178 Mr. W. M. Hicks on some Effects of Dissociation 



We know that the mean internal energy of the molecules is in 

 a constant ratio to the energy of agitation; and it is also 

 highly probable that when the internal energy of a particular 

 molecule is greater than a certain quantity, the molecule can 

 no longer exist. This would modify the distribution of the 

 velocities slightly ; but the number breaking up in any time 

 from this cause will be expressed by ihQ number of molecules 

 existing multiplied by a coefficient which is a function of the 

 temperature. This only adds to the equations terms of the 

 form —\x, — /i-y, —''^7 and, as before, we shall only get one 

 set of solutions. None of these hypotheses, then, accounts 

 for more than one state of a gas at a given temperature. Is 

 it possible that, as some think, the action between two atoms 

 is alternately attractive and repulsive, and hence that colli- 

 sions with blows between (say) c and c^ make the molecule 

 split up, those with blows between c^ and c'^ produce a combi- 

 nation, &c», where c < c' < c^^ < . . . ? It is probable that in this 

 ease two states of the gas at the same temperature may be 

 possible ; but the reactions appear too complicated and arbi- 

 trary to be consistent with the general simplicity of nature. 



Any hypothesis which would allow us to write the first two 

 equations in the form 



aziiu—a/f — x^ ...] =0, &c., 



where a is a positive function of the temperature < ^, might 

 allow two or more states, as is evident by putting x=OyX=a, 

 .2?=^ in succession, when the left-hand member becomes posi- 

 tive, negative, and possibly positive alternately. But I cannot 

 see any physical justification for this form. We seem driven, 

 then, to the conclusion that, though dissociation may exist to 

 some extent at all temperatures, it is not sufficient to account 

 for the fact that two gases may exist combined or uncombined 

 at the same temperature. Some modification will therefore be 

 necessary ; but what, is not clear : most probably a combina- 

 tion of the three just suggested. 



27. Whatever our hypothesis may be, not only will it 

 be necessary that the solutions of our equations satisfy the 

 relations in § 23, but they must be such that the resulting 

 state of the gas is a stable one. It is necessary therefore to 

 determine the conditions of stability. Suppose, after elimina- 

 ting a/ and y^ , that the equations are 



dz J, . . 



