156 
THE MASS-LUMINOSITY RELATION 
the method used for Capella.' For e Hydrae the spectroscopic orbit of the 
bright component has to be combined with the relative orbit of the two 
components measured visually; thus a knowledge of the mass ratio is 
required at an early stage. There being no direct measurement of mass 
ratio worth considering, I have used the magnitude difference of the two 
components to determine the mass ratio—an extension of the principle 
adopted for Krueger 60 and other stars. 
Spectral types of most of these stars were taken from Lick Bulletin, 
No. 343; the effective temperatures assigned to the types are still un 
fortunately a matter of judgment. Above 6000° an error in the assigned 
temperature does not make much difference to the comparisons since the 
temperature correction 8 m is set off against the reduction to bolometric 
magnitude Am. In the redder stars the two corrections add up, and in 
the neighbourhood of 3000° where Am is changing rapidly an error is more 
serious. 
When only one residual for two components is determined, it is repre 
sented in Fig. 2 at an abscissa corresponding to the mean of the two masses. 
Table 19. Eclipsing Variables. 
The method of finding the mass and bolometric magnitude has been 
explained in § 105 for V Puppis. In the headings of the Table, R is the 
radius of the star, and a the semiaxis of the relative orbit. The column 
m (bol.) gives the absolute magnitude derived from the formula 
L = 7 racR 2 T e *, 
and the column m (calc.) is derived from the mass by Table 14. 
The results in all cases refer to the bright component which has been 
identified with the more massive component except in ¡3 Lyrae. The 
inevitable uncertainties would probably be magnified if the method were 
applied to the faint components. The photometric results R/a and cos i 
are from H. Shapley’s discussion, the “ darkened ” solution being preferred*. 
The second column gives the grade of the orbit as classified by Shapley, 
Grade 1 being the most trustworthy. The spectroscopic data are chiefly 
due to J. S. Plaskettf. 
In this series of comparisons the effect of an error in the assigned 
effective temperature would be considerable, and it is the more unfortunate 
that many of the stars are of B type where the temperature scale is most 
uncertain. We can show that 
s (0 - C) = - 83 (log 10 T e ), 
* Princeton Contributions, No. 3 (1915). For a few stars better data are now 
available; but it was considered best to use one standard source of data (as in 
Tables 17 and 18) in order to avoid bias in selection. 
f Publications of the Dominion Astrophysical Observatory, Yols. 1 and 2.