of Electrons, and the Spectrum of Canal Rays, 675 



§ 17. (2) In this case the group of systems serves as a 

 model of a radiating gas, e. g. a hot flame, the negative glow 

 of a vacuum-tube, the relatively stationary gas through 

 which the canal-ray particles move. This produces the 

 " irregular" radiation of Stark, seen in the series lines of a 

 flame and the undisplaced lines of the canal-ray bundle. 



We assume that the velocity is on the average equally in 

 all directions, and, in accordance with this, that the axes of 

 the systems are equally distributed, so that the inequalities 

 A 2 o-.. all vanish. We shall, as before, neglect TJ/O in 

 comparison with unity. We get 



X=F=Z=0 (40) 



S= fef(U)dU (41. 



W ~3C 2 J- 



RU 9 /(U)<*U (42) 



The remaining equations are unnecessary. 



We draw the following conclusions from the equations of 

 this and the last section : — 



(1) Whatever be the source of the radiation R from one 

 of the moving systems, the average total radiation per 

 system, S, is of the order It, but the average rate of working 

 of the radiation pressure per system, W, is only of order 



(2) Hence only a very small fraction of the energy 

 radiated can be ascribed to work done by radiation pressure, 

 either for a radiating gas, or for a bundle of canal rays. 



§ 18. We must now consider in what way the values of TY, 

 P' are influenced by the motion, that is to say, we must 

 enquire whether it is possible to satisfy assumption (Bj 

 continually by supposing the system (£) to be suitably 

 disturbed. For this purpose we must calculate the mechanical 

 force acting on any electron of (2). 



Denote this force for the moment by F, and its components 

 by (X, Y, 2), the meanings of these symbols of course being 

 different from those used in § 9. For an electron with 

 charge e and velocity (u -f U, v, w) we have 



r/ , =Y+ ^L-^N, 



z/,=z+^m-;l. 



c ° 2 Z 2 



