in the Analogy between Solutions and Gases. 101 



it is necessary to mention the different forms which it has 

 assumed during the years since its discovery. We shall 

 first give this relation a simple expression in which Guldberg 

 and Waage's conceptions may he included, viz. : — 



2a«logC=K (1) 



This differs from the one given on p. 100 merely in that the 

 terms representing the components of both systems have had 

 their signs changed. The original expression of the Nor- 

 wegian investigators is closely analogous (Christiania Viden- 

 skabs Selskabs ForhandUngar, 1861) : — 



g#logC=K (2) 



except that k has to be determined for each constituent in 

 question by observation of the equilibrium of the system. 



As Guldberg and Waage (Etudes sur les affinites chimiques, 

 1867) repeatedly found the coefficient k equal to 1, they 

 simplified their equation thus : — 



2logC = K (3) 



In their last treatise, however {Jour, fllr prakt, Cliem. xix. p. 69), 

 they introduce the change that the number of molecules a 

 must also be taken account of, and consequently they approxi- 

 mate their formula to that deduced for gases on thermodyna- 

 mical grounds, thus : — 



2alogC = K; (4) 



We have taken this last expression as their final formula. 



The Norwegian investigators maintained this simple 

 formula, with whole numbers as coefficients, even for solu- 

 tions ; but Lemoine has lately revived the original formula 

 (2) in order to represent the results of Schlosing's investiga- 

 tions on the solubility of calcium carbonate in water con- 

 taining carbon dioxide, with constants hereafter to be deter- 

 mined, which are, however, not whole numbers ; for if whole 

 numbers be employed, it is impossible to reconcile fact with 

 theory. 



In view of this uncertainty, the formula which we have 



sufrm.sted has this advantage, that the coefficients which 



• • • • 



occur in it arc a priori determined, and its truth can at once 



be decided by experiment. It will in fact appear that in the 

 instances .-tudied by Guldberg and Waage the simple form 

 which they recommend is completely confirmed ; and that 

 such simplification is in most cases admissible confirms, more- 

 over, the validity of Avogadro's law in its application to solu- 

 tions. On the other hand, the results of Schlosing's in- 

 vestigation, prominent!) ... . moine, cannot be 



