508 Prof. J. S. Townsend on the Collisions of 



4. In order to draw conclusions from these results by 

 representing the motion of the electrons as taking place in a 

 series of free paths between collisions with molecules, it is 

 necessary to specify the distance between an electron and 

 the centre of a molecule when a collision may be considered 

 to take place. This distance most probably depends on the 

 velocity of the electron, but with the velocities which are 

 here considered, the values of k and W as found experi- 

 mentally are in fair agreement with calculations made on 

 the hypothesis that collisions occur with molecules when the 

 distance between the electron and the centre of a molecule is 

 equal to the diameter of the molecule as determined in the 

 kinetic theory of gases. This is seen by means of the 

 formula given by Langevin * for the velocity W in terms of 

 molecular quantities. In the case of electrons where the 

 mass m of an electron is small compared with the mass of a 

 molecule of the gas the formula becomes 



W= Z - e x J x -815, 



m u 



I being the mean free path, and u — u vk the velocity of 

 agitation of the electron. The formula may be applied to 

 test the numbers given in the above table for the smaller 

 values of Z/p where u is large compared with W. The 

 mean free path I is laken as l/na^v, where <r is the radius of 

 a molecule of air, v the number of molecules per cubic 

 centimetre at a millimetre pressure. The value of I thus 

 obtained is 3'2 x 10~^ cm. 



When the above equation is written in the form 



are substituted, it 



so that the ratio of e/m may be calculated from the values of 

 W and h. The values of e/m x 10 ~ 17 thus obtained are given 

 in the fourth row of the above table, and those corresponding 

 to the smaller forces are in good agreement with the known 

 value e/m x 10~ 17 = 5*3. This result confirms the conclusion 

 already arrived at as to the free movement of the electrons. 



5. With forces from 50 to 100 volts per centimetre, the 

 number of ions generated by collisions with molecules of air 



* P. Langevin, Ann. de Chim. et de Phys. (8) v. p. 245 (1905). 









W 2 = 



Z 2 



m 



e x ve 



mvu 2 k 



x/ 2 x 



and 



the 



known vab 



nes 



of ve and 



mvv 2 



reduces 



to 



















e 



m 



-[¥]■• 



k 



2S ; 



