152 
THE MASS-LUMINOSITY RELATION 
curve. For graphical comparison it is more convenient to leave the curve 
alone and apply the correction — Sra to the observed magnitudes. The 
observational points plotted in Fig. 2 represent bolometric magnitudes 
reduced to the standard temperature 5200° in this way. 
We may notice that the curve (or Table) gives quite reasonable results 
beyond the range for which definite observational data can be found. Thus 
the predicted (uncorrected) bolometric magnitude of a star of mass 100 
is _ 7 m ; allowing for the fact that the effective temperature of so massive 
a star would probably be very high the visual magnitude would be about 
— 6 m . This agrees with what is usually considered to be about the extreme 
limit of stellar luminosity—as indicated for example by the brightest 
stars observed in globular clusters. The faintest known star, Proxima 
Centauri, is about + 15 m visual or + 13 m bolometric; this should correspond 
to a mass ^ O—a fairly acceptable value. It is suspected, however, that 
the approximations of our theory begin to fail for these very small stars 
and I daresay that the actual mass is rather smaller. 
The observational data plotted in Fig. 2 are set forth in Tables 17, 18, 
19, 20. The necessary explanations are given in the following notes. 
Tables 17 and 18. Ordinary binary stars. 
The calculation of m is performed by straightforward use of Table 14; 
but where only one residual is given for two components the method 
described for Krueger 60 has been used, that is to say, the mass of the 
system has been divided between the two components in such proportions 
as will give the same residual for both. 
Since an error of 10 per cent, in the parallax or semiaxis produces an 
error of 30 per cent, in the mass leading to residuals from 0 m -5 to l m *3 
(according to the star’s mass), only wide pairs with large parallaxes have 
been included with Capella and the sun as first-class determinations in 
Table 17. Procyon is reckoned second-class because the semiaxis of the 
orbit is not well determined; observations of this star are greatly to be 
desired and would form a most important check on the theory. 
Except for e Hydrae and 8 Equulei the observational data have been 
taken from a table by E. Hertzsprung*. The parallax, combined mass 
and absolute visual magnitude are taken directly from his list; the only 
modifications are (1) the adopted absolute magnitude of the sun, changed 
for the sake of consistency with other parts of this book, and (2) the 
difference of magnitude of the components of Krueger 60, changed from 
l m *5 to 2 m -5 since the former estimate appeared to me incredible. The 
selection of the best possible observational material has thus been left 
in the main to an independent arbiter, who made his choice before the 
* Bull. Astr. Inst. Netherlands, No. 43 (1923).