332 DR. S. CHAPMAN ON THE LAW OF DISTRIBUTION OF MOLECULAR VELOCITIES, 
of numerical calculation. The following are the expressions found for the deter¬ 
minants V (S rs b rs ), V (S rs c rs ) as far as regards the first, four elements :— 
(226) V(J„6 r .) = 
fj__7_l 
114 2 (n—l)\ 
2(n-l) 
f 45_ 4 4 1 
1196 49(n-l) + 49(n-l) 2 J 
^ (< 1,0 = 
1 
f 1 7 ) 
1 14 2(n-l)J 
f 1 7 \ 
114 2 (n— l)j 
(205 4 4 1 
1588 49 ( 71 — 1 ) + 49(n-l) 2 J 
When n is made infinite these become identical with (221), (222); it is interesting 
to notice that the additional terms are the same in the two determinants, though 
whether this is true for other values of r and s is not clear. 
The first approximations to 2/3,., 2 y r are, of course, unity ; the second are found 
to be approximately as follows :—- 
(227) 
16 n —2 
45 45 (n— 1 ) 2 
44 2 1 
11 n-l 
1 48 n — 2 
~ 205 205 (n-l) 2 
= 202 " 
101 n-l 
From §9 (C), (196), we know that when n = 5 the values of 2/3 r and 2y r are 
0 0 
unity, and this is also true of any approximation to their values made in the present 
manner. From § 10 (A), however, we know that for n — co the second approxi¬ 
mations are slightly too small, by 0‘003 and O'OOl very nearly. In the following 
table, therefore, which gives the approximate values of 2and 2y r for various 
values of n lying between 5 and oo, the results obtained from (227) have been 
increased by O'OOl, 0'002, or 0'003, as seemed most appropriate in each case. 
Table Y. — Molecules which are Point Centres of Force varying as r n . 
Maxwell’s 
case, 
n = 5. 
n = 9. 
n = 15. 
n = 25. 
n = co, 
rigid elastic 
spheres. 
O M 8 
A 1 
1 
1-007 
1-013 
1-018 
1-026 
CO 
r 
0 
1 
1-004 
1-007 
1-011 
1-016 
CO CO 
S c = 2/3,./2 7 , 
0 0 
1 
1-003 
1-006 
1-007 
1-010 
