A SWARM OR METEORITES, AND ON THEORIES OF COSMOGONY. 
07 
in § 15, and their various values are illustrated in fig. 1. The horizontal scale in that 
figure gives the ratio of the radius of each size to the radius of the meteorite of mean 
mass. The vertical scales are the ratio of the mean free path of any size to that of 
all sizes together, and the ratio of the mean frequency for any size to that of all sizes 
together. The figure shows that collisions become infinitely frequent for the infinitely 
small ones, because of their infinite velocity; and again infinitely frequent for the 
infinitely large ones, because of their infinite size. There is a minimum frequency of 
collision for a certain size, a little less in radius than the mean, and considerably less 
in mass than the mean mass. 
For infinitely small meteorites, the mean free path reaches a finite limit, equal to 
about four times the grand mean free path; but this could not be shown in the figure 
without a considerable extension of it upwards. For infinitely large ones,-the mean 
free path becomes infinitely short. It must be borne in mind that there are infinitely 
few of the infinitely large and small meteorites. 
Variety of size does not, then, so far, materially affect the results. 
But a difference arises when we come to consider the different parts of the swarm. 
The larger meteorites, moving with smaller velocities, form a quasi-gas of less elasticity 
than do the smaller ones. Hence, the larger meteorites are more condensed towards 
the centre than are the smaller ones, or the large ones have a tendency to sink down, 
whilst the small ones have a tendency to rise. Accordingly, the various kinds are to 
some extent sorted according to size. 
In § 16, an investigation is made of the mean mass of the meteorites at various 
distances from the centre, both inside and outside of the isothermal sphere, and fig. 2 
is drawn to illustrate the law of diminution of mean mass. 
It is also clear that the loss of the system through evaporation must fall more 
heavily on the small meteorites than on the large ones. 
After the foregoing summary, it will be well to briefly recapitulate the principal 
conclusions which seem to be legitimately deducible from the whole investigation; 
and, in this recapitulation, qualifications must necessarily be omitted, or stated with 
great brevity. 
When two meteorites are in collision, they are virtually highly elastic, although 
ordinary elasticity must be nearly inoperative. 
A swarm of meteorites is analogous with a gas, and the laws governing gases may 
be applied to the discussion of its mechanical properties. This is true of the swarm 
from which the Solar system was formed, when it extended beyond the orbit of the 
planet Neptune. 
When the swarm was very widely dispersed, the arrangement of density and of 
velocity of agitation of the meteorites was that of an isothermal-adiabatic sphere. 
Later in its history, when the swarm had contracted, it was probably throughout in 
convective equilibrium. 
The actual mean velocity of the meteorites is determinable in a swarm of given 
mass, when expanded to a given extent. 
K 2 
