The sun's mass must actually be diminishing at this portentous rate, which might raise fears of its disappearance. But its present mass is so great (1.98 x grams) that the existing radiation would use up only a millionth part of it in 15 million years, and the consumption of a moderate fraction would give a life long enough to meet the wildest demands of geology.
Process of Transformation.—What the process of transforma tion is by which mass disappears and energy is liberated—pound for pound—can only be conjectured. The spontaneous disintegra tion of heavy complex atoms, as in the case of radio-activity, liber ates a great amount of energy. The formation of heavier atoms out of hydrogen would furnish still more ; for such an atom weighs about o.8 per cent. less than the corresponding number of hydro gen atoms, which contain protons and electrons enough to make it. The difference may best be attributed to liberation of energy in the reaction of formation. The conversion of a mass equal to the sun's from hydrogen to iron, for example, would liberate heat enough to maintain the present solar radiation for 120,000 million years. Finally, it may be that a proton and an electron, under certain rare conditions, may annihilate one another—the electrical charges being neutralized, the mass disappearing, and the energy escaping and being converted into heat in the surrounding gas. If the whole mass of the sun were expendable in this fashion, and should be steadily consumed at the present rate, it would shine for 15,000,000,000,00o (15 X years before it vanished.
The existence of some transformable material, and the main tenance of radiation by loss of mass, are now generally accepted as inevitable deductions from observed facts. Whether the total change of mass during a star's history is a large or small fraction of the whole is less easy to settle. According to the answer which we give our views of the life-history of a star will be different.
Stellar Luminosity.— Though the manner in which heat is gen erated within a star remains obscure, the manner in which it gets out of a star is now clearly understood. Radiation in the interior is very intense. Light is streaming about in all directions, but going only a short distance before it is absorbed by the hot gas and re emitted. On the average, this results in a flow of energy from the
hotter to the cooler parts, at a rate which is greater the more rapid the fall in temperature per mile, and less the greater the opacity of the gas to radiation. Modern physics makes it possible to de termine pretty closely the laws which govern the emission of radiation and its absorption by the gas, and their changes with the temperature, density, and composition of the material. A detailed theory of the luminosity of the stars has thus been developed by Eddington, which gives results in admirable accordance with the observed facts. The conclusions which concern the present prob lem are that the amount of heat which leaks out from the interior of a star and escapes from its surface, depends very little upon a star's diameter but very greatly upon its mass. If a star of given mass contracts, the temperature inside rises and the tem perature gradient becomes steeper. The opacity remains nearly constant, but the area of the surface diminishes. The effects of these changes almost balance one another, so that the total radia tion of the star is changed but little. The amount which escapes per square mile, however, increases steadily, so that, as the star contracts, its surface must become hotter and its light whiter.
Whether the total radiation increases or diminishes as the radius grows smaller depends on the finer points of the theory. Eddington, after a careful investigation, concludes that it in creases slightly; but the possibility that it remains constant, or even diminishes a little, cannot be excluded from consideration.
For a star of the same size, but smaller mass, the temperature gradient is less and the opacity greater, so that much less heat escapes from the surface. These conclusions apply strictly only to stars which are built upon the same law of internal distribution of density, but it is not hard to prove—following Eddington—that for a wide range of laws of internal density, of the type that appear at all plausible, the calculated total radiation will differ but little.