206 
VARIABLE STARS 
If the pulsation theory is correct there should be a broadening of the 
spectral lines by the Doppler effect as well as an average displacement 
of them at times of maximum and minimum velocity, since different 
points of the surface have different velocities in the line of sight. Owing 
to the “darkening at the limb” of a star the broadening of the lines is 
considerably less than would be predicted for a disc of uniform brightness 
and perhaps we can scarcely expect the effect to be observable. It has 
escaped detection hitherto*. 
Long-Period Variables 
140. Variables of this class have, with few exceptions, periods ranging 
from 100 to 500 days with a strong preference for periods near 300 days. 
The light-range is comparatively large, averaging about 4-8 magnitudes; 
it is seldom, if ever, less than 3 magnitudes. The stars are all of type M 
or of the closely allied rare types S (zirconium type) and N (carbon type). 
Great changes in the spectrum occur between minimum and maximum, and 
bright emission lines of hydrogen and other elements appear. The periodicity 
is imperfect and the star may be some weeks behind or ahead of the pre 
dicted phase; the amplitude of the variation is not always the same in 
successive periodsf. 
There is growing evidence that long-period variation and Cepheid 
variation are essentially the same phenomenon. The very low density 
and temperature of the long-period variables exaggerates and renders 
more erratic the effects of the same kind of pulsation as in the Cepheids. 
This is still a very speculative conclusion, but we shall consider the evidence 
pointing in this direction. 
It has been shown by Pettit and Nicholson J that the range of variation 
in heat is very much less than the light-range. For example, y Cygni gives 
1300 times as much light at maximum as at minimum, but only 1-7 times 
as much heat. The following results were obtained from direct measure 
ments of the heat received from o Ceti§— 
Near minimum, visual magnitude 8-9, bolometric magnitude 1-5. 
Near maximum, visual magnitude 4-5, bolometric magnitude 0-2. 
The heat range is generally about 1 magnitude, so that in this respect the 
variation is quite similar to that of the Cepheids. * * * § 
* For a detailed discussion see Shapley and Nicholson, Proc. Nat. Acad. Sci. 5, 
p. 417 (1919). A curious feature of the observations is that the lines at minimum 
light are much broader than at maximum although the Doppler broadening should 
be the same at both times. 
| Collected data are given by T. E. R. Phillips, Journal B.A.A. 27, p. 2. 
j Mount Wilson Report, 1924, p. 101. 
§ Mount Wilson Report, 1922, p. 238; we have applied a correction of - 0 m -3 
to reduce to the standard of bolometric magnitude used in this book.