Electric Discharge in Hydrogen, 305 



On repeating the experiments, however, with tubes of 

 various lengths nnd with induction coils giving various 

 E.M.F.'s, I found that the rotatory phenomenon is observ- 

 able in hydrogen as in other gases, but the conditions have 

 to be carefully adjusted for the purpose, for reasons which 

 will appear from the theoretical discussion which is given in 

 the present paper. This discussion, however, is necessarily 

 incomplete, in view of our ignorance of the intricate 

 mechanism of the processes which obtain in a discharge- 

 tube. 



We know that the equation of continuity in a discharge- 

 tube is [J. J. Thomson, ' Conduction of Electricity through 

 Gases,' art. 137] 



~dn ~dnu , s no, 



where a -=- =no.of corpuscles generated by collision per unit 

 length of the tube per unit time, 



f3 -j- =no. that disappear through recombination, 



ft = no. of corpuscles per unit length of tube, having 

 average velocity c , 



l~ length of mean free path. 



For steady rotation we must have 



a-/3 = 0, 

 and, moreover, 



«=F(X^=/(y), 



where F, /are unknown functions, and X = electric intensity 

 and p the pressure. 



The condition accordingly depends not merely on the 

 pressure of the gas, but also on X and (3. 



Now, both experiment and theory have amply shown that 

 X depends not merely on the voltage of the induction-teoil, 

 but also on the nature of the gas. We must, therefore, admit 

 that /3 also depends on the nature of the gas ; it follows 

 accordingly, that the rotation stage will depend on this 

 quantity, as well as on other factors (pressure, length of the 

 tube, and the voltage of the induction-coil). 



That j3 depends on the nature of the gas is a priori evident. 

 The following investigation, further, shows that it ought to 

 be so. 



Phil. Mag. S. 6. Vol. 41. No. 242. Feb. 1021. X 



