SOME fifty years ago, Kelvin announced that the temperature of the earth could not have been anything like its present value for more than some 20 to 30 million years. This estimate was based upon three independent considerations, namely: the temperature gradient inside the earth's crust, the amount of tidal friction, and the total amount of energy radiated by the sun. The first of these arguments has been invalidated completely by the discovery of the radio-active elements. The other two arguments are scarcely affected by this event. The geologists always found some difficulty in compressing the history of the earth, more especially of the sedimentary strata, into the period allowed them by Kelvin. Prof. Harker's presidential address before the Yorkshire Geological Society, seems to show that there is a general impression abroad that Kelvin's estimates have been superseded, and that the discoveries in radioactivity allow one to assume a period of the order of thousands of millions of years since the earthhas reached a constant state as regards climate. I should like to be allowed to state as succinctly as possible what difficulties this view entails. The mean temperature of the earth is about 280 degrees absolute. It, therefore, radiates about 1.7X 1024 ergs per second into space. cal. Assuming the latest value 1.92 for the solar cm.'mn. constant, the earth receives 1.72 X 10” ergs per second from the sun. Therefore, the radiation from the sun just compensates the amount lost by the earth; in other words, the temperature of the earth is determined by the temperature of the sun. The possibility that the earth's temperature might have been maintained by radio-active processes before the sun was incandescent, and that the radio-active substances have died off since then need scarcely be discussed seriously. Forquite apart from the well-known sterilizing effects of the rays, any radioactive substances with asuficiently long life to keep up the temperature of the earth for any considerable length of time would not disappear quickly. Uranium, for instance, only diminishes at the rate of about 1.5 per cent. in 100 million years. One may conclude, therefore, that the time during which the ^^th can have existed in its present state cannot be greater than the time since which the effective temperature of the sun has been about degrees, its present value. This time cannot exceed about thirty million years. For the sun loses energy atthe rate of about 3.8 X 10” ergs, and the total energy to be gained sec. by a mass of 1.97 X lOSs gm., contracting to a radius 6.96 X 10”> cm., is 2.2 X 1048 ergs, assuming approximate homogeneity. (Taking the increase in density toward the center into account does not alter these figures much). Now even if one assumes that the whole of this energy was radiated at a rate of about 3.8 X lOS3—, sec i. e., at the present rate, it will only last 18.3 million years. But any other supposition, namely, that the sun at one time emitted more or less energy per second, leads to a shorter period for the earth in its present state. To explain a greater age it was necessary to find other sources of energy, and since neither the heat of chemical combination nor any possible increase in the specific heat was anything like large enough, the heat of radioactive transforations was invoked. This was, perhaps, excusible in the early days before very much was knownwn about the laws governing these processes, but it seems quite inadmissible to-day. It has been suggested that at the enormous pressure and temperature inside the sun radio-active processes might be modified, and even that ordinary elements might break up. A consideration of the quantitative relations involved shows that this is most unlikely. Though one can scarcely apply ordinary thermodynamics to radio-active processes, one can certainly apply the general rule, which may also be developed from the quantum theory if desired, namely, that a reaction the energy of which is A ergs per molecule is affected chiefly by the collisions of atoms of energy of the order A. Now A is of the order ergs in radio-active processes, and one can, therefore, only expect the temperature to afect those if an appreciable number of atoms have an amount of energy of this order. The average energy of an atom would be 10-s ergs at about 5.1010 degrees. Therefore, even at million degrees only one atom among 10<° would be moving fast enough to influence a reaction which liberates 10-s ergs. Obviously, 500 million degrees is quite beyond the bounds of possibility in part of the sun. One must conclude, therefore, that any process which liberates anything like the requisite energy is unaffected by solar conditions, and takes place at the same rate on the sun as on the earth. Thus, one must fall back upon the ordinary radio-active materials, and as Sir Ernest Rutherford has pointed out, one would only gain a paltry five million years even if the whole sun were composed of uranium. The only way out would seem to be to suppose that the sun was created some 10 s or 1010 years ago out of special radio-active material which produces an enormous amount of energy, ana at it has been breaking up ever since. This material does not exist on the earth though, so the earth would have to be the object of a special creation. Such an assumption, of course, can neither be controverted nor even discussed. But, unless some such hypothesis is introduced, i. e., unless the presumably radio-active solar material which liberates a quantity of energy sufficient to keep up the sun's heat for the desired 10' or 1010 years, is supposed to have been created by some inconceivable force at the epoch at which the sun is supposed to have begun to radiate, this material would have disintegrated