( 391 ) 



points ai some distaiicc from tlie critical tempcrahirc, appear outside 

 in the realisable part of the diagram before the critical point is 

 reached? The answer to this (piestion is the following: the minimum 



{,i\ = ,(■„) approaches one ol the maxima (( -— ., 1 = 0) and at a 



dp 

 given temperature coincides with it; from the expressions for —— and 



d' T> 



— -, or bv geometry, it follows that both coefficients vanisli in tliis 



d.r^-' 



point ajid that the p — .i\ curve has a point of inflexion witii a tangent 

 parallel to the .I'-axis. Immediately afterwards the iwo points in 

 question have passed each other and have exchanged tiieir charactei-, 



/ /- H \ 

 i. e. the point, where ( — —\ = 0, is now a minimum') and the 



\d.i\y 



other point, where ,i\ = .v.^, is a maximum : the latter point lies 



at first in the metastable })art of the diagram between the minimum 



and one of the liquids of the three-phase equilibrinm ; a further 



change of temperature makes it coincide with this liquid and ultimatel}- 



brings it outside into tlie stable part of the ligure. The maximum 



and minimum in the non-stable part approach each other and Unall}' 



coincide, as explained before. 



For the sake of clearness we will once more go through die 

 ^•arious changes as deduced above in the op[)Osite order, i. e. while 

 the temperature falls towards and passes through the critical point. 

 Above the critical mixing-i)oint there is a separate two-liquid curve 

 turning its critical point towards the ^'apour-li(plid curve: in the 

 latter ^ve assume a well defined maximum {a\=^x^). When the 

 temperature falls the two curves approach and at a given moment 

 come into contact; this contact takes place in the critical point of 

 the liquid curve, but in general at a smaller or larger distance 

 from the maximum on the vapour-licpud curve : doubtless the distance 

 may in some cases be small, but that does not affect the general 

 argument; on further hjwering of the tem|)erature the maximum 

 is in many cases taken up inside the three-phase equilibrium and 

 so disappears from tlie realisable portion of the diagram; it passes 

 successively the connochil and the spinodal curves and lies then 

 ultimately in the non-stable region, ^^ here it is found at low temperatures. 



It was mentioned in the beginning tiiat similar changes occur in 

 other cases, e.g. wiien the two-liquid curve lies inside the vapour- 



2) Compare the figure for sulphurous acid and water, van der Waals, Gonti- 

 nuitat II, p. 18, fig. 3. 



