610 
NATURE 
[May 5, 1923 

The first idea of the image of the fluid state which 
was gradually developed by van der Waals came to 
him when he combined the kinetic theory of gases 
with the determination of the cohesion in Laplace’s 
theory of capillarity. With the aid of very happy 
approximations he built up the kinetic theory of the 
fluid state. Such a simplification gave in the first 
place the calculation of a molecular pressure which 
represents the cohesion, and the result of the calculation 
led him to the profound conception that the molecules 
of the gaseous and the liquid state are identical and 
exert identical forces. Secondly, he accepted as by 
inspiration an exceedingly appropriate form for what 
would be the outcome of the calculation of the kinetic 
pressure at higher densities. The simple equation of 
state which he obtained in this way reproduced the 
well-known diagram of Andrews-Thomson, as the 
representation of a series of stable and unstable states 
of mechanical equilibrium. It gave a deeper insight 
into the continuity of the liquid and gaseous state 
as well as a luminous explanation of the critical 
phenomena. It stood even the crucial test which van 
der Waals only with apprehension undertook to apply 
to it; that is, the calculation of the critical data of 
carbon dioxide of Andrews from the deviations from 
Boyle’s law according to Regnault. Finding correct 
values for these meant a great "discov ery. The various 
thermal properties of fluids treated until then in 
different chapters of physics proved now to be at 
least approximatively contained in a single equation 
with only two specific constants, the volume and the 
attraction of the molecules, their molecular weights 
being given by their composition. Later researches 
have proved, more and more, the greatness of the 
genius which led van der Waals to his equation of 
state. Even now it is the most appropriate one 
to discuss qualitatively the properties of fluids. 
Directly from this can be derived the second great 
discovery of van der Waals, namely, that it is only 
necessary to introduce the reduced values of volume, 
temperature, and pressure obtained by dividing the 
values of these variables by their critical values into 
the equation of state, to reduce this equation to the 
same equation for all substances. Simple as this 
substitution is, it took seven years before it was 
arrived at, and then only by van der Waals himself, 
who had been wrestling for a long time with the 
explanation of the deviations between his equation 
of state and reality. He had followed many false 
tracks in order to find some regularity in the devia- 
tions of the different substances, and had reached 
the conviction that to compare substances they 
have to be considered in corresponding states ; that 
is, at the same values of the reduced variables. At 
that moment he found the law of corresponding states. 
Its scope is far wider than that of the equation of 
state. It involves the bold idea that the thermal 
properties of all substances can be derived from those 
of a single one simply by numbers of proportionality ; 
and, what is marvellous, the law approximates more 
closely to Nature than the equation from which it is 
derived. How much I was under the influence of its 
great importance as much as forty years ago may be 
best judged by my taking it then as a guide for my 
own researches. It has had a great effect on the work 
NO. 2792, VOL. 111] 

of liquefying the permanent gases (in his thesis van 
der Waals predicted that air had to be cooled below 
—158° C. to be liquefied, which has proved nearly 
correct) and of attaining the madir of temperature. ; 
This cannot be better illustrated than with the words 
of our deeply mourned Sir James Dewar in a letter 
to me, expressing that van der Waals was “the 
master of us all,’ “whom we cannot honour too 
much.” All substances, except for small differences, 
appear in the light of the law of corresponding states, 
as van der Waals expresses it, as individuals of the 
same kind. He liked to direct attention to the fact 
that his friend Dewar had proved that, taking tem- 
perature as a measure, hydrogen was, according to 
his prophecy, a dwarf. To read to van der Waals a 
report of the experiments which proved that helium, 
though a very small dwarf, was yet well shaped, was 
a happy moment in my life, especially as the report 
showed the profit derived from van der Waals’ law 
of corresponding states and at the end referred to his 
words that ‘‘ matter would always show attraction.” 
As all normal substances are almost copies of the 
same model, van der Waals was anxious to bring his 
equation of state in closer approximation to this’ 
general model and to understand the differences 
between the various substances. To his pondering 
on the influence of association into double molecules 
on the deviations, we owe his theory of binary mixtures, 
which covers a yet vaster and more varied field than 
his previous discoveries. It is especially this theory 
to which, in connexion with the beautiful work of our 
deeply mourned Kuenen, I owe the strong ties which 
united me to van der Waals. For many years I went 
to his study at Amsterdam for a “ monthly private 
course,” that is, a consultation on the Leyden work, 
and I found van der Waals always at his table filled 
with papers, with the portrait of his wife, who died at 
an early age, on the chair in front of him. In these 
hours it often occurred that from an unpublished 
calculation he could rightly predict some error to be 
found in the diagrams of the experiments; and it is 
from them that I have got an idea of the amount of 
work from which his genius came to his intuitions. 
It would occupy too much space here to refer in 
detail to the work of van der Waals, which groups 
itself around these three great discoveries. I can 
only point out that he tried to combine the theory 
of specific heats with that of the equation of state, 
and that in the end he was occupied with the very 
interesting problem of the influence of the conglomera- 
tion of greater number of molecules ; that of quasi- 
association. Rounding off in this way the chapter 
he wrote in the history of science, he gave us, at the 
same time, a glimpse of that chapter which the next 
generation has to write, containing a rational applica- 
tion of quantum considerations in van der Waals? 
theory of the fluid state. .t 
Not less than the extraordinary intellectual gifts 
which made possible his great life work, his friends 
admired his severe culture of the ideal and his noble 
character. We remember the pious heart, in whose 
friendship we rejoiced, and with a feeling of deep 
sorrow at the loss of his presence, we give him here 
the tribute of our profound gratitude. 
H. KAMERLINGH ONNES. 
a en 

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vc. rong 
