568 JAMES CLERK MAXWELL. 



and the product of pressure and volume remaining the same, 

 it follows that the virial must be unaffected by expansion. 

 But the virial must depend on the density if there be any 

 sensible forces between the molecules when at sensible dis- 

 tances, unless the force between two molecules varies in- 

 versely as the distance between them, a law which Newton 

 showed to be inadmissible in the case of molecular forces. 

 We must therefore conclude that the force between two mole- 

 cules is sensibly zero, unless the distance between them be 

 very small compared with the average distance between mole- 

 cules, and that the virial is therefore sensibly zero in a gas, so 

 that the energy and pressure of a gas depend on the motion 

 of the molecules and not on the forces between them. 



The experiments of Regnault indicated that in most 

 gases as the density increases the pressure falls below that 

 indicated by Boyle's law, which shows that when the 

 particles approach very near together the virial is positive, 

 or there is attraction between the molecules. When the 

 pressure is made still greater the gas reaches a condition in 

 which a small increase of density is accompanied by an 

 enormous increase of pressure, so that the virial is negative, 

 and the forces between the particles repulsive. This is the 

 case in the liquid s.tate. Maxwell infers that as the 

 particles of a gas approach each other the forces between 

 them become attractive, attain a maximum, then diminish, 

 and when they are within a certain distance become re- 

 pulsive, the repulsion increasing so rapidly " that no attain- 

 able force can reduce the distance of the particles to zero." 

 The same conclusion as far as the attraction between the 

 particles at small distances is concerned, was indicated by 

 the experiments which Joule conducted, in company with 

 Sir William Thomson, on the expansion of air into a vacuum, 

 when very careful measurements indicated that a slight 

 cooling effect took place. 



The greatest difficulty which the kinetic theory of gases 

 has to face is the observed relation between the specific 

 heats of gases at constant pressure and at constant volume. 

 Boltzmann showed that if each molecule possess n " degrees 



