The Universe in the Light of New Research1.

W. Nernst.

Introduction. Statement of the problem. — The universe in the light of new research. — Addenda. — The temperature of world space. — The reversibility of radioactive processes. — The energy of gravitation and heat. — The lifetime of fixed stars. — Uranium as an explosive substance. — The radiant energy of the sun. — The chemical composition of meteorites. — The zero energy of the luminiferous ether. — The so-called Hess radiation. — The formation of planets and double stars. —

Introduction. Statement of the problem.

In 1886, when I was a student in Graz, Professor Boltzmann delivered at the Vienna Academy of Sciences his inaugural address on the second law of heat. (Boltzmann, Populäre Schriften, p. 25, Leipzig, 1905.) He remarked, among other things, that all attempts to save the universe from heat death had not been crowned with success, and that he did not intend to make any such attempt himself.

These words, which I read in my student years, made an enormous impression on me, and since then I have constantly watched to see whether any way out might appear. For there can hardly be any serious doubt that the indicated consequence of the second law is, in the highest degree, improbable. Moreover, every natural-scientific theory of the Cosmos must proceed, contrary to the above-mentioned conclusion of thermodynamics, from the assumption that the universe is in a stationary state, that, on the average, as many stars go out in the world as are kindled anew1.

At the present time it may be considered beyond doubt that the dissipation of the capacity for work of the energy of the universe occurs practically almost exclusively owing to radiation, as a result of which, as is known, energy passes from more heated matter into the ethereal sea; the hypothesis that is to cover the loss of capacity for work which the second law of heat postulates for irreversible processes therefore cannot dispense with calling upon the energy of the world ether (or, if one likes, of “empty space”).

In the speech “Toward a New Development of Thermodynamics”2, delivered by me at the congress of natural scientists in Münster in 1912, I did, in passing, develop such a hypothesis in the following terms:

“The discovery of the radioactive decay of elements has acquainted us with sources of energy of such power that previously we had no conception of them. Let us suppose—and any other assumption would obviously be quite arbitrary—that all elements are capable of radioactive decay, but that only the greater part of the elements disintegrates into simple constituent parts too slowly for this decay to be traceable; in that case we come to the conclusion that within the atoms of all elements there are accumulated stores of energy in comparison with which the stores of heat, i.e. the kinetic energy of atoms and the potential energy connected with it, as well as every chemical energy, appear vanishingly small.

However, in radioactive processes the thermodynamicist will also note another, extremely important point, namely the phenomenon of irreversibility. Whereas any, however complex—for example chemical—process that proceeds in one direction can, without doubt, be made to go in the opposite direction by corresponding changes in the conditions of the experiment, in radioactive transformations, on the contrary, there is not the slightest indication that experimental conditions are possible which would allow uranium, or another radioactive element, to be formed from its decay products. We are not even in a position to alter—

the rate of radioactive decay by any external influences, for example, by temperature or by any other factors. This circumstance means that the second law of thermodynamics, which is applicable only to reversible processes, is powerless before the phenomena of radioactivity, at least insofar as the quantitative treatment of these processes is concerned.

However, it is possible that the phenomena of radioactivity can in another respect be brought into connection with the consequences of the second law. As is known, the second law, when applied to the world as a whole, leads to a fatal conclusion, and all attempts to save the universe from this consequence have hitherto ended in failure. The point is that any conversion of heat into work, or, what is the same thing, into the living force of moving masses, is either altogether impossible or possible only in part; and, conversely, all processes in nature proceed in such a way that a greater or lesser part of the work passes into heat, is transformed, one may say, into degraded energy. Thus all the events of the world inevitably lead to an increase of this degradation, and hence it follows that all tensions that might still perform work gradually disappear, and with them, in the end, all visible motions in the universe must cease.

The validity of this conclusion is indisputable, and one may assert in advance that no combination of diffusion, thermal conduction, attraction of masses (phenomena that must constantly be accompanied by the transition of visible living force into heat), electrical phenomena, in general of processes that, each taken separately, are all subject to the second law of thermodynamics—no combination of such processes can, with correct calculation, lead to a result that would contradict the above-mentioned general consequence of the second law.

In exactly the same way, the phenomena of radioactive decay are processes connected with the degradation of energy. Therefore, in principle, they cannot change anything in the result stated above, although the stores of energy hidden in atoms signify a previously unforeseen increase in the world’s capacity for work; as a consequence, the so-called heat death of the universe is merely postponed, but, in the end, its onset remains inevitable. One may even say that the theory of radioactive decay of the elements places, alongside the increasing degradation of energy, an equally continuously occurring degradation of matter, and thereby only doubles the prospect of the twilight of the gods advancing upon the universe.

Nevertheless, salvation seems possible if we admit a process opposite to radioactive decay; namely, if we suppose that the atoms of all the elements of the universe decompose over time into a primary substance, which we might identify with the world ether, this hypothetical interplanetary medium; in the ether

all possible groupings may take place, even the most improbable, just as kinetic theory allows for gases, and in this way, from time to time, atoms of some elements could again be formed (most probably even elements with a high atomic weight).

It is enough that the indicated process should in reality occur only exceptionally rarely; this follows, first, from the enormous duration of the life of ordinary chemical elements and, second, from the extraordinary sparseness with which matter is distributed through world space (on average, for every hundred kilometers there is a grain of matter the size of a pinhead!). Unfortunately, precisely for this reason there is no hope of detecting experimentally this supposed phenomenon of the reversal of radioactive decay and thereby giving empirical support to the train of thought outlined here. Nevertheless, it seems to me not without interest to point out that at the present time a conception is possible that is not wholly improbable, according to which the matter existing in the universe, together with its store of energy, is to a certain extent in a stationary state, and that therefore the cessation of all that is taking place should not be regarded, at least, as an unconditional consequence of our modern views of nature.

It should be added that the supposition which, so far as I know, was first expressed in the passage set forth above, and according to which the luminiferous ether must be regarded as filled with enormous quantities of energy, seems inevitable for our modern views of nature. The chief content of the further exposition therefore consists in a deeper justification and further application of my cosmic hypothesis outlined above.

The Universe in the Light of New Research

The contemplation of the vault of heaven on a clear night belongs among the spectacles that make the strongest impression upon man; some savage peoples looked upon the stars as simple little fires, while others devoted themselves to the cult of the stars; even the Catholic Inquisition still believed that the planets were in the power of demons; even so outstanding an astronomer as Tycho Brahe, who already stood on the threshold of the newest investigations, considered it acceptable to justify predictions by the arrangement of the heavenly bodies; the modern cultured man is convinced that the greater part of the fixed stars are formations similar to our Sun, and that neither stars nor planets can have any bearing on human destiny. Among the results of the astronomical investigations of the last century there is, further, the conclusion that our Sun is a member of an enormous-

of a star cluster, approximately lenticular in shape, while the outer boundaries of this cluster we discern in the form of the Milky Way.

The effect of works of art upon the human soul is deepened by reflexes that always occur beyond the threshold of clear consciousness; thanks to this, every great work of art impels one toward thoughtful analysis. A strong impulse arises to reveal the sensation slumbering in the depths of the soul.

What, then, is the cause of the powerful aesthetic influence of the content of the vault of heaven? First of all, it is the consciousness of the utter insignificance of everything taking place on our earth in relation to infinite space, in which “myriads of worlds grow like nocturnal grasses”; the thought of the double infinity of space and time, like a dark premonition, shakes the spectator.

