392 
Variable Stars 
[oh. XV 
correspond to alternations of stability and instability in the temperature-* 
luminosity diagram shewn in fig. 12 (p. 159). Fission can only commence 
when the star has a liquid or semi-liquid centre, and for this reason stars in 
process of fission are on or near the left-hand edges of the regions of stability, 
while spectroscopic binaries, which are permanent structures, must of course 
be actually on the bands of stability. 
The foregoing consideration would seem to suggest that the long-period 
variables may be of the same nature as Cepheids, namely stars in which the 
process of fission is either about to start or is under way. There is a certain 
difficulty, however, in supposing that the long periods of these variables can be 
those of the rotation of Jacobian ellipsoids. Corresponding to a period of 300 
days, we have seen that equation (360T) requires a density of only 0*00002. 
This hardly suggests matter in a sufficiently liquid state for ellipsoidal con 
figurations, although it must not be overlooked that eclipsing binaries exist, 
such as W Crucis, in which both components are giants of low density, and 
these must, so far as we can tell, have broken up by fission. Moreover, there 
are two distinct types of long-period variables; in one of these, the regular 
variables, the light-curve repeats itself indefinitely with perfect regularity, as 
in the Cepheid variables, but in the other types the light-curve is irregular 
both in period and shape. It seems possible that the fission theory may 
adequately account for the former. But the irregular variables do not shew 
the features to be expected in a star breaking up by fission. 
Irregular Variables. 
365 . The irregular long-period variables give various indications which 
suggest that they are in a state of pulsation. The diameter of Betelgeux has 
already been found by interferometer observations to vary from 0*047" to 0*034". 
Moreover in most of the irregular long-period variables which have been 
studied in detail, the spectrum and effective temperature appear to vary exactly 
in phase with the visual luminosity. 
From an exhaustive study of o Ceti, Joy* finds an approximately linear 
relation between the spectral type (ranging from Mo to M 9*5) and the 
logarithm of the visual magnitude (ranging from 0*45 to 1*0). Vogtf has given 
observational curves for R Scuti in which the maxima and minima of the 
effective temperature agree exactly with those of the visual magnitude. 
If this is accepted as being generally true of long-period variables, then 
equation (360*2) shews that R, the radius of the star, must be in phase with 
both the spectral type and the magnitude, which is precisely what is required 
of a pulsating star. It is true that Joy finds that the displacements of spectral 
lines of o Ceti, if interpreted as radial velocities, would indicate changes 
in the star’s radius which are out of phase with both these quantities, but 
* Astrophys. Journ. lxiii. (1926), p. 290. 
f Heidelberg ( Konigsstuhl ) Obs. vm. (1926) No. 5.