The Age of the Earth

J. Joly.

The words “age of the earth” are somewhat ambiguous. From the geological point of view they are ordinarily taken to mean the age of the ocean: in other words, the age of the earth reckoned from the beginning of those geological changes of the surface which are caused by denudation. However, another meaning may also be put into these words. We may, for example, refer the initial moment to the time when a strongly heated shell cooled to the point of solidification. In that case we shall increase the age of the earth by those long periods of Archean time during which the role of water was only secondary, while the chief importance for the semiliquid masses of the terrestrial globe belonged to volcanic activity. A third interpretation carries the moment of birth into an even more remote and indefinite epoch, during which the differentiation of the earth as an independent planet took place under the action of forces of a nature unknown to us. The greater part of astronomical considerations and conclusions relates precisely to this last interpretation. What I shall speak of here has in view almost exclusively the first interpretation of the words “age of the earth.” By the age of the earth I mean the period of time that elapsed after the surface of the earth became the arena of destructive forces on a world scale and the foundations of organic evolution were laid. The fact of the existence of denudational forces gives us certain methods for estimating the age, which are valid insofar as we may assume that the rate of denudation processes in our time differs only insignificantly from their average rate during geological time.

Such an assumption has the following grounds:

a) Of decisive importance in the processes of denudation is the quantity of rain falling on the land, which is determined in turn by solar heat and the circulation of the atmosphere. From the existence of organic life on the terrestrial globe, beginning from very early times, it follows that the temperature fluctuated only within narrow limits; in other words, in the past there were no prolonged and significant changes in the intensity of solar radiation that could have affected the rate of denudation. Fluctuations within the usual

changes in climate cannot have any appreciable influence on the erosive action of water. The same may be said of variations in the circulation of the atmosphere, since the latter depends chiefly on the rotation of the earth and on the distribution of solar heat.

b) Since a considerable part of the land surface is in fact deprived of rain, a change in the extent of the surface of the continents cannot strongly affect the dimensions of denudation; the only consequence of these changes is some shifting of the belt subject to erosion. Moreover, from paleogeographical data and from the distribution of sedimentary deposits it follows that the present area of land does not differ very much from the average area in former times.

c) Since the secondary factors that influence the rate of the erosive action of water and of weathering are very numerous and diverse in their nature, it is unlikely that, over a sufficiently long period, there has ever been observed a combination of such changes in these factors as would all have acted in one direction and could have caused a considerable deviation from the average.

Lack of space does not permit me to enter into a more detailed consideration of these assertions. I shall touch only briefly on those methods by means of which, proceeding from the statistics of the destructive action of water and air, one can determine the age of the ocean.

1) The key to this question is the chemical composition of the ocean and of rocks. On the basis of a comparative study of primary or igneous rocks and secondary or sedimentary rocks, we find that, say, \(n\) grams of sodium enter the ocean for every ton of igneous rocks transformed into sedimentary ones, while in the ocean we find \(N\) grams of sodium. The total quantity of washed-away volcanic rocks over all geological times, expressed in tons, is therefore equal to \(\frac{N}{n}\). Our investigation also gives us the average magnitude of the total loss accompanying the transition from primary rocks to sedimentary rocks, so that we can also learn the total mass of sedimentary rocks in tons. Turning now to the most important rivers of the whole world and using estimates of the quantity of sedimentary-rock material carried by them from the land into the ocean, we can calculate the number of years required for the enormous mass of sedimentary rocks formed in former times to have been deposited on the ocean floor. Making the known allowances, we thus arrive at the figure of 100 million years.

2) From the total quantity of sodium in the ocean one can also calculate the age of the earth in another, more direct way. We know that the greater part of this sodium was brought into the ocean during geological time by rivers. Turning to analyses of river water, we can estimate the total annual supply of this element to the ocean. Dividing the first

number by the latter, and making certain assumptions, we again arrive at the figure of 100 million years.

3) The third, more difficult method does not depend on our knowledge of the chemistry of denudation. We estimate the maximum thickness of all sedimentary deposits and, knowing the weight of the solid matter that is carried annually by rivers, determine the thickness of the annually formed layer of sedimentary rocks; dividing the first number by the latter, we again arrive at the figure of 100 million years.

