502 Prof. D. N. Mallik : Theory of Electric 



4. Next consider the effect of masses moving through 

 the fluid, supposed perfect. 



If p = density of the fluid, a the radius of a positive ion 

 supposed spherical, and r the distance between them ; then 

 it can be shown that the repulsion between them, when 

 moving with velocities q, is 



a 6 ., 



If, then, there are n positive, N negative charges in either 

 stream per unit length, and b is the radius of a negative sphere 

 and — q' its velocity, the repulsion per unit length of either 

 stream will be 



^ [n 2 ay + N 2 Z>V 2 - 2nN aH?qq f ] 



= 7 ^(na*q-m 3 q') 2 (4) 



That is, the effect is always a repulsion which decreases as 

 the pressure of the gaseous medium decreases. The resultant 

 repulsion per unit length of either stream will, therefore, 

 be equal to the sum of (1) and (4). 



On taking account of these two sets of forces, it is easy to 

 see that the observed phenomena must be due to repulsion 

 and attraction between various streams of ions issuing from 

 the various points of the cathode. While, of course, the 

 resultant effect must depend on the relative values of N, n, 

 q, q', the simplest supposition that we can make is that 

 whenever these streams carry mostly one kind of electricity, 

 they will spread all round the tube, but when the streams 

 contain an equal number of both kinds of electrified particles, 

 and the pressure is not too high, the various streams will be 

 attracted together and form a band. 



Although it is not possible to trace in detail the change in 

 the value of the above expression, it seems to be possible to 

 follow the course of events in a general manner. Thus, let 

 N x = number of corpuscles shot off from the cathode, n 1 = 

 number of ions produced at the anode, 



N s = tt 2 = no. of negative or positive particles produced 

 by collision. 



N 3 = no. of corpuscles lost through combination with 

 positive ions or neutral molecules of the gas. 



n 3 = no. of positive ions lost through recombination. 



