A SWARM OF METEORITES, AND ON THEORIES OF COSMOGONT. 
47 
Now, 
fi”' dcp __ E 
Jo (1-^2 sin3 0)-5 “ 7/= ’ 
and in the present case ~ h''^ = -1. 
Hence. 
where E and E' qsq the complete elliptic integrals with modulus sin 45°. 
In Legendre’s Tables, we find 
£’= 1-350644, £’= 1-854075, and 2£’— 7^ = -847213. 
Then, 
The mean free path 
and thus 
T=? yfv/(2-E-r)= 1-91377. 
y TV 
L= UT= 1-9138 VT — 
1'9138 mip 
5-3318 ^3 
£ = 
1 mjp 
2-786 (29)- 
(51) 
If the spheres had all been of the same size, we should have had 
4- 
mip 
(29) V 2 
4-44 
( 29 )- • 
(52) 
Hence, finally from (49) to (52), if there be a number of spherical meteorites, of 
uniform density, of all sizes with radii grouped about a mean radius according to the 
law of error, and if S be the diameter of the meteorite of mean mass m, and p be the 
density of the distribution of meteorites in space, and \mV'^ their mean kinetic 
energy of agitation, then the mean free path £, mean free time T, and mean velocity 
U are given by 
L 
1 
2-786 
mjp 
5 ™/P 1 
-14 nearly. 
T = 
U = 
1 m/p 
3 «LP 1 
iir nearly. 
1-9138 V = 2V nearly. 
i 
(53) 
Also the mean free path is about i^-ths, and the mean free time about f of that 
which would have held if the meteorites had all been of the same size m and had had 
the same mean kinetic energy m 
* I owe tills to l\[r. FoESYTH, 