Of these methods, the most direct is the one that operates only with figures relating to sodium. The reason why precisely this element was chosen as the criterion lies, of course, in the great solubility of its compounds, thanks to which it, unlike all the other dissolved constituent parts of the ocean, was protected from chemical precipitation and absorption by living organisms. This method was analyzed by many critics, especially by Sollas, who subjected it to detailed consideration in his presidential address to the Geological Society in 1909. He finds that, under certain assumptions, one may arrive at a period of 175 million years and that this is, to a close approximation, the possible maximum. My own discussion of this method has convinced me that it is possible, with its aid, to arrive at the figure of 150 million years, but that the figure of 200 million years is incompatible with our present knowledge of the factors taking part in these processes. All this applies, as I have already said, only to the duration of sedimentary processes and cannot be compared with dates that go back into the depths of Archean times.

However, even in Archean times there were some insignificant deposits of sedimentary rocks. We cannot take account of their influence either on the magnitude of our numerator or on the magnitude of our denominator; we can only, apparently, consider it insignificant. “The Archean epoch was a time of worldwide volcanism and, in respect of the ratio of the quantities of erupted and sedimentary rocks, represents a deviation from the uniformity of conditions of later geological times,” so say Van Hise and Leith in their monograph.

Before turning to the results based on radioactive methods, I must discuss in greater detail one objection to accepting the present rate of denudation as a basis for measuring time. Namely, the assertion has been made that we live in a period of abnormal uplift of the continents, which entails an excessive increase in the erosive action of water. With some attention to the nature and conditions of this erosive action, it would be easy to refute this objection, but it is enough to refer to the following data. The average elevation of the continent of North America is 700 meters; it is being eroded at a rate of 79 tons per

per square mile per year; for South America the corresponding figures are 650 meters and 50 tons. Europe, however, has a much lower mean elevation—only 300 meters. The corresponding rate of denudation, nevertheless, is 100 tons per square mile per year. Thus experience shows that the rate of the destructive action of water is the smaller, the higher the land is situated, as theory also requires; so that, if the objection under consideration had any basis, we should have had to conclude that the figures cited above are too high.

So far as I know, before the appearance of methods for determining the age of the earth based on the radioactive transformations of the elements, no serious objections were raised against the results obtained by the geological method. Some investigators even considered the numbers found to be too high. Thus, for example, Becker came to lower figures by taking into account the increasing exhaustion of the constituent parts of the surface over geological times. The correctness of this correction, however, remains in doubt. Others thought that organic changes, recorded by rocks, required a longer period of time. It seems to me that Sollas gave a clear answer to these objections in his Age of the Earth. In any case, Lyell, Geikie, and Poulton during past years defended the doctrine of the uniformity of geological conditions. However, with the appearance of the new radioactive method, based on the study of the uranium family, it seemed necessary to accept a much higher value for the age of the earth and to draw the unexpected conclusion that the intensity of the destructive action of water at the present time is not less than four, and may be eight (or even more) times greater than the average intensity in former times.

The first considerations concerning the possibility of using the accumulated products of radioactive transformations were expressed by Rutherford. He, and later Strutt (now Lord Rayleigh), made an estimate of geological time on the basis of the amount of helium formed. Strutt gave a geological chronology, the first of its kind, considering, however, that he was dealing only with lower limits. Boltwood used the final product of uranium transformation—lead—and for Archean (?) materials arrived at so high a figure as 1640 million years. As I have already said above, the geological method cannot be applied to these remote times. In any case, however, such results as \(430 \times 10^6\) years for Silurian or Ordovician deposits and \(1200 \times 10^6\) years for post-Atulian ones are wholly inconsistent with the data of the geological method. In any case, the following has now been established: a series of figures obtained from carefully selected material shows that the ratio of the lead content to the uranium content

increases on passing to deeper layers and decreases on passing to less deep layers, while preserving a sufficient degree of agreement even for very remote localities.

One can be satisfied with such a result, however, only by ignoring the following extremely interesting and thought-provoking fact: if the lead content in carefully selected thorium minerals is taken as the basis of the calculations, then numbers are obtained which are in sufficient agreement with the results obtained by the geological method. Such agreement between the results of methods that are completely different in their nature is a serious confirmation of their correctness.

It had long been known that thorium minerals, such as, for example, thorite, constantly lead to lower age values than uranium minerals; following the example of some investigators, however, it became customary to regard these values as unreliable. We now know that such a point of view is in no way justified; on the contrary, those who reject the indications of thorium-lead and the denudation statistics are under the obligation to explain the reasons for their remarkable agreement.

