A SWARM OF METEORITES, AND ON THEORIES OF COSMOGONY. 
5 
into kinetic energy. When the condensation of a swarm is just beginning, the mass of 
the aggregation towards which the meteorites fall is small; and, thus, the new bodies 
arrive at the aggregation with small velocity. Hence, initially, the kinetic energy is 
small, and the volume of the sphere within wdiich hydrostatic ideas are (if anywhere) 
applicable is also small. 
As more and more meteorites fall in that volume is enlarged, and the velocity with 
which they reach the aggregation is increased. Finally, the supply of meteorites in 
that part of space begins'to fail, and the imperfect elasticity of the colliding bodies 
brings about a gradual contraction of the swarm. 
I do not now attempt to trace the whole history of a swarm, but the object of the 
paper is to examine its mechanical condition at an epoch when the supply of meteorites 
from outside has stopped, and when the velocities of agitation and distribution of 
meteorites in space have arranged themselves into a sub-permanent condition, only 
affected by secular changes. This examination will enable us to understand, at least 
roughly, the secular change in the velocity and in the distribution of the meteorites 
as the swarm contracts, and will throw light on other questions. 
§ 3. Formulce for Mean Square of Velocity, Mean Free Path, and Interval between 
Collisions. 
We have to investigate whether, when the solar system consisted of a swarm of 
meteorites, the velocities and encounters could have been such that the mechanics of 
the system can be treated as subject to the laws of hydrodynamics. The formulse 
which form the basis of this discussion will now be considered. 
For the sake of simplicity, the meteorites will, in the first instance, be treated as 
spheres of uniform size. 
The sum of the masses of the meteorites is equal to that of the Sun, for the planets 
only contribute a negligible mass. If M^ be the Sun’s mass, and m that of a meteorite, 
their number is MJm. 
If, at each encounter between two meteorites, there were no loss of energy, the sum 
of the kinetic energies of all the meteorites would be equal to the potential energy 
lost in the concentration of the swarm from a condition of infinite dispersion, until it 
possessed its actual arrangement. In such a computation the rotational energy of the 
system is negligible. 
Suppose the Sun’s mass to be concentrated from infinite dispersion until it is 
arranged in the form of a homogeneous sphere of radius a and density p. Then let 
the sphere be cut up into as many equal spaces as there are meteorites, and let the 
matter in each space be concentrated into a meteorite. When the number of 
meteorites is large, the poteiitial energy lost in the first process is very great compared 
with that lost in the subsequent partial condensation into meteorites."^ Thus, the 
energy lost in the ])artial condensation is negligible. 
* It depends, in fact, on the square of the ratio of the diameter ‘2a to the linear dimcrsion of one of 
the equal spaces. 
