142 MAGIE— THEORY OF SOLUTIONS. [April 19, 



same as the heat capacity of the solid solute. A similar rule has 

 been shown to hold for the volumes of aqueous solutions of cane 

 sugar by Wade and by Wanklyn, and examples of its applicability 

 to solutions of other non-electrolytes can be obtained by simple cal- 

 culations from the data given in the tables of specific gravities. 

 The few cases in which this rule does not hold good, notably those 

 of aqueous solutions of the alcohols, may fairly be considered as 

 exceptions which perhaps cannot now be explained, but which we 

 may expect to explain in harmony with our main hypothesis. 



With regard to the electrolytes, the observations of Thomsen 

 and other observations made in the physical laboratory at Princeton 

 by Mr. R. E. Trone, can be represented by the formulas with great 

 accuracy and completeness. As I expect soon to publish (in the 

 Physical Review) an extended comparison of the data of observa- 

 tion with the numbers calculated from the assumed formulas, I 

 shall content myself here with giving a few typical examples. 



The formulas to be illustrated are : 



For the heat capacity H =W + A(i — p) + Cp, 



For the volume V = U ^ D(i — p) -^ Fp, 



in which W and U are respectively the heat capacity and the vol- 

 ume of the water used in making up the solution, and p is the 

 dissociation factor, or the number of dissociated molecules of the 

 solute, expressed as a fraction. In the tables A^ represents the 

 number of gram-molecules of water in which one gram-molecule 

 of solute is dissolved. 



The constants C and F express, for the heat capacity and the 

 volume respectively, the effect of both ions of the dissociated mole- 

 cule. Either one of them may be considered as the sum of two 

 similar constants, each expressing the effect of one of the two ions. 

 If, therefore, we consider solutions of two binary electrolytes, each 

 containing a common ion, the difference between their values of 

 C or of F should be independent of the effect of the common ion, 

 and so should be the same for the same pair of other ions, what- 

 ever may be the common ion with which they are connected. This 

 conclusion from the hypothesis is illustrated by the sodium and 