Light from the suns situated in the Milky Way, according to the latest measurements, takes tens of thousands of years before it reaches us, although the speed of light (300,000 kilometers per second) far surpasses all other speeds known to us; the distance of the outermost stars of the Milky Way may be estimated even at thirty thousand light-years. However, world-systems are probably accessible to our observations with the aid of telescopes whose distance is immeasurably greater than that indicated, and which form star clusters similar to our Milky Way. This assertion cannot yet be regarded as unconditionally correct, for it is possible that the observed formations also belong to our Milky Way. Nevertheless, it is beyond doubt that at a great distance from the sun, i.e., at the boundary of the system of our Milky Way, the number of stars falling within a definite volume of space—the so-called density of stars—noticeably diminishes, so that our Milky Way should indeed be regarded as a star cluster in cosmic space.

Just as, when contemplating the vault of heaven, our ideas of space must operate with dimensions other than our earthly distances, so too for cosmic events intervals of time of an entirely different order of magnitude are significant than those that play a role in the history of the human race—in so-called “world history.” The determination of the intervals of time applicable there is still more difficult than the determination of spatial distances; the discussion and consideration of what the latest investigations say on this subject will constitute the most important chapter of the forthcoming exposition.

The question arises whether, with so enormous a change in scale, our concepts of space and time, obtained from experience, retain their original meaning. Since until now the investigation of nature has been accessible to the control of experience, this has been so. But can the laws be transferred to the entire universe ...

physics and chemistry, derived on the basis of empirical data which we obtained from measurements on a very limited scale? This was allowed in all discussions concerning the structure of the heaven of the fixed stars and, since it could be checked, was allowed with full justification. But still, of course, one cannot be completely certain of this. Let us admit that the transfer of our laws of nature, verified only on a very limited scale of space and time, to the problems posed before us by the contemplation of the firmament, may lead to incorrect, or at least inaccurate, conclusions.

One must make peace with this in all such reasoning. To this is added yet another great difficulty. Every theory of the universe is based on that body of knowledge which exists at the time of its origin. Thus Helmholtz, developing further the hypothesis of Kant and Laplace, which he, incidentally, considered the happiest achievement of natural science, did not yet possess the profound information on this question that appeared thanks to the later discovery of radioactivity. And even now no one would venture to assert that similarly essential discoveries do not still lie dormant in the depths of the future.

Therefore we can approach our present task only with great reservations: to create, on a natural-scientific basis, a picture of the formation and disappearance of celestial bodies. Helmholtz, who devoted an extraordinary amount of attention to cosmic questions, expresses himself on this subject in the following words (Vorträge und Reden, Bd. II, p. 58): “It may perhaps seem audacious that we, confined in the circle of our observations—with respect to space, by our sojourn on a small earth, a speck in the system of the Milky Way; with respect to time, by the brief history of humanity—should venture to apply, to the whole boundlessness of immeasurable space and time, laws established in the narrow realm of facts accessible to us.” Yet he justly adds further that precisely such reasoning may help to establish clearly the limits of natural-scientific methods and of the applicability of the laws established up to the present time.

The essence of the Kant–Laplace theory, in that part of it which has withstood the test of time, consists, as we can set it forth now, in the following. Somewhere in world space matter, gas or dust, accumulates in a state of extreme rarefaction. Owing to Newtonian attraction between the masses, compression arises, as a result of which, through the action of these forces, an enormous amount of work is performed. At the same time, as Helmholtz showed, using the law of conservation of energy, the masses undergo strong heating and form an enormous nebula, also called a giant star, such as we can observe in the sky, although not in very large ...

number. With further contraction the density and temperature increase; a star arises, shining with white light, the so-called “dwarf star.” Then cooling sets in. The white light becomes yellowish, then reddish, until at last all luminosity ceases; thus there arise dark stars, inaccessible, of course, to direct perception; however, thanks to the action of attraction manifested by them, we can not only prove their existence—for example in double stars, as an invisible companion of a bright star—but even draw conclusions about their mass. Red stars may be either very bright—in that case they are very extensive, weakly heated nebulae—or very dark, and then represent dense suns that have already cooled greatly.

All the successive stages of development described here we can study in the sky in numerous examples. However, it seems that there are also certain exceptions which do not fit entirely into the scheme described. Therefore we cannot assert that all stars traverse precisely the path of development indicated here, and must allow that some of them have their own special destiny. Yet this does not impair the Kant–Laplace hypothesis, for it represents, so to speak, the normal development of a star. Our sun, with its yellowish light, is thus on the descending branch; as a fixed star it has already passed its highest point.

When, with further contraction of the mass of gas, a ring separates from it, which subsequently contracts into a sphere, planets with their moons arise. Laplace was the first to devote special attention to this question; however, such a conception, as later scholars showed, encounters at present great difficulties in a consistent development if one operates exclusively with Newton’s law of force. We shall see later that in the process of planet formation large electrostatic forces probably take part, so that future calculations must be based on a somewhat altered foundation. But, be that as it may, many striking regularities of the planetary orbits can be explained only on the assumption that the masses of the planets were once united in a nebula. The chief merit of Kant’s work lay precisely in clarifying and substantiating this point, and such a view has never seriously been called into doubt. Anticipating here the chief result of our further investigations, we shall indicate that, in general and on the whole, the Kant–Laplace hypothesis retains its force, but that in certain essential points it requires additions consistent with the requirements of new investigations, chiefly those of the last fifteen years.

The extraordinary refinement of experimental art over the last decades, which in its consequences is undoubtedly the most important achievement of the natural-scientific epoch of our time, has сказ—

extended in the most brilliant manner also to investigations of the starry sky. The system of the Milky Way has been investigated to such an extent that the number of its luminous stars may with a certain confidence be estimated at approximately half a billion. For a large number of stars we know their distance from the Sun, their proper motion, their temperature, and their transverse dimensions. This sounds simple; yet one can hardly imagine at what cost of the most delicate observations and theoretical acumen it has been possible to assemble this great quantity of data in stellar catalogues. We must not forget that, in contrast to the planets, fixed stars in the telescope appear only as bright points, having, so to speak, no dimensions, and that therefore the determination of their actual transverse dimensions, for example, is possible only by indirect means. Time does not permit, of course, even an approximate outline of these methods; but in order to show how successfully their further development is now proceeding, I must briefly mention that Professor Michelson in America has recently succeeded, by applying the phenomenon of the interference of light, even in directly measuring, with astonishing accuracy, the diameter of stars.

Among the many remarkable results obtained in the new investigations of the starry sky, the following is especially striking. The mass of an enormous number of stars varies within very narrow limits. Differences in the masses of stars do, of course, occur; in particular it turns out, as Professor Ludendorff in Potsdam has shown, that very hot white stars on average possess a greater mass, which is understandable: the greater the mass, the greater the heating that accompanies its contraction. Yet these differences are small; in numbers they are expressed as from \(10^{33}\) g to \(10^{34}\) g. We shall see later what explains this. From the point of view of the original Kant–Laplace theory this is, of course, incomprehensible, for it can say absolutely nothing about the quantity which, having accidentally accumulated somewhere in world space, condenses into a blazing sun. Yet, naturally, one cannot see in this any contradiction of the theory mentioned.

