﻿deduced from the Electrical Theory of Matter. 79 



Putting in the values of p\ f, r given by (9), and the 

 values of V, m, n' given above, and remembering that 



1 = 1 — -—- and Iv = v s , 



€ 



we readilv obtain 



^•-^-^(l-^Xi+S)-; 



Now this is the quantity which, in the moving system, 



replaces S(l r~) * n * ne expression for yjr in the fixed 



system, so that since, as is readily seen from (5), 

 A,= f^^'i we have, at corresponding points and times, 

 tf^e^ + fftvA*. 



Again, making nse of the relation (5) and substituting the 

 values of p\ </, r', in terms of p, q, r, we have, at corre- 

 sponding points and times, 



(A,', A,', A,'). ,( '+<' ) "'"1 



[»(i -"■)]' •-"•[K'-5)]' 



1/2 



e€ -l/2, 



e -l/2 



or 



A,', A/, A,' = e v^JL ^ + A l \ ky> A „ 

 Writing 



(J' »." J' t"\ I M* t t f -MO. M2 VX \ 



[a , y , z , t J = ^e 1 /-^ ,y\z r ,€ W-e 1 ' 2 ^-J, 



we see that the above is equivalent to the statement that 

 y(r', A x ', A/, A z ! are the same functions of «", y", s" and *" 

 in the moving system, as in the fixed system, 



«*(^+*A x ), e*(£* + A.), A* A, 



are functions of a?, ?/, ~, and £. Since ,c = x—vt, we have 

 A = ,1/2 _^ -1/2 V S B __ el/ o , B , o t-3 





(10) 



