88—90J 
Configurations of Equilibrium 
97 
ExM°(\ + iy *g*Tf 
( 90 * 4 ) 
Table X. Solutions for various internal arrangements of stars. 
K 
n 
*i 
Pc 
p 
o 
1 (M 
B 
£(0=1) 
(n + ljti* \pj 
1-4 
2-5 
5-42 
24-1 
6-60 
0-235 
1-02 xlO 69 
255 
1-33 
30 
6-90 
54-4 
6-04 
0-285 
1-27 XlO 69 
319 
1-31 
3-25 
8-00 
88 
5-84 
0-322 
1-43 X 10 69 
358 
1-29 
3-5 
9-52 
152 
5-67 
0-374 
1-60 XlO" 
400 
1-25 
4-0 
15-00 
623 
5-42 
0-554 
2-00 x 10 69 
500 
1-222 
4-5 
32-14 
6378 
5-20 
1-124 
2-46 X 10 69 
614 
1-204 
4-9 
169-47 
934,800 
5-20 
5-524 
3-03 X 10 69 
758 
1-200 
5-0 
00 
00 
5-20 
00 
3-19 x 10 69 
799 
1-14 
7-0 
00 
00 
5-20 
oo 
— 
— 
Further progress can only be made by assigning a definite value to l. As 
the labour of continuing the calculations for all values of l would be excessive, 
we may confine our attention to two values for l, namely l = ^ and 1 = 0, 
trusting to interpolation or extrapolation to give an adequate idea of the 
solutions for other values of 1. 
Solutions when j = 0 and l = \ (Eddingtons model). 
90. When l~\, equation (89'3) gives n = 3, independently of the value 
of X c ; this, as we have already seen (§ 76), is the model discussed by Eddington. 
For this value of n, Table X gives p c =54 , 4p, so that the central density is 
always equal to 54’4 times the mean density, and 5 = 319. 
Equation (891) now becomes 
X c V 4 if 2 = 319 (1 + X c ) 3 (901), 
which gives X c at once in terms of M and g, and we have already noticed 
that X is constant throughout the star, as is also obvious from equation (82'7). 
Equation ( 88 * 6 ) gives the central temperature in the form 
r,= 19 ' 8 xl 0 ‘rTx( i r) (90-2) 
The total emission of radiation E is in general equal to MG, where G is 
measured at the surface of the star, and when all stars are supposed built 
on the same special model (n = 3), this is proportional to MG where G is 
measured at the star’s centre. Inserting the value of G from equation (81-3), 
or from Eddington’s integral (761), we find that 
E x 
M J 
.(90-3). 
X (X "I - 1) 
Using equations (901) and (90‘2), and also the relation E = ±Trar 2 T e \ 
where T e is the effective temperature of the star’s surface, we find that