/ 
THE SOURCE OF STELLAR ENERGY 
291 
This observational result refers to only one particular phase in the life 
of the star; but if we take it as a general hint that the Kelvin time-scale 
needs to be multiplied by a factor of at least 150 we arrive at an age of 
the sun (>3.10 9 years) satisfying modern requirements. Even if the 
pulsation theory of Cepheids is rejected our argument is probably valid. 
The law II oc p~i is directly deducible from observation without reference 
to the pulsation theory (Table 25). Moreover, it is inconceivable that a 
periodicity intrinsic in the star should be practically unaffected by large 
changes of density. If, for example, the period of the light-fluctuation 
were that of the rotation of the star, as some writers have supposed, the 
conservation of angular momentum requires that II oc p~i so that an even 
faster change of period would be looked for. 
203. In seeking a source of energy other than contraction the first 
question is whether the energy to be radiated in future is now hidden in 
the star or whether it is being picked up continuously from outside. 
Suggestions have been made that the impact of meteoric matter provides 
the heat, or that there is some subtle radiation traversing space which the 
star picks up. Strong objection may be urged against these hypotheses 
individually; but it is unnecessary to consider them in detail because they 
have arisen through a misunderstanding of the nature of the problem. No 
source of energy is of any avail unless it liberates energy in the deejp interior 
of the star. 
It is not enough to provide for the external radiation of the star. We 
must provide for the maintenance of the high internal temperature, 
without which the star would collapse. The temperature gradient from the 
surface to the centre cannot be maintained by supplying heat at the bottom 
end. If, for example, sufficient heat is developed by meteoric impact to 
maintain the surface of Capella at 5200°, the temperature throughout the 
interior will fall gradually to this level and the star will no longer be 
distended to low density. In fact the evolution of the star goes on unmoved 
by what is happening at the surface, and if extra heat is generated there 
it is thrown off as extra radiation (cf. § 143). 
We may glance also at the suggestion of a modification of the laws of 
radiation such that a body radiates only in directions in which there is 
something to intercept and, as it were, appreciate the radiation. This would 
economise the heat flowing from the star into space, but it makes no 
difference to the flow in the interior where in every direction there is 
matter to intercept the radiation. The suggestion is not helpful because 
it is the internal flow which decides how much energy is going to be 
squandered, and it is too late to check the waste by economy at the 
surface. 
19-2