330 DR. S. CHAPMAN ON THE LAW OF DISTRIBUTION OF MOLECULAR VELOCITIES, 
By taking these determinants with one, two, three, and four columns we get 
successive approximations to V, V' (cf. § 8 (E)), and to the actual coefficients /3 and y, 
as follows :— 
Table II.—Rigid Elastic Spheres. 
v (U- 
V (c rs ). 
v q V (8 rs 5 rs ) 
V (8 r As) ' 
v.. v (<WW) 
/r v (8 rS c rs ) ' 
1st approximation 
2nd 
3rd ,, 
4 th „ 
1-000,00 
0-224,49 
0-019,13 
0-000,79 
1-000,00 
0-343,54 
0-062,15 
0-005,54 
1-000,000 
1-022,727 
1-024,818 
1-025,134 
1-000,000 
1-014,851 
1-015,879 
1-016,065 
The determinants V (8 rs b rs ), V (o rs c rs ) are obviously much more convergent in form 
than V (6 rs ), V (c rs ). Table II. shows that in each case these determinants converge 
rapidly to the value zero, but that the principal minors of the former determinants 
converge also to the same value in nearly constant ratios. These ratios, the 
successive approximations to which are given in the two last columns of Table II., 
are the quantities ~E/3 r and 2y r which we require ; they evidently converge rapidly, 
the successive differences being as follows :—- 
Table III. — Rigid Elastic Spheres. 
2ft. 
Differences. 
Sy r . 
Differences. 
1st approximation 
1-000,00 
2273 
1-000,00 
1485 
2nd 
1-022,73 
209 
1-014,85 
103 
3rd 
1-024,82 
31 
1-015,88 
29 
4th 
1 -025,13 
1-016,07 
We may therefore conclude that, within a small fraction per cent., 2/3 r and 2y r 
have the following values for rigid elastic spheres:— 
(225) 2ft = 1*026, 2y r = 1*016, 2ft/2y r = 1*010. 
0 0 0 0 
It should be noticed that even the second approximations to these quantities give 
results which are very nearly accurate, owing to the rapid diminution of the successive 
differences. 
