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.
The amount of energy generated by the falling together of the matter of the sun from universal diffusion to the dimensions which the sun has at present, is only about 13,000,000 times the amount now radiated per annum. In Thomson's paper Pouillet's estimate of the energy radiated per second is used, and this number is raised to 20,000,000. Taking the latter estimate, the whole potential energy exhausted by the condensation of the sun's mass to uniform density would suffice for only 20,000,000 years' supply. But the sun is undoubtedly of much greater density in the central parts than near the surface, and so the energy exhausted must be much greater than that stated above. This will raise the number of years provided for. On the other hand, a considerable amount of energy would be dissipated during the process of condensation, and this would reduce the period of radiation estimated. Thomson suggests that 50,000,000, or 100,000,000, years is a possible estimate.
It is not unlikely that the rate of radiation in past time, when the sun had not nearly condensed to its present size, was so much less than it is at present that the period suggested above may have to be considerably augmented. Another source of radiation, which seems to be regarded by some authorities as a probable, if not a certain, one, has been suggested in recent years—the presence of radio-active substances in the sun. So far as we know, Lord Kelvin did not admit that this source of radiation was worthy of consideration; but of course, granted its existence to an extent comparable with the energy derivable from condensation of the sun's mass, the "age of the sun's heat" would have to be very greatly extended. These are matters, however, on which further light may be thrown as research in radio-activity progresses. Lord Kelvin was engaged when seized with his last illness in discussing the changes of energy in a gaseous, or partially gaseous, globe, slowly cooling and shrinking in doing so; and a posthumous paper on the subject will shortly be published which may possibly contain further information on this question of solar physics.
But Thomson put forward a third argument in the paper on Geological Time, which has always been regarded as the most important. It is derived from the fact, established by abundant observations, that the temperature in the earth's crust increases from the surface inwards; and that therefore the earth must be continually losing heat by conduction from within. If the earth be supposed to have been of uniform temperature at some period of past time and in a molten state, and certain assumptions as to the conductive power and melting point of its material be made, the time of cooling until the gradient of temperature at the surface acquired its present value can be calculated. This was done by Thomson in a paper published in the Transactions, R.S.E., in 1862. We propose to give here a short sketch of his argument, which has excited much interest, and been the cause of some controversy.
In order to understand this argument, the reader must bear in mind some fundamental facts of the flow of heat in a solid. Let him imagine a slab of any uniform material, say sandstone or marble, the two parallel faces of which are continually maintained at two different temperatures, uniform over each face. For example, steam may be continually blown against one face, while ice-cold water is made to flow over the other. Heat will flow across the slab from the hotter face to the colder. It will be found that the rate of flow of heat per unit area of face, that is per square centimetre, or per square inch, is proportional to the difference of the temperatures in the slab at the two faces, and inversely proportional to the thickness of the slab. In other words, it is proportional to the fall of temperature from one face to the other taken per unit of the thickness, that is, to the "gradient of temperature" from one face to the other. Moreover, comparing the flow in one substance with the flow in another, we find it different in different substances for the same gradient of temperature. Thus we get finally a flow of heat across unit area of the slab which is equal to the gradient of temperature multiplied by a number which depends on the material: that number is called the "conductivity" of the substance.
Now, borings made in the earth show that the temperature increases inwards, and the same thing is shown by the higher temperatures found in deeper coal mines. By means of thermometers sunk to different depths, the rate of increase of temperature with depth has been determined. Similar observations show that the daily and annual variations of temperature caused by the succession of day and night, and summer and winter, penetrate to only a comparatively small depth below the surface—three or four feet in the former case, sixty or seventy in the latter. Leaving these variations out of account, since the average of their effects over a considerable interval of time must be nothing, we have in the earth a body at every point of the crust of which there is a gradient of increasing temperature inwards. The amount of this may be taken as one degree of Fahrenheit's scale for every 50 feet of descent. This gradient is not uniform, but diminishes at greater depths. Supposing the material of uniform quality as regards heat-conducting power, the mathematical theory of a cooling globe of solid material (or of a straight bar which does not lose heat from its sides) gives on certain suppositions the gradients at different depths. The surface gradient of 1° F. in 50 feet may be taken as holding for 5000 feet or 6000 feet or more.
