A Theory of the Widening of Lines in Spectra. 321 



electrostatic repulsion between the corpuscles, we can easily see 

 that similar effects are produced by the forces due to electro- 

 magnetic induction. 



The effect of these forces can be represented by introducing a 

 term 



e 2 fdx 1 dx 2 dy x dy 2 dz 1 dz 2 \ 

 ~Wr \dt ~dt + ~dt ~dt + di dt) ' 



in the expression for the kinetic energy of two corpuscles, V being 

 the velocity of light, the rest of the notation being the same as 

 before. The introduction of this term, if we neglect squares and 

 products of the velocities, leads to the equations 



d 2 x<, e 2 d 2 x x 



m W + ^ = WrW 

 Hence p 1 and p 2 , the two periods, are the roots of the equation 



O - mpj = (J^ p\ 



e 2 

 or fju — nip 2 = + j=£- p 2 , 



V 



or Sp = ± 



e~ p 



V 2 mr 2 ' 



Thus in the case of two corpuscles the shift due to the electro- 

 magnetic induction would be the same on the two sides of the 

 original line ; the effect in this case is proportional to p while for 

 the electrostatic repulsion it is proportional to 1/p. It is also 

 proportional to 1/r instead of 1/r 3 so that though the electro- 

 magnetic effect of a single corpuscle is less than the electrostatic 

 effect, the effect of more distant corpuscles will be relatively more 

 important and we have to integrate the effects over a larger 

 volume. The general conclusions drawn from the consideration of 

 the electrostatic effect apply also to the electromagnetic. 



