16 Prof . J. H. Jeans on the Interaction 



2. A single ray of light propagated parallel to the axis of 

 x may be taken to be given by 



X=0, Y=Acosjr(ar + Vt), Z = 0, 

 a=0, j3 = 0, 7 =— A cos ic(x + Yt). 



The equations of an electron moving freely in this field 

 according to the classical laws, will be 



mx =-eA V T C0S tc {x + V*) + \~ ~ z x + ..."] 



my — eA cos k (x -f- Y/) -f eA^-cos /c(x ■+■ V*) + |.7 -p y + . 1 



mc = L3Y- + -J' (1) 



in which the terms in square brackets represent the retard- 

 ing force on the electron produced by its own emission of 

 radiation. If the frequency of the light is p, so that p = kY, 

 the ratio of these terms to those on the left-hand sides of the 



2 e 2 

 equations is of the order of magnitude J— ^p. Giving to 



2 e 2 ° m\ ir fe 



m its electromagnetic value . T -^, this ratio is equal to 

 pa/Y or 2ira/\. 6 aV 



We are searching for the point of departure between the 

 true laws and the classical laws, and this departure is known,, 

 from observation, to be most pronounced at low tempera- 

 tures, at which all the radiation is of great wave-length, and 

 the motion of free electrons is very slow. We may ac- 

 cordingly limit ourselves to the consideration of the problem 

 for low temperatures, in the certainty that if a break with 

 the classical laws is necessary, this special problem will 

 disclose it. This limitation makes it legitimate to neglect 

 aj\, and therefore to omit all the terms in square brackets 

 in the above equations. Further, it permits us to disregard 

 variation of mass with velocity, and so to treat m as 

 constant. 



The equations simplified in this way become 



mx = — eA ~ cos tc(x + Yt) 



my = eA cos k(x 4- Vt) + ^Ar f cos k{x.+ Yt) I ' 