The determination of the atomic weight of the thorium isotope of lead, carried out by Soddy in 1917, provided material for estimating the age of rocks on a very broad scale; its value was especially high by the very nature of such an investigation. Soddy worked with Ceylon thorite from rocks directly overlying the charnockite series. The latter must be regarded as extremely ancient, Lewisian or Lower Archean. Reading in Nature Prof. Soddy’s report on his determination of the atomic weight of lead obtained from these rocks, I came to the conclusion that, judging by the quantity of lead extracted from the thorite, 130 million years had elapsed since the time when this mineral arose; having communicated this conclusion to Professor Soddy, I became convinced that he had arrived at approximately the same result.

At that time, however, it was still possible to suppose that thorium-lead was not entirely stable. It was considered especially possible that its final product is thallium. These doubts, however, were resolved by the following experimental data: Cotter, working with thorianite in my laboratory, did not succeed in detecting even spectroscopic traces of this element; in the thorite with which Prof. Soddy worked, too small a quantity of thallium was found. Later, in a letter to Nature, Prof. Soddy indicated that an investigation carried out at the Radiological Institute in Vienna confirmed the stability of both isotopes of lead obtained from thorium. I shall now give additional evidence that the transformations of the thorium family end in lead.

Holmes, in a letter to Nature devoted to the defense of the hypothesis of the instability of thorium-lead, gives data for a selected specimen of uraninite, according to which the age of the rocks containing

Coddi thorite, judging from the uranium–lead ratio, is equal to 512 million years. Previous determinations of the uranium–lead ratio gave much higher numbers, but even in this case the results are contradictory: the uranium number is four times greater than the thorium one. According to the uranium time scale the thorite should be older than the Silurian rocks, for which uranium–lead indicates an age of 430 million years; it probably belongs to the Cambrian or even to pre-Cambrian time. On the basis of the considerations set forth above, we must regard the figure of 130 million years for early Paleozoic times as compatible with the maximum indicated by the geological method. A later determination of the quantity of lead in a Norwegian thorite from Langezundfjord, also belonging to the beginning of the Paleozoic era, apparently leads to the figure of 150 million years. In this case too, confidence is increased by the presence of a determination of the atomic weight. We have no right to discredit these results by assuming the instability of lead. Why, indeed, should we reject them in favor of numbers obtained with uranium–lead, which are in hopeless contradiction with all the data on processes taking place on the surface of the globe? I believe that it will not be too bold to consider the whole situation at the present time changed, and to call into question the significance of the particular uranium–lead quotient. And indeed, as we shall see, there are many obscure points in the question of the initial transformations in the uranium series; the discovery of isotopes, moreover, points us to possibilities that were not even thought of in the first days of the study of radioactivity.

I shall now turn to the conclusions to which the study of pleochroic halos leads us.

Halos allow us to investigate certain facts concerning the decay of radioactive elements in the remote past. The dimensions of halos, however small they may be, can be determined with considerable accuracy; and these dimensions are determined by the combined action of several groups of $\alpha$-rays emitted by the transforming elements. Bragg and Kleeman observed and measured entirely analogous total ionization effects in air. The scale of the ionization curves in a mineral, thanks to its high stopping power, is 2000 times smaller than in air. Nevertheless, they are hieroglyphs on which one can rely, and they make accessible to our knowledge an almost infinitely remote epoch.

A definite $\alpha$-ray gives a well-known ionization curve, measured by Geiger. The magnitude of the range of the $\alpha$-ray does not affect the general character of the curve. If we imagine that uranium or thorium, as parent elements, are enclosed in a microscopic crystal, say of zircon, then to each of the $\alpha$-rays acting on the surrounding substance—let it be mica—there corresp...

corresponds to a concentric spherical layer, corresponding to the radial distance at which the ionizing action of the various $\alpha$-rays has its maximum value. These layers more or less overlap one another. As a result, on mica plates split along cleavage planes, we see colored concentric rings reflecting the ionizing action of the rays.

In order to establish the theoretical distribution of these rings, we must add up all the ionization effects observed in air; in other words, to each ray one must assign a Geiger curve, taking into account the magnitude of its range, and sum all the ordinates.

