Pressure of Gaseous Vibrations. 371 



In all that precedes, the motion of the gas has been in one 

 dimension, and even when we supposed the gas to be confined 

 in a cylinder, we were able to avoid the consideration of 

 lateral pressures upon the walls of the cylinder by applying 

 the virial equation in its one-dimensional form. We now 

 pass on to the case of three dimensions, and the first question 

 which arises is as to the value of the virial. In place of (27) 

 we have now 



itmU^-iKXx-t-Yy + Zz) . . . (30), 



U being the resultant velocity, Y, Z impressed forces 

 parallel to the axes of y and z. Let us first apply this to a 

 gas at rest under pressure p . The total virial, represented 

 by the right-hand member of (30), is now zero ; that is, the 

 internal and external virial balance one another. As is well 

 known and as we may verify at once by considering the case 

 of a rectangular chamber, the external virial is §p i', v denoting 

 the volume of gas. The internal virial is accordingly — §po v j 

 and from this we may infer that whether the pressure be 

 uniform or not, the internal virial is expressed by 



—%\\\pdxdydz, (31). 



The difference between the internal virial of the gas in 

 motion and in equilibrium is 



-^(p-p )d.vdych. . , . (31*). 



According to the law of Boyle, (31*) must vanish, since the 

 mean density of the whole mass cannot be altered. The 

 internal virial is therefore the same whether the gas be at 

 rest or in motion. 



A question arises here as to whether a particular law of 

 pressure may not be fundamentally inconsistent with the 

 statical Boscovitchian theory of the constitution of a gas upon 

 which the application of the virial theorem is based. If, 

 indeed, we assume Boyle's law in its integrity, the incon- 

 sistency does exist. For Maxwell has shown (Scientific 

 Papers, vol. ii. p. 122) that on a statical theory Boyle's 

 law involves between the molecules of a gas a repulsion 

 inversely as the distance. This makes the internal virial for 

 any pair of molecules independent of their mutual distance, 

 and thus the virial for the whole mass independent of the 

 distribution of the parts. But such an explanation of Boyle's 

 law violates the principle upon which (31) was deduced, 

 making the pressure dependent upon the total quantity of 

 the mass and not merely upon the local density ; from which 



