470° 
NATURE 
[SEPTEMBER I1, 1902 
‘molecules. No one, however, had attempted to make a com- 
plete study of a liquefiable gas throughout wide ranges of tem- 
perature. This was accomplished by Andrews in 1869, and his 
Bakerian Lecture ‘‘On the Continuity of the Gaseous and 
Liquid States of Matter” will always be regarded as an epoch- 
making investigation. During the course of this research 
Andrews observed that liquid carbonic acid raised to a tem- 
perature of 31° C. lost the sharp concave surface of demarcation 
between the liquid and the gas, the space being now occupied 
by a homogeneous fluid which exhibited, when the pressure was 
suddenly diminished or the temperature slightly lowered, a 
peculiar appearance of moving or flickering striz, due to great 
local alterations of density. At temperatures above 31° C. the 
separation into two distinct kinds of matter could not be effected 
even when the pressure reached 400 atmospheres. This limiting 
temperature of the change of state from gas to liquid Andrews 
called the critical temperature. He showed that this tem- 
perature is constant, and differs with each substance, and that 
it is always associated with a definite pressure peculiar to each 
body. Thus the two constants, critical temperature and pres- 
sure, which have been of the greatest importance in subsequent 
investigations, came to be defined, and a complete experimental 
proof was given that ‘‘ the gaseous and liquid states are only two 
distinct stages of the same condition of matter and are capable 
of passing into one another by a process of continuous change.” 
In 1873 an essay ‘‘On the Continuity of the Gaseous and 
Liquid State,” full of new and suggestive ideas, was published 
by van der Waals, who, recognising the value of Clausius’ new 
conception of the Virial in Dynamics, for a long-continued 
series of motions. either oscillatory or changing exceedingly 
slowly with time, applied it to the consideration of the mole- 
-cular movements of the particles of the gaseous substance, and 
after much refined investigation, and the fullest experimental 
calculation available at the time, devised his well-known 
Equation of Continuity. Its paramount merit is that it is based 
entirely on a mechanical foundation, and is in no sense empiric ; 
we may therefore look upon it as having a secure foundation in 
fact, but as being capable of extension and improvement. 
James Thomson, realising that the straight-line breach of 
continuous curvature in the Andrews isothermals was untenable 
to the physical mind, propounded his emendation of the 
Andrews curves—namely, that they were continuous and of S 
form. We also owe to James Thomson the conception and 
execution of a three-dimensional model of Andrews’ results, 
which has been of the greatest service in exhibiting the three 
variables by means of a specific surface afterwards greatly 
extended and developed by Prof. Willard Gibbs. The 
suggestive work of James Thomson undoubtedly was a valuable 
aid to van der Waals, for as soon as he reached the point where 
his equation had to show the continuity of the two states this 
was the first difficulty he had to encounter, and he succeeded in 
giving the explanation. He also gave a satisfactory reason for 
the existence of a minimum value of the product of volume and 
pressure in the Regnault isothermals. His isothermals, with 
James Thomson’s completion of them, were now shown to be 
the results of the laws of dynamics. Andrews applied the new 
equation to the consideration of the coefficients of expansion 
with temperature and of pressure with temperature, showing 
that although they were nearly equal, nevertheless they were 
almost independent quantities. His investigation of the capillarity 
constant was masterly, and he added further to our knowledge of 
the magnitudes of the molecules of gases and of their mean free 
paths. Following up the experiments of Joule and Kelvin, he 
showed how their cooling coefficients could be deduced, and 
proved that they vanished at a temperature in each case which 
is a constant multiple of the specific critical temperature. The 
equation of continuity developed by van der Waals involved the 
use of three constants instead of one, as in the old law of Boyle 
and Charles, the latter being only utilised to express the relation 
of temperature, pressure, and volume, when the gas is 
far removed from its point of liquefaction. Of the two 
new constants one represents the molecular pressure arising 
from the attraction between the molecules, the other four times 
the volume of the molecules. Given these constants of a gas, 
van der Waals showed that his equation not only fitted into the 
general characters of the isothermals, but also gave the values 
of the critical temperature, the critical pressure and the critical 
volume. In the case of carbonic acid the theoretical results 
were found to be in remarkable agreement with the experimental 
values of Andrews, This gave chemists the means of ascertain- 
