360, 36i] The Fission Theory 389 
the wave in longitude will lag behind that of the ends of the major axis of 
the ellipsoid which are causing the wave. 
These two factors necessarily result in an absence of fore-and-aft symmetry 
both in the radial motion of the star’s atmosphere and in the light-curve of 
the radiation. Moreover, although the details remain to be worked out, 
the general nature of the asymmetry would seem likely to be of the nature 
observed in Cepheid variation, a rapid increase both in radial velocity and in 
light emission being followed by a slow decline. As a very rough approxima 
tion, let us suppose that the wave which advances over the surface of the 
star has an absolutely vertical wall-like front, and that the whole difference 
in luminosity between maximum and minimum results from high temperature 
radiation emitted by the front of this wave. Then each time this wave appears 
from behind the limb of the star, the star’s luminosity will increase with 
great rapidity to its maximum. This maximum is attained as soon as the 
whole front of the wave is fully visible, after which a foreshortening effect 
will result in a slow decline to minimum. The spectral lines will shew a 
maximum velocity of approach exactly when the star is at its maximum, 
which is precisely what is observed in Cepheid variation. 
As a better approximation we can imagine two systems of waves travelling 
over the surface of the star, one resulting from the variations of the gravita 
tional field at the star’s surface, caused by the rotation of the elongated core 
inside, and the other produced by the transmission of the mechanical upheaval. 
The succession of two such waves would account for the double maxima 
observed in Cepheids of the 8 Sagittae type. 
The period of the variation would be half the period of rotation of the 
ellipsoid. For a Jacobian ellipsoid fairly near to its maximum elongation 
(which is the configuration in which variability would be most likely of 
detection), the value of (o 2 /2Tr^p is 015, so that the period n r/o> is equal 
to 3'2 ( 7 p) 
Thus the fission theory leads to the same qualitative relation between P 
and p as the pulsation theory, namely P oc p~^, but the numerical factor is 
different. In place of equation (3571) the fission theory gives 
P> = 0*021 (360-1), 
where P is again measured in days, but p is no* longer the mean density of 
the star but the mean density of its core. The values of p given by equation 
(360-1) are about ten times the values of p calculated on the pulsation theory, 
and for the Cepheid variables these were about six times as great as the mean 
densities estimated by Seares (cf. Table XXXI). Thus for numerical agree 
ment with observed periods, the fission theory requires that the mean 
densities of the cores shall be about 60 times the mean densities of the stars 
as estimated by Seares. This factor of 60 is not an unreasonable one; a core 
which had a mean radius equal to a quarter of that of the star and contained