(11) 



ïnnm pressure of the mixture wliose .i- = /r/)', and will therefore have" 

 an element in common with tiic isotherm of the concentration xjo'. 



As for the sign of - — we may remark that it is positive outside 



the points D and D and negative inside them. 



The ordinary case being supposed in the diagram, viz. Vs <C Vj\ 

 we may draw two tangents to the above mentioned isobar from the 

 point Ps with the points of contact R and E. These points of con- 

 tact now, indicate the points where the quantity l^,y=0, as van 

 DER Waals ^) showed. 



This quantity is represented by the equation : 



and denotes the decrease of volume per molecular quantity when 

 an infinitely small quantity of the solid phase passes into the coex- 

 isting fluid pliase at constant pressure and temperature. 



For the case that the coexisting phase is a vapour phase, Vsf is 

 negative, but this quantity can also be positive, and when the pres- 

 sure is made to pass through all values, there is certainly once 

 reversal of sign, for the case F) 0> ^^s even twice. 



To elucidate this Prof, van der Waals called attention to the 

 geometrical meaning of V^f. 



Let us call the coordinates of the fluid phases Q coexisting with 

 Fs, Vf and Xf and let us draw a tangent to the isobar in Q. 

 Then Ps F will be equal to Vsf if P is the point where this 

 tangent cuts the line drawn parallel to the axis of v through Ps. 



If the point P lies above Ps, Vsf is negative, and if P' lies under 

 Ps, then Vsf is positive. For the case that the tangent to the isobar 

 passes thi'ough Pg, which is the case for the points E and R', Vsf=^ 0. 



In this way it is very easy to see that for the points outside those 

 for which Vsf = 0, the value of Vsf is negative, and for the points 

 within them, Vsf is positive, but this latter holds only till the points 

 D and D' have been reached, where Vsf=^o:>- Between Z) audi)', 

 Vsf is again negative. The transition from positive to negative takes 

 therefore place through od . 



As each of the lines of equal pressure furnishes points where 



1) These Proc. VI, p. 234. 