The matter is otherwise with three further consequences of the dominant theory which, even if they do not refute it completely, must nevertheless make us reflect seriously. Specifically, I have in mind the so-called thermodynamic world problem, then a second world problem, which I would call the “radioactive problem,” and finally the so-called “cosmic world problem.” What is involved here is a consideration simple in essence, but of fundamental significance.

In this we proceed from the following ideas. A natural scientist cannot admit that at a certain time the whole world was in a chaotic state, from which incandescent suns began to condense, in order in the end to arrive at a state,

in which the further formation of suns becomes more impossible. In other words: the notion that everything that takes place in the world began, so to speak, on one definite day and will finally cease on some definite day is so improbable that any theory which necessarily leads to this consequence must be regarded by us as improbable in the highest degree and therefore imperfect.

Neither Kant nor Laplace could have had a clear conception of the fact that their theory of the formation of worlds necessarily presupposes a limited duration for the life of all that exists; otherwise they themselves would probably not have acknowledged their views as having universal applicability. Only the development of the doctrine of heat compelled the drawing of the above-mentioned, highly unpleasant conclusion, with that degree of certainty with which conclusions from the laboratory to the universe can in general be transferred. The celebrated English physicist Lord Kelvin was the first to draw attention to the fact that, on the basis of the doctrine of heat founded by Carnot and Clausius, the total store of energy of the world is, though slowly, yet inexorably transformed into heat, and that likewise, inexorably, all the heat available tends toward temperature equilibrium. But at the same time the world is condemned to eternal rest; thus the application to the ideas of Kant and Laplace of the law of the doctrine of heat—in other words, of the most general and most reliable law that we possess at all—entails the appearance of the dreadful thought that the world is tending to turn into an eternal cemetery. This is usually expressed by saying that the universe is threatened by inevitable heat death.

We shall try to present the thermodynamic world-problem set forth here in a somewhat more limited and vivid form. As a consequence of radiation, the incandescent suns of our starry heaven continuously give up heat to world-space; and since any energy expended in some other way must, in the course of events, likewise be transformed into heat, we may say that the energy reserves of matter pass irreversibly into the form of thermal radiation wandering in infinite space. According to existing views, this energy is inevitably lost for any further transformation into work, i.e. for any event. Thus we become convinced that only the admission of a process acting in the reverse direction could be of help here.

We can take one further step. In recent years, through the work of Einstein, it has been established that when matter gives up energy, its mass also decreases; in most cases the quantities involved are so negligible that this decrease of mass proves immeasurably small, so that for practical purposes the mass may be considered entirely constant. However, in principle we may say that mass continuously escapes into world—

space, but we are still not in a position to indicate a process that would compensate for this loss.

The thermodynamic problem set forth above is the most general problem of this kind; the two following ones are, in fact, only special cases and a certain development of it. About twenty years have passed since, following Röntgen’s discovery, the remarkable atomic disintegration of certain elements was established—in other words, radioactive transformation. In its essential features this phenomenon consists in the fact that elements of large atomic weight continuously and spontaneously split into elements with a smaller atomic weight. As products of disintegration in radioactive transformation, along with electrons, atoms of helium always appear. By means of the so-called displacement rule of Russell, Fajans, and Soddy, we are even able to indicate precisely the chemical character of the elements newly formed along with helium; we may say, especially thanks to Rutherford’s investigations, that we are better informed about radioactive processes than about ordinary chemical reactions, which, of all the phenomena known to us, stand closest to radioactive transformations. The reverse of the radioactive process, i.e. the construction of a complex atom from simple atoms, has not yet been observed; but with the aid of the methods of the new thermodynamics we can calculate with great confidence that such construction can take place only under utterly exceptional conditions, namely at a temperature of more than ten thousand million degrees. According to new and well-founded views, such temperatures, which we of course cannot even approximately realize in laboratories, do not exist even inside the hottest fixed stars. But even if in individual cases such temperatures were possible, this would in principle change nothing in the subsequent considerations.

Radioactivity has so far been observed experimentally only in a small number of elements. But many circumstances, especially the surprising relations between the atomic weights of the elements, have nevertheless led to the conviction that what we have here is not a special property, but a quite general phenomenon—as, indeed, one could hardly have doubted from the very beginning.

Thus, since, as was indicated above, we do not assume a beginning of the existence of the world, we arrive at the following conclusion: if, thanks to radioactive processes, helium (and probably also hydrogen) is being produced continuously, though extremely slowly, yet with inexorable regularity, then the remaining chemical elements ought long ago to have disappeared, and the world would present an entirely different picture from that which we observe at the present time. Instead of the fullness of the phenomena of the universe—a fullness which, in the final analysis

rested on the diversity of its constituent elements, a gloomy veil of uniformity and an infinite desert would long since have had to descend upon the whole universe. Or, if we prefer to proceed from some definite moment of time when all changing matter, with its numerous elements and their countless combinations, was given to us, then we must acknowledge that there must befall it—and at no very remote date—the end indicated above, when all material differences will be almost completely smoothed out. It is obvious that this special prospect of the death of matter is little more cheering than the already described general prospect of the thermal death of the universe.

Finally, I must briefly touch upon the so-called cosmic problem, treated in a series of articles chiefly by the well-known Munich astronomer Seeliger. World space, filled with masses—even on the assumption that their mean volume density is extremely small—must act upon every material particle, generally speaking, with an infinitely great force, which, of course, cannot be admitted. This consequence, as Seeliger showed, disappears if one assumes an absorption of gravitation at very great distances. Yet under continuous action gravitation must nevertheless necessarily lead to accumulations of the masses scattered in world space, in particular of the stars of the Milky Way system. For what follows we must therefore accept that, to put it briefly, in order to secure the normal state of the universe there must also exist some cause that would bring about the dispersion of accumulating masses. Such a role, as we saw above, is performed by thermal radiation, but in a quantitatively quite insufficient degree and, moreover, at the cost of an enormous expenditure of the working capacity of energy. Comparing all that has been set forth, we may say: the hypothesis of Kant and Laplace has, over time, received so many confirmations that it undoubtedly contains a sound kernel; however, it alone is insufficient, for it leaves us helpless before questions of the highest importance. Logical necessity compels the natural scientist to think about correcting it, even at the risk that, owing to the insufficiency of our data, these questions are at present not yet fully prepared for resolution.

The most outstanding minds have taken the liveliest part in elucidating the question of the structure of the world. Among earlier investigators, besides Kant and Laplace, I shall mention only the names of Lord Kelvin, Helmholtz, and Boltzmann. Further progress in this field can be expected only on the basis of new information and the ideas flowing from it. In general one may say that in questions of natural science it is rather hopeless to take up problems over which the greatest investigators have worked attentively

of the past, provided that since then there have not appeared at our disposal experimental facts or means of analysis that were unknown to our outstanding predecessors. But this is precisely what has occurred in the present case, and therefore it will not be too presumptuous to expect certain consequences from a new examination of the problem. I must therefore now turn to a brief account of those advances in the natural science of the most recent period which, in my opinion, are especially promising for the consideration of cosmic questions.

