of Electrons, and the Spectrum of Canal Rays. 673 



Multiply by iP;(cos 6) sin 6d6 and integrate from = to 

 6 = 7r ; we find 



Qi = 2 (A is cos sD, + B is sin *n)**P^( - U/C), . (29) 

 where, as before, k— sjl — U 2 /(J 2 . Again write 



F cos;2f ^=*S < D i sin 2 tfP^cos 0) . . 



IP 

 2ttJ 



*=o ls y 14-2 L 4 I i + s-4 



"We find 



7+7— < 



,i + * J 1 * + *-3 



s+1 p( s+1 V_Ti/nu q *p(«) 



/k' +1 PS'^(-U/C)) 



+ l (1 _ u . A7) ffi=™l 



| »+«-i | T r u "-'' ;i + ,-i J" • 



Also write 



Q^iC T (T' 2 -P'>' 2 . P-(cos (9) sin 3 Odd. . (31) 

 We find 



S^^(l-g) 2 .{R + C 2 .R 2 + a.R 4 +...}. (32) 



We notice that S x , S 2 , S 2 ' involve inequalities of even 

 order only ; in general the existence of such inequalities 

 produces polarization of the normally emitted light, and 

 vice versa polarization may be regarded as a test of the 

 existence of such inequalities. 



In the particular case when the distribution is symmetrical 

 about the direction of motion, and thus does not involve II, 

 the only coefficients involved in S 2 , S 2 ', are A 20 , A 40 ..., just 

 as in Si. 



§ 16. We must now average for all values and directions 

 of the velocity U. Two cases are of special interest : 



(1) All the systems move in parallel lines. 



(2) The velocities of the systems are distributed equally 

 in all directions. 



(1) In this case the group of systems may serve as a model 

 of a bundle of canal rays. The model is not a perfect one ; 

 for in the canal-ray bundle, owing to collisions, the velocities 

 of the particles cannot all be in the same direction, though 



Phil. Mag. S. 6. Yol. 13. No. 78. June 1907. 2 Z 



(30) 



