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NATURE 



\Oct 15, 1874 



theory of liquids. A dynamical theory of "perfect" 

 gases is already in existence ; that is to say, we can ex- 

 plain many of the physical properties of bodies when in 

 an extremely rarefied state by supposing their molecules 

 to be in rapid motion, and that they act on one another 

 only when they come very near one another. A molecule 

 of a gas, according to this theory, exists in two very 

 different states during alternate intervals of time. During 

 its encounter with another molecule, an intense force is 

 acting between the two molecules, and producing changes 

 in the motion of both. During the time of describing its 

 free path, the molecule is at such a distance from other 

 molecules that no sensible force acts between them, and 

 the centre of mass of the molecule is therefore moving 

 with constant velocity and in a straight line. 



If we define as a perfect gas a system of molecules so 

 sparsely scattered that the aggregate of the time which a 

 molecule spends in its encounters with other molecules 

 is exceedingly small compared with the aggregate of the 

 time which it spends in describing its free paths, it is not 

 difficult to work out the dynamical theory of such a 

 system. For in this case the vast majority of the mole- 

 cules at any given instant are describing their free paths, 

 and only a small fraction of them are in the act of en- 

 countering each other. We know that during an encounter 

 action and reaction are equal and opposite, and we as- 

 sume, with Clausius, that on an average of a large number 

 of encounters the proportion in which the kinetic energy 

 of a molecule is divided between motion of translation of 

 its centre of mass and motions of its parts relative to 

 this point approaches some definite value. This amount 

 of knowledge is by no means sufficient as a foundation 

 for a complete dynamical theory of what takes place 

 during each encounter, but it enables us to establish cer- 

 tain relations between the changes of velocity of two 

 molecules before and after their encounter. 



While a molecule is describing its free path, its centre 

 of mass is moving with constant velocity in a straight 

 line. The motions of parts of the molecule relative to the 

 centre of mass depend, when it is describing its free path, 

 only on the forces acting between these parts, and not on 

 the forces acting between them and other molecules which 

 come into play during an encounter. Hence the theory of 

 the motion of a system of molecules is very much simpli- 

 fied if we suppose the space within which the molecules 

 are free to move to be so large that the number of mole- 

 cules which at any instant are in the act of encountering 

 other molecules is exceedingly small compared with the 

 number of molecules which are describing their free paths. 

 The dynamical theory of such a system is in complete 

 agreement with the observed properties of gases when in 

 an extremely rare condition. 



But if the space occupied by a given quantity of gas is 

 diminished more and more, the lengths of the free paths 

 of its molecules will also be diminished, and the number 

 of molecules which arc in the act of encounter will bear a 

 larger proportion to the number of those which are 

 describing free paths, till at length the properties of the 

 substance will be determined far more by the nature of the 

 mutual action between the encountering molecules than 

 by the nature of the motion of a molecule when describing 

 its free path. And we actually find that the properties 

 of the substance become very different after it has reached 



a certain degree of condensation. In the rarefied state 

 its properties may be defined with considerable accuracy 

 in terms of the laws of Boyle, Charles, Gay-Lussac, 

 Dulong and Petit, &c., commonly called the "gaseous 

 laws." In the condensed state the properties of the sub- 

 stance are entirely different, and no mode of stating these 

 properties has yet been discovered having a simplicity 

 and a generality at all approaching to that of the " gaseous 

 laws." According to the dynamical theory this is to be 

 expected, because in the condensed state the properties of 

 the substance depend on the mutual action of molecules 

 when engaged in close encounter, and this is determined 

 by the particular constitution of the encountering mole- 

 cules. We cannot therefore extend the dynamical theory 

 from the rarer to the denser state of substances without at 

 the same time obtaining some definite conception of the 

 nature of the action between molecules when they are so 

 closely packed that each molecule is at every instant so 

 near to several others that forces of great intensity are 

 acting between them. 



The experimental data for the study of the mutual 

 action of molecules are principally of two kinds. In the first 

 place we have the experiments of Regnault and others on 

 the relation between the density, temperature, and pressure 

 of various gases. The field of research has been recently 

 greatly enlarged by Dr. Andrews in his exploration of the 

 properties of carbonic acid at very high pressures. Ex- 

 periments of this kind, combined with experiments on 

 specific heat, on the latent heat of expansion, or on the 

 thermometric effect on gases passing through porous 

 plugs, furnish us with the complete theory of the sub- 

 stance, so far as pure thermodynamics can carry us. 



For thefuither study of molecular action we require expe- 

 riments on the rate of diffusion. There are three kinds of 

 diffusion — that of matter, that of visible motion, and that of 

 heat. The inter-diffusion of gases of different kinds, and 

 the viscosity and thermal conductivity of a gaseous 

 medium, pure or mixed, enable us to estimate the amount 

 of deviation which each molecule experiences on account 

 of its encounter with other molecules. 



M. Van der Waals, in entering on this very difficult 

 inquiry, has shown his appreciation of its importance in 

 the present state of science ; many of his inves igations 

 are conducted in an extremely original and clear manner ; 

 and he is continually throwing out new and suggestive 

 ideas ; so that there can be no doubt that his name will 

 soon be among the foremost in molecular science. 



He does not, however, seem to be equally familiar, as 

 yet, with all parts of the subject, so that in some places, 

 where he has borrowed results from Clausius and others, 

 he has applied them in a manner which appears to me 

 erroneous. 



He begins with the very remarkable theorem of 

 Clausius, that in stationary motion the mean kinetic 

 energy of the system is equal to the mean virial. As in 

 this country the importance of this theorem seems hardly 

 to be appreciated, it may be as well to explain it a little 

 more fully. 



When the motion of a material system is such that the 

 sum of the moments of inertia of the sjstem about three 

 axes at right angles to each other through its centre of 

 mass does not vary by more than small quantities from a 

 constant value, the system is said to be in a state of sta- 



