( 687 ) 



for different densities and entropies and the crystal form will be 

 different for various modifications. 



The increase of the vibration energy will gradually efface the 

 mean predominant most probable distribution and orientation as the 

 crystal is raised in temperature and although the whole continually 

 approaches a uniform mean distribution and orientation still some 

 different groups will remain in arrangements of most probable predo- 

 minant distribution and orientation. In particular if this hypothesis 

 Is applied to the case of a gaseous and a solid phase in equili- 

 brium which are brought together to a higher temperature, fresh 

 hypotheses must be made to render it clear that no identity of the 

 two phases can become possible and therefore no continuity of solid 

 and gaseous states will be found. Of course it does not matter if 

 the temperature under consideration is above the liquid-gas critical 

 point. Further there is no reason known why it should not be 

 allowed to extend the double convex part of the Gibbs' surface, — 

 containing essentially states of equilibrium, to higher temperatures and 

 pressures, so that it surrounds the critical point at the end of the plait. 



Is is quite in harmony with our assumptions of ^ 1 that, in the 

 gaseous phase of a substance occurring also as solid, molecular groups 

 will at all times be found (produced always from different indivi- 

 duals) in which the particular attraction betw^een not equivalent 

 points ^), predominating in the solid state, will also be manifest. 

 Below a certain temperature it will then be necessary to momenta- 

 rily consider certain portions of the gas as crystalline. We are here 

 only following the method employed by Boltzmann for the deter- 

 mination of the equilibrium distribution, which is the most probable. 

 We apply it to a given densitj- and velocity distribution but also 

 extend it to orientation and arrangement. 



We have mentioned above the existence of more ridges wiiich 

 appear successively on the Gibbs' surface towards the side of 

 diminishing volume. This case appears to us to be the normal one. 

 It is probable that the various solid modifications are not known for 

 most substances. If we further consider that a small change in the 

 course of the isotherms can cause one ridge to rise above another and 

 thus to represent more stable i)hases or not, it is not at all probable that 

 just those modifications of the various substances are known, which 

 belong to corresponding ridges. It is therefore, possible that in the solid 

 state the various substances would differ- less than now appears to be 

 the case if one were acquainted with all their modifications; finally the 



J) Gomp. Reinganum, Drudes Annalen. 1903. 10 p. 334. 



