( 187 ) 



necessity. This is in fact an argument that speaks for fig. 2, but 

 Avhich did not seem to me perfectly conclusive. For who warrants us, that 

 these very special circumstances do not occur here ? It is chiefly to 

 decide this point, that I have also examined the course of the (p,7')a,- 

 lines. And this examination has taught me, that the particularities 

 which occur in these lines, do not clash with the assumption which 

 leads to fig. 2 — whereas we should be confronted with difficulties, 

 when we concluded to fig. 1. 



Then fig. 3 is drawu up on the supposition that there are still 

 hidden complications beyond the values of Te and Ta- In this figure 

 is drawn in the first place the projection on the {T, cv)-plane of the 

 phases coexisting at the three phase pressure, viz. the continuous 

 curve DEAC. So this line represents the locus for the points .A'-4^" of 

 the figs. 4, 5, 6 of the paper of March 1905. The value of T for 

 the point E is therefore Te, and for the point A, T has the value 

 of Ta. That this broken line consists of three almost straight pieces 

 is not essential, but it has been assumed that it does not change its 

 direction continuously at the points E and A. 



In the second place the projection of the plaitpoint line has been 



given by: . It consists of a piece which may be considered as 



the projection of the points P of the figures of March J 905, i.e. the 

 left part up to the point E. The part lying on the right from the 

 point A represents then the projection of the points Q of the figures 

 1. c. Every part of this line l}ing between E and A is projection 

 of the hidden plaitpoints. 



As we make one double plaitpoint disappear at T^ Te, and 

 the other at T <| Ta, this middle part starts on the left still 

 running to higher values of T, (the piece EM) and on the right 

 there is a piece inA, that also runs to higher values of T. The remaining 

 part of this plaitpoint projection curve, viz. the piece Mm descends 

 therefore with increasing value of x. That this plaitpoint curve 

 possesses a maximum and a minimum value will be shown presently. 

 This middle piece is the locus of the plaitpoints R of the figs. 4, 5, 

 6 1. c. The part between E and M, and also the part between A 

 and m is the projection of the higher plaitpoint of the hidden 

 complication in the cases that this complication still exists either 

 above Te or below Ta. 



In the third place the three phase pressure is traced. In the points 

 of the line DE thinner lines have been drawn parallel tothe^>axis, 

 increasing in length as we reach the point E. The three phase 



pressure itself is denoted by . We must, of course, take 



care that points of the branch of the three phase pressure lying 



13 



Proceedings Royal Acad. Amsterdam. Vol. VIII. 



