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sufficiently accurate temperatures at our disposal: the liquefaction 
of hydrogen .soon appeared upon the programme: the piezometry 
and thermometry of low temperatures had to be studied. In the 
meantime were discovered the monatomic gases whose molecules 
probably answer best the assumptions made by vaN DER Waats, and 
helium at once usurped the place originally set apart for hydrogen. 
And now helium itself has been liquefied, but the number of 
isotherms of different gases that have been determined is small while 
the region covered by them is narrow, and although the problem 
that is being worked out at Leiden has undergone important exten- 
sions, it still retains the same character as before. 
Helium is now the substance to which one would «@ priori ascribe 
an equation of state most resembling the var DER Waars equation. 
In this connection it remains to be shown how, from the surfaces which 
represent the reduced equations of state for ordinary normal sub- 
stances (passing over first those for oxygen, nitrogen, etc. argon, 
then those for neon and hydrogen) that for helium may be derived 
by continual deformation ; to this one would like to aseribe a limiting 
form. . 
Comms. No. 71 (June 1901) and 74 contain a reduced equation 
of state obtained by combining the different portions given by various 
measurements with hydrogen, oxygen, carbon dioxide, ether and 
isopentane, each for the region of reduced temperature which 
corresponds with the ordinary temperature for that particular 
substance. In the Leiden researches this mean equation of state 1s 
regarded as an envelope which is in contact with each of the special 
surfaces of state in that region to which it has contributed to form 
the mean equation, while the special reduced surfaces for the 
various substances separate from each other and from the enveloping 
surface in the other regions, the helium surface in this respect 
exhibiting the greatest deviations. In fact, the special reduced equation 
for hydrogen (VII, H,, Comm. No. 109a $ 7 equation (16), March 
1909) differs markedly from the mean (VI, 1, Suppl. No. 19, p. 18), 
and measurements already made with helium (cf. Comm. No. 108, 
Aug. 1908) confirm the fact that its equation of state differs from 
that for hydrogen in the same way as this has been found to differ 
from oxygen and nitrogen. 
The deformation of the surface representing the reduced equation 
of state is accompanied by a deformation of all corresponding lines 
on it, thus occasioning a change in the reduced values of all magni- 
tudes deduced from the equation. This point will be treated in 
greater detail in an article by H. KAMERLINGH ONNEs and W.H. KEEsomM 
