If then, the proportion of expendable matter within a stays small it will remain of nearly the same brightness all through its evolution, until it becomes so dense that calculations based on the simple laws of gases are no longer applicable. But if a consider able portion of its mass is lost by radiation it will be fainter in its old age than in its youth.
Stability.—A new difficulty now arises. If the rate at which heat escapes from a star of given mass is so nearly fixed, whatever its size, what will happen to a star in which the rate of income of heat from sub-atomic sources is out of balance with this fixed outgo? If the income is too small, it is evident that the star will have to draw on its gravitational store and will contract ; if the income exceeds the outgo, the process will be reversed and the star will expand, storing up the excess energy by means of the work done against gravitation.
Whether the energy-account will remain unbalanced after these changes depends on the way in which the rate of income from sub-atomic sources changes as the star contracts, and the pressure and temperature in its interior increase. If these changes increase the rate of generation of energy, then a star of deficient income, as it contracts, will find its income gaining on its expenditure and will approach a state of equilibrium. Should it overshoot this and contract too far the income would exceed the outgo and ex pansion would be forced, tending again to restore the equilibrium.
In this case, and in general, when income of heat gains, rela tive to outgo, as the star contracts, the equilibrium will be stable. The rate at which equilibrium of this sort is approached is slow, being comparable with that of a "Kelvin contraction," so that the adjustment will require tens of thousands of years even for the most rarefied giant stars, and tens of millions for stars like the sun. In the opposite case, when the outgo gains relative to the income, equilibrium, if it existed, would be unstable, the smallest deviation tending to increase indefinitely.
If a star's expenditure of heat increases as it contracts, stability demands that the rate of sub-atomic change shall increase more rapidly; if, on the other hand, the expenditure diminishes, sta bility may be possible with a fixed income, such as radioactivity might furnish.
Overstability.—Too rapid an increase in income, however, leads to other dangers. Any external disturbance affecting a star may set it "pulsating"—alternately expanding and contracting, under the influence of its own gravitation. Eddington has shown that the leakage of heat from one part of the star to another should act like friction to damp out the pulsation. But, if heat is generated most rapidly when the star has contracted to its smallest size, this gives a succession of well-timed impulses, which may overcome the damping effect, and, if great enough, cause the pulsation to increase to a large amplitude. This condi tion, called by Eddington "overstability," will (in the case studied by him) occur if, when the star contracts, the percentage increase of the rate of heat production is more than about twice that of the temperature. There remains, however, a considerable range in which stability of both kinds is assured.
Appeal to Observation.—To find out more about the laws of release of sub-atomic energy we must go to the stars themselves, and in the present state of knowledge our answers must be tenta tive, showing that a certain assumed law may account for the observed phenomena rather than proving that such a process actually happens. The conclusions previously stated appear to be well founded ; those which follow may be greatly changed by future investigation. Our guides must be the observable proper ties of the stars, and, in particular, their luminosities and temper atures. We might add "their masses," if it were not that ob servation fully supports Eddington's conclusion that the stars of a given luminosity all have nearly the same mass.
Colour-Brightness Diagrams.—These relations may best be exhibited by means of "colour-brightness" diagrams, in which the brightness of a star (its absolute magnitude) is plotted as vertical co-ordinate, and its colour (which is intimately related to its surface temperature and its spectral type) as horizontal co ordinate. When such a diagram is made from all reliable observational data, it is found that the points representing the stars are far from being distributed at random.