148 Prof. 0. W. Richardson on the 



These relations are not sufficient to determine the distribu- 

 tion of the velocity among the particles. But we should 

 expect the asymmetry to be more marked the greater the 



u 

 value of - and hence the greater the value of v. Thus those 



radiations which give rise to the emission of electrons with 

 the greatest velocities should exhibit the greatest degree of 

 asymmetry in this emission. This is known to be the case. 



u 

 According to formula (2) the maximum value of is J, and 



is the limit to which the fraction approaches as the velocity 

 of the emitted electrons approaches that of light. To illus- 

 trate the possibilities it is perhaps worth while devoting a 

 moment's consideration to this particular case. 



We do not know with absolute certainty whether the fact 

 that u is not zero is due to v being different in different 

 directions, or to v being the same and the number different 

 in different directions, or to both these causes. For 

 simplicity suppose that v is the same and the number 

 different. This supposition seems a little more probable 

 than the first alternative and is also supported by experi- 

 mental evidence, at least in the case of the Rontgen rays *. 

 If 4:7rn is the total number emitted and ne the number per 

 unit solid angle making the angle with the direction of the 

 radiation, 



±7rn= ] n . 2tt sm d6 .... (3) 

 Jo 6 



and since u= v cos 0, 



rnj . 27r cos sin dO . . . (4) 



4-7m J 



Thus if cos = x and n lt -=n 



u 



\ n xd x = v ) 



xrixdx (5) 



When - =J, particular values of n x which satisfy (5) are: 

 v 



n x = const, x (1 + d-) 2 , —!<.«<+!, . . (6) 



and 



n# = 0, — 1<#<0: n. r = const, 0<#<+l. . (7) 



• Cf. R. T. Beattie, Phil. Mag. vol. xx. p. 320 (1910). 



