602 
Physics. — “Contribution to the theory of binary systems. XXI. The 
condition for the existence of minimum critical temperature.” 
By Prof. J. D. van DER WAALS. 
Already in the theory of binary systems concerning perfectly 
miscible substances we repeatedly found the case of a minimum 
critical temperature, and already in my “Théorie moléculaire’ I 
derived the condition for the existence of such a minimum, and ex- 
pressed it in the form: 
: 5 and —2 En 
12 De 
In my investigations of recent times, in which I chiefly intended 
to ascertain the conditions for the only partial miscibility, my 
attention was again directed to the possibility of the existence of a 
minimum (7; ,, and I have come to the conclusion that there is 
also question of such a minimum (7%), for the mixture ether-water, 
but that the value of 2 for 7}, minimum lies very close to the ether 
side. If as second component we always take the substance with 
the greater value for the size of the molecules, so ether in the 
case under consideration, the value of w is 1 or nearly 1. In 
the experimental investigation by Dr. ScHprreR my expectations 
have proved to be correct, and he has even succeeded in observing 
the course of the p,7-line for given value of 2 up to a certain 
distance from the ether side, and found it in perfect harmony 
with the course predicted by theory for completely miscible sub- 
stances. He has even succeeded in reaching the value of z at which 
the plaitpoint entirely coincides with the critical circumstances for 
such a mixture taken as homogeneous. According to this experimental 
investigation, of which I express my sincere admiration, the value 
of xv at wkich the minimum value of (7%). occurs, is so close to 
the ether side that we may put this value —1, and the second value 
mentioned of z is at a distance of more than 0,3 from the ether 
side, so that we may put it smaller than 0,7. For smaller value of 
« the non-miseibility, as a new circumstance occurring in this 
system, prevents the observation of the course of the ordinary plait- 
point line. 
In my investigation of the causes of imperfect miscibility and of 
the different forms which can occur for oniy partial miscibility, I 
was led to apply a simplification in the theory, which I thought that 
though certainly of influence on the quantitative accuracy, would 
be of little or no intluence on the qualitative course of the pheno- 