This gradient of diminution of temperature outwards leads inevitably to the conclusion that heat must be constantly flowing from the interior of the earth towards the surface. This is as certain as that heat flows along a poker, one end of which is in the fire, from the heated end to the other. The heat which arrives at the surface of the earth is radiated to the atmosphere or carried off by convection currents; there is no doubt that it is lost from the earth. Thus the earth must be cooling at a rate which can be calculated on certain assumptions, and it is possible on these assumptions to calculate backwards, and determine the interval of time which must have elapsed since the earth was just beginning to cool from a molten condition, when of course life cannot have existed on its surface, and those geological changes which have effected so much can hardly have began.
Considering a globe of uniform material, and of great radius, which was initially at one temperature, and at a certain instant had its surface suddenly brought to, let us say, the temperature of melting ice, at which the surface was kept ever after, we can find, by Fourier's mathematical theory of the flow of heat, the gradient of temperature at any subsequent time for a point on the surface, or at any specified distance within it. For a point on the surface this gradient is simply proportional to the initial uniform temperature, and inversely proportional to the square root of the product of the "diffusivity" of the material (the ratio of the conductivity to the specific heat) by the interval of time which has elapsed since the cooling was started. Taking a foot as the unit of length, and a year as the unit of time, we find the diffusivity of the surface strata to be 400. If we take the initial temperature as 7000 degrees F.—which is high enough for melting rock—and take the interval of time which has elapsed as 100,000,000 years, we obtain at the surface a gradient approximately equal to that which now exists. A greater interval of time would give a lower gradient, a smaller interval would give a higher gradient than that which exists at present. A lower initial temperature would require a smaller interval of time, a higher initial temperature a longer interval for the present gradient.
With the initial temperature of 7,000 degrees F., an interval of 4,000,000 years would give a surface gradient of 1° F. in 10 ft. Thus, on the assumption made, the surface gradient of temperature has diminished from 1⁄10 to 1⁄50 in about 96,000,000 years. After 10,000 years from the beginning of the cooling the gradient of temperature would be 2° F. per foot. But, as Thomson showed, such a large gradient would not lead to any sensible augmentation of the surface temperature, for "the radiation from earth and atmosphere into space would almost certainly be so rapid" as to prevent this. Hence he inferred that conducted heat, even at that early period, could not sensibly affect the general climate.
Two objections (apart from the assumptions already indicated) will readily occur to any one considering this theory, and these Thomson answered by anticipation. The first is, that no natural action could possibly bring the surface of a uniformly heated globe instantaneously to a temperature 7000° lower, and keep it so ever after. In reply to this Thomson urged "that a large mass of melted rock, exposed freely to our earth and sky, will, after it once becomes crusted over, present in a few hours, or a few days, or at most a few weeks, a surface so cool that it can be walked over with impunity. Hence, after 10,000 years, or indeed, I may say, after a single year, its condition will be sensibly the same as if the actual lowering of temperature experienced by the surface had been produced in an instant, and maintained constant ever after." The other objection was, that the earth was probably never a uniformly heated solid 7000° F. above the present surface temperature as assumed for the purpose of calculation. This Thomson answers by giving reasons for believing that "the earth, although once all melted, or melted all round its surface, did, in all probability, really become a solid at its melting temperature all through, or all through the outer layer which has been melted; and not until the solidification was thus complete, or nearly so, did the surface begin to cool."
Thomson was inclined to believe that a temperature of 7000° F. was probably too high, and results of experiments on the melting of basalt and other rocks led him to prefer a much reduced temperature. This, as has already been pointed out, would give a smaller value for the age of the earth. In a letter on the subject published in Nature (vol. 51, 1895) he states that he "is not led to differ much" from an estimate of 24,000,000 years founded by Mr. Clarence King (American Journal of Science, January 1893) on experiments on the physical properties of rocks at high temperatures.
It is to be observed that the assumptions made above that the physical constants of the material are constant throughout the earth, and at all temperatures, are confessedly far from the truth. Nevertheless Thomson strongly held that the uncertainty of the data can at most extend the earth's age to some value between 20,000,000 and 200,000,000 of years, and that the enormously long periods which were wont to be asked for by geologists and biologists for the changes of the earth's surface and the development of its flora and fauna, cannot possibly be conceded.
