410 Mr. "W. M. Hicks on some Effects of Dissociation 

 fore, is that — x—ay — by + ax must be negative, or 



£ + « + &>«£, 

 or, substituting for f , 



l>a— */-a? + b, 



which is clearly the case, and the value of £ therefore gives a 

 stable state. 



The condition may be stated in a different form as follows. 

 When x increases through the root, f(xy) must change from 

 positive to negative. From this again we see that the positive 

 root of by 2 — 2axy — x 2 = gives a stable state. For when 

 ^ = the expression is positive, and when #==co it is negative, 

 whence, as there is only one positive root, f(xy) must change 

 from positive to negative as x increases through it. 



13. The expression above found for f gives twice the ratio 

 of molecules to free atoms in the gas at any given tempera- 

 ture 0. The proportion of molecules to the whole number of 



moving particles in the gas is therefore = t =7] suppose 



whilstthe whole number of moving particles — c ly-\-x = \ -z — | N. 



In order to obtain some idea of the law of variation of the pro- 

 portions of molecules and free atoms with the temperature, I 

 have traced the curve in fig. 1. The abscissas denote the tem- 



perature measured in terms of O , whilst the ordinates give the 

 proportion of free atoms to moving particles. The particular 



curve represented belongs to the case where s x = 2 (which 



seems very likely the case) and s — § s 2 (or the radius of action 

 of a molecule equal to the sum of the radii of action of the 

 atoms of which it is composed) ; but the general form of the 

 curve does not depend on the values of s, s 1; s 2 , and only varies 

 very slightly with their variations. It is noticeable that there 



