t DE 
Physics. — “On the value of the critical quantities”. By Prof. Dr. 
J. D. vaN DER Waars. 
(Communicated in the meeting of March 25, 1911). 
Originally by the term critical quantities we understood the volume, 
the pressure, and the temperature of the critical point. For the value 
oe Eca 8 a 
of these three quantities ve = 36,, p; = S57» and RTG Has 
27 by 27 bo 
been derived. But in the determination of these values it has been 
supposed that the quantity 6, which had proved to be variable 
with the volume, would have changed only so little in the 
critical point that it might be put equal to the value which it 
has in infinitely large volume, and which will be denoted by the 
symbol 6,. But this equation beb, implied at the same time 
9 
db d*b 
the neglect of fe and of ol In course of time the value 
k NS Ad 
av 
of other quantities, as they appeared to be in the critical point, have 
come to the foreground. 
In my communication on Quasi association (These Proc. XIII p. 107) 
pen 1 RT; T dp a faa 
d = == FS, ( ) = a 
RP ie al Spe pal) i. “ei ae 
I have mentione 
v : 5 Ae 
and ( :) == Í ‚ which together with the above three quantities 
v a k 8 
a 1 . : a sr 
ve = rb, and Pk= GD and Ba Go 
of 8 quantities, which, however, are not independent of each other. 
If the quantities a and 6, are determined by the choice of the 
substance, the knowledge of 3 quantities, viz. 7, s, and fis sufficient 
to calculate them all. 
From the property of the critical point follows that it is that point 
Bete) * 3 a, (P dp 
of the tsothermie line for which the quantities B and ( i 
dv) dv? JT 
are equal to 0. So two equations must suffice for the determination. 
By means of these two equations the quantities vj, and R7/ are 
determined, and further the value of pj. by means of the equation 
for p itself. Also the other critical quantities mentioned are then 
derived by simple mathematical operations. If we put for p: 
RT a 
;» forms a number 
the two equations for the determination of vj, and RT, are: 
