252 Rate of Recombination of Ions in Gases. 



1 e \ 



According to the formula v— the ratio of the 



° 2m c 



velocities of the ions under unit fields for two different gases 



should be =—(—,) , where m, m are the masses of the 

 a \m J 



corresponding ions. In the case of air and carbon-dioxide 



the mean of the values of the ratio found by Zeleny for the 



positive and negative ions in the dry gases = *497. This 



gives for the ratio of the masses of the ions — =1*54. The 



m 



ratio of the densities of carbon-dioxide and air is 1*53, a 



result which indicates that an ion in carbon-dioxide at high 



pressures contains the same number of molecules as an ion 



in air. Since it has been shown that a negative ion in air at 



high pressures probably consists of three molecules held 



together by a corpuscle, presumably the same is the case for 



a negative ion in carbon-dioxide. 



Objection may be made to the present theory on the ground 

 that almost any function might be capable of being repre- 

 sented by a formula such as that given on p. 247 by taking 

 a sufficient number of terms, each involving one of the un- 

 determined constants a»_i, &c. This is not, however, a valid 

 objection. In the first place, the constants a are not arbi- 

 trary ; they are always positive and less than unity, which 

 they rapidly approach as n increases. In the second place, 

 reference to fig. 2 shows that in the case of air a single term of 

 the series, viz. r 3 , is sufficient to represent all the points but one 

 within the limits of experimental error, and even that is not 

 very far out. So that this very complex curve can be repre- 

 sented with almost the desired amount of accuracy by a formula 

 containing only one arbitrary constant, which is equal to the 

 ratio between the radius of one of the prescribed spheres and 

 the mean free path of an ion when the pressure equals unity. 

 In the case of carbon-dioxide the points which fall off the 

 curve cannot be brought on to it by manipulating the con- 

 stants without making the theory lose all its physical signi- 

 ficance. The constants a ought to be capable of being- 

 calculated by making some hypothesis about the effect of a 

 collision. At present the experimental results are not 

 sufficiently accurate to enable us to more than guess at their 

 values. 



It will be noticed that roughly speaking the present theory 

 makes e=f(p) for different gases depend solely on one para- 

 meter X, the value of the mean free path of an ion in the gas 

 in question. The smaller the value of X the more the curve 

 e=/(p) is displaced towards the axis of e. 



