380 



h P 



T^O, and i=zloq R -\- — — ^ — 1, i. e. the chemical constant ^), 



R R 



equation (25) becomes, 



r T 



''^''=-^'+H-'"' ï'+.+i ƒ -/.(ï)'"- ±JMr)<iT+... (25', 



o O 



We thus tind, as might be expected, a vapour-pressure formula 

 of the form assumed by Neknst. ^) 



13. The equation contains two indeterminate functions/,(7') and 

 f^iT), the former being governed by the internal meciianism of the 

 single molecule and determining the change of the specific heat Cj 

 with the temperature, while the latter depends upon the internal 

 mechanism of the associated molecule and in connection with the 

 former determines the change with T of the specific heat C of the 

 condensed state. The fact that we are free to choose these functions 

 as we like might give the impression as if the equation of state 

 which we have deduced and which is independent of that internal 

 mechanism, would be compatible with the properties of the amorphous- 

 solid condition without any modification. Siill this is clearly impossible: 

 for it is evident that the pressure must also depend upon that 

 internal mechanism '), and from this point of view something- 

 must be lacking in our equation of state. 



It is, however, not impossible that it will be sufficient to make 

 a small modification in the law of dependence of h ^) in order to 

 obtain the devised correspondence with the equation of state of the 

 solid condition, and that by establishing the "equation of state of 

 the molecule" ^), not only of the single molecule, but also of the 

 complex one, the object might be attained. Still, so long as the 

 equation of slate of the solid condition itself is not better founded 

 than it is, it would be premature to go into this question any further. 



1) I. W. Gedeeberg (Die thermodynamische Berechnung chemischer Affinitaten, 

 Berlin, 1906, p. 25) puts i — logjJic; in our result this constant remains in- 

 determinate. 



^) This is known not to be the case with the original equation of state (cf. e.g. 

 Planck, Thermodynamik, p. 277). 



5) Comp. H. Kamerlingh Onnes and W. H. Keesom, loc. cit., p. 887 (273) 

 etc. Vid. also Max B. Weinstein, Ann. d. Phys , (4) 51 (1916) p. 465; (4) 52 

 (1917) p. 203; (4) 52 (1917) p. 506. 



*) As an instance : whereas according to the previous assumptions the condensed 

 state would be completely incompressible at r=0, the hypothesis of a change 

 with pressure of the limiting volume biim would give the substance in that condition 

 a certain degree of compressibility. 



^) See e. g. van der Waals, these Proceedings, III, p. 515, 571, 643. 