As a result of the study of radioactive phenomena, we have succeeded, especially thanks to the work of Rutherford and Bohr, in penetrating deeply into the structure of the atoms of the chemical elements. According to these conceptions, each atom consists of a positively charged heavy nucleus, around which revolve much lighter negative electrons, the elementary atoms of negative electricity. Thanks to the memorable discovery of Professor Laue (v. Laue), we are even able to arrange all the elements in the order of numbers indicating the magnitude of the charge of the nucleus or, what is the same thing, the number of electrons revolving around it; in other words, to renumber the elements reliably. The ordinal number of the last of the elements known to us, uranium, is 92. We know all the members of this series, with the exception of five, and even with respect to these missing members we are able to enumerate in great detail their chemical and physical properties. Obviously these missing elements are extremely rare, and some, perhaps, are so strongly radioactive that they have long since died out. In any case, one cannot refuse high praise to the work of the chemists, spanning, in round numbers, a century, for they discovered in the group of the rare earths, despite great difficulties, almost everything that could be discovered; this is a truly striking example of the enormous certainty with which exact natural science is able to work.

Whether elements with atomic numbers higher than uranium exist, we do not know; however, one can hardly doubt that precisely these elements must be strongly radioactive, which perhaps explains why they, as for the most part extinct elements, are not found, perhaps, on our earth, at least in places accessible to us.

At the same time, another remarkable circumstance also becomes comprehensible, one which has long attracted the attention of investigators. Among the most interesting phenomena are meteorites, which fall upon our earth in great numbers and are of very diverse size. These messengers of distant heavenly bodies most probably originate, at least in part, from other solar systems. Naturally, chemists carefully analyze meteoric stones; however, no new elements have ever been found in them. This

had long given grounds for supposing that all heavenly bodies, in their essential features, consist of the same elements as the earth or our sun, from whose depths it arose.

Spectral analysis has transformed this supposition into certainty; and if the known spectral lines of the sun and of other fixed stars do not completely coincide with the lines of terrestrial elements, then, according to the latest investigations, this is explained by the fact that here we are dealing with terrestrial elements well known to us, from which, under the action of the extremely high temperature prevailing on the stars, several electrons have been split off, as a result of which they must inevitably exhibit a somewhat different spectrum. Various considerations have led to the supposition that the chief constituent part of the earth and the sun is iron; in agreement with this, there are many meteorites which consist almost exclusively of this element.

How well the assumption of the uniformity of the chemical composition of all heavenly bodies is confirmed is clear from the following, especially striking example. In 1879 Nilson and Cleve discovered the element scandium, an analogue of aluminum; however, it occurred only in exceptionally small quantities, so that it seemed to belong among the rarest companions of the so-called rare earths. But spectral analysis revealed, in many fixed stars, lines characteristic of this element. On this basis Professor Eberhard, of the Potsdam Astrophysical Observatory, arrived at the idea that scandium must also be rather widespread on the earth. After Prof. Eberhard had worked out a reliable spectroanalytical method for determining scandium, it became possible—chiefly thanks to the efforts of Professor R. J. Meyer in Berlin—to obtain scandium, previously so rare, from numerous ores (wolframites, tin ores, zircon), so that now we have at our disposal almost unlimited quantities of this element. Here is an interesting example of how observations of distant stars can lead to tangible, practical results on our earth.

The identity of the chemical composition of the various heavenly bodies might once have seemed astonishing, when the possibility of innumerable chemical elements appeared conceivable; but since, in recent years, as shown above, a finite, quite limited number of elements has been established, the circumstance mentioned above has become readily understandable. Kant and Laplace could still admit that, in the formation of the fixed stars, the original nebulous matter might in different cases have had an entirely different composition; a theory which at the outset excludes this possibility obviously gains in its intrinsic plausibility.

Let us now briefly acquaint ourselves with the conditions for the formation of organized matter, i.e. the origin of life according to our modern

views, although this question also lies outside the sphere of our immediate consideration, for such a miniature heavenly body as our insignificant Earth cannot, of course, be of any special interest. Animate matter is undoubtedly connected with the existence, in the highest degree, of complex molecules, i.e. with the possibility of a very varied linkage of atoms.

Of all the chemical elements—and we may consider that we know sufficiently the properties of all the elements that come under consideration—the question can concern only carbon and, perhaps, nitrogen; and indeed these two elements, in combination with oxygen and hydrogen, constitute the principal components of all terrestrial living beings. The very complex molecules that figure here prove sufficiently capable of reactions only within a narrow interval of temperature. We thus see that the conditions for the formation of living beings are rather restrictive, and that only on a few planets, and then only at certain times, are these conditions fulfilled to the necessary degree. But since we may suppose that both the Sun and other fixed stars possess numerous planets, there can hardly be any doubt that there is an enormous number of planets within and outside the system of our Milky Way whose conditions are very close to those of our Earth. Thus, in the question of the development of life no limits are placed on the flight of imagination; but, of course, we absolutely do not wish to assert anything definite. True, there is another element, in many respects chemically similar to carbon—namely silicon—and one might suppose the formation, on remote planets, of living beings in which carbon is replaced by silicon. However, the latest investigations of Professor Stock at the Kaiser Wilhelm Institute in Dahlem have shown that silicon does not possess, even approximately, so great a capacity for forming compounds as carbon, and, above all, that under the action of water it easily passes into inactive silicic acid. The development of silicon beings must be regarded as a fantasy, even if a chemical fantasy. In any case, at present we have no further grounds for doubting that on the planets of cosmic space under consideration there exist, just as on Earth, the elements necessary for the construction of organized matter.

Let us now turn to Einstein’s well-founded relation between matter and energy, which we have already, incidentally, made use of. The meaning of this relation is that a body, in giving up energy, at the same time loses mass. The loss of mass is equal to the energy given up divided by the square of the speed of light. This formula is so reliable that we shall regard it as given. How important it is precisely for cosmic questions is evident from the following vivid argument. Our Sun, from the moment when out of the nebula it ...

has condensed to a somewhat greater density, continuously radiates enormous quantities of energy, the magnitude of which we can determine precisely by direct measurement of solar radiation; in this way we can calculate with certainty that the sun loses annually \(10^{20}\) grams, i.e. a gigantic mass of hundreds of billions of tons. But above we saw that fixed stars have approximately the same mass, i.e. stars at the end of their stellar life, already greatly cooled red stars, are on the average not much lighter than bright-white stars; this proves that the loss of mass through radiation during the lifetime of a star cannot in any case amount to a significant part of its total mass. If the sun had radiated for \(10^{13}\), i.e. ten trillion years1, in the same way as it radiates now, then by now nothing at all would be left of it.

Thus, the duration of its life must be much shorter, especially if one takes into account that in former times, when the sun was a brighter star, it radiated much more heat. We thus obtain a reliable upper limit for the duration of the life of bright fixed stars. On the basis of considerations into which I cannot enter here in detail, it may be considered improbable that the sun has lost through radiation more than one hundredth of the magnitude of its mass, so that the duration of its life, and together with it the duration of the life of hot stars in general, may be estimated at no more than 100,000 million \((=10^{11})\) years.

However, Einstein’s relation gives us grounds for another, probably more important, conclusion. Once we accept that the loss of mass is to be attributed to the expenditure of energy, the natural conclusion seems to be that the existence of mass is due exclusively to the accumulation of energy. In the last few years we have learned that in the atom enormous quantities of energy are accumulated in the form of so-called zero energy; some part of this energy, in any case only a small one, is released, for example, in radioactive decay. Thus, the atoms of the various elements are exclusively accumulations of energy, and accumulations of extraordinary dimensions at that. From this point of view, radioactive decay appears to be only one of the possibilities of obtaining enormous quantities of energy from matter. The technical utilization of this energy does not, in principle, appear impossible. It seems that even Rutherford has recently succeeded—though, it is true, on an insignificantly small scale—in obtaining such energy in the splitting of nitrogen by the rays of radioactive substances. However, one should beware of the illusion that the technical utilization of these stores of energy has become in any appreciable sense near enough that one could speak of the depreciation of coal;

but, in any case, it cannot be denied that here lies one of the greatest technical problems.

