160-162] The Virial 145 



We suppose that the force between two molecules at distance r is an 

 attractive force < (r), a function of the distance r only. If the centres of 

 the molecules are at x, y, z, x', y', z' ', and if X, Y, Z, X', Y', Z' are the com- 

 ponents of the forces acting on them, then 



Zj. / \ " ~v j. / \ & 

 = r - % =<>r. 



The contribution to *2<xX made by the force between these two particles 



= xX + x'X' 



r 

 The contribution to S (xX + yY + zZ) is therefore 



-*> {(x - xj + (y- yj + (* - zj] = r<f> (r), 

 so that the part of the virial which arises from intermolecular forces, is 



where the summation extends over all pairs of molecules. 

 Equation (334) may now be replaced by 



iSwc 2 = fpft - 22r< (r) 

 so that the pressure is given by 



(r) ...................... (335). 



162. Clerk Maxwell* makes an important observation on the subject of 

 this equation. By obliterating one or other of the terms on the right-hand 

 side, we notice that a pressure may be produced either wholly by molecular 

 motion or wholly by intermolecular force. The latter is a hypothesis on 

 which attempts have been made to account for the pressure in a gas. If this 

 were the true account, then Boyle's Law that pl is constant could be 



satisfied only by making 2Sr< (r) constant, and therefore by taking <f> (r) = - . 



In other words, two molecules would have to repel one another with a force 

 proportional to the inverse distance. This is, however, an impossible law for 

 a gas. It would make the action of the distant parts of the mass prepon- 

 derate over that of the contiguous parts, and would not give a pressure 

 which, for a given volume and temperature, would be constant as we passed 

 from one vessel to another, or even from one part to another of the surface 

 of the same vessel. We therefore conclude that the pressure of a gas cannot 

 be explained by assuming repulsive forces between the molecules ; it must 

 arise, at any rate in part, from the motion of the molecules. 



* " The Dynamical Evidence of the Molecular Constitution of Bodies." Collected Works, 

 ii. p. 422. 



J. 10 



