200 
VARIABLE STARS 
Heat content, K + H (T = 1-55)* = 6-75.10 14 ergs per gm. 
= 134,000 years’ supply of radiation. 
Mechanical energy of pulsation = 1*3.10 11 ergs per gm. 
Dissipation of mechanical energy =0*5 ergs per gm. per sec. 
Time of decay = 8000 years. 
Maintenance of the Pulsation. 
135. It has sometimes been supposed that the pulsation is started by 
some accident—possibly the near approach of another star. The frequent 
occurrence of Cepheids in star clusters where the stars are closer together 
might be held to favour this view. But we see that a pulsation so originated 
would decay in about 8000 years. According to present views this is so 
small a fraction of the life of the star, that we should rarely observe a star 
in this condition. It would scarcely be possible to account for the observed 
abundance of Cepheids on this hypothesis. 
The alternative hypothesis is that there are causes at work within the 
star tending to increase and maintain a pulsation. If these are stronger 
than the dissipative causes discussed above, any infinitesimal pulsation 
will grow until either it reaches the natural limit explained in § 131, or 
it reaches an amplitude for which the dissipative forces balance the 
assisting forces. If we are right in believing that for many of the observed 
Cepheids the amplitude reaches the natural limit this view is supported. 
Since it is only at a certain stage of the evolution of a star that Cepheid 
pulsation occurs, we must suppose that at this stage the maintaining cause 
is especially strong, but that during most of the life of a star (and in stars 
of small mass) it is too weak to overcome the dissipation. 
The heat that is continually being liberated in the star is an abundant 
source from which the energy required to keep up the pulsation might 
be derived. Thus in 8 Cephei 160 ergs per gm. is liberated, and only 0*5 ergs 
per gm. is required to maintain the pulsation. But this heat can only be 
made available as mechanical work if the star behaves as a thermodynamic 
engine; that is to say, excess heat must be added to matter when at a 
high temperature and withdrawn at a low temperature. We require, in 
fact, something corresponding to the valve-mechanism of a heat engine. 
136. We first consider the obvious position for placing the “valve,” 
viz. at the point of entrance of the subatomic energy into the engine. 
On the steady supply e 0 there must then be superposed a periodic supply 
e 0 e x , representing positive supply at high temperature and negative supply 
or withdrawal of heat at low temperature. Since the liberation of sub 
atomic energy is likely to be stimulated by increased temperature, and 
* A comparatively high T is adopted here because the low value used for the 
pulsations refers only to differential changes of heat content at the temperature of 
the Cepheids.