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Stedman and Hutchinson, comps. A Library of American Literature:
An Anthology in Eleven Volumes. 1891.
Vols. IX–XI: Literature of the Republic, Part IV., 1861–1889

Source and Duration of the Solar Heat

By Charles Augustus Young (1834–1908)

ASTRONOMERS generally, while conceding that a portion, and possibly a considerable fraction, of the solar heat may be accounted for by the meteoric hypothesis, are disposed to look further for their explanation of the principal revenue of solar energy. They find it in the probable slow contraction of the sun’s diameter, and the gradual liquefaction and solidification of the gaseous mass. The same total amount of heat is produced when a body moves against a resistance which brings it to rest gradually as if it had fallen through the same distance freely and been suddenly stopped. If, then, the sun does contract, heat is necessarily produced by the process, and that in enormous quantity, since the attracting force at the solar surface is more than twenty-seven times as great as gravity at the surface of the earth, and the contracting mass is so immense.

In this process of contraction, each particle at the surface moves inward by an amount equal to the whole diminution of the solar radius, while a particle below the surface moves less, and under a diminished gravitating force; but every particle in the whole mass of the sun, excepting only that at the exact centre of the globe, contributes something to the evolution of heat. To calculate the precise amount of heat developed, it would be necessary to know the law of increase of the sun’s density from the surface to the centre; but Helmholtz, who first suggested the hypothesis, in 1853, has shown that, under the most unfavorable suppositions, a contraction in the sun’s diameter of about two hundred and fifty feet a year—a mile in a trifle over twenty-one years—would account for its whole annual heat-emission. This contraction is so slow that it would be quite imperceptible to observation. It would require nine thousand five hundred years to reduce the diameter a single second of arc (since 1 second equals 450 miles at the sun’s distance), and nothing less would be certainly detectable.

Of course, if the contraction is more rapid than this, the mean temperature of the sun must be actually rising, notwithstanding the amount of heat it is losing. Observation alone can determine whether this is so or not.

If the sun were wholly gaseous, we could assert positively that it must be growing hotter; for it is a most curious (and at first sight paradoxical) fact, first pointed out by Lane in 1870, that the temperature of a gaseous body continually rises as it contracts from loss of heat. By losing heat it contracts, but the heat generated by the contraction is more than sufficient to keep the temperature from falling. A gaseous mass losing heat by radiation must, therefore, at the same time grow both smaller and hotter, until the density becomes so great that the ordinary laws of gaseous expansion reach their limit, and condensation into the liquid form begins. The sun seems to have arrived at this point, if indeed it were ever wholly gaseous, which is questionable. At any rate, so far as we can now make out, the exterior portion—the photosphere—appears to be a shell of cloudy matter, precipitated from the vapors which make up the principal mass, and the progressive contraction, if it is indeed a fact, must result in a continual thickening of this shell and the increase of the cloud-like portion of the solar mass.

This change from the gaseous to the liquid form must also be accompanied by the liberation of an enormous quantity of heat, sufficient to materially diminish the amount of contraction needed to maintain the solar radiation.

Of course, if this theory of the source of the solar heat is correct, it follows that in time it must come to an end; and looking backward we see that there must also have been a beginning. Time was when there was no such solar heat as now, and the time must come when it will cease.

We do not know enough about the amount of solid and liquid matter at present in the sun, or of the nature of this matter, to calculate the future duration of the sun with great exactness, though an approximate estimate can be made. The problem is a little complicated, even on the simplest hypothesis of purely gaseous contraction, because as the sun shrinks the force of gravity increases, and the amount of contraction necessary to generate a given amount of heat becomes less and less; but this difficulty is easily met by a skilful mathematician. According to Newcomb, if the sun maintains its present radiation it will have shrunk to half its present diameter in about five million years at the longest. As it must, when reduced to this size, be eight times as dense as now, it can hardly then continue to be mainly gaseous, and its temperature must have begun to fall. Newcomb’s conclusion, therefore, is that it is hardly likely that the sun can continue to give sufficient heat to support life on the earth (such life as we now are acquainted with, at least) for ten million years from the present time.

It is possible to compute the past of the solar history upon this hypothesis somewhat more definitely than the future. The present rate of contraction being known, and the law of variation, it becomes a purely mathematical problem to compute the dimensions of the sun at any date in the past, supposing its heat-radiation to have remained unchanged. Indeed, it is not even necessary to know anything more than the present amount of radiation, and the mass of the sun, to compute how long the solar fire can have been maintained, at its present intensity, by the process of condensation. No conclusion of geometry is more certain than that the contraction of the sun from a diameter even many times larger than that of Neptune’s orbit to its present dimensions, if such a contraction has actually taken place, has furnished about eighteen million times as much heat as the sun now supplies in a year; and therefore that the sun cannot have been emitting heat at the present rate for more than that length of time, if its heat has really been generated in this manner. If it could be shown that the sun has been shining as now, for a longer time than that, the theory would be refuted; but if the hypothesis be true, as it probably is in the main, we are inexorably shut up to the conclusion that the total life of the solar system, from its birth to its death, is included in some such space of time as thirty million years. No reasonable allowances for the fall of meteoric matter, based on what we are now able to observe, or for the development of heat by liquefaction, solidification, and chemical combination of dissociated vapors, could raise it to sixty million.

At the same time, it is of course impossible to assert that there has been no catastrophe in the past—no collision with some wandering star, endued, as Croll has supposed, like some of those we know of now in the heavens, with a velocity far surpassing that to be acquired by a fall even from infinity, producing a shock which might in a few hours, or moments even, restore the wasted energy of ages. Neither is it wholly safe to assume that there may not be ways, of which we yet have no conception, by which the energy apparently lost in space may be returned, and burned-out suns and run-down systems restored; or, if not restored themselves, be made the germs and material of new ones to replace the old.

But the whole course and tendency of Nature, so far as science now makes out, points backward to a beginning and forward to an end. The present order of things seems to be bounded, both in the past and in the future, by terminal catastrophes, which are veiled in clouds as yet impenetrable.