long ago. It might be objected that the same holds good of uranium, that the fact that uranium exists in measurable quantities proves that it has not existed for a time great in comparison” to 5.10' years. This is doubtless true, but there is no real difficulty about ass^ing uranium or other radio-active substances to have been produced if one supposes the solar system to have been formed by the collision of two stars. At the moment of collision the velocity of two stars half the mass of the sun would be 1.15 X 10” cm. V sec. ' r being the distance between the centers of gravity. Suppose they both contained some lead, this would reach a temperature of the order 1.1 X 1010 i > r i. e., of the order 2.10' degrees at the moment of coUision. As has been shown above, an appreciable quantity of radio-active material might be formed at such a temper ture if some helium were present. But, of course, the heat used up in forming these substances would cool the rest of the ^.ss: any energy gained in radio-active form would be lost in the form of heat. It could never avail to explain a solar constant such as has been measured for longer than Kelvin's 20 million years. In other words, radio-active substances produced would act only as accumulators of energy, not as primary batteries. To recapitulate: As Kelvin showed, gravitational energy can only account for 18.3 miUion years of sunshine at the present rate. Invoking radio-activity as a source of energy implies the assumptionthat unknown radioactive materials liberating considerably more energy than uranium were created by some unknown agency within a measurable period of time, and that these are now breaking up. Thisassumption is not necessary to account for the existence of uranium, as it is quite conceivable that a certain amount of radio-active matter might be produced afresh during every stellar collision. The energy of substances formed in this way would not be available to explain a greater amountofenergy on the sun as their energy is abstracted from the gravitational ene^^, and has already beentaken into account. A correspondent of Nature, C. E. Stromeyer, sends to that publication the following comment on theabove article. While reading through Dr. F. A. Linde^nn's defense of Lord Kelvin's estimate of the age ofthe earth, I was reminded that in spite of the sympathetic spirit in which he always entered into any discussion, he would never allow the least doubt to be thrown on the correctness of his estimate of the earth's age. Yet it is open to several objections: he assumed that the solidifiedcrust, as it was being formed, would sink toward the center of the earth until it was solid throughout, whereas, there can be no doubt about its core being so heavy that the crust material couldnot possibly sink. He also assumed a diminishing rate of cooling, whereas, the greater pol'- tion of the earth's surface is cov^ed by water, the bottom temperature of which must have been practically constant for millions of years. He also cuts down the temperature in the earth's center from 410^00 deg. Fahr., which it would be, according to his asumption, to deg. Fahr.; whereby, the available heat is reduced enormously. However, if radio-active processes can supply the earth's radiation losses, there is no need to deal with the older question. I notice that Dr. F. A. Lindemann draws the conclusion that the sun's radiation just compensates the amount lost by the earth, but this is not correct. The earth's loss is estimated fromthe known temperature gradient in the earth's crust; it is a net loss over and above any possible interchange of heat with the sun. Then, also, Dr. Lindemann limits the earth's age by the sun's age, but among the several possible sources of its heat supply he does not even mention the heat-producing power of a meteoric bombardment. Yet, as I have shown in my work, “Unity in Nature,” in the chapter on matter (pp. 85-92), it is not at all unlikely in comparatively recent time the sun may have passed through a large cloud of heavy meteoric matter. One effect of a comparatively slight addition of heavy meteoric matter would have been to increase its density from, say, 1.00 to 1.38, and the other effect would have been to raise the sun's surface to such a high temperature that it would have evaporated and formed an atmosphere extending, perhaps, beyond the orbits of the asteroids. In fact, the difference in the densities of the inner and outer planets and the sun, and the fact that practically- all rotations and revolutions are in the same sense, suggest that our solar system once consisted of a sun and the outer planets, all having a very low density, and that in passing through a cloud of heavy meteoric matter, the density ofthe sun was slightly increased, and the inner heavy planets created; but it is impossible here to go into the details of these interesting questions. As regards the nearer evidence of the earth's age to be sought for in the sedimentary rocks, no notice seems to have been taken either of the time required for the innumerable raisings and lowerings of level which certainly occurred during the coal periods or of the time which it must have taken to tilt horizontal strata through 90 degrees and more. Thus, Japan is being tilted at the rate of about 0.5 seconds per century, and if this tilting rate were steadily maintained in one locality, which is highly improbable, the Japanese strata would stand on end like our Cambrian strata in about forty million years' time. Yet, a few such tiltings were completed before some of our oldest strata were formed and over- thrusts suggest a stili greater antiquity for the age of sedimentary rocks.
This article was originally published with the title "The Age of the Earth" in s , , 183 (March 2013)