A SWARM OF METEORITES, AND ON THEORIES OF COSMOGONY. 
31 
describinof a circular orbit about the centre of the swarm, D is the deflection from 
the straight path in the mean interval between two collisions. Then the criterion is 
that the deflection shall be small compared with the mean free path. 
We may consider the criterion from again another point of view, and state that 
the arc of circular orbit described in the mean interval shall be a small fraction of 
the whole circumference. 
The linear velocity v in the circular orbit is given by 
V 
2 
a 
Tn!_. I . 
G 
And the mean interval T ~ Ll\y S/Stt]. Hence, if A be the arc described with 
velocity v in time T, 
8^3 
I? n , . Stt 
• - nearly, since —, 
v'/ry- Gx, 8/3" 
•988. 
But the whole arc of circumference C is ^TTajx. 
Therefore, 
A Z 1 [_glG']i 
C 2a IT v/Vq 
_ / m J 1 [glG]ix^ 1 _ I m „ 
2a M A [tt [r/rj [w/ip] J 2a M s~ 
(38) 
The factor F.^ has been tabulated above, in Table III. 
§ 10. On the Densittj of Meteorites and Numerical Ai)'plication, 
It is necessary to make assumptions both as to the mass and the density of the 
meteorites. We have a right to assume, I think, that the density 8 is a little less 
than that of iron, say about 6, and we may put f ttS equal to 25, Then we have 
m = and — = \-s. 
There is but little information about the average size of meteorites ; but, if we retain 
the symbol s, it will be easy, by merely shifting the decimal point in the final results, 
to obtain results for all sizes. Thus, if s = 1 cm., m = 3;g- grammes ; if 5 = 10 cm., 
m = 3^ kilogrammes; if s = 100 cm., m = 3^ tonnes, and if = 1000 cm., 
m = 3125 tonnes. I shall, therefore, keep s in the analytical formulse, and put it 
equal to unity in the numerical results. 
In the first place, making no assumptions as to the density or masses of the 
meteorites, we have 
= 2-1767 X M, i/3" = -39723. 
