( 65 ) 

 seek how man\ limes a straight line may be drawn parallel to the 



6 



ü-axis, so that p(Vb — v a ) = j pdv. It' this can take place only once, 



the extremities of this straight line indicate the value of v of the 

 phases coexisting with each other, and the distance of this straight 

 line above the v-axis the value of the pressure for this pair of coexist- 

 ing phases, and the chosen (/-line cuts then no other branches ot 

 the binodal line. This may take place several times, when the chosen 

 q-Yuie passes 4 times through the binodal curve, or when there are 

 6 points of the binodal curve on the chosen (/-line. To ascertain 

 whether this can take place times, or 1, 2 or more times, we have 

 to pay attention in the first and foremost place whether or not the 

 chosen q-liae intersects the spinodal curve, and if it does, how many 

 times. For every time when a (/-line cuts the spinodal curve, there 

 is cither maximum pressure or minimum pressure for the points of 

 this </-line. In the points of the spinodal curve a p-line touches the 

 chosen (/-line, and one and the same //-line, having either larger or 

 smaller value than the /.(-line which touches, will pass through two 

 points lying on either side of the spinodal line. Thus in fig. 7 (p. 738j 

 there is maximum pressure in point 4 of the gyline, and minimum 

 pressure in point 2, but for larger volume than that of point 4 the 

 pressure is always smaller than in 4, and the smaller as r is larger, 

 and in points of the same (/-line in which v is smaller, the pressure 

 is always larger than in 2, and the larger as we follow the gyline 

 to its initial point, where p = x. If we now construe p as function 

 of v, the _/j-line has a shape similar to that of an ordinary isotherm. 

 For v = oo , ft = 0, there is a maximum and a minimum pressure, 

 and for v = 6, p = oo. Maxwell's rule may then be applied, but 

 only once. 



So this gyline will possess two points of the binodal curve. In 

 fig. 7 this will be the case for every q-Yme. For the line j = qd, or 

 for the first substance we find the coexisting phases of that substance, 

 and for q = — oo or for the second substance, the coexisting phases 

 of the second substance. If starting from a certain point of the v,x- 

 diagram we draw both the p-curves as function of v, viz. the p-curve 

 when we follow the (/-line which passes through the chosen point, 

 and the //-curve when we remain at constant value of x, then the 

 2 nd curve has always greater value of p than the first for all values 

 of i' smaller than that of the point chosen. Thus in fig. 7 the pressure 

 in a point lying more to the left to which the (/-line moves is smaller 

 than is the case for constant value of x at the same value of v. 



5 



Proceedings Royal Acad. Amsterdam. Vol. X. 



