210 
VARIABLE STARS 
of the radiative theory on this point. The dimensions that have usually 
been given are very improbable on general grounds. We now abandon 
the hopeless task of utilising the light measurements of the faint com 
ponent, and without testing the theory apply it to the bright component 
alone. After some trials a mass ratio M 1 = 5 M 2 is found to fit satisfactorily. 
This gives 
a = 6oq = 10,200,000 km., 
whence M 1 = 4-30, M 2 = 0*86, 
R x = 2,140,000 km., R 2 = 2,450,000 km. 
The absolute magnitude of the bright star predicted from the mass is 
then — l m -21 and from the radius and effective temperature is — l m *14. 
The absolute visual magnitude would be — 0 m -45, and the parallax 0"*028. 
Referring to Table 23 we notice that the mass 4-3 is just right for a58 
star on the main series—a fact which increases our confidence in the result. 
The faint component is a giant as in most eclipsing variables*. 
Reflection Effects. 
143. In a number of eclipsing variables the components are so close 
that the reflection by the faint component of the light of the bright 
component is conspicuous in the light-curve; superposed on the eclipse 
effects there is a brightening of the star as the faint component changes 
from “new” to “full.” Another cause of continuous variation is the 
spheroidal form of the stars; but this can be disentangled from the reflec 
tion effect by the difference of phase. It is usual to investigate and allow 
* [When this was sent to press I was unaware that a trustworthy determination 
of the dimensions of the Algol system had been made by an interesting new observa 
tional method (D. B. McLaughlin, Astrophys. Journ. 60, p. 22) which gives the radius 
R 1 =2,180,000 km. During the progress of the eclipse different portions of the disc 
remain unobscured so that differential radial velocities between portions of the disc 
can be measured; hence the equatorial speed of rotation is found. Multiplying by 
the rotation period (which can be assumed to be the same as the revolution period 
when the components are so close together) we obtain the circumference of the star, 
and hence R 1 is found. As the differential velocity amounted to 35 km. per sec. the 
determination is presumably satisfactory; indeed it is probable that the radius of 
Algol is now more accurately known than that of any other star except the sun. 
McLaughlin determined from this the mass ratio M 1 fM z = 5-0 in agreement with 
our result above. 
It has also transpired that our failure to determine the correct mass ratio from 
the light of the faint star is not the fault either of the photometric data or of the mass- 
luminosity relation. The Algol system contains a third distant component with 
period 1-885 years. Light is coming from this at the time of deepest eclipse, and 
this has been falsely attributed to the faint hemisphere of the secondary. The mass 
ratio 0-41 determined above is presumably the ratio of the tertiary to the primary; 
and the secondary may well be extremely faint as the value M 1 /M 2 = 5 would require. 
This is a rather striking confirmation of the theory by a star which at first seemed 
unfavourable to it.]