216 Prof. Townsend on the Conductivity produced in 



In order to obtain values of a for the range of forces that 

 has been used, it is necessary to find 7 coefficients in equation 

 (10). When ft is taken equal to 21, the coefficients so found 

 will be less than ft, and, according to the theory, it is neces- 

 sary that the coefficients should satisfy this condition. 



When the following values of b are substituted in (10), the 

 equation will represent very accurately the curve through 

 the points in figs. 7 and 8. 



b x = # 03 when the velocity of impact 



is intermediate between I { and I 5 



b 2 = -75 „ ,, I 5 ,, ] 10 



fr 3 = 2*7 ,, „ I 10 ,, I 15 



"4 = ''*0 „ ,, 1 ]5 „ I 20 



6 6 = 13-0 „ „ I 20 „ I 2 5 



b Q =16-0 „ ,^ I 25 , } I 50 



6 7 = 20*0 for velocities over J 50 



The values of a, have been calculated for the different 



pressures from equation (10), by replacing - and — for ai 



and X l9 and taking the above values of the coefficients. 

 The results are given in the fifth column of the tables in 

 Section 4. 



We have thus obtained results which enable us to find 

 approximately the number of ions that would be generated 

 by a single ion in moving through a gas with a fixed velocity. 

 The maximum number is 21 xp per centimetre, which corre- 

 sponds to large velocities. The number is 13 xp when the 

 velocity is about T 22 , and for velocities of the order I 5 the 

 number is comparatively small. 



8. The mean free path which we have deduced can be 

 shown to agree with what we should expect from physical 

 considerations of a more familiar kind. 



The mean free path of a molecule of air at pressure 

 760 mm. and temperature 0° C, is * 0'96 x 10 " 5 centim. 



We may therefore take the mean free path in air at 20° C. 

 to be 1-03 x 10- 5 . 



The free path here has not quite the same meaning as the 

 free path that we have been considering — that of an ion 

 travelling through a gas supposed to beat rest. The formula 

 used in finding the mean free path from the coefficients of 

 viscosity takes into account the fact that all the molecules are 

 in motion. The collisions that a single molecule would 

 make with other molecules would be less frequent if the 



* Meyer, Kinetic Theory of Gases. 



