VARIABLE STARS 
209 
/ 
calculated mass thus obtaining a residual for each star. If the theory is 
correct it should be possible to find a mass ratio which makes both residuals 
vanish simultaneously. If not, we vary the mass ratio until the two 
residuals become equal, and their common value measures the discrepancy 
between theory and observation. 
It is, I think, an accident that no suitable example for discussion 
presents itself*. We desire to illustrate the method but have to use an 
unsuitable star ft Persei (Algol). The photometric orbit of Algol was obtained 
by J. Stebbinsf by selenium photometry but we shall (unjustifiably) treat 
the results as though they were visual observations. 
The ratio of surface brightness of the primary to the faint hemisphere 
of the secondary is J X \J 2 = 20, or a difference of 3 m -25. Adopting T 1 = 13,000° 
for the effective temperature of the primary (observed type B 8) we find 
T 2 = 5350° by Table 16. 
From Stebbins’s results the ratio of the radii is R 2 /R 1 = 1*14. Hence 
the difference of bolometric magnitude (reduced to standard T e for direct 
comparison with Table 14) is 
m 2 ~ m 1 = — 5 log 1-14 + 8 log (13000/5350) = 2 m -80. 
We expect a star of type B 8 to have a mass about 4. Examples of 
pairs of masses in Table 14 with magnitude difference 2 m -80 are 5-67, 2-20 
and 3-44, 1-50, the mass ratios being 0-39, 0-43 respectively. Hence we 
adopt provisionally M 2 /M 1 = 0-41. 
The observational data give 
= 1,700,000 km. 
hence the above ratio gives 
a — a x + a 2 = 5,850,000 km. 
Combining this with the period 2-867 days we find the mass of the system 
M 1 + M 2 = 0-97, 
so that = 0-69, M 2 = 0-28. 
The photometric data also give R l — 0-2 la, B 2 — 0-24«, so that 
R 1 = 1,230,000, R 2 = 1,400,000. 
We can now calculate the bolometric magnitude from the M’s and 
R’ s respectively; but it is clear that there will be a hopeless discordance 
since the masses are much too small. We cannot therefore pursue the 
calculation further. 
Since much interest has been taken in the dimensions of the system of 
ft Persei on account of its celebrated history, we may give the conclusions 
* Excellent photometric orbits are known for a number of eclipsing variables 
(enumerated in Table 28 a below); but only two besides fi Persei have spectrographic 
orbits and for them the orbits of both components have been measured. 
t Astrophys. Journ. 32, p. 185. 
e 14