( 739 ) 



point at which the two branches have joined at a volume v = (vk)x, and 



has a point of inflection there. Two 



parts of (/-lines have been drawn 



as touching the ;>line. The two 



points of contact (1) and (2) 



are points of the spinodal curve, 



and lie again outside the curve 



dp 



— = 0. For a higher ;>line these 



dv 



points will come closer together. 

 And the place where they coin- 

 cide is the plaitpoint. As in 



point (1) ( — ) >( — ) and re- 



ctor 



dx* 



versely in point(2) 



Fig. 76. 



fdH\ 

 \d?) h 



d'v 

 dx 1 



q 

 > 



d u v 

 dx~* 



rd'v\ 



= ( Jjji) wh en (1) and (2) 



have coincided, and this may be considered as the criterion for the 

 plaitpoint so that in such a point the two equations: 



"dv\ /dv' 



and 



hold. 



dxj f 



da 



d'v 



\dx*) p \dx 2 J t/ 



The following remark may not be superfluous. In point (2) 



d*v\ fd'v\ 



is not only smaller than { -7-7 J, but even negative. In order to 



da 



find the plaitpoint, the point in which 2 points of contact for the gaud 



'd*v\ fdH\ 



the p-lines coincide, and so { t~z I and ( ~rz ) have the same value, 



dx* 



dx* 



( — ) must lirst reverse its sign in the point (2) with increase of 

 \dx*J p 



(d*v\ 

 the value of p for the isobar before the equality with ( — J can 



be obtained. And that, at least in this case, this reversal of sign 

 must take place with point (2) and not with point (1), appears from 



the positive value of 



d'v 

 dx~ 7 



So we arrive here at the already known 



theses that in the plaitpoint the isobar surrounds the spinodal curve, 

 and also the binodal one. 