Let us first consider the case of a thorium halo. Figure 1 shows the curve obtained by the method just described. Its ordinates are proportional to the total ionization produced by the elements of the thorium series that emit $\alpha$-rays. In the upper part of the figure I have marked, after recalculating them for air, the positions of the colored rings that surround in biotite a small particle of a mineral containing thorium and all the subsequent products of its transformations. In doing so, of course, we produce a very great magnification of the dimensions of the halo—more than 2000 times. As you see, the halo corresponds very well to the outlines of the air curve. It may perhaps be of some interest to mention that the discovery of the third ring led to the detection of the prominence on the curve which corresponds to it (this part of the curve had originally been drawn from an insufficient number of ordinates). The close agreement observed is extremely curious.

Fig. 1.

The character of the air curve depends on the value of the range of the $\alpha$-rays that we measure at the present time in our laboratory. The measurements of the halos, however, relate to radioactive effects that began to leave their trace in the mica in Carboniferous times—perhaps even considerably earlier. The halos reveal no signs of changes in the magnitude of the corresponding ranges. As is known, the rate of decay (or the transformation constant of radioactive elements) is closely connected with the range. Thus, in the case of the thorium series, in these ancient microscopic records we can find a guarantee that the accumulation of the final product—the thorium isotope of lead—took place in remote times at exactly the rate that we have derived from the results of the brilliant investigations of our own time. This certainty we owe

given by thorium halos. They also show us the improbability of instability of the lead being formed, since if the latter took place, we would have had to establish the presence of yet another kind of ray, in addition to those which we used in deriving the ionization curve. It is true that the corresponding rays might, owing to the coincidence of the ranges, be hidden in one of the halo rings, but the structure of the halo fits so exactly each bend of the curve that such a case appears extremely improbable. One may also observe the successive stages in the development of thorium halos. The first to appear are the rings corresponding to the two most conspicuous crests of the curve in Fig. 1. If the central nucleus is too small or weak, nothing more appears.

Fig. 2.

Let us now pass to the uranium curve. Arranging all eight separate ionization curves according to the magnitude of the range of each ray and adding the ordinates, we obtain the curve shown in Fig. 2. Above it are arranged the rings observed in uranium halos.

In considering these rings, we notice that the outer outlines of the halos are apparently in good agreement with the present-day values of the ranges. The inner ring, however, has a larger radius than could have been expected from the curve. This observation was subjected to a very careful check. In Devonian mica from County Carlow these halos can be found in all stages of development, depending on the size and activity of the nuclei. The uranium halo first appears as a dark single ring surrounding a microscopic central nucleus. It can be measured from the stage of its development that borders on invisibility to that in which its central part has already darkened and the first cloudy signs appear of the outermost ring itself, formed exclusively under the action of radium C rays. A series of measurements carried out recently by various investigators on these embryonic halos has confirmed the value of the mean radius of the first ring given in the paper communicated to the Royal Society in 1916. The discrepancy with the theoretical curve is small; it amounts to from 10 to 12% of the value of the outer radius. Some inaccuracy is unavoidable owing to the difficulty both of measuring the size of the nucleus and of

introducing the corresponding correction. The discrepancy between the theoretical curve and the dimensions of the halo evidently has great significance. I have already pointed out that the range of the α-rays emitted by the disintegrating element is connected with the rate of its decay. The range is the greater, the smaller the mean lifetime of the element. And so we see that the first ring of the uranium halo in mica indicates a range greater than we could have expected from modern observations of the air curve. The agreement that exists in other cases shows that there is here no unknown effect that would influence the retardation of α-rays by mica. The position of the first uranium ring is determined chiefly by α-rays of small range, which are emitted in the initial transformations of the uranium series. We may conclude from this that, at least, one group of these rays must formerly have had a larger range and that, consequently, the corresponding period of decay must have been shorter. Of especially great significance in the formation of the halo are the slowest α-rays, which are emitted in the decay of uranium I. It is possible that the observed discrepancy arises precisely because these rays had a greater range in early geological times. In any case, the existence of such a discrepancy obviously suggests to us that the rate of transformation of uranium into lead was once considerably greater than in our day.

I can now touch upon some measurements made recently on halos belonging to comparatively recent and to very remote geological times. In doing so I must make the reservation that these results, owing to the difficulty of the measurements and by their very nature, require very careful confirmation. The initial problem may be formulated in a few words as follows: is there a dependence between the magnitude of the deviation of the dimensions of uranium halos from theory and the antiquity of the rocks in which the halo was formed?

