( 680 ) 



Mi 



Fig. 3. 



from the side of large v, we 

 >^ should see a succession of ridges, 

 and where we for simplicity con- 

 sider the case of a single solid 

 state of aggregation, we should 

 see the resulting ridge rising at 

 lower temperatures above the 

 liquid ridge (cf. fig. 3). 

 To find the coexisting phases from the region a' a" or from the 

 region U with the vapour phase from the region c, one must lay 

 the common tangent plane on the curved surface in c and the given 

 ridge. In the case that a rarefied gas phase occurs in c, the ridges 

 would be represented approximately by curved lines. This is then 

 also to be permitted in the search for the corners a and b of the funda- 

 mental triangle of the triple point. The general thermodynamical 

 character of a solid state occurring together with the Van der Waals 

 state (liquid, gas and labile intermediate states) would be thus obtained 

 by representing it on a Gibbs' surface by a ridge of a somewhat 

 other position and form but generally analagous to the liquid ridge. 

 There is thus every reason to suppose that outside the region 

 of observations and towards the large volumes the first continuations 

 of the isotherms obey an analogous law as to form and change 

 of form with temperature as tlie liquid isotherms, and thus by 

 a slight extension really produce a ridge. This appears to be more 

 probable when one notices that there is also a ridge on the Gibbs' 

 surface which does not correspond to the original equation of 

 VAN DER Waals where a and h are taken as unchangeable but 

 which belongs to the equation into which this changes when a and 

 h are taken as functions of temperature and volume. Thus when 

 shifting the variable or corrected isotherms (cf. ls\ 66 § 3 end) in 

 place of the original constant one a similar ridge as that Avhich 

 we have considered would also be always formed, though the suc- 

 cessive isotherms are no longer equal and similar, but show a small 

 continuous change with temperature. In this way one cannot escape 

 the conclusion that metastable states occur at the side of the solid 

 s'ate between solid and gas. 



The observed part of the isotherm on the vapour side for tempe- 

 ratures far below the furthest limit of the observed undercooling of 

 liquid does not extend beyond the sublimation line. Still from ana- 

 logy with what is known for vapour at higher temperatures, it must 

 be assumed until the contrary is proved, that the Gibbs' surface extends 

 inside the sublimation line to metastable and even to labile equili- 



