VARIABLE STARS 
181 
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maximum velocity of approach. This fact rules out any interpretation 
of the variation as an occultation effect. 
The absolute magnitude is a definite function of the period. This was 
first shown by Miss Leavitt from a study of the variables in the Lesser 
Magellanic Cloud. A full confirmation was obtained by H. Shapley from 
the variables in globular clusters. In the same cluster the absolute mag 
nitude differs from the apparent magnitude by a constant (depending on 
the unknown distance of the cluster) so that the period-luminosity re 
lation is given directly without the intervention of parallax. It is found 
that the period determines the absolute magnitude to within a probable 
error of ± 0 m -25. Having thus found the period-magnitude curve applicable 
to all Cepheids except for the unknown constant, we proceed to anchor 
the curve by combining our knowledge of the mean luminosity of the 
nearer Cepheids (derived from their parallactic and cross motions) into 
a single mean determination of the constant. 
There is a progression of spectral type in the direction from A towards 
M as the period (and luminosity) increases. 
The Cepheids are more luminous than ordinary giant stars of the same 
spectral class, although some giant stars of high luminosity, called pseudo- 
Cepheids, are found which seem to resemble them very closely without 
showing any light-variation. Cepheids and pseudo-Cepheids are sometimes 
described as “super-giants.” 
124. Tables 24 and 25 contain results for those Cepheids which have 
been sufficiently investigated. The observational data have been taken 
from a compilation by Margarete Güssow*. 
In Table 24, column 3 gives for most stars the range of spectral type 
since the type changes during the light-period. In column 4 an effective 
temperature is assigned to correspond to the median spectral type. The 
basis adopted in this assignment is 4900° for type G 0 with an increase of 
log 10 T e by 0-0140 for each tenth of a type between M and A, so that 
A 0 = 9300°, M 0 = 2600°. The temperatures are taken rather low, partly 
because these stars are super-giants of low density, and partly because the 
types here used (mostly due to Shapleyf) are systematically ^ or T % of a 
type bluer than those assigned by Adams and Joy. The absolute visual 
magnitude in column 6 is derived from the period by Shapley’s period- 
luminosity curvej. Differentially these magnitudes should be correct to 
within 0 m -25, but the zero point of the period-luminosity curve is not so 
well determined, and there may be a constant correction applicable to the 
whole series. I suspect also that there may be a progressive error (originat- 
* “Kritische Zusammenstellung sämtlicher Beobachtungsergebnisse der Verän 
derlichen vom S Cephei-Typus und Kritik der Eddingtonschen Pulsationstheorie” 
(lithographed, Berlin, 1924). 
f Astrophys. Journ. 44 , p. 274. t Ibid. 48 , pp. 114, 282.