338 DR. S. CHAPMAN ON THE LAW OF DISTRIBUTION OF MOLECULAR VELOCITIES, 
(251) Centres of force r~ n , 
M 
(1 + 0 
7 5m 
8A A,r(4-_^) 
n +3 
2te-l) 
f — f (i+0- 
In these formulae e a and e c denote the values of 2y r in the cases respectively when 
0 
the molecules are attracting spheres and centres of force, and S a and S c similarly denote 
S/3 r /2y r ; their values are given in Tables V. and VI., and in no case differ from 
unity by more than two per cent. 
The mode of variation of /x with the temperature affords a guide to the law of inter¬ 
action between the molecules of actual gases. By comparison with experimental 
determinations of /x at various temperatures it is thus found that of the above models 
the one which most closely represents the behaviour of actual molecules in this respect, 
at ordinary temperatures, is the second, i.e., a rigid elastic attracting sphere.* 
Comparison of the present formula for /x and S with those of my previous paper. 
§ 11 (E) The general formulae (237) and (248) for viscosity and thermal conductivity 
00 00 GO 
agree with those of my former paper,! except that the factors 2/3 r and 2 ^ r / 2 y r were 
0 0 0 
there omitted. This was in consequence of the assumption on which the analysis of 
that investigation was based, that F (U, V, W) is sufficiently represented by the 
terms of the first three degrees in U, V, W. We have seen in § 9 (C) that this is true 
for a gas composed of Maxwellian molecules, but not otherwise. It seems of interest 
to consider why the neglect of all the coefficients /3 r , y r after r — 0 led to results of 
such accuracy ; for the errors arising from the assumption are represented in the 
special cases (249)-(25l) of (237) and (248) by the factors 1'016, 1‘010, l + e a , l+<b, 
1 + e c , 1 + S c , so that the necessary corrections to my previous formulae do not exceed one 
or two per cent. Enskog, on the other hand, after deducing formulae similar to (237), 
(248), but without evaluating the coefficients /3 r , y r , made a first approximation by 
neglect of all these coefficients after r — 0, and arrived at the result f — 5 for rigid 
elastic spheres. J This was due to the fact that such a use of (237), (248), as they 
stand, involves not only the neglect of all the coefficients after r — 0 , but also requires an 
assumption as to the values of (3 0 , y 0 themselves, as, for instance, that they are approxi¬ 
mately the same as for Maxwellian molecules ; a comparison of (196) with Table IV. 
(p. 331) will show that this is far from being the case. 
It may readily be seen, however, that the method of my former paper required no 
* At very low temperatures, however, the n th power centre of force is the molecular model which gives 
by far the best representation of the relation between /x and T, in the case of helium; cf. Kamerlingh 
Onnes and Sophus Weber, ‘Comm. Phys. Lab. Leyden,’ 134b, p. 18, or Jeans’ ‘Dynamical Theory 
of Gases,’ 2nd ed., §§ 405, 407. 
f Chapman, ‘Phil. Trans.,’ A, vol. 211, p. 433, et seq. 
1 Enskog, ‘Phys. Zeit.,’ XII., p. 58, 1911. 
