( 1101 ) 
still smaller, and the mean value would be found to be only 
f= 0.9, from which it would follow that 7), = 6.°4, a value that 
considering the temperature of the Borre point, must certainly 
be too high. 
It is worth remarking that this value of / differs very much from 
the values, ranging from 2 to 3, that have been found for ordinary 
normal substances). Helium, then, shows in a greatly exaggerated 
form the deviation from the mean /= 2.7 for ordinary normal sub- 
stances that is already noticeable in the case of substances whose 
critical temperature lies below O° C. which give a value f= 2.2. 
Associative substances deviate in the opposite direction; for instance, 
for water f = 3.26 and for isobutyl alcohol f= 4.17. 
The new light now thrown upon the vapour pressure law for 
helium also allows a new estimate of the lowest temperatures that 
were reached in the experiments published in the vaN BrmMMELEN 
Jubilee book, which were then estimated upon a basis of f = 2.2. 
With the value now obtained, the temperature for a vapour pressure 
of 1 mm. should be 1°.33 K., and for 0.15 mm., which was the 
lowest pressure reached, the temperature should be 1°.15 K., while, 
to reach a temperature of 1° K., the vapour pressure would have 
to be lowered to 1/25 mm. 
§ 5. Densities of Liquid Helium. In the following table containing 
the experimental results, densities are expressed in terms of the 
normal density of the gas. 
From these values oj, is obtained by multiplying by o = 
N 09C. 760 mm. 
= ().0001787, so that we now get o. = 0.122, where the 
2 N liqcoex.4.°29 : 
roughly approximate value 0.15 was given before. 
The great decrease in the expansibility as the temperature is lowered 
is remarkable. In the experiments of 1909 described in Comm. N°. 112 
the impression had already been created that this would prove to 
be the case; the density values then obtained are given in column I. 
The results are shown graphically in fig. 2, Pl. IL, and it is parti- 
cularly noteworthy that there seems to be a maximum in the density ; 
from the figure this seems to be at about 2°.2 K. Furthermore, it 
was clearly observed that, when the temperature was being lowered 
and passed 2°.1 K., the meniscus in the stem of the dilatometer 
became stationary, and rose again as the temperature sank further 
to 1°.48 K., while the reverse phenomenon was observed as the 
temperature rose again from this point to 2°.37 K. The following 
') Kuenen, Zustandsgleichung p. 142. 
72 
Proceedings Royal Acad. Amsterdam, Vol. XIIL 
