( 684 ) 



The extension of this idea to associated substances was necessarily 

 excluded since the law of corresponding states w^as taken as the 

 basis of the development. The existence of a maximum density for 

 water need then bring no difficulty for the representation of the 

 liquid state in the consideration that in general p, and thus i] also, 



1 



is ffiven along an isotherm by powers of — . The question, if the 



V 



connection between i] and v, which follows from the mechanism of 

 the liquid or gaseous states, can in general be given by expressing 



1 



11 in powers of — , could be left out of account. Kow that we wish 



V 



to introduce the solid state into the polynomial — until now not used, 

 but after some change perhaps applicable for this purpose — we meet 

 the difficulty that with many substances solidification is accompanied 

 with increase of volume. For water, which falls in this case, the 

 question is treated more fully in §§ 3 and 4. Still if this case could not, 

 as we have supposed, be explained by association, and if in general 

 the complete knowledge of the mechanism of the solid state for the 

 isotherms of gas, liquid and solid leads to an implicit relation between 

 tj and V, still for one part of the range of i] it will be possible to 

 express this directly by one value in terms of v. It appears to us 

 to be quite possible that with certain normal substances p can be 



empirically expressed in powers of — over the whole range under 



consideration. 



The GiBBs' surface, which we have constructed for this first class 

 of substances, will serve to give not improbable corresponding Aalues 

 of p and V for an isotherm in the liquid-solid plait, and to permit 

 computation of useful values for the virial coefficients — the coeffi- 

 cients in a polynomial 



pv = A-^ h— + 



V V' 



If we seek for the values which these coefficients can have, we 

 find a second connection between this investigation and Comms 

 Nos. 71 and 74. In both of these it is shown that values will be 

 found for the reduced virial coefficients of different substances, which 

 are sufficiently, but still not quite, equal. These differences in Ö S 

 etc. will just give the deviations of the various substances from the 

 law of corresponding states. They express parts of the molecular 

 interaction which cannot be explained or represented by the actions 

 of homologous points which last actions are those whose mechanical 



