﻿<*>! Dr..'W. F. G. Swann on the Effects of Uniform Motion 



system are, in view of the alteration of the accelerations 

 produced by unit forces on the electron, 



d\r \ 



— = n oe -3/ 2Fl(e i V ,y,.',f")% 



^='»»oe- 1 V 1>l Fi(€ ,/B *',y , ,s , ** , 0- 



Now the orbit of the electron in the system at rest is the 

 curve of intersection of two surfaces, 



$(%, y, .:) = 0, and x(*> V> z ) = °> 

 which are obtained by eliminating t from equations (17). 

 The question is, shall we on eliminating t from equations (18) 

 obtain two surfaces of the form 



<£<V V, y\ _-') = 0, and % (e' V, y' , ,') = ? 

 Now observing that 



«? v*,ldx'\ d 



d _i _ 1/2 w r/a? \ « _ r , (I v z /ldx \ a 



<ft "~ dt 



we see that, neglecting the second term of the 1 ist expres- 

 sion, which we are entitled to do, to the degree of approxima- 

 tion to which we are working, we can write - as e_1 ^ 2 T77? 

 and our equations (18) take the form 



(/VV) 



f ^ ) 



^ 2 ==n F 2 (eHW J y',z>,t"\i . . (19) 



I 

 r/V 



^ = »oF,(e 1 /V,y,y,<"); I 



from which it is obvious, that if 



0(.r. y, z) = and x fa y, z) = 

 are the surfaces obtained by eliminating t from (17), then 



c5 (e 1 V, y\ z') = and % (W, y' ; *') = ' 

 are the surfaces obtained by eliminating t" } and consequently 



* Strictly, we should write — '— where x — x'+vt. Since v is cou- 

 . * r/-.r d\v' (lt ~ 



Btant, however. - - = - — . 

 dt- dt- 



