150 
THE MASS-LUMINOSITY RELATION 
We perhaps naturally think that data for the sun must be more 
accurate than for any other star, but that is not true of its absolute 
magnitude which may be one or two tenths of a magnitude in error. 
Hertzsprung, for example, adopts as most probable + 4 m -67 visual 
corresponding to + 4- m 62 bolometric. If he is right the discrepancy is 
only 0 m -10. 
I have considered the desirability of shifting our standard of reference 
from Capella to the sun; but it has seemed too daring a step whilst the 
notion of perfect gases of density 76 gm. per cu. cm. is still unfamiliar to 
us. It would perhaps be more accurate to determine k x from the sun; 
but the uncertainty of the sun’s absolute magnitude would be a dis 
advantage for differential comparisons with other stars. 
(5) Krueger 60. 
Absolute visual magnitudes of components ll m -25 and 13 m -75; combined 
mass of system 0-43 x O; both components of type Ma indicating 
effective temperature 3100°*. 
Here the difficulty is that only the combined mass is known. It is 
true that several determinations of the ratio of the masses have been made 
but these range from 6 : 5 to 3 : 1, and we cannot place reliance on them. 
To avoid this difficulty we may predict the mass from the absolute 
magnitudes as we did for S Cephei. The results are— 
bright component: bol. mag. 9-82, 1 — = -00747, M = -354, 
faint component: bol. mag. 12-32, 1 — ¡3 = -00264, M = -209. 
This gives a combined mass 0-563 compared with the observed mass 0-43. 
There is some reason to think that the discrepancy is real and that in 
trinsically faint stars deviate systematically in this direction, although 
the evidence in any particular case is not very strong. Assuming that the 
orbital elements of Krueger 60 are accurate, the mass 0-43 corresponds 
to a parallax 0"-260 and the mass 0-56 to a parallax 0"-238. The trigono 
metric measures of parallax are perhaps accurate enough to exclude the 
latter value. 
If it is preferred to express the discrepancy in magnitudes (which is 
more convenient for comparison with other stars) we divide the mass 0-43 
* A later orbit by R. G. Aitken ( Lick Bulletin, No. 365) was not available when 
this calculation was made, but the mass is only changed to 0-45 Q. Aitken gives 
the magnitudes as 11-3, 12-8 following most recent writers in ascribing a difference 
l m -5. I think I am right in saying that in observing this star in company with 
Dr Aitken we both agreed that the difference was considerably greater. Burnham 
gives a difference 3 m . With an assumed magnitude difference l m -5 the individual 
masses 0-25, 0-18 are obtained ( Monthly Notices, 84, p. 312) as compared with 0-27 
and 0-16 here found.