In order to make the reality of these questions as vivid as possible, let us remain on experimentally reliable ground. Let us imagine a vein of pitchblende, with respect to which we know with certainty that the uranium contained in it can, through various intermediate stages, be transformed into lead, and that enormous quantities of energy are liberated in the process, in comparison with which the energy developed by our most powerful explosives appears as an utter trifle; let us further suppose that this transformation, instead of lasting, as at ordinary temperature, for thousands of millions of years, takes place instantaneously. The immediate consequence of this would be an explosion whose power exceeds all imagination; moreover, probably, as a result of such an initial impulse, the remaining matter of the planet, in a considerable part of it, would also begin to be transformed.

I think it can be calculated with sufficient accuracy that such a transformation could be achieved if one were to set fire to pitchblende, just as gunpowder is ignited with a match, but, of course, not with an ordinary match, the flame temperature of which may be estimated at 1500 degrees, but with a match whose temperature would have to reach approximately ten thousand million degrees. We cannot realize such a temperature, and, in all probability, it is not attained anywhere in nature. Like uranium, however, all or almost all elements behave in the same way. And in order to illustrate with complete clarity the exceedingly remarkable property of matter mentioned above, we might compare the existence of mankind with the existence of savages who inhabit an island consisting mainly of pyroxylin and who have no fire. The colony would perish at the very instant that Prometheus handed one of its inhabitants a burning brand.

What has been set forth above proves that, at the present time, in considering the cosmic problem, we possess other auxiliary means than was possible, for example, for Helmholtz. Let us now consider the significance of the new achievements for the investigation of the starry heavens.

First of all, here one should mention the ingenious theory proposed in 1916 by the English astronomer Eddington, which, it seems, very successfully explains the already mentioned remarkable circumstance that the fixed stars possess approximately equal masses. A hot star may be regarded as a gaseous sphere; gas pressure counteracts, of course, the gradual compression due to attraction. Another factor opposing compression is—and in this consists the essence of the new theory—light pressure, which comes from the inner, considerably more heated layers and repels, according to a definite

according to the law, layers more distant from the center. Calculation shows that for very large stars this latter repulsive action, in conjunction with gas pressure, exceeds attraction, so that the existence of stars of such dimensions becomes impossible. The striking result of Eddington’s theory consists in the fact that stars with a mass exceeding \(10^{34}\) grams cannot exist, which agrees with astronomical data.

Among the assumptions that Eddington had to make, the magnitude of the gas pressure plays a known role, that is, the mean molecular weight of the substance of the star. Eddington takes, as the principal mass, iron vapor, i.e. a mean molecular weight of 56; however, owing to the high temperature prevailing within the star, many free electrons separate from the iron vapor, whereby the molecular weight is greatly reduced. Eddington calculates a value with a mean molecular weight of 2.8. Now, however, with the aid of the new thermodynamics, we can take rather accurately into account the influence of the splitting off of electrons from iron vapor. Dr. Eggert (Eggert)1, at my suggestion, carried out the corresponding calculation and, on the basis of a careful discussion of the relations encountered, arrived at a mean molecular weight of 3.2, which serves as very good confirmation of Eddington’s assumption. Thus his theory gains considerably in reliability. It is very important that Eddington can also calculate the pressure and temperature inside the star, concerning which until now we knew nothing; in investigating the light radiation of a star we find, of course, only its external temperature, which reaches, for the sun, for example, 6000 degrees, and in white stars may considerably exceed 12000 degrees.

Inside, i.e. near the center, the temperature and pressure prove to be approximately constant, namely several million degrees and, correspondingly, several million atmospheres.

Stars of smaller dimensions are, of course, stable in themselves; but if we accept that in the formation of stars there is no shortage of mass, then it follows that there are formed chiefly stars of the maximum possible magnitude, such as we in fact find in great abundance in the sky.

An entirely different field is concerned with the success consisting, one may say, in an unexpectedly precise method of determining the age of the earth—a result that also has great significance in estimating the age of the fixed stars. By the age of the earth we shall here understand the time that has elapsed since our planet, from a molten fragment of the sun, turned into a celestial body with a solid crust. The method applied here, which rests on data relating—

relating to the field of radioactivity, leaves nothing to be desired in its originality.

A radioactive element disintegrates at a constant rate, independently of temperature, independently of whether the given element is in a free state or enters into the composition of some chemical compound. This has not only been proved by numerous experiments, but is also excellently substantiated theoretically. Indeed, radioactive decay takes place inside the atomic nucleus, upon the state of which, according to the principles of the modern quantum theory, the aforementioned external circumstances can have no influence whatsoever.

Only at extremely high temperatures, which, according to the preceding, apparently do not occur in the universe, could one expect an influence on the rate of atomic disintegration; within the limits of the temperatures involved in our problem, this rate may with complete confidence be regarded as exactly constant.

Thus uranium, this most important initial product of the radioactive series, disintegrates at an entirely constant rate; its continuously occurring splitting into other elements is, as it were, the hand of a chronometer running with maximum precision. And, of course, these clocks have the advantage that they never need to be wound up: a radioactive element carries within itself so much energy that the clocks run until the element is completely destroyed. And in order to make the described time-measurer ideally perfect, it is furnished with a registering device. For the products of radioactive decay accumulate, of course, in the very same measure in which the element decomposes. First of all helium is formed, a volatile gas; but if we are dealing with a splendid solid crystal of uranium ore, then the helium, at least in considerable part, remains enclosed within the crystal. Since, by means of electrical measurements, the rate of formation of helium, which is identical with the intensity of the radioactive radiation, is measured with extreme accuracy, it is possible to calculate how much helium is formed in the course of a year from a kilogram of uranium; thus the quantity of helium enclosed in a piece of uranium ore gives directly the time during which the crystal, as such, has remained unchanged.

Since one must reckon with an inevitable loss of helium over millions of years, determination by helium gives a minimum value for the age of solid ores. Still more reliable are the results of the “lead method.” The final product of the radioactive decay of uranium is lead, which, being deposited in solid crystals, certainly cannot volatilize.

Here one might object that the lead found in uranium ores may perhaps only in part arise as a consequence of radioactive decay, and may in part have become admixed with the ore as a result of...

the action of some geological processes (helium, on the contrary, cannot be included in the solidifying uranium ore). But even this difficulty is easily overcome, as though nature had taken care to provide us with the fullest reliability of this incomparably important method of determination. Uranium lead of radioactive origin, being chemically the purest lead, has an equivalent weight noticeably different from that of ordinary lead; it is an isotope of lead. In other words, accidental original admixtures of ordinary lead in the ore can be precisely distinguished from lead of radioactive origin. Uranium clocks give reliable indications.

In view of the great interest connected with the determination of lead in uranium ores, various investigators have engaged in such analyses. Uranium ores have been found with a relatively small content of uranium lead which, as calculation shows, are not very old; namely, their age can be estimated at several hundred million years, that is, such a time has elapsed since they separated from an igneous-liquid melt, perhaps during some volcanic eruption. However, there are also uranium ores from various deposits which show a certain maximum lead content, namely approximately 20%, which corresponds to an age of 1500 million years; and this figure must indicate very precisely the moment of formation of the solid earth’s crust; it is possible that this formation occurred still earlier.

