( 623 ) 



ilir quantitatively accurate shape of the spinodal curve will, indeed, 



not be known, but vet in large traits the reasons max be stated, 

 why in many cases the shape of the plait is so simple as we are 

 used to consider as the normal course, whereas in other cases the 

 plait is more complex, and there are even cases that there is a 

 second plait. 



Particularly with regard to the y>-lines, it. is possible to forecast 

 the course of these lines from the properties of the components. 

 With regard to the g-lines this is not possible to the same extent, 

 but if there is some uncertainty about them, we shall generally have 

 to choose between but few possibilities. 



The course of the /j-lines. 



In fact the most essential features of the course of the />-lines 

 were already published by me in "Ternary Systems" — and only 

 little need be added to enable us to determine this course in any 



O 1 • -1 1 ^*f' 



given case ot two arbitrarily chosen components. As p = 



dv xT 



dp" 



and — ) = ,, ' - , it is required for indicating the course of 



K&Jp f<¥\ 



\dv)xT 



these >>-lines to know the course of the curves ( — ] =0 and 



\dvJ xT 



The former curve has a continuous liquid branch, and a continuous 



gas branch, at least when T lies below every possible Tk, when we 



denote by Tk the critical temperature for every mixture taken as 



homogeneous that occurs in the diagram. If there should be a minimum 



value of Tk for certain value of ,v, and 7' is higher than this mini- 



fdp\ 

 mum Tk, the curve I — 1 =0 has split up into two separate curves. 



In either of them the gas and the liquid branch have joined at a 

 value of v — v/ : . In this case a tangent, may then be traced // to 



the r-axis to each of these two parts of the curve f — J = 0. 



\dvj xl 



fdp\ 



The second curve I— I = is one which has two asymptotes, 

 \dxJ vT 



and which may be roughly compared to one half of a hyperbola. 



The shape of this curve derived from the equation of state follows 



from the equation: 



