in the former case prevents us from making practical use 

 of these equations ; but their theoretical application gives I 

 think a clearer view of the energetics of electromagnetic (and 

 magnetic) action than can be obtained without them. 



1 shall now consider from this dynamical point of view the 

 inductive magnetization produced in iron and other sub- 

 stances when placed in a magnetic field. As is well known, 

 the expression in (1) or (3) for the electrokinetic energy can 

 be reduced to a definite integral. The following method of 

 performing this reduction seems more direct and simple than 