NO. 1715, VOL. 66] 
ing the critical constants, provided sufficiently accurate data 
derived from the study of a few properly distributed isothermals 
of the gaseous substance were available. Such important data 
came into the possession of chemists when Amagat published 
his valuable paper on ‘‘ The Isothermals of Hydrogen, Nitrogen, 
Oxygen, Ethylene, &c.,’’ in the year 1880. It now became 
possible to calculate the critical data with comparative accuracy 
for the so-called permanent gases oxygen and nitrogen, and this 
was done by Sarrau in 1882. In the meantime a great impulse 
had been given to a further attack upon the so-called permanent 
gases by the suggestive experiments made by Pictet and Cail- 
letet. The static liquefaction of oxygen was effected by 
Wroblewski in 1883, and thereby the theoretical conclusions 
derived from van der Waals’ equation were substantially con- 
firmed. The liquefaction of oxygen and air was achieved 
through the use of liquid ethylene as a cooling agent, which 
enabled a temperature of #zzmws 140 degrees to be maintained 
by its steady evaporation zz vacwo. From this time liquid 
oxygen and air came to be regarded as the potential cooling 
agents for future research, commanding as they did a tempera- 
ture of 200 degrees below melting ice. The theoretical side of 
the question received at the hands of van der Waals a second 
contribution, which was even more important than his original 
essay, and that was his novel and ingenious development of 
what he calls ‘‘The Theory of Corresponding States.” He 
defined the corresponding states of two substances as those in 
which the ratios of the temperature, pressure and volume to 
the critical temperature, pressure and volume respectively were 
the same for the two substances, and in corresponding states he 
showed that the three pairs of ratios all coincided. From this 
a series of remarkable propositions was developed, some new, 
some proving previous laws that were hitherto only empiric, and 
some completing and correcting faulty though approximate laws. 
As examples, he succeeded in calculating the boiling-point of 
carbonic acid from observations on ether vapour, proved Kopp’s 
law of molecular volumes, and showed that at corresponding 
temperatures the molecular latent heats of vaporisation are 
proportional to the absolute critical temperature, and that under 
the same conditions the coefficients of liquid expansion are 
inversely proportional to the absolute critical temperature, and 
that the coefficients of liquid compressibility are inversely 
proportional to the critical pressure. All these propositions 
and deductions are in the main correct, though further experi- 
mental investigation has shown minor discrepancies requiring 
explanation. Various proposals have been made to supplement 
van der Waals’ equation so as to bring it into line with experi- 
ments, some being entirely empiric, others theoretical. Clausius, 
Sarrau, Wroblewski, Batteli, and others attacked the question 
empirically, and in the main preserved the co-volume (depending 
on the total volume of the molecules) unaltered while trying to 
modify the constant of molecular attraction. Their success 
depended entirely on the fact that, instead of limiting the 
number of constants to three, some of them have increased 
them to as many as ten. On the other hand, a series of very 
remarkable theoretical investigations has been made by van 
der Waals himself, by Kammerlingh Onnes, Korteweg, Jaeger, 
Boltzmann, Dieterici, and Rienganum, and others, all directed 
in the main towards an admitted variation in the value of the 
co-volume while preserving the molecular attraction constant. 
The theoretical reductions of Tait lead to the conclusion that a 
substance below its critical point ought to have two different 
equations of the van der Waals type, one referring to the 
liquid and the other to the gaseous phase. One important 
fact was soon elicited—namely, that the law of correspond- 
ence demanded only that the equation should contain 
not more than three constants for each body. The simplest 
extension is that made by Reinganum, in which he increased 
the pressure for a given mean: kinetic energy of the particles 
inversely in the ratio of the diminution of free volume, due to 
the molecules possessing linear extension. Berthelot has shown 
how a ‘‘reduced’’ isothermal may be got by taking two other 
prominent points as units of measurement instead of the critical 
coordinates. The most suggestive advance in the improve- 
ment of the van der Waals equation has been made by a lady, 
Mme. Christine Meyer. The idea at the base of this new 
development may be understood from the following general 
statement: van der Waals brings the van der Waals surfaces 
for all substances into coincidence at the point where volume, 
pressure and temperature are nothing, and then stretches or 
compresses all the surfaces parallel to the three axes of volume, 
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