328 DR. S. CHAPMAN ON THE LAW OF DISTRIBUTION OF MOLECULAR VELOCITIES, 
It is useful also to recall that If ( r , s) — B* ( s , r), and that B* (r, s) — 0 if 
r < k or s < k. 
By using these formulae in connection with (143), (144), (147) and (204)—(208) the 
elements b rs , c rs , have been calculated,* as above mentioned, and are given in the 
following expressions :— 
(217) 
m,) = 
1 
15 
41 
741 
2.7 
cy2 cp 
2 3 7.11 
15 
269 
5993 
7571 
2.7 
2 2 7 2 
2 3 3 2 7 2 
2 4 3.7.11 
41 
5993 
152537 
1517873 
2 2 3 2 
2 3 3 2 7 2 
2 4 3 4 7 2 
2 5 3 3 7 2 11 
741 
7571 
1517873 
50375871 
2 3 7.11 
2 4 3.7.11 
2 5 3 3 7 2 11 
2 h 3 3 7 2 1 l 2 
(218) 
v (e„) = 
1 
15 
41 
741 
2.7 
2 2 3 2 
2 3 7.11 
15 
877 
6893 
3889 
2.7 
2 2 3.7 2 
233272 
2 4 3 2 11 
41 
6893 
193329 
6202777-f- 
2 2 3 2 
2 3 3 2 7 2 
343472 
2 5 3 4 7 2 11 ‘ ' 
741 
3889 
6202777-f- 
225937695 
2 3 7.11 
2 4 3 2 11 
2 5 3 4 7 2 11 
2-3 4 7 2 ll 2 
or, writing 
out the elements in decimals to six places, 
(219) 
V (&„) = 
1 - 000,000 
1-071,429 
1 *138,889 
1-202,922 . . 
1-071,429 
1-372,449 
1-698,696 
2-048,431 . . 
1-138,889 
1-698,696 
2-402,006 
3-259,364 . . 
1-202,922 
2-048,431 
3-259,364 
4-916,968 . . 
( 220 ) 
V (c„) = 
rooo,ooo 
1-071,429 
1 '138,889 
1-202,922 . . 
1-071,429 
1-491,497 
1-953,798 
2M55,177 . . 
1 "138,889 
1-953,798 
3-044,359 
4M39,790 . . 
1-202,922 
2-455,177 
4-439,790 
7-350,929 . . 
* A considerable part of the computations of § 10 (A) have been made by Mr. J. Marshall, Scholar 
of Trinity College, Cambridge, who has thus been of much assistance in bringing the results into a 
useful form. 
