A SWARM OF METEORITES, A^B ON THEORIES OF COSMOGONY. 
45 
The second of these two integrals cannot, I think, be evaluated algebraically, but 
its value is easily found by quadratures. I find, then, 
r(2 — (1 — z^ydz = 1- 
Jo 
2999 . 
The former of the two integrals may be evaluated as follows 
Let 
I = e~^ dx, 
J A 
then, 
^co p 
■ 0 Ji 
/•CO .1 
= 4 | J’ 
Jo Jo 
e J'" dx dy 
= f dzd<p 
Jo Jo 
'0 
= 2rj dtd<i> 
J 0 J 0 (1-2 sin- (/)) 
~ Jo U - isi 
= 7r*F(45°), 
siiH 0 )^ 
where F iq the complete elliptic integral with modulus sin 45'^ 
Hence, 
We thus have the frequency of collision given by 
■F^ • 1-2999 
V5 . 
8 
3 ". 2 " . F(29) 
mip 
Now, Legendre’s Tables give 
logjl’^ - 2681272 , 
with which value we easily find for T the mean free time, or IjT the frequency, 
i = 5 . 33,8 = nearly. 
mIp 
( 49 ) 
If l/Tg he the frequency of collision when the spheres are all of the same size and 
mass ? and m, and are agitated with mean square of velocity L", wm have, by the 
ordinary theory, 
l=4yf.riM= 4-0935 .(50) 
/q ^6 mip onip ' ' 
I owe tFis to Mr. Fobsyth, fmd the result verifies an evaluation by quadratures which I had made. 
