Recombination of Ions in Gases. 251 



r is independent of the gas. Also since ,/' = r/X, all we have 

 to do is to find the value of A, corresponding to a particular 

 value of x for an}- one gas. This may be done by means of 

 the formula for the velocity of an ion under unit field, which 



is given by the kinetic theory of gases, viz., t?= \ ', where 



c is the mean velocity of agitation of the molecule. The 

 author* has recently shown that the value of the velocity of 

 the ions indicates that they have a definite complex structure, 

 which is a function of the pressure and probably also of the 

 temperature. 



In the paper referred to it is shown that at pressures greater 

 than atmospheric the negative ions are practically all com- 

 plex, and probably consist of three gas molecules cemented 

 together by a corpuscle. Hence the mass of a negative ion 

 will be equal to three times the mass of an average molecule 

 in air. The formula for X may be written 



X = \/ hnc 2 sj'lm— . 

 e 



Substituting the following values : 

 imc 2 =3*6 xlO-^ 

 m =101 xlO" 24 

 t7 =505 and <? = 3'1 x lO" 10 , 



we find X at atmospheric pressure =8*8xl0 -6 cm. This 

 value for X, seems to be obviously too high, being midway 

 between the values for oxygen and carbon-dioxide. In the 

 absence of any other evidence bearing on the question, we 

 shall take the true value to be somewhere about 4 x 10 — 6 cms. 

 at atmospheric pressure. The value of x at atmospheric 

 pressure we find from the curves to be 1*1. This gives for 

 the radius of the prescribed spheres ? , =4*4 X 10 -6 . The work 

 done on the ion by the electric forces before it reaches the 

 boundary of the sphere is seen to be = 2'2 x 10 — 14 ergs, and 

 the kinetic energy thus set free would be equivalent to raising 

 the temperature of the ion to about 200° C. The work done 

 inside the sphere on an ion which recombines is about two 

 hundred times that done outside. 



If we may assume that the value of r is independent of the 

 gas, the ratio of the pressures corresponding to any given 

 value of e for two different gases should be the ratio of their 

 mean free paths. Assuming that the values for carbon- 

 dioxide at low pressures are the ones which the curve ought 

 to fit, this gives for the ratio of the mean free path of an ion 

 in C0 2 to that of an ion in air \'/'\=z m 635. 



* Phil. Mag. [6] vol. x. p. 177 (1905). 



