( ^''^'^ ) 



experimental pressure and temperature ranges. For many years a 

 similar investigation has stood on the program of the Leiden Labo- 

 ratory. 



IV. The Gibbs' surface for H^O for great densities. 

 {Model for the equilibrium of Tammann's ice varieties and water). 



The Gibbs' surface 'suffers a deformation from association in the 

 case of water, and the general character of the change has been 

 already given in § 3 according to our \iews. Having once arrived 

 at a given idea about the general form, we can more exactly deter- 

 mine the form to be ascribed to the ridges according to this idea 

 by the help of the experimental numbers. The model that we have 

 obtained by our method is shown on PI. II fig. 4. As Tammann has 

 already indicated, t^vo other ice varieties (ice II and ice III) are 

 found, in addition to ordinary ice (ice I). The general position of 

 the ridges belonging to these values follows from Tammann's measu- 

 rements concerning the volume change and heat of transformation 

 for the transition of one ice variety into another or into water. If 

 we give the value to the last and 1, 2 and 3 to the three ice 

 varieties, Tammann finds at T =: 251 (triplepoint w\ater — ice I — ice III) 



Lv,, = — 0.05 

 A?'3, = + 0.193 

 r„j = — 73 cal. 



?'o3 = — 70 ,/ 



Also Tammann finds that Av^^ is very nearly equal to Ai\^. We 

 have assumed that Ar,^ is somewhat greater than Av\^. We then 

 find the general arrangement given in PI. IV fig. 1 for the water 

 and three ice varieties. The dashed line gives the isotherm through 

 the triple point w^ater — ice I — ice III, the dotted line the isopiestic. 

 We have not taken these from pi. II, fig. 4, where no isotherms 

 or isopiestics are drawn, because this figure is not sufficiently worked 

 out for this purpose. We have drawn on PI. IV. schematic figures 

 in order that they may be used in continual comparison with the 

 surface, whenever we wish to further explain the properties of the 

 surface. From these we can show easily that they agree with the 

 model of PI. II, fig. 4. 



We now further specify our ideas for the modification and 1. 



Here - is negative for points on the binodal line, and this also 

 dt 



