( 682 ) 



and the great change of the time of relaxation with the above men- 

 tioned further change of b at the transformation from solid to liquid 

 is explained on the same grounds. Still keeping this in view we may 

 say that by prolonging the line hi till it reaches the solid state we 

 have given what van der Waals calls the eqnation of state of the 

 molecule. 



Now it follows immediately from this representation that the form 

 of the connecting line Id must be taken as dependent upon the tem- 

 perature and the inflection as decreasing and finally vanishing with 

 rising temperature. Thus the above consideration of the form of the 

 liquid ridge on the Gibbs' surface necessitates the assumption that the 

 solid can be joined to the liquid ridge by a plait. This wdll be gene- 

 rally perpendicular to the ^'-axis and will end in a plaitpoint i.e. this 

 indicates the continuity of the gaseous and solid states of aggregation. 



With these considerations we have not treated the question whether 

 the conditions in the plait which we assume to exist in the gap 

 between the two states of aggregation (c.f. § 2 for outside the plait) 

 are also conditions of equilibrium, labile or ollierwise. We have 

 advanced no reason for this. This is as far as we know not done 

 by othei'S either who have assumed the existence of similar condi- 

 tions '). [n considering the vapour, we slated that there have not 

 been observed metastable states connecting the solid with the gaseous 

 and liquid states. However these appear very clearly and markedly 

 between the gaseous and liquid states, and have an important bearing 

 in the theory of van der Waals. 



Also it is not unlikely that van der Waals has never in his 

 writings treated the continuity of the gaseous and solid states, and 

 has expressly kept it in the background, because the use of such 

 intermediate states as those above considered is only allowed theo- 

 retically when it is shown — as van der Waals did for the inter- 

 mediate vapour-liquid states — that these intermediate states may be 

 treated as conditions of equilibrium. However we do not propose to 

 determine "the molecular equation of state" from a given mechanism, 

 but to seek for an empirical form for this from the known facts by 

 induction. In this case we must use the most obvious analogies as 

 indications and it is not allow^ed to deviate from the most simple 

 suppositions without proving each step. With variable molecules it 

 is probable that relations between entropy and volume can exist 

 other than those which van der Waals has already treated in 

 his equation of state based on the theory of cyclic motion. In order 



1) See especially Ostwald, Textbook of general cliemislry. 



