A SWARM OF METEORITES, AND ON THEORIES OF COSMOGONY. 
57 
The solution now becomes different according as M or /3 is tlie smaller. 
First, suppose M is the smaller. Then the limits of integration are ]\I and 0. 
If we put 
rr'‘ ( I 
\ 
-\\lx 
13/ 
«+1 -,i 
, n.n — 1 3 
nz-\- 2 ' 
so that the numerator and denominator of m are easily integrahle. 
If now we write 
Q=i 
M 
•M / 
(M — a;) ( 1 
0 \ 
-<?•)-I (2 3) ( 1 -Cl) 
+ “■ 3^ (1 — Q’’) + iV (1 — C*') 
= 2/3‘ 
7.1: u “ *? + sh “ 7^ + <):fi 
- !)• ch = 2/3”' 
Then, since yS = (1 — Q)IM, we have 
,,i _ _ 4 . ^ + f Qk — 2Q" + tV Q"-' 
If- + 
This expression has a high order of indeterminateness when ^ = 1, but I find that 
when Q is nearly equal to unity 
jvJ = 2[1 - T^o (1 - Q^)] iiearly.(65) 
Thus, the mean mass is -|-M where r — a, which we know to he correct. 
Secondly, suppose that yS is smaller than M. Then effecting the integrations in the 
same manner as before, we have 
(64) 
j (M — a;) ^ dx = 2yS 
M 
-1 - 
1 /2M 
— 3 
2.8 
(~ - 
MDCCCLXXXIX. — A. 
I 
