( 590 ) 



At /n coiilact of a spinodal line and tiie itlaitpuiiit line takes 

 place for the third time, viz. at the branch f VI mentioned. Again at 

 somewhat lower temperatnre a three phase eqiiiJibriiim will be fonnd 

 at M by the repeated splitting np of 2 into 1 and '1, and now for 

 good and all, down to the lowest temperatures. All this is quite 

 identical with the case treated with type II. 



Theoretically of importance for this remarkable third (very ab- 

 normal) pi'incipal type is therefore this, that after the two liquid 

 phases 1 and 2 have become identical at M' (t^), there must again 

 take place splitting up of the homogeneous liquid phases into two 

 separate phases with sufticient lowering of the temperature, viz. at 

 31, somewhat below R^ (cf. also fig. 12). 



We point out that the point M in fig. 4 and 6, and in fig. 7 is a 

 so-called upper mixing-point, i.e. that at temperatures hlc/her than the 

 temperatures corresponding Avith that point the two phases 3,1 or 

 2,1 will form one homogeneous phase. The same thing is also the 

 case for the points M and Af' of figs. 8 and 12. Above the tempe- 

 rature of 3[ 1 coincides with 2, above that of 31" again 1 with 3. 

 But the point 31' is there a so-called loiver mixing-point, for at 

 temperatures lotn-r than that of 31' the phases 1 and 2, distinct at 

 higher temperatures, coincide to one homogeneous phase. 



For the plaitpoint line C,C^ of the third type (fig. 8) all the points, 

 lying between 31" somewhat before R^ and 31' somewhat beyond 

 R'^, are not to be realized. They form again the series of hidden 

 plaitpoints p', indicated in the figs. 9 — 11. 



The p, .«-representations are again omitted. 



In the figs. 12 and 12a the p, 7'-representations of the plaitpoint 

 line are drawn of the type mentioned. We again notice the three 

 ciisp)s R^, R^ and R'.,. In fig. 12 the three phase pressure lies between 

 the vapour pressures of the components; in fig. 12a above them. 

 Ci R^ has then again, as in fig. 6a, a retrogressive course. 



We shall put off the discussion of the remaining points to a 

 following paper. Those points are : a. The transition case between 

 type I and II with the double point; l>. the discussion of the possi- 

 bility of the occurrence of type III ; c. some remarks on the special 

 case (9^1; d., the proof, that in the ^v,7'-representations the different 

 points R^, R, and R', are cusps. 



