( 053 ) 



Por this wc shall start with the case that b increases and a decreases 



fd r \ 

 with increasing a, so that r l\ : decreases strongly, and I — 1 is positive 



\oxJ v 



everywhere; and for the present we confine ourselves only to the 



solidification of the least volatile component, so x 8 = 0. Let us write 



the value which N gets at the rim by the aid of the value derived for 



d P \ ' 



— J from the equation of state, in the form: 



OX Jo 



I MRT db '^l d A 



(V-*) h TT3 'i~[-MRT. . . . . (1) 



f (r — by dx v ) 



It is clear that this value will become negative for v = oo , on 

 the contrary positive for v = b *); so there will always have to be 

 a point on the axis x = 0, where A r = 0. The value which N 

 assumes for a? = l, is: 





and this expression will, accordingly, be negative for x = 1 for all 

 possible liquid volumes, and even negative infinite. Krom this follows 

 that from the point of intersection of N = with the axis ./; = 0, 

 the locus jV=0 will run to smaller volumes. Now whether A r = 

 and D = will intersect in our figure depends on the place where 

 jty"=0 cuts the axis x = 0. In this we may distinguish three cases: 



1. The point of intersection of A 7 = and the axis lies at smaller 

 volume than the points where D = cuts the axis. Then no inter- 

 section of* A — and D = () will take place; the points Q and Q' 

 lie quite outside the axes x = 1 and x = 0; 



2. The point of intersection A r =0 with the axis lies between 

 the points of intersection of D = with it. Then the point of 

 detachment does fall inside the figure, but not the point of contraction ; 



3. The point of intersection of JSÏ = and the axis lies at larger 



') If we should object to putting v = b, yet assuming that v/ > v s , we shall 

 in any case have to grant that there is nothing incompatible in the assumption 

 that at a certain high pressure the volume in the solid state can be smaller than 

 that in the liquid state, and that yet a great increase of pressure may be required 

 to keep the substance in the same volume after we have replaced some of the 



molecules by much larger ones (so j ^ J = oo) . 



2 ) As said, in every point of the line N = the ij-line passing through it, is 

 directed to the point indicating the solid substance. Every (/-line for infinite volume 

 being / / v-axis, and terminating in the point v — b, it follows from the existence 

 of the line iV = that every (/-line cutting this locus, must at least possess one 

 point of inflection. 



