A SWARM OF METEORITES, AND ON THEORIES OF COSMOGONY. 
21 
Let 
and vve have 
a 
dj) 
IV dr 
_ _5 
3 3/x7If /x-^ . 1-1 
iTTfjLcr =-= —, since ivq = ^ p rigorously, 
M 
w, 
Vq^CI 
Hence, our equation is 
(29) 
It is obvious the f /3^ M dzjdx is the whole mass (expressed in terms of the mass of 
the isothermal sphere) enclosed inside of radius a/x. The differential equation to be 
satisfied is 
A 
6 
(30) 
We have seen in the last section that ^ = '39723, and, hence, |/3" = '99308. 
This equation is not so easy to solve as that in the last section, and I have not 
succeeded in finding the general law of the coefficients in an expansion. Nevertheless 
it is easy to find a series which will do all that is required. 
Let c be any value of x for which we know 2 and dzjdx, and let 
Assume 
^ = X — c. 
2 = 2o {1 + + ^ 2 ^^ + ^ 3 ^'^ + ...]. 
Then, if the suffix 0 indicates the value of a symbol when x 
have 
c and ^ = 0, we 
But 
2 
0> 
2^2^0‘ 
5/8- d ’ 
0 
