(443 ) 

 only at a temperature, at which either there is nol yei question of 



</'-'l|' r/-|f' 



contact <>t lie.' two curves = and . or at which this contact is 



long over, the complication in the course of the p-line will have 

 disappeared for the spinodal line. At the moment of the disap- 

 pearance this p-line possesses a horizontal tangent and a point of 

 inflection in the point in which maximum and minimum pressure 

 coincide. It* further in such a figure we drew a third line indicating 

 the pressure along the binodal curve, this third line would have a 

 complicated shape - but U>v this I refer to some Communications 

 occurring in These Proceedings 1905. 



But from all this we further conclude that is not necessary that 



(/'■'if' ,/-i r 



the two curves = and =0 intersect for the occurrenceof 



the pair of heterogeneous plaitpoints on the spinodal line. If they 

 only draw near enough to each other, the spinodal line can already 

 pos>ess the described complication, and there can even he three- 

 phase-pressure. 



It follows from this that for mixtures the properties of whose 

 components are represented besides by ;/. by positive e, and f„, 

 the presence of the heterogeneous plaitpoints is not restricted to the 

 space OPQ below the parabola for e, and a s ; but that this space must 

 be extended with a part of the parabola itself - - a part lying in 

 the neighbourhood of the top. The theoretically exact shape of this 

 part can only be determined by investigation of the spinodal line 

 itself. But in view of the difficulties attending this investigation, I 

 shall content myself here with an indication of the way in which 

 I have tried to form an idea for myself of the accuracy of ni\ 

 expectations that this part would again be approximately bounded 

 by a parabola, which compared to the preceding one, would have 

 shifted in the direction of the axis, though what follows must 1 1 « » i 

 be looked upon as much more than a certain kind of empirical 



calculation. W hen the curve - = lies entirely within — <). 



,/y* ' dv' 



bul in the neigbourhood of the latter curve, two other curves, vi/.. 



</> </' J if 



= at lower temperature? and = at another still lower 



dv' ' dm* 



temperature will show intersection and contact in the space outside 

 = 0. where the spinodal curve lies, and where the pair of 



heterogeneous plaitpoints are found, at a certain distance apart or 

 coinciding. 



