VARIABLE STARS 
185 
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the principal star. Allowing for the large eccentricities the secondary 
must dip deeply into the principal star at periastron. The orbital inter 
pretation has to be discarded because there is not enough room for the 
hypothetical orbits*. 
A disproof of the binary hypothesis does not necessarily compel us to 
adopt the pulsation hypothesis. We are, however, reduced to the considera 
tion of a single star, and the period of light variation must therefore be a 
period intrinsic in that star. If the period is not that of some form of 
pulsation, the only alternative seems to be that it is the period of the star’s 
rotation. We do not know of any theory connecting the variations with 
the star’s rotation, sufficiently plausible to be discussed here. No doubt 
there are other kinds of pulsation which might claim some attention 
besides the symmetrical mechanical pulsations which we consider and 
advocate in this Chapterf. 
126. Accepting the pulsation theory the relative amplitude SR/R has 
the kind of value which would be anticipated. It is large enough to produce 
important changes of internal temperature and density and so cause the 
rate of radiation to fluctuate. There is some indication that SR/R is pro 
portional to the temperature amplitude ST e /T e ; the fact that the corre 
spondence is not very exact can be attributed to errors of the observational 
data. For the 15 stars (omitting X Cygni) the mean values are 
SR/R = -052, S T e /T e = -066. 
But SR/R must certainly be increased a bit because the spectroscopic 
measures of SR refer to the integrated light of the hemisphere and do not 
give the true rate of expansion of R. If the law of darkening of the disc 
is the same as for the sun the values of SR/R have to be multiplied by ff , 
giving a mean value -073. But I think that the pulsation may cause the 
light at maximum to rush out more in a normal direction than in a static 
star and the correction is probably not so large. It seems then that SR/R 
* The chief arguments against the binary theory and in favour of the pulsation 
theory were put forward by H. Shapley ( Astrophys . Journ. 40 , p. 448 (1914)). The 
pulsation theory was previously advocated by H. C. Plummer, chiefly because 
deviations from elliptic motion were detected of a kind impossible to ascribe to 
gravitational perturbations by a third body (Monthly Notices, 73 , p. 665; 74 , p. 662). 
f [Recently there has been a recrudescence of criticism of the pulsation theory, 
and rival theories have been advocated. A summary of these discussions will be 
found in Monthly Notices, 86 , p. 251. I have never regarded the hypothesis of 
symmetrical pulsations as conclusively established but I am not persuaded that 
anything has transpired in the recent discussions to weaken the case for it as here 
set forth. Those theories which identify the light period with the period of the star’s 
rotation seem to be ruled out by the following consideration. I or 8 Cephei the radius 
2.10' km. and period 5*4 days give an equatorial velocity 270 km. per sec., so that 
between different portions of the stellar disc there would be a differential velocity of 
540 km. per sec. in the line of sight. The spectral lines would be extremely diffuse 
with total width 8 A and effective width (not counting faint margins) at least 3 A.]