CHAPTER XV 
VARIABLE STARS 
353. Over 2000 stars are known to be variable, and of these about 1000 
are definitely periodic. These periodic variables fall into the two main classes 
of Cepheid and long-period variables. 
It is still uncertain whether Cepheid and long-period variables are 
essentially different objects or varieties of essentially similar objects. If the 
latter, the varieties are quite distinct. Long-period variables have periods 
ranging from about 60 to 500 days, whereas no Cepheid is known whose period 
exceeds 38 - 7 days ( U Carinae), and most have periods substantially shorter than 
this. Apart from their different ranges of period, the two classes of variables 
have many features in common. The light curve of Cepheid variables does 
not shew a regular symmetrical rise and fall, but rather a fairly rapid rise to 
maximum brightness followed by a slow decline to minimum, and many long- 
period variables shew the same features, although generally to a less degree. 
The Cepheid variables shew a very marked correlation between period and 
spectral type, shorter periods accompanying the earlier speetral types. Adams 
and Joy* find a similar correlation in the long-period variables, and this 
proves to be a direct extension of that already established for Cepheids. In 
a diagram in which spectral type and period are taken as co-ordinates, they 
find that a single smooth curve runs through the positions occupied by the 
long-period variables, the normal Cepheid variables and the cluster variables 
which form a special short-period group of Cepheids. 
Without deciding whether these variables are different or similar types of 
object, it will be convenient to discuss them together until we are compelled 
to differentiate between them. 
354. Observationally the most marked characteristic of both classes is 
their extreme rarity. In part, this is a necessary consequence of the fact that 
they are extremely bright, since extremely bright stars are in any case rare. 
Cepheids have an average absolute magnitude of about —2, and we have seen 
(Table V) that for every million stars as bright as the sun there are only 450 
stars of this absolute magnitude. But Cepheids are even more rare than this, 
only a small fraction of stars of the requisite degree of brightness being 
Cepheids. Within a distance of 100 parsecs of the sun, there must be about 
400,000 stars. Only two of these (Polaris and /3 Cephei) shew Cepheid charac 
teristics, and both are so non-typical that there is some doubt as to whether 
they are true Cepheids or not. Within a sphere of radius 1000 parsecs there 
* Proc. Nat. Acad. Sci. xm. (1927), p. 391.