170 
The Evolution of the Stars [oh. vi 
and Joy, and by Eddington revealed no abrupt break in the correlation 
between mass and luminosity such as might have been expected to occur at a 
transition from the gaseous to the solid state, while, as already mentioned, 
Eddington met with a substantial measure of success in explaining the mass- 
luminosity correlation in terms of a theoretical formula which supposed all 
stars, including dense dwarfs such as Kruger 60, to obey the gas-laws. 
This led Russell to propound an alternative theory of stellar evolution in 
1925*, based on an acceptance of the hypothesis that the source of stellar 
energy was the transformation of matter into radiation. 
Russell believed that all main-sequence stars have approximately the same 
central temperature of about 30,000,000 degrees, and based his theory on this 
supposed fact. He obtained his supposed fact by calculating all his central 
temperatures in terms of Eddington’s special model for which n = 3 (§ 90). 
We have seen that when n is given the proper value required by the mass of 
the star and by Kramers’ opacity law, the values of n generally differ very 
appreciably from 3, with the result that the central temperatures of main- 
sequence stars vary considerably, although still not enormously, inter se. The 
supposed constancy of the central temperatures led Russell to conjecture that 
the transformation of matter into radiation could not occur, at any rate in 
main-sequence stars, until the matter reached a temperature of 30,000,000 
degrees, after which energy could be supplied to a practically unlimited extent. 
If for instance the central temperature of the sun fell at any instant to below 
30,000,000 degrees, the transformation of matter into radiation would instantly 
cease. The sun would continue to radiate energy from its surface, and as this 
energy would not be replaced, the sun would contract, getting hotter throughout 
in so doing. In time the central temperature would again reach 30,000,000 
degrees, after which the generation of energy would restart, and so on. If too 
much energy were generated at any instant, the star would expand until the 
central temperature fell to below the critical 30,000,000 degrees, when the 
cycle would repeat itself. 
One cannot but admire ohe ingenuity of this theory, but our analysis has 
shewn (§ 114) that it comes into fatal conflict with dynamical principles. We 
have seen that oscillations of the type described would increase indefinitely 
in amplitude, so that the star would be violently unstable. 
Apart from this the theory meets very grave difficulties in explaining the 
giant branch. As a matter of calculation the central temperatures on this are 
well below 30,000,000 degrees, and shew no very marked approximation to 
constancy. Russell accordingly found it necessary to postulate that in addition 
to normal matter which begins to be transformed at 30,000,000 degrees, there 
must be innumerable other types of matter which transform themselves into 
radiation at the various temperatures of the centres of the giant stars. The 
Nature, cxvi. (1925), p. 209.