530 The Viscosity of Gases and Molecular Force. 



and 



l*=w(w'ir 9 /3)*(l + ?w/tl/2a)/i?)* ; 

 hence 



2N 

 3 B 



l-££,r(2«)» 



_/ mf(l/2a) \* Nmf b_ 



\ v* ) B 2 1-A/B' 



showing that for attracting molecules tie virial of the colli- 

 sional forces is (1 + mf(l /2a) /v**)* times its value when the 

 effect of molecular force on the number of collisions is neglected. 

 The form of the characteristic equation is soon obtained in 

 both cases, for the virial of the molecular attractions 

 | . \ SER^r reduces to the form 3a/2B or 3a/2v ; hence when 

 the effect of molecular force on collisions is neglected, 



_ ^mv* , ^ T mv 2 b „a 



^ 2 2 v — b z v 



v? + t?*r 3 V + t>-V w-a i 



y. (A) 



(p+^) Cv -^ )=RT; J 



this form depending on the fact that the coefficient of b/(v — b) 

 is unity. When the effect of molecular force on the number 

 of collisions is allowed for, the coefficient of b/{v—b) becomes 

 {l + w/(l/2a)/i?}* or (1 + C/T)*, and thus the characteristic 

 equation is 



^=Rt|i + (1 + C/T)^}-^. . . (B) 



Now of the two forms (A) and (B), it has been shown 

 (Phil. Mag., March 1893) that (A) represents fairly well the 

 facts of Amagatfs experiments down to the critical volume, so 

 that (B) cannot do so, seeing that it implies at low volumes 

 or high pressures a considerable variation of "dpfftT with T, 

 which does not occur at volumes above the critical. 



How are we to explain that the more accurate equation 

 represents the experimental facts worse than the less accurate ? 

 Simply in this way, that we have no right to expect to get 

 the virial of the collisional forces of actual molecules by treating 

 them as smooth spheres. There are certain properties of 