However interesting these determinations may be for the history of our earth, still greater importance for us belongs to the conclusions that can be drawn concerning the age of the sun. By the time the earth arose, the sun evidently must already have passed through a long period of contraction, during which it was transformed from a nebula of gigantic dimensions into a relatively dense star. The age of the sun in the stage of such a more dense star must, consequently, amount to at least 1500 million years; probably it is considerably greater. Taking into account that, according to the remark made above, the age of a fixed star can hardly be greater than one hundred thousand million years, and that, on the other hand, according to what has just been found, it must significantly exceed one thousand million years, we see that the age of the stars proves to be reliably determined within rather narrow limits. In what follows we may estimate the duration of the life of shining suns at approximately ten thousand million years.

The extraordinarily important result, according to which the duration of the life of shining suns is reckoned at least in thousands or even tens of thousands of millions of years, leads, however, in modern research to new difficulties, to which various astronomers have pointed in recent years. The point is that, knowing precisely the action of the forces of attraction, one can cal-

to calculate the amount of heat developed in the formation of a fixed star from a nebula, and what heat must cover the losses due to radiation. However, the amount of heat obtained proves to be far less than what is necessary; instead of many thousands of millions of years, the radiation of a star with the intensity with which it now occurs could be maintained, as Helmholtz showed long ago, for at most only a few tens of millions of years. The Kant–Laplace theory is here completely powerless. In addition to the mutual attraction of masses, there must exist another, incomparably more powerful source of energy in order to make possible the considerable duration of life of shining suns. The supposition naturally arises that radioactive processes supply the necessary energy.

However, even if we admit, for our purposes, the most favorable case—namely, if we suppose that, for the formation of a star in the Kant–Laplace scheme, pure uranium dust served as the material—we shall find by calculation that even then only a moderate part of the heat radiated during the lifetime of the star can be covered. It is true that this supposition partly removes the discrepancy between calculations and observations. Yet the assumption that the primordial nebula of Kant–Laplace must have consisted exclusively of radioactive elements seems so fantastic that it is hardly worth dwelling on it any longer.

In the preceding exposition I have tried to sketch a picture of contemporary views on the structure of the world. In general and on the whole, we arrive at the pressing necessity of further developing the Kant–Laplace theory, and the observational astronomy of recent times has furnished us, for this purpose, with impressive material concerning the nature and properties of a large number of fixed stars, both giant nebulae and their later products, dwarf stars or suns proper. Yet there still remain substantial gaps which do not allow us to speak of a harmonious picture of the world. Heat death, with all its consequences, is logically most unsatisfactory and at the same time extraordinarily improbable; likewise, the admission that we do not know whence the Sun’s own energy actually comes is a very palpable imperfection.

The few minutes that are still granted me by your kind attention I should like to devote to a brief description of an attempt based on an assumption—still, to be sure, hypothetical—which, as it seems to me, simply and radically removes the above-mentioned difficulties. I developed this attempt at explanation, though only in passing, in a speech at the congress of naturalists in Münster (see p. 152); now we shall dwell on it in greater detail.

We have seen above that the so-called heat death of matter may ultimately be reduced to the scattering of matter in world—

in the world space, and radiation is delayed in the world ether of the universe. Perhaps you know that at the present time the existence of the world ether has repeatedly been called into question; but if one must agree that a large complex of phenomena can be interpreted without using the hypothesis of the luminiferous ether, then on the other hand it is beyond doubt that for many processes, for example for explaining the constancy of the speed of light, one cannot do without the hypothesis of a weightless intermediate medium. In any case, when I speak unconditionally in favor of the existence of the luminiferous ether, I have on my side many outstanding physicists. Further, the new atomic theories teach us that even at absolute zero, animated motions are preserved within the atom, and that consequently part of its mass must be attributed to a store of energy, the so-called zero-point energy. Under such circumstances, of course, the simplest assumption will be to recognize that all matter consists of zero-point energy. If we add to this the further consequence that this energy is in equilibrium with the energy of the luminiferous ether, then it can be shown that the luminiferous ether must possess enormous stores of energy. We may now put forward the hypothesis that atoms of the chemical elements can arise in world space as a result of random fluctuations in the energy stores of the luminiferous ether; in that case, of course, we must also admit the converse, i.e., that in the process of the so-called radioactive decomposition, atoms of the chemical elements—chiefly the final products of radioactive decay, atoms of helium and hydrogen—can again be transformed into the zero-point energy of the ether. Thus we admit the continuous appearance and disappearance of matter in the universe.

Let us now ask ourselves whether, in that case, we ought not directly to observe the formation of atoms of the chemical elements. The lifetime of most elements must be much greater than the decay time of uranium, whose transformation, right down to lead, we can trace experimentally, that is, much more than a thousand million years.

The average density of matter in our Milky Way system is such as if in every hundred liters there were one atom of uranium. In order to maintain the mass of the world on average constant, it is necessary that in the named space there arise one atom of uranium in a period incomparably greater than 1000 million years1. We see, therefore, that our supposition cannot stand in any contradiction with experience.

As for the reverse transition of matter into the sea of ether, we observe it, in principle, in every radiation—of course, in this case only in imperceptible quantities. A more noticeable disappearance of matter occurs in radioactive processes. But, of course, the principal loss of matter—the disappearance of helium and hydrogen atoms—we cannot yet observe experimentally, for the same reasons for which the formation of atoms is inaccessible to direct observation, since in both cases the matter concerns processes exceptional in their rarity. That these processes are rare follows, at the very least, from the great duration of the life of matter, at least of its principal constituent parts; and this longevity is confirmed by two entirely different experimental facts: first, by the extraordinary slowness of the radioactive decay of the greater part of the elements, and, second, by the extraordinarily great duration of the life of the fixed stars.

As for the type of atoms formed directly from the zero energy of the luminous ether, we shall specialize our hypothesis by assuming that there are formed chiefly, or even exclusively, elements with a very high ordinal number—that is, those standing in the series of elements above uranium; these are very strongly radioactive elements, which undergo a long series of transformations, and therefore develop far more heat than has been measured for uranium.

It is now not difficult to show that with the aid of our—at any rate hypothetical, as I perhaps have not sufficiently emphasized—assumption, one can explain in a simple and graphic way the formation of the fixed stars, their extraordinarily prolonged shining, and finally their continuous new formation. For this purpose let us apply our hypothesis to the Kant–Laplace theory of the formation of worlds.

The newly formed atoms of elements of very high ordinal number, extremely dispersed in world space, gradually combine into a cold nebula of gigantic dimensions, whose faint glow is caused by radioactive radiation. Owing to the increasing condensation, a high temperature arises, which leads to ordinary light radiation. Then, as a result of further compression, a hot, so-called dwarf star is formed, that is, a world-body similar to the Sun. At first, however, such a sun still possesses a powerful store of radioactive substance, which is precisely what maintains its high temperature and prolonged radiation. Then this store is gradually exhausted; the temperature, having remained approximately constant for a long time, begins to decrease; the white star relatively quickly passes into a yellow and then into a reddish star, in order finally to cool completely. Subsequently the cooled star decays radioactively, with extreme slowness, and, as was explained above, after an enormous period of time thus disappears entirely from view.

world. At the same time, on the average, new stars are formed in approximately the same number from the newly arisen radioactive atoms. When radioactive decay has essentially come to an end, as, for example, in the case of the sun, ordinary chemical elements must remain present, always in approximately one and the same quantitative ratio; that is, stars in a later stage must have approximately the same chemical composition, which, in accordance with the foregoing, is very plausible.

