122 Mr. Gr. H. Livens on the 



Again, we have, quite generally 



X =2q(uR)- i(«V)A + u»(tiV)fc 



which depends on the time through the terms in f, rj, £, u r 

 and R. We must, however, notice that since the magnetic 

 force always acts on the electron in a direction perpendicular 

 to its motion, the parts o£ the vector R depending on this 

 force will contribute nothing to the product 



OR). 



We may thus use for R in the expression x simply the 

 acceleration due to the electric force, or in other words, we 

 may take 



m 



We may thus take ^ simply to depend on the time through 

 the factors (f, tj, f, u). Again, however, we may neglect 

 the parts of the variations of these quantities which are 

 brought about by the electric force itself. We may thus 

 use simply 



7j t =.-. 7] cos nt + f sin nt, 



£ t =% cos nt — 7] sin nt , 

 whence 



and is independent of the time. We conclude, then, that 

 A 1 «-** , Xl «ft 1 =A*-^l xi*i 



Jh=t-T Jh=t-T 



= Ae -5 " 2 |~— (P «t + (Em + E.£) sin m 



\jnn l * » 



+ (E 2 ,r-E,,M)(l-cosnr)} 



1 f t M ■/ BA , „dA\ . 



