( 183 ) 



Physics. — "Contribution to tin' theory of binary mixtures. VI. 

 The plaitpoint line" By Prof. J. D. van der Waals. 



Continued. See p. 123. 



By the plaitpoint line we understand the continuous series of points, 



in which the mixture is in the plaitpoint state. It' we think the 



points of the surface of saturation determined by the coordinates 



T, p and x, then ihe plaitpoint line is a curve lying on this sin face, 



and its projections on the planes of coordinates are expressed by: 



p=f 1 (T), p=f t (x) and x=f t (T). If the surface of saturation 



is given by the coordinates T, v and x, its projections have the 



form: v=f A {T), v=f i (x) and x=f t (T). The two surfaces of 



saturation mentioned may be derived from each other by the aid of 



the relation p = <p (.<', v, T). If we have t lie first mentioned surface, 



the substitution of p leads to the second. However, we might also 



have eliminated T, and obtained a surface of saturation of the form 



F(p,v,x) = 0, also one of the form F^ {p, v, T) = 0. A point of 



saturation being determined and known in all respects if the 4 



quantities T, x, v, and p are known and the equation of state giving 



a relation between these 4 quantities, we may imagine as many 



surfaces of saturation as the number of combinations of 4 quantities 



three and three. The number of projections of the plaitpoint line 



is then the number of combinations two an J two. For the direction 



dT dp dv dp dp dv 



of the projections — , — , — , -zx, » — .and-— present themselves for 

 1 J dx da das dT dv dT 



consideration, which of course, are not independent of each other. 



The best known shape of the plaitpoint line is that for which the 

 initial point lies in the critical point of the first component, and the 

 final point in the critical point, of the second component. 



In this case there is a point in which the plaitpoint line begins, 

 and another in which it terminates ; but such initial and final points 

 lie necessarily in such places as are to be considered as natural 

 boundary points. Thus initial and final points might also occur for 

 boundary volumes (v = b) — but a plaitpoint line can never have 

 an initial or final point for arbitrarily chosen value of v and x. 

 Thus in the case that there is minimum or maximum Tk the mentioned 

 well-known shape of the plaitpoint line will, it is true, make its 

 appearance only in a certain point with gradual increase or decrease 

 of the temperature for certain definite value of T — but such a 

 point is then necessarily a double plaitpoint, and the plaitpoint line 

 itself retains its character of continuous series of points; the double 



