424 UNPUBLISHED FKAGMENTS. 



Let us next consider the case in which the solutum appears with 

 more than one molecular formula in the liquid or gas or both. Now 

 there are two cases, that in which the quantities of the substance 

 with the different molecular formulae are independently variable, and 

 that in which they are not. In the [first] case there is no question. 

 If, for example, hydrogen appears with the molecular formula H 2 

 and also in molecules with the molecular formula H 2 0, these are to be 

 treated as separate substances, and we have the two equations 



At , 

 lir- lo gyH 2 > 



and 



At 

 2 o = f unc (0 + M-- lo g 7 H 2 o , 



and also if free oxygen is present 



At 



//o 2 = f unc (0 + -^- log yo 2 . 

 "*O| 



But when the quantities of the substance associated in the different 

 molecular combinations are not independently variable, then we have 



the equation 



[13] 



which is exact and certain, and the considerations adduced on p. (*), 

 which are not limited to gases, seem to show that in this case the 

 equations of the form (t) all continue to subsist, but we have also the 

 equation of form (J). 



It would therefore appear that we may regard the equation 



At 



as expressing a general law of nature, where the letter M is the 

 molecular weight corresponding to any molecular combination in the 

 liquid and y is the density of the matter which has that molecular 

 formula, provided that the density y is so small that of the molecules 

 which it represents only a negligible fraction at any time are within 

 the spheres of each other's attraction. It goes without saying that 

 the law is approximative, as the last condition can only be satisfied 

 approximately for any finite value of y. (Need of verification on 

 account of the unknown M.) 



[The author's manuscript for the proposed supplement ends, so far 

 at least as a connected treatment is concerned, at this point. The 

 following notes are appended."] 



* [Although left blank in the MS., this probably refers to p. 423.] 

 t [Probably equation [ 12]. ] J [Probably equation [13]. ] 



