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similarity results in the law of corresponding states. The various 

 substances certainly differ widely in the solid state when they are 

 expressed with reduced coefficients. Thus the mechanical dissimilarity 

 of the actions of unhomologous points appears at once. When the 

 same isotherm passes through the gaseous liquid and solid states, 

 the higher coefficients of the polynomium must without doubt differ 

 considerably. It is thus to be expected that the lower coefficients, 

 will also exhibit certain but smaller differences, which are connected 

 with those in the higher coefficients. In this manner, in the compa- 

 rison of two substances, the deviations from the law of corresponding 

 states would be clearly connected with the solid properties of the 

 two given substances. 



Further, as the virial coefficients give the deviations from the 

 Boyle Gay-Lussac law we may say that these deviations do not only 

 express the properties of the liquid state as given by van dee Waals 

 but also those of the solid state. Really a connection between the 

 deviations and the properties of the solid state is also implied in 

 VAN DER Waals' last development of the equation of state after the 

 method of cyclic motion. 



§ 2. The best possible connection of the known part of the solid 

 with the liquid ridge by a continuous surface has some similarity with 

 the use of the continuous line by which J. Thomson connected the 

 liquid and gaseous states found by Andrews. Still there remains a 

 marked difference. Thomson could start from the existence of a cri- 

 tical point. A continuous change from the solid to the liquid state 

 is not experimentally proved, it is doubted by some and as to the 

 crystalline modification it is directly contradicted by Tammann. If 

 Tammann's theoretical considerations were correct, then it would already 

 be clear that we had produced only a simple empirical interpolation 

 when we intended to have constructed a group of intermediate states 

 which beforehand would be at least probable on physical grounds. 



Tammann's objections are certainly not conclusive. They rest in 

 the same way as our assumptions on extrapolations outside the 

 experimental region, and it appears that our extrapolation is more 

 probable than his. Also Tammann's combination of the fusionline of 

 water, an associating substance, with that of other substances as if 

 they were two cases which could pass one into the other by change 

 of temperature and pressure, presents some important difficulties. We 

 have not to consider these conclusions so long as we exclude asso- 

 ciated substances and substances of perhaps very complicated character. 

 Instead of giving immediately a general treatment of cases so 



