164 
the two methods of calculation are evidently leading to considerably 
different results for hydrogen too. 
§ 3. His opinion that the polarisation of the molecules caused 
by their mutual influence, is of great importance, is based by 
DepisE principally on the values of the coefficients of the mean 
reduced equation of state. This mean equation of state has been 
given by KAMERLINGH ONNES for a systematic summary and discus- 
sion of the material of observations and of the deviations from the 
law of corresponding states. At the same time, however, he declared 
emphatically *) that for no substance this mean reduced equation of state 
will coincide with the real reduced equation of state. [t would only 
do so, when the substances the data of which have been used in 
the derivation of the mean reduced equation of state, strictly 
obeyed the law of corresponding states. Now this is by no means 
the case, especially not for hydrogen compared with nitrogen and 
oxygen, which gases gave the data for the higher reduced tempera- 
tures, which are of most interest for our question. This is a.o. 
evident from the following fact. When for the great volumes and 
for the dominion of reduced temperatures corresponding to the tem- 
perature interval in which Amacar has made measurements on O, 
and NV, we want to make the reduced equations of state of H, cor- 
respond with those of O, and N,, we must choose as critical reduction 
temperature for H,*) 43, whereas however the critical temperature of 
H, is 33. Now in the mean reduced equation of state the reduced 
second virial coefficient DS is represented as a function of the reduced 
temperature t that is obtained by combining the values taken from 
H, with those of O, and N,, ete. and reduced as well for H, as 
for O, and N, by means of the experimental values of 7x. And it is 
evident that this function can show a quite different character from 
that which corresponds to the behaviour of each of the substances. 
For the discussion of questions as those considered here, we do 
better not to use the mean reduced equation of state. 
It would be preferable to start from the special reduced equation 
of state of hydrogen *). In the above question however the special 
equation of state would lead to trustworthy results only then, 
when it was fitted to high temperatures. But this is not the case. 
1) See e.g. Leiden Comm. N°. 74 8 4, 1901. 
3) H. KAMERLINGH ONNEs and C. BRAAK. Leiden Comm. N°. 9768, p. 39. 
H. KAMERLINGH Onnes and W. H. Krersom. Die Zustandsgleichung. Math. 
Enz. V 10. Leiden Suppl. N°. 23, note 399. 
3) See Leiden Comm. NO. 109a, § 7, 1909. 
