of Electrons, and the Spectrum of Canal Rays, 659 



Relative to the moving axes its coordinates at time t are 

 {x-TJt, y, z). 

 Write 



t' TJ r f 



TT, 1 t f . ° • *-» «*' 



x-bt = tcx, y=y, z = z, t=-+-^; 

 and 



U = K 2 u', V = /cv', IV = tCW 1 . 



[vide Note II.] 



For a point fixed relative to the aether we have, since 



t U.r 

 t'=— — -j-r,, dt=icdb f ; for a point fixed relative to the 



moving origin we have dt= — ; for in the first case (x, y, z) 



K 



and in the second case (V, y', z') are unchanged. 



We shall choose the system (20 so that corresponding- 

 elements of volume, and therefore also corresponding electrons, 

 have equal charges: this assumption makes 



p' = /cp, p dx'dydz' = pdxdydz, e f = e. 



§ 5. The following relations hold between the electro- 

 magnetic fields o£ the two systems at corresponding places 

 and times : — 



X=X', *Y = Y' + ^N', «Z=Z'~^m / 



>• • (1) 



L=L', «M=M / -2 Z / «N=N / +^Y / . 



() C j 



E', H' are given in terms of a scalar potential <j>' and a 

 vector potential A', (F', G' H') by the equations 



e ""^If~ v ^ + c" vf ' H - curiA '^ 



div.E'=4flr(l-^y> div.H' = 0, 

 while </>', A' are given by the equations 



> 



(2) 



J 



V 2 4>' 



L' 3 Be' 3 



iirp' = 0, 



1 9«'_U BF' 



C*B7" c?Bi r+dlvA=0 - 



(3) 



2 Y2 



