Pressure of Gaseous Vibrations. 373 



rarefaction as potential. It was, however, on the lines of the 

 kinetic theory that I first applied the virial theorem to the 

 question of the pressure of vibrations. In the form of this 

 theory which regards the collisions of molecules as instan- 

 taneous, there is practically no potential, but only kinetic, 

 energy. And if the gas be monatomic, the whole of this 

 energy is translational. If V be the resultant velocity of the 

 molecule whose mass is m. the virial equation gives 



} i?1 ir=iSmV 2 (37), 



p 1 denoting, as before, the pressure upon the walls, assumed to 

 be the same over the whole area. If necessary, p x and %mY 2 

 are to be averaged with respect to time. 



It is usually to a gas in equilibrium that (37) is applied, 

 but this restriction is not necessary. Whether there be 

 vibrations or not, p x is equal to § of the volume-density of 

 the whole energy of the molecules. Consider a given chamber 

 whose walls are perfectly reflecting, and let it be occupied 

 by a gas in equilibrium. The pressure is given by (37). 

 Suppose now that additional energy (which can only be 

 kinetic) is communicated. We learn from (37) that the 

 additional pressure is measured by § of the volume-density of 

 the additional energy, whether this additional energy be 

 in the form of heat, equally or unequally distributed, or 

 whether it take the form of mechanical vibrations, i. e. of 

 coordinated velocities and density differences. Under the 

 influence of heat-conduction and viscosity the mechanical 

 vibrations gradually die down, but the pressure undergoes 

 no chano-e. 



o 



The above is the case of the adiabatic law with 7 = If 

 already considered in (35), and a comparison of the two 

 methods of treatment, in one of which potential energy plays 

 a large part, while in the other all the energy is regarded as 

 kinetic, suggests interesting reflexions as to what is really 

 involved in the distinction of the tw^o kinds of energy. 



If we abandon the restriction to monatomic molecules, the 

 question naturally becomes more complicated. We have 

 first to consider in what form the virial equation should be 

 stated. In the case of a diatomic molecule we have, in the 

 first instance, not only the kinetic energy of the molecule as 

 a whole, but also the kinetic eaergy of rotation, and in 

 addition the internal virial of the force by which the union 

 of the two atoms is maintained. It is easy to see, however, 

 that the two latter terms balance one another, so that we are 

 left with the kinetic energy of the molecule as a whole. For 



