285 
1907-8. J The Problem of a Spherical Gaseous Nebula. 
sphere, and which are, according to the definition given in § 3, inconsistent 
with a condition o£ convective equilibrium, we are still forced to conclude 
that Homer Lane’s exquisite mathematical theory gives no approximation 
to the present condition of the sun, because of his great average density. 
“ This was emphasised by Professor Perry in the seventh paragraph, headed 
‘ Gaseous Stars,’ of his letter to Sir Norman Lockyer on £ The Life of a 
Star ’ {Nature, July 13, 1899), which contains the following sentence : — 
‘It seems to me that speculation on this basis of perfectly gaseous 
stuff ought to cease when the density of the gas at the centre of the star 
approaches 0T, or one-tenth of the density of ordinary water in the 
laboratory.’ ” * 
§ 57. According to a promise in the 1887 paper to the Philosophical 
Magazine “ On the equilibrium of' a gas under its own gravitation only,” I 
now give examples of the application of this theory of convective equi- 
librium to spherical masses of argon and of nitrogen ; choosing, for illustra- 
tion, amounts of matter equal to the masses of the sun, earth, and moon, 
with density at the centre 0T in each case. 
Assuming 
* = C©[£C" k * _1) ] (67) 
as the solution of equation (24), which gives central density 0T, we find 
from equation (19) 
0-i = (~j (68); 
and, as in this case we suppose the total mass M of the nebula to be known, 
we can determine C by applying equation (25) above. Thus 
E e 
where q denotes the value of x for which ® K (q) — 0. Eliminating A and 
by means of equations (22) and (68), we obtain 
(69), 
C = ( L )*3770. 
1 /M\ § 
(70). 
k + iVe, 
From equations (68) and (22) we can determine the following expressions 
for A and or : — 
K — 3 
. . . (71) 
Jl) 
• ='8122^®' K (g) 
k — 3 
■i -iiWMy 
K + l \E/ 
1366.© , K (g) 
K — 3 
l“ r 
/M nS 
j (k+i^-dve. 
(72). 
* Quoted from “ On Homer Lane’s Problem of a Spherical Gaseous Nebula,” Nature , 
Feb. 14, 1907. 
