241 
been left out of account in the first deduction of the equation. For 
example, we may refer in particular to the recent researches of 
VAN DER Waars on the influence of apparent association. On the 
other hand, there has been collected much valuable experimental 
material, which has already, on various occasions, been compared 
with the results obtained from theoretical assumptions. In the mean- 
time, while tbese researches are being continued, it seems desirable 
and opportune to undertake a systematic investigation of the equation 
of state over a region in which not only reliable experimental data 
can be obtained, and are in fact already accessible in part, but 
which also permits of a rigorous theoretical investigation. 
KAMERLINGH ONNES *) has started to systematically collect, arrange 
and incorporate into his empirical equation the experimental results 
already accessible over the whole region which has been already 
investigated for the equation of state. Amongst other effects of this 
empirical equation is that it makes it easy to compare different 
substances from the point of view of the principle of similarity, 
and in this respect it has already led to a number of valuable 
conclusions. For a general review of these conclusions we may refer 
to an article on, the equation of state which is to appear in the 
Eneyklopädie der Mathematischen Wissenschaften and is now passing 
through the press; we shall refer to this paper as Suppl. N°. 23. 
In investigating the most suitable expression for the equation of 
state preference was finally given (cf. Comm. N°.71 § 3) to a series 
of increasing powers of v-l (omitting the odd powers above 2 
and closing the series with v-®). With a small deviation from the 
notations of Comms. N°. 71 and 74 we may write the equation in 
the form 
EN alone here 
pe A ee a er a Sees om ot Lj 
Vv 
(cf. Suppl. N°. 23). 
The form of this equation shows that, from an experimental point 
of view, the method most immediately indicated for proceeding to 
obtain correspondence between theory and experiment is to successively 
determining, both theoretically and experimentally, the various 
virial-coefficients A, B, C etc., over a temperature region as extensive 
as possible for substances for which one would expect it necessary to 
make the least complicated assumptions regarding molecular structure 
1) H. KameruincH ONNes, Comm. No. 71 (June 1901), No. 74, Arch. Néerl. (2) 
6 (1901), p. 874. 
