A SWARM. OP METEORITES, AND ON THEORIES OP COSMOGONY. 
But now suppose that there are spheres of all possible sizes, and that in unit 
volume the number whose radius lies between s and 6’ + is 
4n 
Since the inteoTal of this from oo to 0 is n, it follows that n is the number of 
spheres of all sizes in unit volume. 
If p be the total mass in unit volume, or the density of distribution, 
^ X/'TT J 0 0-" 
4w r“ 
= —•17780-3 x ^ e-^dx 
\/Tr 
4% 
^77 
477 8a'3 
If m be the mean mass, m = pjn ; but 77^ = f77S?3; hence, 
3 4 . 
^0 _ - 
and 
+ LH = 
So 
3 4 
a/77 
o-\3^ /(r\3' 
If the A spheres of radii 5^ are those whose radii lie between 5^ and 5^ + ds^, and 
the B spheres of radii s.^ are those whose radii lie between % and 
A = 
B = 
Hence, the formula for collisions between the A’s and B’s is 
4?!/ 
V 77 
W/ 
1 (J 
in 
fsj 
ch 
\/77 
V 0-/ 
/ cr 
64%^ 
- +c 
2/ j 
or, if we write a? = .s^/cr, ?/ = s^/cr, it is 
64?7^ 
r(iiTV^)-a^(x + ijy(x‘+fy(xyye ^ r'clxdi/ 
. (48) 
* If the spPei’es are grouped about a mean mass, instead of about a mean radius, according' to a law of 
tbis kind, the subsequent integrals become very troublesome. Any law of the kind suffices for the 
discussion. If, bowever, I bad foreseen tbe investigation of § IG, I sbould not have taken tbis law of 
frequency. 
G 2 
