184 
VARIABLE STARS 
its spectral lines are never detected. The explanation often given for the 
light variation is that there is a resisting medium surrounding the whole 
system, and as the principal star moves through the medium its front 
surface becomes heated by the resistance. Consequently the star goes 
through phases like the moon according as the cooler hemisphere or the 
heated hemisphere is presented towards us; in particular the brightest 
phase is presented when the star has its maximum velocity towards us— 
in agreement with the observed relation of brightness and velocity. To 
generate so considerable an increase of heat the resistance must be great 
enough to alter the period fairly rapidly; to meet this objection it has 
sometimes been suggested that the resistance does not actually generate 
the heat, but it brushes aside the outer layers of the star exposing a hotter 
substratum. The suggestion does not seem to us very intelligible; one 
would think that there must be an accumulation rather than a deficiency 
of absorbing matter on the front side of a star pushing its way through a 
medium. 
First suspicions of the orbital interpretation of the observed radial 
velocities were aroused by the general tendency of the element co to fall 
near 90°. It is absurd to suppose that the orbits can have a systematic 
orientation with respect to the line of vision from the sun. But the 
tendency is too well marked to be a matter of chance; the conspicuous 
exceptions Y Ophiuchi and £ Geminorum both have small eccentricities 
so that the value of co for them has not so much significance. 
The regular relation between period and density which makes Hy/p c 
practically constant (Table 25) also tells against a binary theory. We shall 
see later that such a relation would naturally be expected if the period is 
intrinsic in a single star. 
But the most convincing disproof of the binary theory is afforded by 
a consideration of the dimensions of the system, which shows that there is 
no room for the supposed orbits and the binary model is a geometrical 
impossibility. The column 8R/R (i.e. a x sin i/R x on the binary interpreta 
tion) shows that a x sin i is on the average -054^. Now the distance 
a x + a 2 between the two components cannot be less than the radius R x 
of the principal star. Hence the ratio of the masses is 
Cosec i will not in general be much greater than 1, and it certainly will 
not be large for all the stars in our Table; hence in general M 2 is not 
more than, say, -£ 2 M X . Practically we can consider M x (i.e. M in Table 25) 
to be the whole mass of the system. That being so, the semiaxis of the 
relative orbit is the quantity tabulated as a '. But in most cases a' is a 
little less than R\ that is to say, we have to place the secondary inside 
M 
M 
•054 cosec i 
1 — -054 cosec i '