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CHAPTER XI 
THE SOURCE OF STELLAR ENERGY 
The Contraction Hypothesis. 
201. The energy radiated by the sun into space amounts to 1-19.10 41 
ergs per year. Its present store of heat energy is as follows (§ 103)— 
Radiant energy 2*83.10 47 ergs 
Translatory energy of atoms and electrons 26-9.10 47 
Energy of ionisation and excitation ... < 26-9.10 47 
This constitutes 47 million years’ supply at the most. We do not, however, 
think that this capital is being used for expenditure; it is being added to 
rather than exhausted. 
It is now generally agreed that the main source of a star’s energy is 
subatomic. There appears to be no escape from this conclusion; but since 
the hypothesis presents many difficulties when we study the details it is 
incumbent on us to examine carefully all alternatives. 
Formerly the contraction theory of Helmholtz and Kelvin held sway. 
This supposes that the supply is maintained by the conversion of gravita 
tional energy into heat owing to the gradual contraction of the star. The 
energy obtainable from contraction is quite inadequate in view of the 
great age now attributed to the sun. It is perhaps worth while to give a 
revised calculation of the age of the sun according to the contraction 
hypothesis taking account of two recent conclusions: (1) that the material 
is a perfect gas and therefore concentrated to the centre more strongly 
than used to be supposed, and (2) that the sun’s rate of radiation cannot 
have varied very much in the past if its mass has been constant. The 
gravitational energy lost in contracting from infinite diffusion to the 
present radius is q = 3QM*/R = 5-66.10 48 ergs. 
Of this, 2-97.10 48 ergs has been saved in the form of material kinetic energy 
and radiant energy (as above). An unknown part of the balance 2-69.10 48 
ergs has also been saved as energy of ionisation and excitation. Ignoring 
this last deduction (which is probably substantial) the balance allows of 
radiation at the present rate for 23 million years. Allowing for the rather 
smaller rate of radiation in the past according to the law L cc T^ <x 
(equation (98-3)) the age is just doubled. 
If we measure the sun’s age from the time at which it reached an 
effective temperature of 3000° the result is 15 million or 19 million years 
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