4 
SURVEY OF THE PROBLEM 
since the star remains apparently steady for exceedingly long periods of 
time, the radiation of the star must be just equal to the amount of energy 
converted in the interior. It is now believed that this conversion process 
is the liberation of subatomic energy. The critic contends that, since the 
outflowing heat represents the energy liberated by subatomic processes, 
the amount can only be calculated if we know the laws of liberation of 
subatomic energy, and any procedure which evades this difficult problem 
begs the question. 
Now it is quite true that a theory of the rate of liberation of sub 
atomic energy is a conceivable approach to the problem of stellar radiation. 
In the present state of our knowledge such theories are little more than 
guess-work and results are rudimentary. But it is unsound to argue that 
no other procedure is permissible. The amount of water supplied to a 
town is the amount pumped at the waterworks; but it does not follow 
that a calculation based on the head of water and diameter of the mains 
is fallacious because it evades the problems of the pumping station. 
It may seem puzzling to understand how two radically different ways 
of calculating the theoretical radiation from a star can be made to agree. 
Appealing again to the analogy, the two modes of calculating the water 
supplied to a town may not agree; but in that case there will be a flood 
at the pumping station. Similarly in a star a disagreement would involve 
the blowing up or collapse of the star. Accepting it as a fact that the 
stars generally are in a nearly steady state, we must infer that for actual 
stars (but not necessarily for a model star of arbitrarily assigned constitu 
tion) the two modes of calculating the radiation would give the same result; 
and in Chapter xi we shall try to follow up the question how the adjust 
ment has occurred by which the supply of subatomic energy just meets 
the demand. Meanwhile we note that, flood or no flood, the flow of water 
must conform to the pressure gradient and diameter of the pipe; and so 
also the radiation from a star must in any case conform to the temperature 
gradient and opacity in the interior. 
We may thus proceed with our method of determining the expenditure 
of radiation by the star without reference to the supply of subatomic 
energy. How the star manages to accommodate its supply to balance its 
expenditure, and so avoid collapse or expansion, is an independent problem. 
Lane’s Theory. 
5 . The pioneer investigation of the distribution of temperature within 
a star is contained in a paper published in 1870 by J. Homer Lane en 
titled, “On the Theoretical Temperature of the Sun, under the Hypothesis 
of a Gaseous Mass maintaining its Volume by its Internal Heat, and 
depending on the Laws of Gases as known to Terrestrial Experiment*.” 
* American Journ. of Sci. and Arts, Series 2, 4, p. 57.