loNIZATION BY NEGATIVE IONS 29 



corresponding to the potential fall V. A theory worked 

 out on these lines would make the expression for a in 

 terms of X very complicated, and would not add much 

 to the information which is obtained by comparing the 

 experiments with the simple formula involving one 

 exponential term. 



13. Molecular dimensions deduced from the mean free 

 paths of negative ions. 



The mean free paths of the negative ions in the 

 different gases at 1 millimetre pressure are the recipro- 

 cals of the numbers N. As might be expected, the mean 

 free path is longer in hydrogen than in other gases, and 

 in general the sectional area of the molecule which is 

 proportional to N is larger in the heavier gases. The 

 most notable exception occurs with helium. Although 

 the density of this gas is twice that of hydrogen, a 

 negative ion makes twice as many (5-^2*4) collisions in 

 travelling a given distance in hydrogen as it does in 

 helium at the same pressure. 



It is interesting to compare the mean free paths of 

 the ions as obtained by this method with the mean free 

 paths of molecules of gases obtained from the determina- 

 tions of the viscosity. If a collision occurs between two 

 molecules when their centres come within a distance 

 2o- from each other, then a negative ion, being of small 

 dimensions, would on this view collide with the molecule 

 when it came within a distance o- of the centre. It will, 

 however, be seen that the ion makes fewer collisions 

 than would occur under these circumstances, or, in other 

 words, that the ion must come within a distance R from 



