﻿80 Dr. W. F. Gr. Swarm on the Effects of Uniform Motion 

 so that at corresponding points and times 



B^_ "b± _^_^±, BAor erf'dA.T ) 



B.i- ~ e B^ u 2 B* +ev Ba- C 2 ~dt ' 



Bj/ \ 03/ o,y / B~ VB^ 03- /' 



3A^_erd^ BA? et^B^ BAr 



B* " ^ 2 3* B* ~ C 2 B* et " 3# ' 

 BV_ 1/2 /BA y BAy\ BA/ _ 1/9 /BA g BA*n 

 " 3* ~ e V B* l ' B* /' Bf -~ € \ ~dt v B.i- ) 



Kn) 



Making use of equations (4) and alsp of equations (3) for 

 the magnetic vector, we obtain, on substituting the values of 



W. . . &c. from (11), 



B-? 



T ,_ B^ BAa_ Y } 



x -~B^~i>r- A ' ! 



Bv an exactly similar process, on making use of the 

 expressions for the magnetic vector, and substituting the 

 values of the spacial derivatives of Ar', Ay\ A z ' in terms of 

 the derivatives at the corresponding point and time in the 

 fixed system, we obtain 



a = «. 





(13) 



By a mere algebraical combination o£ (12) and (13) it 

 follows that, at corresponding points and times, 



^(e-VV, /S'+^Z', y-£T', 6-V'X', Y'-r 7 ',Z' + r/3')| (14) 

 = («, & 7 , X, Y, Z). ) 



