302 DR. S. CHAPMAN ON THE LAW OF DISTRIBUTION OF MOLECULAR VELOCITIES, 
being excluded.* The corresponding portions of Ii (xi 2 ) will be denoted by I (r x Si, X 12 ) 
and I (r 2 s l5 X 12 ) respectively. Then 
(81) I (riS h X 12 ) = 
( 2hfi 1 m 0 ) r+s+1 U\C / i 2s UiCi 2r de d cos 6 0 d cos 0 R d<f> 0 d<p R , 
(82) I (r 2 .s u xi 2 ) = II (2 hm 0 ) 
Yr + s+1 
Mi S+ W + ' U / iC'i 2s U 2 C 2 2 ’' de d cos 6 0 d cos d R dfc d<f> R , 
(83) b 12 (nsi) = (miM 2 ) v ’(—— 
- A ?? 1 q (Cn“ + C R 2 ) 
(I (n«i, xia)-I (ns l5 0)} C 0 2 C R 3 _p dp dC 0 dC R , 
(84) &i2 (r^j) = — Vl v 2 (miM 2 ) ’ /2 (~ 
-WC 0 2 +C r 2 ) 
{I (>Vh, 
X 12 ) I (?Vh, 
0)} C 0 2 C R 3 _p dp c£C 0 dC R . 
The similar quantities relating to will be denoted by c 12 (r^), c 12 (r 2 s 2 ) and 
J i r i s i> X 12 )? J ( r 2 5 D X 12 ) respectively, so that 
(85) J (mjSi, X 12 ) 
1(2/W^) r+S+2 
U^CV 5 (oily —C/) C 1 2r cZe c7 cos d cos 0 R d(p 0 d<j> R , 
(86) J (r 2 s 1} X 12 ) 
0 / +s+2 Ml s+1 M2 r+, U / 1 2 C , i 2s (3U 2 2 -C 2 2 ) C 2 2r ded cos 6 0 d cos 0 R d<p o d<p 
R) 
(87) ^(r^) — — !'i^ 2 (miM 2 ) 1/2 l j 
\7r/ 
HIg-ta.iwv){j(,. S]i Xl 3 )_j( rAj 0)} (tfCVjp dpdC„dC B , 
(88) c 12 (r 2 s 1 ) = "'^j 
\ 7T / 
III e -^ (W+0 ,, { J ( rA , Xi2 ) _ j ( rAi 0)} C/C e 3 r dC 0 <2C B . 
* We have here included a, factor (2Am) 1 /* which does not occur in F; this will be allowed for 
subsequently. 
