306 Electric Discharge in Hydrogen. 



If n = number of electrons in unit volume, then the 

 number of electrons which have speeds lying between c and 

 •c + dc 



n _^- 2 . 



<*-T6 a2 c 2 dc; 

 ar 



where a is the most probable speed and varies as c. 

 Then the corresponding number of collisions 



c n — 

 <x T . ~ d e~« 2 c 2 dc. 



Hence the total number of collisions corresponding to the 

 range of velocities to c 



n_C* 



no. c , nc c 



If, therefore, only the collisions lying within the range 



c 4 

 and c (supposed, small) result in recombination, 6 x ~. 



c 



Now, we may reasonably suppose c oc - for any gas, and 



therefore c oc - for different gases. 



P . Xe 



Also c oc Xe, i. e. we ma} r take c a — p. 



Moreover, if the kinetic energy corresponding to c is 

 supposed to arise in accordance with the equation 



e 2 

 ■^inc = -y , 



where V is the distance [supposed, constant] at which the 



o 4 

 velocity of corpuscle is zero, then -j 



c 

 ? 

 1 



* (i ) c 



In order to satisfy the condition for steady rotation, 

 therefore, we must have 



