( 843 ) 



value of x for the two coinciding heterogeneous piaitpoints is larger 



than the value of x for the plaitpoint P„. With further rise of the 



<Z> dSp 



temperature, when — = rises further above — = 0, the plait- 



points P 1 and P a move further apart. P, moves towards larger 



values of x, and P a (the hidden piaitpoints) to smaller value of ,v. 



And the two heterogeneous piaitpoints P t and 1\ coinciding at still 



higher value of T, there is a continuous series of values of x from 



# = up to x = 1, for which piaitpoints occur. For every value of x 



only one. I have drawn (These Proc. VII, p. 626) the transformation 



of what I called there a principal plait and a branch plait. But 



this transformation refers, properly speaking, more to the binodal 



curve of such a complex plait than to the spinodal curve. If we 



then draw T p i as function of x, such a line has a maximum and 



a minimum value, both lying above 1\ . The minimum value at 



the origin of the double plaitpoint P 1 and P a , and the maximum 



value at the disappearance of P a and P 3 in consequence of their 



coinciding. Also when P p i is drawn as function of x, we get a 



dp dp fdp\ dT dT p i 



similar curve. As in general — = 1- 777, 7— > will be 



dx d.rx \dlj x dx dx 



dPpi fdp\ 



= 0, if = 0, because — is equal to in a plaitpoint. But 



dx \d.vjT 



the value of P p i as function of T p i exhibits a more intricate form. 



As T—^-— T ( '-£- ) 4- — 1 ~ is determined by the proper- 



dl \dJ J V)X fd^v \ dT 



dx' /pT 



d'v 

 ties of the substance in the plaitpoint, e. g. by — . This quantity is 



dx* v T 



dPpi 

 the same for double plaitpoint, and so — — has two equal values 



dT 



in such a double plaitpoint. The plaitpoint curve has therefore two 



cusps in the case treated. The left branch extends from 7^ to the 



temperature at which P a and P, coincide. The right branch begins 



at Tk„, and runs then back to the temperature at which the double 



plaitpoint P, and P 2 originates. The middle branch gives the hidden 



piaitpoints. But here, too, we must again notice that not the whole 



outside branches can actually be realised, the splitting up into three 



phases when we draw near the cusps having a greater stability 



then the homogeneous plaitpoint phase. These are the phenomena 



observed by Kuenen for the mixtures of ethane and alcohols with 



greater values of b than that of ethane. Perhaps the change of 



