( 193 ) 



takes place. This may be assumed as alread}^ known from the properties 

 of a (p, 7')^-curve, when there are no complications by hidden 

 equilibria. It might possibly be expected that in a plaitpoint, where 



besides — , also — - is equal to 0, double intersection and so 



contact would take place. If, ho^ve^•er, we develop the equation 



fdp\ 

 which teaches us the value of -7" I viz. 



\d.vJr 



fdp\ fd^^^ 



\dxjT \d,v,^y^ri 



for the case of a plaitpoint in the form : 



'd'v,'\ {•v-,v,yfdp^ \(.v,-.v,y fd^^ 



fd^\ 



,,T 2 yd.vjr 'I 2 \dx 



'1 // 



or 



S''-=("---'^-' 



Jt 



\dx^'JpT 



it appears that in the case of a plaitpoint, the quantity ( — ) 



\dxjT 

 is only once equal to on account of the factor a\ — ol\. 



It may be remarked here for the better understanding of the series 

 of figures {a, h, c etc.) that the first set of four viz. a to d holds 

 for values of .r lying betAveen a point halfway xe and xa and the 

 point E itself, ,t moving to continually smaller values. Fig. d 

 holds for XE- The second set of four values holds for x between 

 XE and xn, and Fig. g is the representation for T z= Tt,-. 



The remaining figures {h' , d etc.) hold for values of x lying on 

 the right side. Fig. g^ is the representation for 7'= Tu- on the right 

 side and fig. d' holds for x = xa- 



Physics. — ''The {T,x)-equilibna 0/ solid and fluid phases for variable 

 values of the pressure", by Prof. J. D. van der Waals. 



In two communications (October and November 1903) I discussed 

 and represented in diagrams for the case of equilibrium between a 

 solid and a fluid phase 1*^' the (j), .i')-figures for constant value of 

 T and 2°"^ the {p, 2") -figures for constant value of x. So only the 



