374 Momentum and Pressure of Gaseous Vibrations. 



general purposes a theorem is required of which I have not 

 met a complete statement. For any part of a wider system 

 for which we wish to form the virial equation, we may omit 

 the kinetic energy of the motion relative to the centre of 

 gravity of the part, if at the same time we omit the virial 

 of the internal forces operative in this part and treat the 

 forces acting from outside upon the part, whether from the 

 remainder of the system or wholly from outside, as acting at 

 the centre of gravity of the part. In applying (37) to a gas 

 regarded as composed of molecules, we are therefore to 

 include on the right only the kinetic energy of translation of 

 the molecules. If a gas originally at rest be set into vibration, 

 we have 



^(p 1 —p Q )v = additional energy of translation . (38). 



The pressure p>\ does not now, as in the case of monatomic 

 gases, remain constant. Under the influence of viscosity and 

 heat-conduction, part of the energy at first translational 

 becomes converted into other forms. 



A complete discussion here would carry us into the inner 

 shrine of the kinetic theory. We will only pursue the subject 

 so far as to consider briefly the case of rigid molecules for 

 which the energy is still entirely kinetic — partly that of the 

 translatory motion of the molecules as wholes and partly 

 rotatory. Of the additional energy E representing the 

 vibrations, half may be regarded as wholly translational. Of 

 the other half, the fraction which is translational is 3/m, where 

 m is the whole number of modes. The translational part of 

 E is therefore iE(l + 3/m) ; so that 



fo-jPo)«=Eg + i) .... (39) 



If m = 3, as for monatomic molecules, we recover the 

 former result ; otherwise p L — p is less. In terms of y we 



have 7 = l + 2/m (40), 



and accordingly 



(B-Po>=E(J-^). . . . (41), 



in agreement with (34) where what was there called the 

 total energy is now regarded as the additional energy of 

 vibration. In the case of a diatomic gas, m = 5, 7= If. 



Terling Place, Witham, 

 July 26. 