The considerations set forth may, in a certain respect, be confirmed by observations; indeed, our view leads to the exceedingly simple consequence that those states of stars which have the greatest duration of life should occur most often in the sky. According to our considerations, these are, first, the brightest stars, which are near the maximum of their development, and, second, stars that have completely or almost completely gone out. Observation confirms this conclusion in an astonishing way for the first category; as for the second, it cannot be reliably verified, since we cannot see these stars; however, at present, on the basis of indirect indications coming from various quarters, the opinion is gaining ground in astronomy that the total mass of extinct, that is, faintly shining stars (including meteorites and dark cosmic dust) cannot be insignificant in comparison with the mass of shining stars.

If meteorites (at least in part) originate from fragments of extinct stars, then they must represent the later stage in the decomposition of the chemical elements, such as we can observe on the earth, where matter, according to what has been set forth above, must be in approximately the same state as on the sun (white stars, and especially nebulae, must be at an earlier stage, that is, contain elements with a higher atomic weight than those known to us). It is therefore remarkable, and deserves thorough investigation, that in meteorites elements with high atomic weight seem to be absent (see the note).

Kant and Laplace reckoned exclusively with gravitation as the force having significance in the formation of the solar system. We must now recognize that, especially at the beginning of the formation of fixed stars, forces of electrical origin, appearing as a consequence of radioactive actions connected with strong electrification, likewise play an outstanding role. Since in fact it has proved that, in order to explain the formation of the planets according to Laplace, Newtonian attraction alone is insufficient, new points of departure are thereby given for the further development of the theory. With this, in particular, may be connected the strange appearances and disappearances of new stars, which occur, as Guthnick has shown in his recently published Physics of the Fixed Stars,

so regularly that the corresponding processes should, as it were, be counted as belonging to the normal development of stars.

Finally, I must mention one more point, to which Professor Zeeliger, the physicist and son of the astronomer mentioned earlier, recently drew my attention.

Namely, perhaps one may see support for the views developed above on the occurrence of radioactive atoms in world space in the fact that this space appears to be filled with radioactive rays, and moreover with so-called gamma rays ($\gamma$-rays) of an extraordinary hardness, such as we know in no known element. The investigations of Hess, Zeeliger, and Swinne show that these remarkable rays are in no case sent out by the earth, the sun, or the moon; however, it is not yet clear whether the upper layers of our atmosphere, and not world space, might serve as the place of their origin. The solution of the question of what part of the measured radiation is of cosmic origin could serve as an important basis for further astrophysical calculations.

Our considerations, in any case, remove heat death, as well as the dispersal of matter. Our gaze is no longer compelled to regard the world in the distant future as a gloomy cemetery; it sees the universe continually filled with the appearance and disappearance of brightly shining stars. Let the sacred fire of suns die out here and there; it flares up again in many places with renewed, youthful force. The matter of the world can no longer be transformed wholly into helium. Finally, matter cannot in the course of time collect anywhere into a gigantic mass—I recall the cosmic problem cited above—for it is continuously formed anew in world space, with approximately constant density.

Cosmic physics is not ordinary physics. What in the latter provokes censure as unproved speculation may here become a logical necessity, occupying an insurmountable place among investigations. We find ourselves compelled to bring into our reasoning assumptions that are not yet proved, but are not implausible. Kant1 already said in the introduction to his “Theory of the Heavens”: “In works of this kind one can never demand geometrical precision and mathematical infallibility. If a system is based on analogies and correspondences established according to the rules of probability and logic, then it sufficiently satisfies all the requirements of the subject.”

Kant went on to say: “Give me matter, and I will construct a world for you from it.” Possibly, but that world will not be our world. Perhaps we shall come closer to the truth if we say: “Give me radio-

active elements of high atomic weight”; in this case we shall also obtain enormous reserves of energy, dispersed throughout the universe, the explanation of which is still the unpaid debt of Kant and Laplace. Let us add to this: “Give us the zero energy of the luminiferous ether,” and we may regard the history of the universe as secured for ages upon ages.

Addenda.

The temperature of world space. The temperature of world space (of the luminiferous ether) may be determined in the following way. Let us imagine, at some arbitrary point, some small speck of a black body—that is, of a body which absorbs all rays falling upon it. This speck, under the action of the radiation present everywhere, will assume a definite temperature, namely the temperature of world space at the given place, since in thermal equilibrium it will absorb as much heat as it radiates in consequence of its own temperature. There is no doubt that, at a sufficient distance from any warm celestial body, this temperature is extraordinarily low, practically scarcely distinguishable from absolute zero.

This result is, obviously, highly surprising; for if we adhere to the view that the Cosmos is in a stationary state, then, according to all our previous knowledge, the temperature of world space ought, on the contrary, to be fairly high. Indeed, the temperature of the accumulations of matter in space—first of all, the temperature of the fixed stars—is very high; likewise all the so-called “dark stars” are heated far above a red heat. In the course of unlimited time—and we must regard it as such by virtue of the “stationary state” of the Cosmos—some average temperature should have been established in world space (in any case of several thousand degrees), which certainly is not in fact the case.

Of course, we might seek a way out in the supposition that enormous masses of very low temperature are distributed in world space, for example in the form of cosmic dust, which in any case could lower this average temperature as much as desired. I do not think, however, that on the basis of our present astronomical knowledge one could propose this solution.

The following supposition seems to me far more acceptable. The luminiferous ether possesses a certain, albeit extremely small,

absorptive capacity for thermal radiation1. According to my views, this absorption should be represented in such a way that, over a very long interval of time, the ordinary energy of radiation is transformed into the zero energy of the luminiferous ether. Given the extraordinary smallness of the phenomenon assumed here, we, of course, do not come into conflict with any laboratory experiments or astronomical measurements. But at the same time we become convinced that the temperature of world space, even in a stationary state, may be extraordinarily low.

Still more important is the following conclusion. Absorption of radiant energy in world space means the disappearance of matter; in such a case, the existence of a stationary state requires a return transfer of matter on the part of the luminiferous ether. And by this very fact my hypothesis, set forth on p. 154 and pursued throughout this article, becomes almost a logical postulate; of course, only “almost,” since one must always reckon with the possibility of some other explanation. It seems, however, that there are only two possibilities for such a way out, namely: first, the above-mentioned assumption of enormous masses of very low temperature; second, a refusal to recognize a “stationary state” in the cosmos; both are, to a high degree, improbable.

It is sometimes said that in the universe there exist regions in which, as in our Milky Way, entropy increases, and others where it decreases. This simply denies our laws of nature. This little book has nothing to do with such a tendency of taste.

Reversibility of radioactive processes. On p. 160 it was pointed out that radioactive processes can be reversed only at extremely high temperatures, which, according to the new views, especially on the basis of Eddington’s considerations, seem nowhere in the universe capable of being realized. This conclusion follows most reliably from a direct application of my thermal theorem2, though, to be sure, on the basis of considerations from quantum theory. In exactly the same way one may conclude that even temperatures of a million degrees and more cannot yet appreciably affect the rate of radioactive transformations. This result is of great importance for all our arguments; without it, it seems, the very reliable foundations would be left completely hanging in the air.

