403-408] Dissociation 335 



the value n + 3 = 92 ; from the values of C p , C v and 7 at normal temperature 

 and pressure, we have (p. 222) found the values 



7i + 3 = 7-66, 6-60, 6-67. 



We may therefore again, with some show of reason, suppose that if the 

 influence of aggregation were removed the value of n + 3 would be six, so 

 that the C0 2 molecule would be a rigid body without an axis of symmetry. 



406. A further instance, as has already been mentioned, is chlorine. 

 The value of n + 3 calculated for chlorine in the table on p. 222, was 6'08, 

 but it is quite conceivable that if we could dispose of molecular aggregation 

 we should find the value n + 3 = 5, so that chlorine would fall into line with 

 the other diatomic gases. 



407. There is no reason why we should not go further. On the evidence 

 which has been obtained, the supposition that we have 



[n + 3 = 3 for all monatomic gases, 

 n + 3 = 5 for all diatomic gases, 

 n + 3 = 6 for all more complex gases, 



seems at any rate to be worth serious consideration. It disposes of the 

 tremendous difficulty of explaining how it is possible for the molecules of 

 a gas to keep up large internal motions without loss of energy, a difficulty 

 which would have to be faced if it were not for the loophole suggested. This 

 difficulty, as we shall see later ( 411), seems almost insuperable in the 

 present state of our knowledge of molecular structure. 



DISSOCIATION. 



408. So far as the mathematical analysis goes, there is nothing in the 

 preceding treatment to prevent it being applied to dissociation. The former 

 molecules must be replaced by atoms, and the former clusters of molecules 

 by single molecules. Dissociation has been treated on these lines by 

 Boltzmann*, whose analysis is almost identical with that which we have 

 just applied to the question of aggregation. The question has also been 

 treated by Willard Gibbs^ and others by a method which, although at first 

 sight appearing very different from that of Boltzmann, will be found, as 

 Boltzmann remarks J, to rest ultimately upon exactly the same physical 

 basis. On the other hand the question has been treated by Prof. J. J. 

 Thomson by a method which rests upon a physical basis entirely different 

 from that of Boltzmann and Gibbs. 



* Vorlesungen iiber Gastheorie, n. p. 177. 



t Tram. Connecticut Acad. in. (1876), p. 108. 



J Vorlesungen, n. p. 211. 



Phil. Mag. [5] xvin. p. 233. 



