80 PHYSICS OF MATTER 



greater than that reckoned on the basis of the number of molecules 

 present, but was to be explained by their dissociation into ions; 

 thus reaching the same conclusion which Clausius had announced in 

 1857, but affording a method by which the precise amount of the 

 dissociation might be measured. Additional evidence in favor of 

 this theory was afforded by the studies of the electrical conductivity 

 of dilute solutions of electrolytes made by Kohlrausch. 



All this was accompanied by an increasing realization of the 

 important relations that might be established by an application of 

 the laws of thermodynamics to chemical problems. Thus van 't Hoff 

 showed in his paper of 1887 that the depression of the freezing-point 

 of a liquid due to a substance in solution depended directly on the 

 osmotic pressure and could be used to measure it; a result which 

 had already been experimentally reached by Raoul. 



In this field, Professor J. Willard Gibbs, in whose recent death the 

 world of science has lost a most profound thinker, was a pioneer. 

 His most important contributions to the subject were in two ex- 

 traordinary papers, On the Equilibrium of Heterogeneous Substances. 

 The first of these related to chemical phenomena, while the second 

 was concerned especially with capillarity and electricity. 



To quote from a recent writer, "The most essential feature of 

 Gibbs 's discoveries consisted in the extension of the notion of thermo- 

 dynamical potential to mixtures consisting of a number of com- 

 ponents, and the establishment of the properties that the potential 

 is a linear function of certain quantities which Gibbs has called the 

 potentials of the components, and that where the same component 

 is present in different phases, which remain in equilibrium with each 

 other, its potential is the same in all the phases, besides which the 

 temperatures and pressures are equal. The importance of these re- 

 sults was not realized for a considerable time. It was difficult for 

 the experimentalist to appreciate a memoir in which the treatment 

 is highly mathematical and theoretical, and in which but little at- 

 tempt is made to reduce conclusions to the language of the chemist; 

 moreover it is not unnatural to find the pioneer dwelling at consid- 

 erable length on comparatively infertile regions of the newly explored 

 territory, while fields that were to prove the most productive were 

 dismissed very briefly." 



"It was largely due to Professor van der Waals that two new 

 and important fundamental laws were discovered in Gibbs 's paper, 

 namely, the phase rule and the law of critical states." 



The phase rule has been the guiding principle in some most import- 

 ant studies of chemical equilibrium. It furnishes a clue by which the 

 polymorphism of such substances as sulphur and tin may be scien- 

 tifically investigated and the conditions of equilibrium between the 

 different polymorphic forms determined. The studies of the case 