In Nature for January 3, 1895, Professor John Perry suggested that very possibly the conductivity of the material composing the interior of the earth was considerably higher than that of the surface strata. If this were so, then, as can be shown without difficulty, the attainment of the present gradient would be very greatly retarded, and therefore the age of the earth correspondingly increased. The question then arose, and was discussed, as to whether the rocks and other materials at high temperatures were more or less conducting than at low temperatures, and experiments on the subject were instituted and carried out. On the whole, the evidence seemed to show that the conductivity of most substances is diminished, not increased, by the rise of temperature, and so far as it went, therefore, the evidence was against Professor Perry's suggestion. On the other hand, he contended that the inside of the earth may be a mass of great rigidity, partly solid and partly fluid, possessing a "quasi-conductivity" which might greatly increase the period of cooling. The subject is a difficult one both from a mathematical and from the physical point of view, and further investigation is necessary, especially of the behaviour of materials under the enormous stresses which they undoubtedly sustain in the interior of the earth.
After the publication of the paper on Geological Time a reply to it was made by Professor Huxley, in an address to the Geological Society of London, delivered on February 19, 1869. He adopted the rôle of an advocate retained for the defence of geology against what seems to have been regarded as an unwarranted attack, made by one who had no right to offer an opinion on a geological question. For, after a long and eloquent "pleading," he concludes his address with the words: "My functions, as your advocate, are at an end. I speak with more than the sincerity of a mere advocate when I express the belief that the case against us has entirely broken down. The cry for reform which has been raised from without is superfluous, inasmuch as we have long been reforming from within with all needful speed; and the critical examination of the grounds upon which the very grave charge of opposition to the principles of Natural Philosophy has been brought against us, rather shows that we have exercised a wise discrimination in declining to meddle with our foundations at the bidding of the first passer-by who fancies our house is not so well built as it might be." To this Thomson rejoined in an address entitled "Of Geological Dynamics," also delivered to the Geological Society of Glasgow on April 5, 1869; and to this, with Professor Huxley's address, the reader must be referred for the objection, brought against Thomson's arguments, and the replies which were immediately forthcoming. This is not the place to discuss the question, but reference may be made to an interesting paper on the subject in the Glasgow Herald for February 22, 1908, by Professor J. W. Gregory, in which the suggestion of Professor Perry, of a nearer approach to uniformity of temperature in the interior of the earth than Thomson had thought possible, is welcomed as possibly extending the interval of time available to a period sufficient for all purposes. In Professor Gregory's opinion, "Lord Kelvin in one respect showed a keener insight than Huxley, who, referring to possible changes in the rate of rotation of the earth, or in the heat given forth from the sun or in the cooling of the earth, declared that geologists are Gallios, 'who care for none of these things.' An ever-increasing school of geologists now cares greatly for these questions, and reveres Lord Kelvin as one of the founders of the geology of the inner earth."
After all, the problem is not one to be dealt with by the geologist or biologist alone, but to be solved, so far as it can be solved at all, by a consideration of all relevant evidence, from whatsoever quarter it may come. It will not do in these days for scientific men to shut themselves up within their special departments and to say, with regard to branches of science which deal with other aspects of nature and other problems of the past, present and future of that same earth on which all dwell and work, that they "care for none of these things." This is an echo of an old spirit, not yet dead, that has done much harm to the progress of science. The division of science into departments is unavoidable, for specialisation is imperative; but it is all the more necessary to remember that the divisions set up are more or less arbitrary, and that there are absolutely no frontiers to be guarded and enforced. Chemistry, physiology, and physics cannot be walled off from one another without loss to all; and geology has suffered immensely through its having been regarded as essentially a branch of natural history, the devotees of which have no concern with considerations of natural philosophy. Lord Kelvin's dignified questions were unanswerable. "Who are the occupants of 'our house,' and who is the 'passer-by'? Is geology not a branch of physical science? Are investigations, experimental and mathematical, of underground temperature not to be regarded as an integral part of geology?... For myself, I am anxious to be regarded by geologists not as a mere passer-by, but as one constantly interested in their grand subject, and anxious in any way, however slight, to assist them in their search for truth."