( 1253 ) 
Physics. — “Some remarks on the value of the volumes of the 
coeaisting phases of a simple substance.’ 1. By Prof. J. D. 
VAN DER WAALS). 
The main features of the curve which represents the volumes of 
the coexisting phases as function of 7, are known. It is a curve 
which possesses a maximum in the critical point for a volume which 
is equal to 7b,. The value of 7 would be equal to 3 for substances 
for which the quantity b is not variable. But for substances for 
which 6 does vary with the volume, 7 is smaller than 3. As this 
variability is greater, 7 will be smaller; it can be found by approxi- 
mation from the relation sr = 8; or more accurately somewhat less 
than 8. In the critical point the liquid branch and the vapour branch 
meet. At this meeting the curve has a continuous course. Though 
this curve can only be experimentally determined at temperatures 
above the freezing point, there is every reason to consider these 
branches as also theoretically existing at lower temperatures. Even 
at temperatures above the freezing-point the liquid volume falls 
below the value of 4,. According to the determinations of SypNey 
1,3583 
Youne the coexisting liquid volume at 0° is e.g. for ether the 
=) 
part of the critical volume, whereas the value of 6, cannot differ 
1 
much from the ET part of vj. And at lower temperatures this is 
’ 
regularly the case. On the vapour side the volume continually 
increases with decrease of the temperature on account of the great 
decrease of the pressure, and the relation pv = RT is fulfilled more 
and more accurately. This holds both for anormal and for normal 
substances. Even for acetic acid, provided we bear in mind that the 
value of BÀ for bi-acetic acid is meant, and do not consider acetic 
acid as an associating, but as a dissociating substance. But as long 
as the volume still has a finite value, there is still deviation from 
the law of the perfect gases, and SypNey Youne’s observations (Proc. 
Royal Dublin Society. June 1910) present a valuable contribution 
to the discovery of the cause of this deviation. 
That there will be a deviation, is of course to be expected according 
to the equation of state, even though we should leave quasi association 
entirely out of account. But the extent of the deviation could be 
accurately calculated in this case. Now the question can be answered 
if besides this cause of deviation there is another — and if we have 
to assume quasi-association to occur in such great volumes as those 
