ing in a faulty reduction from photographic to visual magnitude) which 
makes the first three or four stars too bright and their calculated masses 
too large. The bolometric magnitude is derived from the visual mag 
nitude by Table 16. The light-range in columns 8 and 9 often differs 
considerably from the value given in a former Table of this kind* owing 
to more recent photometric work. The last three columns contain elements 
of the spectrographic “orbits.” The quantity e is not to be interpreted 
literally as an eccentricity, but it serves to measure the deviation from a 
simple harmonic oscillation. The element a> indicates the position of 
periastron according to the orbital interpretation; if a> = 90°, periastron 
is at the point of the orbit farthest from us, so that the drop from greatest 
receding velocity to least receding velocity is sharper than the ascent of 
the velocity-curve. This is generally a characteristic feature. The quantity 
8R is the element a sin i of the spectrographic orbit, but is here considered 
to be the semiamplitude of the pulsation. Strictly speaking, if a> is not 
90° or 270° so that the major axis is not in the line of sight, a correction 
for eccentricity should be applied, but in all these stars the correction is 
trivial. 
In Table 25 columns 3 and 4 give the mass and 1 — /3, deduced by our 
theory from the absolute magnitude and T e . In column 5 the radius is 
obtained as usual from the absolute magnitude and T e . The central density 
and central temperature in columns 6 and 8 are then found by (99-3). 
In column 9 we calculate the radius a' of the orbit of a hypothetical 
satellite revolving round the star of mass M in the period II. In column 11 
8T e is the semiamplitude of a variation of T e which would account for the 
visual light range given in Table 24. Due allowance is made for the change 
in luminous efficiency when T e varies, so that STJT e is not exactly pro 
portional to the range of magnitude. The relation of phase of the light- 
curve and velocity-curve is such that the radius has approximately its 
mean value both at maximum and minimum light. Accordingly it is 
legitimate to ascribe the light-range to a change of effective temperature 
and not to a change of radius; but we may perhaps be in error in assuming 
that the relation of visual light to heat intensity is the same as in a static 
star. 
The stars Polaris and jS Cephei are given for reference at the end of the 
Tables. The light-range is very small, but they are believed to be genuine 
Cepheids. In discussing the Tables we shall, however, confine attention 
to the typical Cepheids with large variation. 125 
125. We shall first explain why the binary hypothesis for these stars 
has been abandoned. 
If there are two stars, the secondary must be relatively faint because 
* Monthly Notices, 79, p. 4. 
VARIABLE STARS 
183