a Spherical Gaseous Nebula. G99 
Eliminating p from (18) by (19), we find 
-1|>-1= — (21) 
Ctrl 1 dr] a* ^' 
where 
§ 24. By putting 
•■=; (23), 
we reduce (21) to the very simple form, 
dH t K 
the equation of the first and third members of (17), modified 
by (20) and (23), Ogives 
m _ (k -\- l)$cr dt {9K\ 
E~ ? dx l ■ y 
§ 25. Let i = ^( t i') be any particular solution of this equa- 
tion ; we find as a general solution, with one disposable 
constant C, 
« = CS[.rCr» (K - 1) ] (26), 
which we may immediately verify by substitution in (21). 
Here %{x) may denote a solution for a gaseous atmosphere 
around a solid or liquid nucleus, or it may be the solution for 
a wholly gaseous globe, in which case %(x) will be finite, and 
%'(je) will be zero, when x = co . Each solution %(x) must 
belong to one or other of two classes : — 
Class A : that in which the density increases continuously 
from the spherical boundary to a finite maximum at the 
centre. In this class we have dp/dr = (dt/dr = 0), when 
r = ; or, which amounts to the same, dp/dx = (dt/dx = 0), 
when x = co . 
Class B : that in which, in progress from the boundary 
inwards, we come to a place at which the density begins to 
diminish, or is infinite ; or that in which the density increases 
continuously to an infinite value at the centre. 
With units chosen to make §(oo)= 1, we shall denote the 
function § of class A by © K , and call it Homer Lane's 
Function ; because he first used it, and expressed in terms of 
it all the features of a wholly gaseous spherical nebula in 
convective equilibrium, and calculated it for the cases, k = 1'5 
and * = 2"5 (k=l^ and & = 1'1). He did not give tables of 
