( 688 ) 



possibility remains that more liquid ridges could exist along which with 

 falling temperature the time of relaxation would not increase to the 

 value required for the solid state, while states of equilibrium between 

 the two are to be expected, so that the same substance could exist 

 in two liquid modifications. 



The reasons why such a case is not known and why the various 

 solid modifications are usually crystalline, must be farther explained 

 by a theory of the solid state. 



§ 3. Following the lines developed \\c have constructed tlii-ee 

 models of Gibbs' surfaces. 



We have first considered an imaginary substance, which partially 

 corref^ponds with carbon dioxide, in the liquid state is in harmony 

 with VAN DER Waals' original equation, and which further can exist 

 in one solid (crystalline) modification. For the Gibbs' surface of this 

 substance constructed according to our ideas, we have only considered 

 that portion where the fusion line of the substance is to be found. 

 This model serves principally to present clearly the views on the 

 solid state advanced in this communication. 



Having assumed that we can express the character of the 

 peculiarities in the transition from solid to liquid by this model, 

 we have further constructed two others, which refer to the actual 

 CO3 and on which all known thermodynamical properties are 

 expressed as numerically exact as possible. 



One of the models represents the whole surface for CO.^ with the 

 exception of the portions for the ideal gas state and for very low 

 temperatures. 



The second gives, on a necessarily larger scale, the region where the 

 transition occurs between the various modifcations with small volumes. 



Finally another model has been formed which demonstrates 



sufficiently, that taking it in general, a substance like water can be 



represented in the manner followed by us. We mean that the 



deviations which this substance exhibits can be brought into line 



with the association. In general a liquid ridge which 



I i corresponded sufTiciently with the van der Waals 



I equation of state, would be pressed upwards and 



J X towards decreasing volume by the association. This 



IK ( \ transformation is represented schematically in the »; v 



"^^ \ projection by fig. 5. To the right lies the undisturbed 



X VAN DER Waals ridge, given by the portion where 

 tiie connodal liquid-vapour, the curve drawn, runs 

 Fig- 5. to the left, the twisted ridge is again given by the 



