388 
Variable Stars 
[ch. xy 
Cepheids can be interpreted as the joint result of two distinct variations, 
a variation in T e which follows the observed changes of spectral type, and a 
variation in R which is generally out of phase with the foregoing. The double 
maximum which occurs in the light curves of Cepheids of the S Sagittae 
type can be naturally interpreted as being caused by T e and R attaining their 
maxima at different epochs. This argument shews that the pulsation theory 
is untenable, quite independently of the interpretation of the observed dis 
placements of the spectral lines. 
Thus all the evidence appears to combine to shew that the pulsation theory 
is inadequate to explain Cepheid variation. 
The Fission Theory of Cepheid Variation. 
361. An alternative theory which I put forward in 1925* escapes the 
particular difficulties which, to all appearances, prove fatal to the pulsation 
theory, although it is yet to be seen what new difficulties it may encounter 
in their place. 
Let us, as in § 253, regard a star as consisting of a liquid or semi-liquid 
core surrounded by a gaseous atmosphere. With slow rotation the core will 
take the shape of a pseudo-spheroid, analogous to a Maclaurin spheroid, and 
the atmosphere will adjust itself to the gravitational field of this core. The 
rotation of the atmosphere is unimportant ; the considerations of § 249 suggest 
that it will in all probability rotate more slowly than the core, in which case 
it must exhibit an equatorial acceleration like that of the sun. 
If the star shrinks, the ellipticity of its core must increase, and finally it 
will assume the shape of a pseudo-ellipsoid.of three unequal axes, the analogue 
of the Jacobian ellipsoid for an incompressible fluid. Even after the core has 
assumed this form, the outer atmosphere, still rotating slowly, would retain 
its nearly spherical shape were it not for the disturbances transmitted to it as 
a consequence of the rotation of the core, which, being no longer symmetrical 
about its axis of rotation, causes an internal upheaval which must be trans 
mitted to the surface of the star, as well as a variation in the gravitational 
field, to which the surface of the star will adjust itself. 
Whatever disturbance is transmitted will travel round the equator in the 
form of a wave, or system of waves, these passing once round the equator 
in the time of a complete revolution of the core. Since these waves must 
travel with a velocity far greater than the velocity of propagation in the outer 
atmosphere of the star, they may be expected to shew the usual characteristics 
of such waves, namely a steeply sloping wall-like front and a gradually sloping 
rear, similar to the bow-wave of a ship, or a tidal bore. Also the position of 
* M.N. lxxxv. (1925), p. 797. The presentation given here varies somewhat from that of the 
original paper, further mathematical analysis (unpublished) having suggested that some of the 
details of the original theory need modification.