Gases by the Motion of Negatively charged Ions. 2 II 



freely between two points differing in potential by P volts. 

 Let a: 1 xX = P and a? 2 xX = Q, X being the force acting on 

 the gas. 



Then the number of times that an ion collides, with 

 velocities intermediate between Ip and Iq, in going through 

 one centimetre is 



X — x "), .... (6) 



/%»(« 



assuming that after a collision the velocity of the ion is small 

 compared with its velocity before collision. (This assumption 

 would not be legitimate for very large velocities of impact, 

 but the hypothesis may be applied to the velocities with 

 which we are dealing, and leads to simple analysis.) 



If the potential P is large, then, according to our theory, 

 a pair of new ions will be formed at each of these collisions, 

 but when P is small (about 10 or 20 volts) new ions will only 

 be made on some of the more favourable occasions. Let /3 P 

 be the number of negative ions formed in ft collisions when 

 the velocity of impact is between I P and Ip+i. 



Then 



»=P* fo (« X -« X ).- - • (?) 



The maximum value that any of the coefficients /3p can 

 have is /3. 



Equation (7) can be expressed in the more general form : 



A ; (8) 



p- / (p)' 



and if no restriction is placed on the form of the function/, 

 it is not necessary to assume that the velocity of the ion is 

 small after impact. 



We can test whether the values of a which we have deter- 

 mined can be expressed by means of an equation of this 

 form. 



If we plot a curve for each pressure, taking as coordinates 



- and — , the five curves should coincide, since they have 

 p p J 



each the same equation (8). 



The points on the accompanying diagrams which are 



marked 1, 2, 3, 4, and 5, have as coordinates the values of 



- and — deduced from Tables I., II., III., IV., and V. respec- 

 tively. 



