SOLUTION OF THE EQUATIONS 
135 
/ 
within a magnitude, since it rests only on indubitable laws of physics 
together with the following conditions— 
(a) constancy of rjk; 
(b) constancy of (x; 
x c) the condition of a perfect gas; 
( d ) the adopted absorption law. 
The first three conditions have been passed in review in §§ 89-97. The 
conclusions are that the uncertainty due to ignorance of 77 is at most 
± 0 m -5 for a star of ordinary mass. Possible variations of ¡x are eliminated 
by using the average value of /x corresponding to f the central temperature. 
Deviation from perfect gas laws in the sense observed in terrestrial gases 
would cause a decrease of L, deviations of the order occurring in terrestrial 
gases being sufficient to produce a marked effect. 
It would seem then that any discrepancy between theory and observa 
tion must be attributed to— 
(а) a wrong physical prediction of the absorption coefficient; 
( б ) a wrong estimate of the value of ¡x to be employed; 
(c) a failure of the condition of a perfect gas. 
If we are not mistaken all other loopholes have been explored and blocked 
up. 
99. In practice a star is generally described by its mass M and effective 
temperature T e . It is desirable to understand how its other properties 
vary with these. Collecting a number of formulae already obtained, we 
have 
L oc B^T^ac M (1 - p)/k c 
ï'oVPc œ (1 - ;3);V/3 
h* pjfiTi* /¡i(i-i3)Ti 
p c oc M/R 3 
T c OC pfxM/R 
1 — /3 x M 2 /?v 4 
(99-1). 
From these are derived 
Roc (1 - 
T c OC M~i (1 - pytfx-iTj 
Pc oz 1 - ¡ 3 )-$fx-%T e V I 
Lac Mi (1 - p)*ix*T* J 
The variation with p has been retained here for completeness, but the 
primary intention of these formulae is the comparison of stars with fixed 
value of p,. In that case (1 — 78 ) is a function of M increasing with M. 
The most important result from (99-2) is that for stars of the same