A SWARM OF METEORITES, AND ON THEORIES OF COSMOGONY. 
29 
angle between the asymptotes is 1/e; and, if I-.? be the radius of either meteorite, 
the pericentral distance (when they graze) is s. Therefore, 
By the law of central orbits 
Therefore, 
1). 
2 
fjbin 
a. 
e 
jxm 
-f- 1. 
But, since ixMja, we have 
e 
+ 1. 
The unity on the right-hand side is negligible, and, since ISO/ire is the deflection in 
degrees, that deflection is 
180 ona 
27r/3- dfs 
degrees. 
Now, if 8 be the density of the body of a meteorite, m = and, therefore, this 
expression becomes 
Sa.^ 
/3- ^ M' 
Let us find what s must be if the deflection is 10“; we have 
We may, for a rough evaluation, take ^ as unity instead of \/6/5, and suppose a to 
be equal to the distance of Neptune from the Sun (viz., 4‘5 X 10^^ cm.), and, as a 
very high estimate of the value of 8, let us suppose the density of a meteorite is 10. 
Then, since the Sun, My =2X10®® grammes, and M is about a half of the Sun’s 
mass, we have 
_ r 2 X 10=^^ 
^ 3 X 4-0 X 10^^ X 10 
= (15 X 10^®)* = 4 X 10®. 
Hence, m = ^7r8s® = ^tt X lOX 64 X 10^ =3 X 10^® grammes, in round numbers. 
But the Earth’s mass is 6 X 10^'^ grammes, and therefore the meteorites are one- 
twentieth of the mass of the Earth. 
It follows, therefore, that, with such small masses as those with which the present 
theory deals, the deflection due to gravity is insensible, and we need only estimate 
actual impacts as encounters. 
Hence, the radius of the sphere of action of a meteorite is identical with the 
diameter of its body. 
