OF THE GASEOUS AND LIQUID STATES. 411 



tions. (See a paper on "Reciprocal Figures, &c." Trans. R. S. Edin., Vol. xxvi. 

 p. 14. 1870.)* 



In gases the virial is very small compared with the kinetic energy. Hence, 

 if the kinetic energy is constant, the product of the pressure and the volume 

 remains constant. This is the case for a gas at constant temperature. Hence 

 we might be justified in conjecturing that the temperature of any one gas is 

 determined by the kinetic energy of unit of mass. 



The theory of the exchange of the energy of agitation from one body to 

 another is one of the most difficult parts of molecular science. If it were 

 fully understood, the physical theory of temperature would be perfect. At 

 present we know the conditions of thermal equilibrium only in the case of 

 gases in which encounters take place between only a pair of molecules at once. 

 In this case the condition of thermal equilibrium is that the mean kinetic 

 energy due to the agitation of the centre of mass of a molecule is the same, 

 whatever be the mass of the molecule, the mean velocity being consequently 

 less for the more massive molecules. 



With respect to substances of more complicated constitution, we know, as 

 yet, nothing of the physical condition on which their temperature depends, 

 though the researches of Boltzmann on this subject are likely to result in some 

 valuable discoveries. 



M. Van der Waals seems, therefore, to be somewhat too hasty in assuming 

 that the temperature of a substance is in every case measured by the energy 

 of agitation of its individual molecules, though this is undoubtedly the case 

 with substances in the gaseous state. 



Assuming, however, for the present that the temperature is measured by 

 the mean kinetic energy of a molecule, we obtain the means of determining the 

 virial by observing the deviation of the product of the pressure and volume 

 from the constant value given by Boyle's law. 



It appears by Dr Andrews' experiments that when the volume of carbonic 

 acid is diminished, the temperature remaining constant, the product of the 

 volume and pressure at first diminishes, the rate of diminution becoming more 

 and more rapid as the density increases. Now, the virial depends on the 

 number of pairs of molecules which are at a given instant acting on one 

 another, and this number in unit of volume is proportional to the square of 

 the density. Hence the part of the pressure depending on the virial increases 



* [Vol. n. p. 176.] 



522 



