CHAPTER XII
THE AGE OF THE EARTH
From his student days throughout his life, Lord Kelvin took a keen interest in geological questions. He was always an active member of the Geological Society of Glasgow, and was its president for twenty-one years (1872-1893). The distribution of heat in the substance of the earth was the subject of his inaugural dissertation as Professor of Natural Philosophy; and previously, as a student, he had written an essay on "The Figure of the Earth," for which he had been awarded a University Gold Medal. He never ceased to ponder over the problems of terrestrial physics, and he wrote much on the subject. His papers are to be found as Appendices to Thomson and Tait's Natural Philosophy, and in vol. ii of his Popular Lectures and Addresses, which is devoted to geology and general physics.
His conclusions regarding the age of the earth have been referred to in the last chapter. The first allusion to the subject was contained (see p. [65] above) in his inaugural dissertation "De Caloris distributione in Terræ Corpus"; but he returned to it again in a communication made to the Royal Society of Edinburgh in December, 1865, and entitled "The Doctrine of Uniformity in Geology briefly refuted." On February 27, 1868, he delivered to the Geological Society of Glasgow an address entitled "On Geological Time," in which the necessity for limiting geological and other changes to an almost infinitesimal fraction of the vast periods at that time demanded was insisted on, and which gave rise to much discussion.
The address began with a protest against the old uniformitarian view of geological changes as expressed by Playfair in his Illustrations of the Huttonian Theory. The first objection taken to the idea that "in the continuation of the different species of animals and vegetables that inhabit the earth, we discern neither a beginning nor an end; in the planetary motions where geometry has carried the eye so far, both into the future and the past, we discover no mark either of the commencement or the termination of the present order" is, that the stability of the motions of the heavenly bodies, to which reference is made in this statement, is founded upon what is essentially an approximate calculation, which leaves out, by intention, the consideration of frictional resistance.
He points out, for example, that the friction which accompanies the relative motion of the waters of the earth and the land is attended by the production of heat, and that, by the doctrine of the conservation of energy, heat cannot be produced without a disappearance of an equivalent quantity of energy, either of motion or of position. The chief source of this energy is the earth's rotation. Since the earth turns under the moon and the tidal spheroid—that is, the earth's shape as distorted by the heaping up of the waters in the tides—remains on the whole stationary with respect to the moon, the solid matter of the earth turns under the distribution of the water, held more or less fixed by the moon, as does a fly-wheel under a stationary friction band round its rim. Then just as the band held fixed retards the fly-wheel, so the earth must be retarded in its rotation by this water-brake. In the earth's rotation there is a store of kinetic energy which, roughly estimated, would not be exhausted in less than ten million million years, although drawn upon continuously by friction, or other actions, at the rate of one million horse-power; so that, no immediate catastrophe, such as that we should be involved in by the stoppage or considerable retardation of the spinning motion of the earth, is possible. But it was pointed out by Thomson that the best results of astronomical observation show that the earth would in one hundred years fall behind a perfect time-keeper, with which its rotation kept pace at the beginning of the time, by about twenty seconds. The tendency is to make the earth turn slower, and the moon to increase its distance and move more slowly in its orbit, but with a resultant effect towards coincidence of the period of the earth's rotation with that of revolution of the moon round the earth. After this coincidence has been attained, however, the solar tides will tend to make the moon fall in towards the earth.
If then the earth be rotating more and more slowly, as time goes on, at present, it must have been rotating more rapidly in past time. A thousand million years ago, at the present rate of retardation, the earth must have been rotating one seventh part of its speed faster than it is rotating at present, and this would give for centrifugal force at the surface one thousand million years ago, greater than the centrifugal force at present, in the ratio of 64 to 49. Apparently therefore the earth must have solidified at a much later date than that epoch, a date when it was rotating much more nearly with the angular speed which it has now; otherwise the figure of the earth would have deviated much more from the spherical form than it actually does. On the other hand, one hundred million years ago centrifugal force would be only three per cent. greater than it is at present, and consolidation of the earth at that less remote period would give a shape to the earth not very different from that which it now possesses. The argument therefore from tidal retardation would cut down the time available for geological and biological changes to something not much more than one hundred million years, perhaps to less.
A second argument for limitation of the time available for such processes is derived from the sun's heat. The sun cannot be regarded as a miraculous body producing its light and heat from nothing. Changes of the constitution of the sun must be continually proceeding, to account for its enormous radiation of energy into space, a radiation of which only an infinitesimal part is received by the bodies of the solar system, and a still more minute portion by the earth. The effects of the sun's light and heat on the earth show how enormous must be the quantity of energy lost from the sun in a year. How is this loss of energy to be accounted for? What is the physical change which gives rise to it? In 1854 Thomson put forward the theory that the sun's heat is kept up by the falling in of meteors on the sun's surface, but he afterwards saw reason to abandon that view. Helmholtz had advocated the theory that the sun was a body heated by the coming together of the matter composing it by its mutual attraction, a process which, although the sun is now a continuous mass, is to be regarded as still going on. It is easy to calculate the exhaustion of potential energy caused by the coming together of the matter of the sun from universal dispersion through infinite space to a sphere of uniform density of the present size of the sun. The result is about as much energy as would be generated by burning seven million million million million million tons of coal. The amount radiated in each hour is about as much as would be generated by burning something like nine tons of coal every hour on every square yard of the sun's surface. It is certain that the sun must be still contracting, and if it contracts sufficiently to just make good this expenditure by the further exhaustion of potential energy involved in the closer aggregation of the matter, it must diminish in radius in each year by as much as 130 feet.