( 188 ) 



above EA, and also of the branch lying above AC must fulfil the 

 condition that for the same value of 7^ the pressure must have the 

 same value for the three branches. 



In the fourth place for some values of T sections parallel to 

 the (j),,^')-plane are given and those parts of these sections are 

 drawn which correspond to the pieces A' PA and AQA" of the figs. 

 4, 5, 6 1. c. We must then, of course, take care that the maxima of 

 the curves fall above the projection of the plaitpoint curve. It is 

 hardly necessary to remark that at any rate as long as T lies between 

 Te and Ta the plaitpoint pressure for the left-hand branch, and 

 also for the right-hand branch is greater than the three phase pressure. 

 But if w^e want to compare the value of the plaitpoint pressure and 

 that of the three phase pressure at the same value of x, we have 

 to carry out another construction. Let G be a point of the projection 

 of the three phase pressure. Let us draw the line GH parallel to 

 the jT-axis, then H (a point of the projection of the plaitpoint curve) 

 has the same value of x, and so above H a point must be sought 

 of the plaitpoint curve itself. How high this point lies depends on the 

 value which the plaitpoint pressui-e has for this value of x. In the 

 point H a somewhat thicker line has been drawn parallel to the 

 ^^-axis, whose length would have to denote the value of this plait- 

 point pressure. This length is left undetermined in the figure — 

 but is clear that it will be smaller than the amount of the three 

 phase pressure for the same value of x. For at the value of 

 T, as it is for the point G, the pressure above G in the section 

 for the chosen value of x is equal to the three phase pressure. 

 The value of T for the point II is smaller than that for G. Between 

 these two values of T the ( 77, 7')a-section of the (p,7^,A')-surface has 

 a continuous course, and in such a (^9, J')a-curve the pressure rises 

 with the temperature. Only in the case that a maximum in the (/>,,f)Z'- 

 curve occurred, the pressure above H, so the plaitpoint pressure could be 

 smaller than that above G. But in our diagrams we shall assume the 

 more general case. Themodifications which would ensue from the 

 assumption that in the region discussed here a maximum pressure occurs, 

 would render numerous new figures necessary, and it will not be 

 difficult to give them when the more common case has been understood. 



According to fig. 3 there is in our case a maximum and a 



minimum for Tpi, so that there are values of x for wiiich — -^=: 0. 



ax 



For a plaitpoint ( -— : ) is equal to 0, because it is a point of the 

 spinodal curve, and at the same time ( — -] is equal to 0. 



