A SWARM OF METEORITES, ARD ON THEORIES OP COSMOGONY. 
03 
In § 9 two criteria, suggested by this line of thought, are found. They measure, 
roughly speaking, the degree of curvature of the average path pursued by a meteorite 
between two collisions. These two criteria, denoted DjL and AjC, will afford a 
measure of the applicability of hydrodynamics in the sense above indicated. 
After these preliminary investigations, we have to consider what kind of meeting 
of two meteorites will amount to an “ encounter ” within the meaning of the kinetic 
theory. Is it possible, in fact, that two meteorites can considerably bend their paths 
under the influence of gravitation when they pass near one another ? This question 
is answered in § 8, where a formula is found for the deflection of the path of each of a 
pair of meteorites, when, moving with their mean relative velocity, they graze past 
one another without striking. It appears from the formuia that, unless tliey have the 
dimensions of small planets, the mutual gravitational influence is practically insensible. 
Hence, notlnng short of absolute impact is to be considered an encounter in the 
kinetic theory ; and what is called the radius of “ the sphere of action ” is simply the 
distance between the centres of a pair when they graze, and is, therefore, the sum of 
their radii, or, if of uniform size, the diameter of one of them. 
The next point to consider is the mass and size which must be attributed to the 
meteorites. 
The few samples which have been found on the earth prove that no great error can 
be committed if the average density of a meteoilte be taken as a little less than that 
of iron, and I accordingly suppose their density to be six times that of water. 
Undoubtedly, in a swarm of meteorites all sizes exist (a supposition considered 
hereafter); for, even if originally of one uniform size, they would, by subsequent 
fracture, be rendered diverse. But in the first consideration of the problem they have 
been treated as of uniform size, and, as actual average sizes are nearly unknown, 
results are given in the numerical table for meteorites w^eighing 3|- grammes. By 
merely shifting the decimal point one, two, or three places to the right the results 
become applicable to meteorites weighing 3|- kilogrammes, 3g- tonnes, 3125 tonnes, 
and so on. 
It is knowm thcit meteorites are actually of irregular shapes, but certainly no 
material error can be incurred when we treat them as being spheres. 
The object of all these investigations is to apply the forraulse to a concrete example. 
The mass of the system is therefore taken as equal to that of the Sun, and the limit 
of the swarm at any arbitrary distance from the present Sun’s centre. The theory is, 
of course, most severely tested the wider the dispei’sion of the swarm; and, accordingly, 
in the numerical example the outside limit of the Solar swarm is taken at 44^ times 
the Earth’s distance from the Sun, or further beyond the planet Neptune than Saturn 
is from the Sun. This assumption makes the limit of the isothermal sphere at 
distance 16, about half way between Saturn and Uranus. 
The results, applicable to meteorites of 3^ grammes, are exhibited in Table IV., § 10. 
The velocity of mean square in the isothermal sphere is U(0/5) of the linear velocity 
