905 
from these the four cone: vertices, we then find as result that the 
rays of the congruence with coinciding foci form a regulus of order 116. 
The curve &*° intersects t; besides in the three cone vertices 
lying in this plane in 57 points more, lying of course on the section 
k® of 2° and ri; to each of these points a ray through 7} is conjugated 
3116 
with coinciding foci; the 4 cone vertices are thus for the surface 2 
57-fold points. 
‘Physics. — “Some remarkable relations, either accurate or approvi- 
mative, for different substances.’ By Prof. J. D. van DER 
W aars. 
(Communicated in the meeting of November 30, 1912). 
In a previous communication (June 1910 These Proc. XIX p. 113) 
I pointed out the perfectly accurate or approximative equality of the 
ratio of the limiting liquid density to the eritical density, and the 
ratio of the critical density to that which would be present for 7, 
Pv 
Vg: and, soit = should always be equal to 1. With the symbols 
used there 
211+ y)= gs 
I have added the factor yg, which must then be equal to 1 or must 
differ little from 1. 
The rule given there has attracted some attention. For first of all 
Dr. Jean TrMMERMANS has informed me that he has found this rule 
entirely confirmed for six substances, for which the observations made 
were perfectly trustworthy. For a seventh substance there was a 
great difference, but he thought that for this real association might 
perhaps occur, as is the case for acetic acid *). Besides this rule has 
also been adopted by KAMERLINGH Onnes and KersOM in their recent 
work for the Encyklopädie: Die Zustandsgleichung. The rule is in- 
deed apt to rouse some astonishment, because it pronounces the 
equality between two quantities, which, at least at the first glance, 
have nothing in common. 
It is to be expected that this approximative equality will have 
to be explained by the way in which the quantity 6 varies with v; 
but it is seen at the same time that perfect equality cannot be put 
1) The numerical values have been communicated in the “Scientific Proceedings 
of the Royal Dublin Society”, October 1912. 
59” 
