A SWARM OF METEORITES, AND ON THEORIES OF COSMOGONY. 
17 
From these relations it is clear that 
^ = 2 /i - 2 log J , 
and 
Then, since /3" dyjdx = 1, when x = 1, and since dy — dy^ and dx = dx^ ajai, it 
follows that 
i ‘'I = ?. 
This relationship has been already used for determining 
It is obvious also that 
p dyjjdxj, when a\ = aja 
p^ dyydx^, when a;i = 1 
Therefore, 
tv 
Jr e^i 
p x^dyydx-^, wlieii x-^^ = aja 
If tVQ be the density when r = a, we have 
i ^ ic’‘. wpn r, =«,;a = _ 1. ^ ^ 
) x’j aypaXj dyydx^ 
If ^:)q be the pressure when r = a, we have 
19 4- 9 9 "^^0 
i^o = 3 ^^^0 = ^rriiay- . • 
If, therefore, we write P = ^irya^p^, 
p- sP ■ P - (rhjjd^,y *' “ ®1'“- 
(24) 
(25) 
(26) 
By (26) we ai-e able to find how the pressure on an envelope of given radius a 
varies with the variation of the temperature of a given*mass M of gas contained in it. 
By means of the formulee (23), (25), (26), we are now able to obtain from the original 
solution any number of other ones; for, after the changes have been effected in the 
notation, we may proceed to magnify or diminish all the various values of a until they 
are of one size, and we shall thus obtain the solution for a gas at any temperature 
whatever. 
I shall now proceed to give a table of results when the standard radius a, which 
may be conveniently called the boundary, is placed successively infinitely near the 
centre, where r = 0 X a^, at r =. T X a^, r = ‘2 X and so on. The first line of 
entries gives the various values of (computed from (23)), on which the elasticity 
of the gas depends; the second line gives wjp (computed from (25)), or the ratio of 
MDCCCLXXXTX.—A. D 
