THEORY OF VISCOSITY AND THERMAL CONDUCTION, IN A MONATOMIC GAS. 331 
While we may thus obtain a close approximation to the values of the series 2/3 r 
and 2y r with little difficulty, the approximations to the values of the individual 
coefficients /3 and y converge by no means quickly, as the following table 
shows :— 
Table IV .—Rigid Elastic Spheres. 
1st approximation. 
2nd approximation. 
3rd approximation. 
4th approximation. 
ho 
1-000,0 
1-340,9 
1-520,2 
1-623,0 
hi 
— 
- 0-318,2 
-0-652,1 
-0-943,2 
hi 
— 
0-156,7 
0-432,8 
hi 
— 
— 
-0-087,5 
yo 
1-000,0 
1-222,8 
1-309,4 
1-366,3 
7i 
— 
- 0-207,9 
-0-368,8 
-0-526,3 
y 2 
— 
— 
0-075,4 
0-221,8 
73 
“ 
— 
-0-045,7 
Evidently the ft s and y’s alternate in sign, and successive terms do not seem to 
diminish quickly, at any rate near the beginning. To obtain an accurate estimate 
of the real values of these coefficients it is clearly necessary to carry the approxi¬ 
mation much further than we have done, but for our purpose this is not required. 
Molecules which are Point Centres of Force varying as r n . 
§ 10 (B) The next simplest case, analytically, to that which has just been discussed 
is the case of molecules which are point centres of force varying inversely as the 
n th power of the distance. By comparison of (186) and (205), in conjunction with 
the general expressions for b rs and c rs , it is easy to see that the difference between 
the values of b rs or c rs in the two cases consists of a power series in —-—, the constant 
n— 1 
term of which is zero, while the term of highest order is (n— l) -(r+s) . Numerically 
the difference is small, as may easily be verified in any particular case ; it appears 
to be of constant sign, b rs and c rs being greatest for molecules which are rigid elastic 
spheres. The behaviour of the determinants V (b rs ), V (c„) or V ( S rs b rs ), V (§ rs c rs ) is 
similar in the two cases, the convergence being slightly the more rapid in the present 
instance. Since for rigid elastic spheres the second approximation to 2/3 r and 2y r 
proved so satisfactory, we shall be content with a second approximation only, for 
molecules which are point centres of force; this very materially lightens the labour 