I tried to find uranium halos in rocks that would be younger than the Leinster granite, which belongs to the beginning of the Devonian period. However, in the Mourne granite, which belongs to the Eocene or to the beginning of the Tertiary era, for a long time it was not possible to find halos suitable for measurements. Only recently was I fortunate enough to find several such early ring-shaped halos, which I was able to measure. Further searches revealed some additional number of them; but in general they occur very rarely and are not easy to find. The nuclei of these halos usually consist not of zircon, but apparently of apatite or allanite; their mean dimensions are larger than in the case of zircon nuclei in mica from Carlow. Taking into account the composition and dimensions of the nuclei in the Mourne granite, it would be necessary in this case to introduce into the observed radius of the halo a large negative correction,

than in the case of halos in mica from Carlow. In reality, however, between the outer radii of the Eocene and Devonian halos there is apparently observed a small discrepancy in the opposite direction. According to a large number of measurements made by several investigators, some of whom were not acquainted with the nature of the matter, the outer radius of the ring in Eocene halos is equal to 0.0135 mm (without correction for the radius of the nucleus). The same persons, in the case of Devonian halos, likewise without correction for the nucleus, found 0.0146 mm. The correction for the nucleus, which is difficult to make, as I have already said, would have increased the discrepancy still more. There is no reason to suppose that more than 1% of this discrepancy can be attributed to the chemical composition or density of the mica that was examined in both cases.

Quite recently I found these primary ring-shaped halos in micas from Arendal and Ytterby, which probably belong to the Archean era and in any case are of very ancient origin. The radius of these halos is equal to, or slightly less than, 0.0160 mm. In this case too the composition of the mica apparently plays no role. Thus, according to these measurements, it appears that the radius of the ring in the Eocene halo must be increased by approximately 7% in order to be comparable with the dimensions of the Devonian halo, while the radial dimensions of the latter are approximately 10% smaller than the dimensions of the Archean halo. An entire geological chronology can be established from the dimensions of these rings.

If the above results are confirmed, they would constitute very strong proof that some factor, changing over the course of geological time, has had an influence on the values of the ranges and periods of certain elements that took part in the formation of uranium halos. One must not, however, attach too much weight to these measurements before they have been confirmed by data relating also to other micas. While awaiting further investigations, I return to the fact that the uranium halos of the Devonian period do not correspond to the ionization curve of the uranium series constructed from modern investigations. Between them there is a considerable discrepancy in the region of rays with short ranges, especially in the region of those primary rays which have special importance for determining the rate of accumulation of uranium-lead.

Apparently we have no grounds for denying the possibility of a decrease in the rate of decay of uranium over geological time. Laboratory experiments similar to those that can be carried out in the case of elements with a short lifetime are unlikely to help us understand this question. In any case, if the explanation given is correct, we must suppose that in the case of thorium the corresponding effects should have been expressed much more weakly. It seems most probable in general to allow for the influence of one or several isotopes of uranium, which at the beginning...

at the present time, may perhaps have almost disappeared. Some outstanding investigators have already tried to invoke hypothetical isotopes of uranium in order to resolve the difficulties connected with the data on ionization in the uranium series. Boltwood considers it possible that what we call uranium consists of three radioactive elements emitting $\alpha$-rays: one parent element and two of its isotopic transformation products (Phil. Mag., July 1920). In 1917 Rikard put forward the supposition that the parent of actinium is a third isotope of uranium, not belonging to the uranium series, with an atomic weight equal to 240. Rikard’s supposition was favorably received by Soddy and Cranston. It removes the difficulties connected with the atomic weight of uranium and agrees well with the atomic weight of radium and of uranium-lead.

To explain the anomalies of the Devonian haloes, one may invoke a hypothesis to some extent similar to Rikard’s hypothesis. The point of departure should be the following facts: the age indicated by uranium for early Paleozoic rocks is approximately more than four times too great in comparison with the age indicated by thorium. We therefore assume that three quarters of the lead found in uranium minerals was formed from some isotope. Since the primary $\alpha$-radiation of this isotope could not have been detected at the present time, it must be assumed that it has almost completely disintegrated. We thus know that a certain mass of this isotope was transformed into lead in a definite interval of time—$130 \times 10^6$ years. Assuming that at the present time only $1\%$ of this isotope remains, we obtain its decay constant $(3.5 \times 10^{-8})$ and, with the aid of the Geiger and Nuttall relation, find the corresponding value of the range (2.6 cm at $0^\circ$ or 2.75 cm at $15^\circ$). At the present time the $\alpha$-radiation of this hypothetical body should amount to only one thousandth of the $\alpha$-radiation of uranium I, but over the whole time since the Devonian period, for every $\alpha$-particle emitted by the longer-lived isotope, there are approximately three emitted by the less long-lived one. The total ionization curve, modified according to this hypothesis, would be in agreement with the results of observations on Devonian haloes. We must also assume that the ranges of the rays emitted by the subsequent decay products of the imagined isotope were such that the outer parts of the haloes remained essentially unchanged. There is nothing improbable in such an assumption.

