between Radiation and Free Electrons. 17 



Put a? + V« = f, so that f=# +V, f=£, and the equations 



become 



y 

 mg=—eA ^cos«?, 



my = <?A ^= cos k%, 

 o£ which obvious first integrals are 



where u, v are new constant velocities. Eliminating y, we 

 obtain as the equation for £, 



p = u 2 — lv-\ ^sin/cf ) , 



or putting 6= tan \k£, 



% ^ = ( M 2 _ „2) (1 + ff2) - ^ ,,0(1 + ff*) + -/-_,, 6» 2 . 



From this the value of 6 may be written down as an 

 elliptic function of the time, but the solution is of greater 

 complexity than is either convenient or necessary for our 

 purpose. 



The same reason which enabled us to limit ourselves to 

 low temperatures also permits us to consider only the case 

 in which the light is of feeMe intensity — we may neglect 

 squares of A. The equation now becomes identical with 



k" v y [_ {u" — v 2 )Km\J 



or, if u 2 — v 2 = iv 2 y so that w is another constant velocity, 



2 * / 9 eAv \ 



k \ iv'icm\ ) 



leading to the integral 



eA.v 



tan ltct= tan ^icwt -\ ^ Tr , 



id- Kin V 



in which we avoid adding a constant of integration if we 

 Phil. Mag. S. 6. Vol. 27. No. 157. Jan. 1914. C 



