THE MASS-LUMINOSITY RELATION 
151 
between the two components in such proportions as will make the residual 
in magnitude the same for both. This is done by trial and error. We find 
Mass 
1-/3 
Boi. Mag. 
(calc.) 
Boi. Mag. 
(obs.) 
O-C 
Bright component 
0-27 
•00439 
11-07 
9-82 
- 1-25 
Faint component 
0-16 
•00156 
13-55 
12-32 
- 1-23 
For the bright component additional results are— 
Pm = 9-06, Pc = 493, T c = 3-22.10 7 . 
Even at a density above 400 there is still no sign of failure of the gas laws, 
for the difference of observed and calculated brightness is actually in the 
wrong direction according to terrestrial analogy. 
106. The last three examples indicate a substantial accordance 
between theory and observation for stars of mass 19-2, 1, 0-27 respectively, 
and bolometric magnitude — 4-7, + 4-9, + 9-8, the comparison being 
differential with respect to Capella (mass 4-2, mag. — 0-4). This covers 
the greater part of the known range of stellar mass and magnitude. It 
will, of course, be necessary to test whether the accordance is confirmed 
by a systematic survey of all the stars available for similar tests. 
In passing it is interesting to note the central temperatures found for 
the five stars. 
Capella ... 
9-08 
8 Cephei... 
6-16 
V Puppis 
42-4 
Sun 
39-5 
Krueger 60 
32-2. 
Allowing for the errors of the determinations there is a possibility that 
the last three temperatures are really the same. The three stars belong 
to what is now called the “ main series ” running from types O and B down 
the dwarf series to type M. The remaining two stars belong to the side 
series of giants whose relation to the main series has become obscure 
since we no longer accept the giant and dwarf theory of evolution. It 
certainly looks significant that along the main series the central tempera 
ture should be so steady through a seventy-fold range of mass and a 
million-fold range of radiation. We shall revert to this result in § 122. 
The Mass-Luminosity Curve. 
107. The values of m and M given in Table 14 are traced as a curve 
in Fig. 2, the ordinates being m and the abscissae log M. 
It will be remembered that before comparison is made with the ob 
served magnitude of a star of effective temperature T e the small correction 
8m = — 2 log 10 (TJ5200) should be added to the value taken from the 
)