122 Mr Olazebrook, A comparison of Maxwell's [Feb. 25, 



Calling k the coefficient of induced magnetization, A, B, G 

 the components of magnetization, a, /3, y components of magnetic 

 force and a, b, c of magnetic induction, we have 



A = ku, etc., 

 a = a + 4>ttA = a (1 + 4tt* ) = A (1 + ^ . 



Thus £, 77, £ correspond to A, B, C; 4nrf, 4nrg, and 4mh to a, b, c 

 respectively, so that if we call &irf, etc. the components of the 

 electric induction, we may say that Maxwell's equations deal with 

 the electric induction, Helmholtz's with the electric polarization 

 produced by the given electromotive force. Moreover /n the mag- 

 netic inductive capacity of the substance is related to k the 

 coefficient of induced magnetization in the same way that K the 

 electric inductive capacity is related to e the coefficient of induced 

 electric polarization, for we have 



fl = 1 + 4777C, 



and K— 1 + 47re. 



With this understood then it is clear that the two equations 



f=KP/M 



f = ,P I « 



are perfectly consistent. 



The value of P depends in part on the electromagnetic action 

 of the medium. Now Helmholtz uses electrostatic units through- 

 out and therefore has to multiply the terms in P which arise from 

 the electromagnetic action by a constant A 2 such that A expresses 

 the number of electromagnetic units in one electrostatic unit of 

 current. If we suppose throughout that our quantities are 

 measured in electromagnetic units we may put A = unity ; we 

 shall do this throughout. 



We have now to consider the electromagnetic effects produced 

 by the currents and magnets in the field. 



Helmholtz treats the two separately; according to him the 

 effects of the currents depend on three quantities U, V, W satisfy- 

 ing certain equations which will be referred to again shortly, while 

 the effects of the permanent magnets depend on three other 

 quantities L, M, JV to be further defined in the sequel. 



According to Maxwell, on the other hand, the electromagnetic 

 effects at any point depend on the electro-kinetic momentum at 

 this point, and this we may write 



F cfa + G dji + H <te^ 



as as as 



We may, in order to compare this with Helmholtz, also divide 



F, G, H into two parts F t and F v etc., where F v etc. arise from 



