( 1103 
An idea of the accuracy of the corrections applied in each case 
may be got from the fact that, in the second experiment, the control 
dilatometer showed a rise of the meniscus of 0.03 as the temperature 
fell, while the caiculated value was 0.028. The mean number 0.134 
that remains after the correction has been applied, must be ascribed 
to expansion between 2°.37 K. and 1°.48 K. As far as a conclusion 
could be drawn from the observation, a maximum density point for 
helium has to be accepted. From a single observation in which the 
vapour pressure of the bath was lowered to 1 mm. it would have 
followed that no further expansion occurs as the temperature is 
lowered still more; bet, in the meantime, this one observation, 
during which the bath was not stirred, is too uncertain to allow a 
definite conclusion as to whether or not the density of helium after 
attaining a maximum decreases till it reaches an invariable value. 
§ 5. Vapour Densities of Helium. The density at a pressure of 
65.54 cm. and a temperature of 4°.29 K. was found to be 69.0 times 
the normal density. Calculating 4 from the equation pr—RT=B/v 
we get L= — 0.000047; and, for the density of the saturated vapour 
at a pressure of 76 cm. a value of 85.5 times the normal. The 
correction for C to be applied according to the mean reduced equation 
of state VII. 1, although undoubtedly appreciable, appears to be too 
uncertain. At 3°.28 K. by extrapolating values of the individual B’s 
deduced from the helium isotherms between O° and —- 216°.56 C. 
(Comm. N°. 102¢, Dec. 1907) B was found to be — 0.000061, and 
this gives at 3°.25 K.asaturated vapour density 24.5 times the normal. 
From these values various characteristic thermal data may be 
calculated for helium. If we deduce the slope of the Maruras diameter 
from 4°.29 K. and 3°.23 K. we find — bj == 0.0033, and, taking 
the critical temperature to be 5°.5 Kk. and hence reaching the value 
01d=0.065, we get for the constant of the Marnras diameter —',—0.255. 
Marmas foretold that the value of — 6g would be small, and he 
suspected that it would be 0.14. The first part of his remarkable 
prophecy is, therefore, hereby fulfilled. 
7 
we get (taking 7, = 50.5 K., 
PEEVE 
and pe = 2.75) from op7 a value 2.68, which is almost exactly the 
theoretical value deduced from the van prR Waars equation of state. 
The value of this constant is thus markedly smaller for helium than 
for all other substances, with the exception of hydrogen, in which 
case if can be obtained only from very uncertain calculation yielding 
the result 2.9. (See Kusnen |, c. p. 60). The smallest known value is 
hae 
For the critical virial ratio A, = 
