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