34 On the Virial Equation. 



by an addition to the pressure of a quantity independent of 

 the temperature and inversely proportional to the square of 

 the volume/' 



By this he means one of two things, namely, (1) the re- 

 sultant force on a molecule is zero on average of time; or 

 (2) the resultant force is actually zero at every instant for a 

 sphere not at that instant undergoing collision. If he means 

 the first alternative, the resultant force must be zero on 

 average of lime if the motion be stationary. If, then, X, Y, Z 

 be the component forces on a molecule, X, Y, Z their values 

 on average of time, X = Y = Z = 0. But it does not follow 

 that X&'-f Yy~\-Zz = Q on average of time, that is that the 

 time average of the Yirial for molecules in the interior is 

 zero. 



In fact, as admitted in Lord Rayleigh's paper, it is not 

 true for the collision forces between elastic spheres. Neither 

 then can it be true if the molecules are centres of repulsive 

 force, becoming evanescent at distances very small compared 

 with molecular distances. There is in fact no proof that 

 Xx -\-Yy -\-7iz = () for molecules in the interior, and therefore 

 no proof that the whole effect "can be represented by an 

 addition to the pressure of a term independent of the tempe- 

 rature and proportional to -| /' 



If we take the second alternative, that at every instant the 

 resultant force is actually zero for every sphere not at that 

 instant undergoing collision, Lord Rayleigh must mean by 

 " symmetry/' that his spheres, although in motion relatively 

 to each other, are at every instant in some symmetrical ar- 

 rangement such, to take an example, as at the angles of cubes 

 or regular tetrahedrons. Is a motion possible in which this 

 shall be the case at every instant ? Without going so far as 

 to say that no such motion is possible, we may say, I think, 

 with confidence that it cannot be motion in accordance with 

 Maxwell's law. Lord Rayleigh's system, then, is not a rare 

 gas. Perhaps it may be a liquid, or a dense gas, to which 

 Maxwell's law is inapplicable. 



In order to form a theory of the motion of a system of 

 mutually acting molecules, to which we cannot apply the 

 ever recurring assumption of infinite rarity, we require to 

 know what part is to be played by the potential, % of the 

 intermolecular forces. In a statical system in stable equi- 

 librium % is minimum. What is the corresponding Liw for 

 stationary motion in a dynamical system ? I think Lord 

 Rayleigh is the man to answer that question, if he could be 

 induced to do so, 



