124 Mr Glazebrook, A comparison of Maxwell's [Feb. 25, 



if a 2 denote the magnetic force due to the magnetization. Ac- 

 cording to Helmholtz the magnetic force is expressed by 



dV dW 



dz dy 2 ' 



a a being as above the part due to magnetization and U, V, W the 



quantities already referred to, and these ■ are consistent with the 



equations F x = fiU, etc. derived from (2) by integrating and omitting 



d\ 

 a function of the form -^- where A, is independent of the time. 

 dec 



Moreover a 2 , etc. being derivable from a potential function, 

 we have 



/dj _ dj3\ _ a\ /dF\ dO x dH t \ _ 2 „ 



\dy dz) dx\dx dy dz J * 



d T 

 = ^-V 2 ^ W, 



if /=— * | d0 i | dH \ 



1 dx dy dz 



But according to Maxwell, Electricity and Magnetism, n. 616, 

 fdy d/3\_dJ 2J? ,. 



f "{Ty-dz-)-dx--^ F (5) ' 



with two similar equations if 



dF dO dH 



dx dy dz 



Also from the values of F 2 , 6r 2 , H 2 it follows that 



dF 3 + dG 1 + dH 2:=0} 

 dx dy dz 



.". J=J t (6). 



Hence from (4), (5) and (6) we have 



v 2 ^=v 2 ^ (n 



Thus on either theory we have satisfied the three equations of 

 which the type is 



fdy d/3\ _dJ t 2jr 



^{dy dz) dx V *' 



or introducing the U, V, W of Helmholtz's notation 

 drt_dfi = d L (dU dV + dW\_ 2JJ 

 dy dz dx\dx dy dz ) 



