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 con- densation 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 i. e., the jihotosphere 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 con- tinual 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 ac- companied 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 calcu- late 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 skillful mathematician. According to Newcomb, if the sun maintains its present radiation, it will have shrunk to half its present diameter in about five millions of 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 millions of 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 com- pute how long the solar fire can have been maintained at its presentintensity by the process of condensation. No conclusion of geometry