Phenomena of some Substances and Mixtures. 193 



point has still the properties of a maximum pressure-point. 



Neither -7- nor ~ can be oo along the plaitpoint-curve at B, 



because that would mean that the temperature went through 

 a maximum or minimum. The result is that at B 



(§0p = (I9 o = (see above) (f ) along raaximum curvej 



i. e. the maximum curve touches the plaitpoint-curve at B. 

 The diagram in my former paper is therefore incorrect, as the 

 plaitpoint-curve was drawn with a break at B. 



33. As to point A, it may be proved that (£■) is infinite 



there. We must use for this the conditions which hold for 

 the point where a plait is split up. A plaitpoint is a point 

 of the connodal curve on the ^ surface, but at the same time 

 of the spinodal curve. The connodal curve is the curve traced 

 out by the double tangent-plane : the spinodal curve, which 

 is inside the connodal curve, separates the part of the surface 

 where the substance is stable from the unstable part. The 

 equation of this curve is 





Inside the curve A < 0, outside A > 0. 



Applying the condition that A = in the plaitpoint, we have 



(dA\ = /^A\ /fcA\ (dx\ /BM (dv\ 

 \dtJ F VfW,* \-dx/ v \dt) P ^{-dv/^dtJp 



Now at A ^— is > 0, because just before the division 

 of the plait A< in that point, and just after A>0*. 



Moreover we have at point A (^— ) = 0, and (^) = 0. 



\oz Jvt \ov J xt 



This will be seen to be true on considering that in the 

 direction of the .r-axis A passes from negative through 

 back to negative, in the direction of v from positive through 

 back to positive. The conclusion we come to is that either 

 doc dv 



It ° r dt i ° r ^ ot ^' are ^ n ^ n ^ e at A. The last alternative is 

 the true one ; but either of the three is sufficient for our 



* A more rigorous proof may be given by working out ^r. : 

 compare van der Waals, /. c. Juni 29, p. 2. "* 



