instance—it ought to produce a very observable effect upon the motions of the planet Mercury—an effect not yet detected.
For this reason astronomers generally, while conceding that a portion, and possibly a considerable fraction, of the solar heat may be accounted for by this 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 center 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 center; but Helmholtz, who first suggested the hypothesis, in 1853, has shown that, under the most unfavorable suppositions, a contraction of about 250 feet a year in the sun's diameter—a mile in 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 9,500 years to reduce the diameter a single second of arc (since 1" 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.
- Leverrier considered that he had detected in the motions of Mercury an irregularity of the kind indicated, but much smaller. It was such as, according to his calculations, would be accounted for by the action of one or several planets, whose aggregate mass should be much less than that of the earth. It was on this basis that he founded his strong belief in the existence of the intra-mercurial planet, Vulcan.