( 509 ) 



entirely realised at T^p. This is only the case at liiglier temperatnre. 

 At T below T,y, there is connection between the unstable part 

 of the transverse plait and of the longitudinal plait. So the liquid 

 branch of the binodal curve of the transverse plait has a metastable 

 and an unstable part. This is also the case at Ts,, . Not until higher 

 temperature, i.e. when the plaitpoint of the longitudinal plait lies on 

 the binodal curve of the transverse plait, this binodal curve is entirely 

 to be realised. But Kuenen's objection makes me doubt whether I 

 have expressed my meaning clearly enough. 



A simple proof for the theorem that — =: at the double 



\cLv-Jpr 



point, is furnished when the spinodal curve is represented by the 

 aid of the S function by : 



dx"-JpT 

 The ditferential quotient is then : 



'd'^\ f d% \ dp 



— 



dx^ J^jT \dp^dpJpT d.v 



/^d'^\ f d% \ 



In case of splitting up both -— and — — — is equal 



\d.vyijT \dx^dpJpT 



to zero, and then — cannot be determined from this equation, hut 

 dx 



must be found from a quadratic equation. Now I — ) = v, and 



\dpJxT 



at a double point the two relations ( — J =i 0, i. e. the condition 



Kdx'JpT 



of a plaitpoint, and ( — ) ^0 hold. At an ordinary plaitpoint 



\dx^Jj,T 



fd''v\ dp 



— is not equal to 0, but then —^0. 

 \dx^)pT dx 



My conclusion is this. At the temperatures at which the splitting 

 up takes place the double point can lie inside the joint realizable 

 binodal curves of the longitudinal plait and the transverse plait. That 

 this is impossible has never been proved as yet, and is not to be 

 proved in my opinion. 



Above Ts,, the lefthand and the righthand convex-convex part of 

 the surface that lies within the binodal curve, have united. 



