of Electrons, and the Spectrum of Canal Rays. 677 



Unless q is large m is practically constant ; hence we may 

 suppose U small compared with q, and write 



, r , ~Uu . , , kJJu' , kJJ cos ylr 



V=g+ — =*Ag' + - a - r +...=»Ay'+ A T + ..., 



,„=/(V) =/(«v) + ^f^/'W) + . .. 



Lastly, in accordance with the equations of transformation 



from system (S) to system (SO, -t-=k—,. Hence we get 

 ./ v / j K n at dt & 



d J t//(V) ! _ r , w' , U/BF ' «' »' a 



7 CHC 9/ C Ss'^' 



d r r y (V ) i ■ «/ „' U /SF ' «' A UV BF ' , . 



p I — i — / - 1 » + d L »-(j* + (TU7 - o*V — cFb7' (4a) 

 <* r «//(V) i _ , «' , •/ , u/b*p,' «■ 7 a pvaF,' 



These equations are general ; U/C is involved explicitly, 

 as well as implicitly, because (u f , v\ w) must obviously 

 depend on U, and X '... L '... F ' depend on (w', v'.w'\ 

 their form being the same as for a system at rest. On the 

 left-hand side U occurs in the first power only in V explicitly, 

 on the right-hand side also in the first power. It follows 

 that in general (u', v r , w f ) also involve first-power terms. 

 On account of the smallness of U/C we shall neglect all 

 powers above the first; hence we put a: = A = 1, 



/O0=/(?') +Uco S f/'( !2 ') = m'+ gcosf . J£, 



V '' here ff=£, m'= m . 



To the first approximation the systems (£), (2') are 

 identical, except for the Doppler effect ; hence we may omit 

 accents everywhere. We shall also omit the suffix as no 

 longer necessary. In all the small terms, the relative velocity, 

 electric and magnetic forces and vector potential may be 

 replaced by their values for steady motion, all disturbances 

 being treated as of the first order. Collecting all small terms 



