﻿1148 The Ionizing Potential of Positive Ions. 



hydrogen taking 11*25 X 10~ 6 cm. as the mean free path 

 in the gas at normal pressure and temperature, which is the 

 mean free path of a molecule of hydrogen given by Jeans in 

 the last edition of his treatise on the Dynamical Theory of 

 Gases. 



On this hypothesis, the number of collisions made by a 

 positive ion in traversing a centimetre of the gas at 8 mms. 

 pressure is 936, and it was found by the experiment that on 

 an average the number of molecules ionized by a positive ion 

 in moving through one centimetre is *059. For a first 

 approximation the velocit} r of agitation of the ions may be 

 neglected in comparison with the velocity in the direction 

 of the electric force. Thus the ratio of the number of mole- 

 cules ionized to the total number of collisions by positive 

 ions is 1 : 16,000. 



If all the ionization by positive ions be attributed to 

 collisions which terminate free paths greater than os, then 

 e xll = 16,000 where I is the mean free path, so that .r = 9 68 x I 

 = '0103 cm., and the potential fall along these paths would 

 be greater than 7*2 volts. The velocity corresponding to 

 this voltage is much greater than the velocity of agitation 

 of the molecules of the gas, so that the longer free paths of 

 the positive ions would exceed the value *0103 cm. by the 

 factor 1*4, and the potential fall would also be greater in 

 the same proportion. Hence the ionizing potential of 

 positive hydrogen ions, as deduced from the above experi- 

 ment, must be at least 10 volts. 



In order to make a more accurate estimate of the ionizing 

 potential it would be necessary to take into consideration 

 the initial velocities of the ions in estimating the number of 

 paths which are terminated by a velocity above a certain 

 value V, so that the above calculation only gives a lower 

 limit to the ionizing potential. If other experiments of the 

 series be considered where the gas is at pressures lower than 

 8 millimetres, it will be found that the ionizing potential of 

 the positive ions in hydrogen is above 15 volts. 



Yours faithfully, 

 7th November, 1922. J. S. ToWNSEND. 



