2 ART. 12. H. HTPtOBE : ON THE FUSION SURFACES OF THE 



be known. And conversely, when the quantitative relations of 

 the heterogeneous equilibria are given, the state of chemical 

 equilibrium in the solution can be determined. Such in short 

 is the essential feature of the theory of dilute solution in its 

 manifold applications. And this is possible because the chemical 

 potential of each chemical species in the dilute solution is a 

 simple function of the concentration, and its variation with tem- 

 perature and pressure can be readily calculated. If the chemical 

 potential in a solution of any concentration were as well known, 

 the general quantitative theory of heterogeneous equilibrium could 

 be developed with equal ease. This is at present by no means 

 the case. But in the solutions, whose component chemical species 

 fulfill the conditions of the ideal solution, the chemical potential 

 has the simple form, whatever may be the relative amount of 

 the various substances. Therefore, when the liquid phase in a 

 ternary system is such a solution, it should be possible to express 

 the fusio7i surfaces in terms of the heat and the temperature of 

 fusion of the solid pliases and the equilibrium constants and the 

 heat of reaction of the reversible chemical changes in the liquid 

 phase. And on the other hand it should be j^ossible to deduce 

 the equilibrium constants etc. of the chemical reaction in the 

 liquid phase from the study of the fusion surfaces. 



In the majority of the ternary systems hitherto investigated, 

 the chemical reactions involved appear to be too complex to lend 

 themselves readily to mathematical treatment. At least it ap- 

 pears premature to attack them without due preparation. More- 

 over, the temperature has in general not been measured with 

 sufficient accuracy, simply because it has not been necessary for 

 the purpose of the investigators. Hence in order to be able to 

 test the foregoing thesis, I had to study experimentally a compara- 