The following facts stand out especially clearly in the study of radioactive haloes: first, the agreement existing between our modern measurements and the outlines of Paleozoic thorium haloes shows that the periods of the elements that took part in their formation have not changed over the course of 130 million years. On this basis, taking also into account the stability of thorium-lead,

we must regard the calculations of geological time constructed on thorium–lead as highly reliable. These calculations are confirmed by concordant indications that we owe to the processes of denudation that have occurred on the surface of the earth. Secondly, the outlines of uranium courtyards contradict the period that we presently assign to uranium; this discrepancy is emphasized still further by the impossibility of reconciling uranium time with the concordant indications of thorium time and of the time calculated from denudation.

The whole question cannot yet be considered definitively exhausted, but in general I think that 150 or 200 million years appears to be the most probable value for the age of the earth, reckoning from the time of the establishment of modern geological conditions on the terrestrial globe.

Astronomical investigations into the question of the age of the earth operate primarily with the far greater age that must be assigned to the earth as a planet. For this age extraordinarily high values have been indicated. The latter can, however, be reconciled with the comparatively small values of geological time. For this purpose, so far as I can judge, it is enough for us to make use only of the necessary conclusions from our information about the radioactivity of terrestrial materials. I should like to go further, remaining, as it seems to me, quite consistent, and to attribute to radioactive energy a far greater influence on planetary and stellar evolution than has been done up to now.

The only planet that we can investigate in detail is, of course, our earth. And what do we find? In the materials of which its surface is built there are enough radioactive elements to explain, as Lord Rayleigh first showed, the mean observed temperature gradient, assuming that surface conditions are preserved down to a certain depth, equal to approximately 19 kilometers. For many reasons, however, it is extremely improbable that there should exist such a precisely defined radioactive layer. It is also improbable that the inner parts of the earth should contain no radioactive substances. We find both thorium and uranium in meteorites with a high percentage of iron and nickel; it is true that these elements have not hitherto been discovered in meteoritic iron, but we know from the mean density of the earth that its central part cannot consist of pure iron. Probably a considerable quantity (about 40%) of siliceous materials is admixed with it, and whenever the latter are found in meteorites, we also find radioactive elements in them. What forces, finally, could one conceive that might separate all the uranium and thorium and transfer them to the surface?

The view according to which the radioactive elements are contained in the middle of the earth often encounters the formal objection-

...the possibility of an increase in the internal temperature of the earth. On what data is such a denial based? If the temperature of the central core of the earth, with a radius, say, of 2000 kilometers, were to rise by 1000°C over the course of a geological period (and for this, taking low values for internal radioactivity, 150 million years would be required), could we detect it? Would the length of the day be noticeably increased? Would there be any effect at all, if the outer parts were at the same time cooling as a result of the loss of primordial heat? We must further take into account that suitable observations exist only for a short period of historical time. In general, as far as I can judge, this denial is based on absolutely nothing.

Let us now assume that the internal temperature of the earth is in fact increasing. Does a threatening end then await our geological epoch? Kelvin showed how complete the thermal insulation of the middle of the earth is, and there is no doubt that the internal heat is not at present being lost. The rise of temperature within must continue until the modern epoch falls victim to the accumulated energy. It must be followed by a period of volcanism, which will destroy life on earth and reverse the chemical changes accumulated over many years by the processes of denudation and organic activity. The whole sequence of events—rapid cooling as a result of radiation, the return of the oceans and, possibly, the rebirth of life with its evolutionary history—would be repeated again. From this point of view the age of the earth, whose determination has occupied us, is perhaps only one of many and must inevitably have its upper limit. But then a rebirth must come, and it is possible that the day will arrive when the epoch of this rebirth will occupy the thoughts of other minds, different from our own. It should not be forgotten that after some ten billion years there will still exist 50% of the heat-producing elements, and that the decrease in their quantity will cause only an increase in the duration of the recurring geological epochs. It is possible that other planets of our system are at various stages of such cyclical changes.

Translated by A. N. Frumkin.