96 
Gaseous Stars 
[ch. Ill 
Inserting the numerical values R/m = 8’26 x 10 7 and 7 = 6’66 x 10~ 8 , and 
further measuring M and r in terms of the mass ( 2’00 x 10 33 ) and radius 
( 6*95 x 10 10 ) of the sun, this assumes the form 
in which M and r are measured in terms of the mass and radius of the sun. 
From equation (82'6) we obtain at once 
This completes the analysis necessary for the evaluation of internal tem 
perature, density, etc. Starting from any values of n, we calculate the value 
of \ c from relation (85‘2) ; equation (88'7) next gives the mass of the corre 
sponding star, and equation ( 88 ‘ 6 ) then gives the central temperature for a 
star of this mass. 
weight is constant throughout the star. In this casey = 0, so that from 
equations (88‘7) and ( 88 ' 8 ), 
The value of B now depends only on n, and is readily determined from 
Emden’s numerical solutions. 
Emden gives solutions only for the values n = 2*5, 3, 4, 4*5, 4*9 and 5, so 
that solutions for intermediate values of n must be obtained by interpolation. 
The interpolation becomes easy on noticing that the values of l/r 1( and of 
from Emden’s solutions, those corresponding to the values n = 325 and 35 
being obtained by interpolation. 
The table refers to the case in which g is constant throughout the star so 
that j — 0, and the relation (85*2) between n and X c reduces to 
so that, on substituting for T c ' from ( 88 ‘ 2 ) 
x/ + lj (pf = B( 1 + x.)« 
(88-7), 
where 
( 88 - 8 ). 
Stars with uniform effective molecular weight. 
89. The problem assumes its simplest form when the effective molecular 
X c > 4 if 2 = 5(1+ \ c ) 3 
(891), 
where 
Table X (p. 97) gives values calculated 
4 + \ c 
1 + 4\ c + 2 1 
n = 3 + (l-2Z) 
(89-3).