126 Mr Glazebrooh, A comparison of Maxwell's [Feb. 25, 



From (10) and (11) we have by differentiation 



T _ T _ dF t j_ dG 1 dll 1 _ _ , <M? . 



1 dx ' dy dz dt 



an equation which can also be obtained directly from the values of 

 F v G x , H x found by Helmholtz; and since 



J=J 1} v*f=v 2 K, 



Helmholtz's fundamental equations may be written 



^ F + l ~irfx = -^ u (18) ' 



etc. 



■■• V*-s~V-js-» <")• 



etc. 

 Hence from (5) 



(dri dfi\ . ldJ . d 2 <& ..,_ 



etc. 



Also differentiating these with reference to x, y, z and adding 

 du dv dw 1 2 j_ _ , . 



dx dy dz ^ir/xk 



Maxwell's equations differ from these. According to him we have 

 instead of (15) 



p& = 4*u (17)> 



dy dz 



Hence -j-n = 0> etc., 



dxdt 



and therefore f- = 0. 



k 



Hence either J = or k = oo . 



If J is not to be zero then to make Helmholtz's theory coincide 



d<& 



with Maxwell's we must put k = oo and -j- = 0. According to 



Helmholtz the two agree if k = 0. We shall have to return to this 

 point again. 



In order to proceed further we require to evaluate P, Q, R the 

 components of the electric force in terms of the other quantities, 

 and here a further difference between the two occurs. The value 



