/
THE MASS-LUMINOSITY RELATION
147
by (87-1) and (58-4). Eliminating M by (84-4)
T _ 477 cG (1 - 0) 39? (1 -p) (G R' ppj /489? 4 if' a \* (I — /3)%
akx arf \4MW lf) l irG 3 a ) p*P*
= 1-443.10 71 V—JlL
Using the value of hy found from the discussion of Capella and adopting
as before ¡i = 2-11, the only unknown in this equation is ¡3. The equation gives
(1 - pft = 0 . 909 ft.
Hence 1 — p = 0-451.
Alternatively, 1 — p may be found as follows. Since the same effective
temperature and molecular weight have been assigned to Capella and
S Cephei, we have in a comparison between them
L oc (1 — /3)*
by (99-2). Since 1 — p oc M 2 P i , we obtain by eliminating M
L oc (1 -.pf* ft*.
For 8 Cephei L is greater by 1-93 magnitudes or in a ratio 5-92; hence
(1 — P) '' ft* has 5-92 times its value for Capella. This gives
(1 _ pft = 0-935 ft,
from which the same value of 1 — p is obtained.
From 1 — /3 the mass is obtained by interpolation in Table 14 or by
direct calculation from (84-6), the result being
M = 9-00 x © = 1-79.10 34 gm.
Other details are now easily calculated—
Pm = -000342,
Pc = *0185,
T 0 = 6-16.10 6 .
(3) V Puppis (brighter component).
Eclipsing variable. Mass 19-2x0; radius 5-28.10 11 cm.; type B 1,
assumed to indicate effective temperature 19,000°.
This star is beyond the reach of ordinary parallax measurement so
that its absolute magnitude is not directly known; but we happen to be
able to determine the radius from a study of the light-curve, etc., and the
absolute magnitude can be calculated as below.
The spectroscopic orbits of both components have been determined*;
* Masses of both components are given in W. W. Campbell’s Stellar Motions,
p. 256; but in J. H. Moore’s Catalogue of spectroscopic orbits, Liclc Bulletin, No. 355,
only the combined mass is given—no doubt with good reason. I am therefore
doubtful whether the mass of V Puppis was obtained in the orthodox way described
here; but the description would apply to nearly all other examples of eclipsing
variables.
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