﻿Ionization by Collision. 405 



to Townsend's measurements, where the values of X/p and 

 not of X are given. Writing IL/p—g, j3=j3 p we have 



V 

 Pb=- Z (H) 



/3o = "oe~ ft ' 7 (15) 



«^=N r K '» (i6) 



i h= f^{n x + n,C^ + l)\e-^i- n -!. . (13') 



It was noted that Townsend's formulae were unsatisfactory 

 because they did not lead to the right value of f(l) when 

 V=V. The formula (13') obviously leads to the right 

 value, for it has been fitted to x = h, and when V = V l = b. 

 It also leads to the right value, f(T)=n 1 for all values of V 

 when p = 0. 



9. The only experiments by Townsend which are sufficiently 

 detailed and accurate to enable a comparison to be made 

 between equations (5) and (13') are those on ionization by 

 ultra-violet light. In these conditions n = 0, and both 

 equations reduce to the simple exponential form 



i/e = ?e% (17) 



where, according to (5), P = w 1 , Q = a, and according to (13') 



n x is the value of i/e when either p = or V is less than 

 V; but, since Townsend does not give the values of this 

 quantity in his experiments, it is impossible to use it to test 

 the two formulae by a comparison of the observed and cal- 

 culated values of P. The test must be made by means of Q. 

 Townsend deduces from his equations the value of Q/p for a 

 number of values of z, and then uses (4) to calculate values 

 for N and V; the concordance between the observed values 

 of Qjp and the values of a Q deduced from N and V is taken 

 as a test of the accuracy of the theory. The same procedure 

 can be adopted if Q, = ; for we have the following equation 

 to determine N and V' from the relation between Q//> 

 and z : — 



log& + /Vj=logN -N„^. . . . (18) 



This calculation has been carried out and the results are 

 given in Tables I.-V11I. Townsend found that the calcu- 

 lated and observed values did not agree for small values 



