326 DR. S. CHAPMAN ON THE LAW OF DISTRIBUTION OF MOLECULAR VELOCITIES, 
the n th power of the distance, the elements b rs and c rs , and the coefficients (3 r and y n 
are pure numbers, independent of the temperature (i.e., of h). 
Molecules which are Rigid Elastic Spheres which Exert Attractive Forces. 
§ 9 (E) Experiments on the phenomena of actual gases, as, for example, on the 
variation of viscosity with temperature, indicate that none of the molecular models 
so far discussed in this chapter gives a really adequate representation of these 
phenomena. The best of all the simple models which have been used in the kinetic 
theory seems to be that considered by van der Waals and Sutherland, viz., a 
rigid elastic sphere surrounded by a weak field of attractive force. This agrees with 
the known fact of slight cohesion in gases. The effect of this field of force on the velocity- 
distribution function, or on viscosity and thermal conductivity, may be referred 
mainly to the deflections of molecular paths for which it is responsible indirectly , 
through the collisions which it induces between molecules which would otherwise 
pass one another without mutual inter-action, rather than to its direct effect in the 
absence of collisions. The latter effect will be expressly neglected in our calculations, 
which will therefore be inapplicable to vapours in which the cohesion is large enough 
to render this neglect invalid. 
A detailed account of the dynamics of collisions in these circumstances is given in 
§ 15 of my former paper, from which the following results are quoted. If the potential 
of the force between two molecules in contact be denoted by \ -b 2 (reckoning this 
potential as zero when the separation is infinite), the condition that a collision may 
take place is 
(209) p <p o where p 0 = 2<r^l+ 
(since the relative velocity, in my former paper written V 0 , is here denoted by 2 C K ). 
The angle x corresponding to such a collision is given by 
(210) . sin ix=p/Po- 
The angle x corresponding to larger values of p, which do not correspond to actual 
collisions, is given by (181) if the molecular forces obey the n th power law, but rve 
will here make no assumption on this point, as the deflections produced by the inter- 
molecular forces alone will be rejected after equation (211). Consequently 
( 211 ) E k {ry) = 2 (4£ + 1 ) <x 2 (1 + b 2 fiC K 2 ) C K + 2 (4/c + 1 ) C K {l-P 2 * (cos x )} p dp 
Jpa 
= 4 (4&+ 1) o - 2 {2hm)- l ^y(l+2hmb 2 /4,y 2 )+f 2k ( y) 
by analogy with ( 202 ) and (183). The latter term f 2k (y) represents the negligible 
