Gases and the Equation of I '/rial. 501 



seem that F must then become an even function of //, so that 

 in (23) B=0. 



As stated, the above argument is probably not quite 

 legitimate, inasmuch as according to (19) a reversal of y! 

 would imply a reversal of the collisional forces as well as of 

 those which operate at greater distances. The introduction 

 of the two sorts ot^ particles is not supposed to alter the 

 repulsive forces called into play during actual collision. I 

 believe, however, that the instantaneous collisional forces may 

 be omitted from (19). The effect of the collisions may be 

 defined without reference to any datum having dimensions 

 other than a, representing the radius of a sphere. The 

 collisions being thus, as it were, already provided for, the 

 argument remains that the virial must be a definite function 

 of X. m. V, fi'. a, v. of which X need not be regarded, the force 

 (outside actual collision) being given by (19). Equation (21) 

 then follows as before with its approximate form (23). If 

 we now suppose that the particles are repellent as much as 

 attractive, (19) may be written 



<k» = ±a»'/W«); ..... (25) 



and. since odd powers of fi' are now excluded, 13 = in (23), 



A\ e have thus discovered a possible theoretical foundation 

 for the empirical conclusion that T should be introduced into 

 the denominator of the cohesional virial, and it would seem 

 to follow conversely that, if the empirical conclusion is 

 correct, the forces must be intrinsically as much repellent as 

 attractive. This argument may be regarded as a strong 

 confirmation of Sutherland's idea, though a question remains 

 as to how the attraction asserts its superiority over repulsion. 



In the above argument the particles are regarded as simple 

 centres of force, half of them being " positive y ' and half 

 " negative/' The advantage is that the form may still be 

 treated as spherical, so that the collisions may be assimilated 

 to those of '"elastic spheres." But a polar constitution, such 

 that the positive and negative elements are combined in 

 every particle, i- certainly more probable. This will intro- 

 duce, as another linear datum, the distance between the poles, 

 and the collisions will admit of greater variety. Moreover, 

 there i- now kinetic energy of rotation as well as of trans- 

 1 ition. However, since the kinetic energies are proportional, 

 the argument remains unaffected, SO far as it relates to the 

 dependence of the virial of a given gas upon volume and 

 temperature, and the- Rankine-Clausius form (24) with B=0 

 <till obtains. 



