on the Physical Proper ties of Gases, 177 



and it must therefore cut the curve C E at one point, and 

 only one. 



24. That the equations possessed at least one set of solu- 

 tions answering the given conditions, we might have known 

 a priori, since the hypothesis is a possible one, and being a 

 possible one, must have some real solution. But we could 

 not assert beforehand that there could only be one ; and this 

 last result is most important, since it shows us that our hypo- 

 thesis is not sufficient to account for the fact that a mixture of 

 two gases may exist at the same temperature in two different 



• states, as, for instance, N + and NO. From a priori consi- 

 derations we might have thought, as I stated in § 6 *, that 

 two such states could be possible. But, further, not only does 

 it show that the particular hypothesis of dissociation we have 

 used is incapable of explaining this fact, but it also leads us 

 to conclude that no other, depending on mutual influence as 

 affected by the motion of translation, is sufficient for the ex- 

 planation. 



25. If w^e consider fig. 1, we see that the reason why we can 

 only have one suitable solution is that the surfaces cut A, 

 B, ... in only one point. If, for instance, A, B D were 

 cut in two points, then we should get two solutions ; if, in ad- 

 dition, B and A D were cut in two points we should get four 

 solutions ; and if C were also cut in two points we should 

 get five solutions, and possibly eight. Hence, in order to have 

 two solutions, one of the three lines A, OB, must be 

 cut in two points. A glance at the equations will show that 

 this can only be the case if the A, B, and C molecules are 

 formed each in more than one way. One way of obtaining 

 this is to suppose that when two molecules impinge, the atoms 

 sometimes interchange : thus, for example, when two mole- 

 cules A A and B B impinge, the result afterwards may be tw^o 

 molecules of ; or when a molecule A A and an atom B im- 

 pinge, the result may be an atom A and a molecule of 0, &c. 

 If we were to take this into account, our equations would then 

 be of the form 



ass^^ + Aza;^ + Cz^ — Ijxy' — x \ 2anX + . . . j. = 0, 

 «44/^ + B^y' + Cz^ - Myx' -y I a^^x +...[= 0, 

 a^^x'y' + \^xy' + 'Wyx' -2Cz^- Kzx' - ^zy' \ 



-'z\a^-^x-\r ...^=0. J 

 But if we now treat these new equations in the same way as 

 the former we shall find that we are no better off, and that we 

 can get only one suitable solution. 



26. Another modification of our hypothesis suggests itself. 



♦ Phil. Mag. June 1877. 

 Phil Mag, S. 5. Vol. 4. No. 24. Sept, 1877. N 