It is extremely surprising that, in astrophysics, so little use has hitherto been made of the new thermodynamics based on my thermal

law. Apart from Eddington’s study mentioned on p. 167, the only exception is a new work by Dr. Saha on the temperature of fixed stars (cf. the review in Zeitschrift für Physik, 6, p. 40, 1921), who, applying my thermal theorem, arrived at a number of excellent results.

Gravitational energy and heat. One might suppose that gravitational energy is not necessarily transformed into heat, i.e. that even over an arbitrarily long interval of time the compression of matter need not come fully to an end. However, even in the most favorable of all conceivable cases—namely, in the case of a central body around which there revolves a single planet, turned, like the Moon, always with the same side toward the central body—it must be borne in mind that, during the revolution, the central body itself, by its various parts, falls within a gravitational field of different strength. And this necessarily entails compression and expansion within it, i.e. the emergence of irreversible temperature differences and, together with this, the damping of the system, which is identical with the transition of gravitational energy into heat. Only at absolute zero do these dampings, according to the new heat theorem, disappear; in reality, however, they are always present. If, moreover, the planet does not revolve exactly in a circle—which is practically the only possible case—then it, of course, also passes through different gravitational fields, and the magnitude of the damping increases.

It should further be noted that if we suppose that both world bodies have one and the same temperature, then, according to the new heat theorem, the specific heat of matter must necessarily change together with the intensity of the gravitational field (compare Grundlagen, p. 182); but this likewise entails a change of temperature with irreversible equalization of it—thereby causing damping. If the temperatures of two world bodies are different, then it may be asserted that the same action must also manifest itself, and indeed even more strongly, for with the gradual equalization of temperature the repulsive force of light pressure diminishes and, consequently, the world bodies will approach one another.

In the case of many celestial bodies, the damping of the system indicated above will obviously increase.

Thus the tendency of matter to contract into ever-increasing clumps cannot be subject to doubt. A cosmic theory that wishes to be general and at the same time proceeds from the hypothesis of a “stationary state,” i.e. does not admit the complete transformation of radiation over an arbitrarily large but finite interval of time—and in this, perhaps, consists the most evident definition of the “stationary state”—must be able to indicate the causes responsible for the continuous dispersal of matter. This requirement, so far as I know, is satisfied up to the present only by the theory substantiated in this little book.

The lifetime of fixed stars.

The brief remarks made in the indicated lecture I later supplemented somewhat. In view of the great general interest presented by the question of the age of the sun in many respects, we shall deal here with this subject in somewhat greater detail.

First of all, as regards the lower limit given by the age of the earth, following the summary of Professor Stefan Meyer (Stefan Meyer)\(^1\), we shall set it at \(1.5 \cdot 10^9\) years; this is the age of pure uranium minerals, obtained on the basis of the content of \(RaG\) (radio-lead) in these minerals. Determinations of the quantity of helium contained in these minerals lead to a considerably smaller value, for, as is assumed, a noticeable quantity of this gas escapes as a result of diffusion from the crystallized ore. However, it is conceivable that this deficiency of helium has another cause as well, namely the conversion of helium atoms into the zero energy of the light ether, which we must, according to our hypothesis, consider possible over such enormous intervals of time. Of course, further proof of this phenomenon (which would also explain to us the astonishingly small content of helium on the earth) is of the highest importance. But in any case, the \(RaG\) method gives, according to our present knowledge, quite reliable results, so that we may regard the figure given above as a trustworthy lower limit for the age of the earth and, at the same time, of the sun.

As for the upper limit, the sun emits per year, in the form of radiation, \(1.20 \cdot 10^{41}\) ergs, which, according to Einstein’s formula, gives a loss of mass of

\[ \frac{1.20 \cdot 10^{41}}{9 \cdot 10^{20}} = 1.33 \cdot 10^{20}\ \text{grams per year} \quad (\text{since } c^2 = 9 \cdot 10^{20}). \]

Since the mass of the sun reaches \(1.9 \cdot 10^{33}\) grams, then over the course of

\[ \frac{1.9 \cdot 10^{33}}{1.33 \cdot 10^{20}} = 1.4 \cdot 10^{13}\ \text{years} \]

the mass of the sun would disappear completely, if the radiation remained constant during this time. But formerly the sun radiated much more energy, partly owing to its higher temperature, partly owing to the much smaller density which it possessed at an earlier stage of development; on average the radiation, as can easily be estimated from comparison with white stars and nebulae, was at least ten times more intense; therefore the interval of time indicated above is reduced approximately to \(10^{12}\) years.

\(^1\) Neuere Ergebnisse der radioaktiven Forschung. Vorträge des Vereins zur Verbreitung naturw. Kenntnisse 58 (H. 7).

Of course, it is quite conceivable that the Sun was formerly a fixed star with a mass twice as great, so that half its mass has escaped. However, stellar statistics, which up to now have been unable to establish any regular decrease in the mass of stars depending on their stage of development, make such a considerable diminution of mass improbable. For the age of the Sun we obtain, one may say thanks to an extraordinarily fortunate coincidence, two rather close limits, from \(10^9\) to \(10^{12}\) years.

So favorable a conclusion encourages us to attempt a further narrowing of these limits. With regard to the lower limit, the radium-lead analysis gives us the time elapsed since the crystallization of the mineral under consideration. The question is how long the Earth could have existed in the form of a fiery-liquid sphere, in order that the full age of the Earth might be estimated. In comparison with the figures given above, this interval proves vanishingly small if one takes into account only cooling due to radiation and performs the calculations with some acceptable value for the specific heat of the Earth’s mass; according to such a calculation, even a Sun of much greater dimensions would undoubtedly have cooled in 10–20 million years. Now, however, when the great influence of the heat developed as a consequence of radioactivity has become clear, such a calculation cannot be considered correct.

We can estimate the influence of the development of radioactive heat by means of the following reasoning. Let us suppose that this heat is capable of maintaining the present temperature of the Earth, if we neglect the influx of energy from the Sun and take into account that, as will be shown below, radioactivity in former epochs was considerably greater, approximately 30–50 times greater than at present; correspondingly, the absolute temperature of the Earth’s surface could have been maintained at a value only 2.3–2.7 times greater than the present one, i.e. only about \(700^\circ\) absolute, for, according to the Stefan–Boltzmann law of radiation, the quantity of heat radiated is proportional to the fourth power of the temperature. Thus, when the Earth was molten, radioactivity played only a secondary role in the question of heat loss. This approximate calculation shows that the interval during which the Earth’s surface remained fiery-liquid must in any case be considerably shorter than the period elapsed since the formation of the solid crust. On the other hand, it should be noted that the number \(1.5 \cdot 10^9\) years, given above for this latter period, although it represents only a lower limit, is in any case a limit that comes rather close to reality.

Thus we may, without much arbitrariness, estimate the age of the Earth at \(2 \cdot 10^9\) years; furthermore, taking into account that the planets (and the corresponding double stars) were formed, in all probability, when the corresponding fixed star was still a nebula (giant-

star), and that the period of development of a giant star, as can be concluded with certainty on the basis of various considerations, proceeds relatively rapidly, we arrive at the final conclusion that the age of the sun should be regarded as somewhat greater than \(3\cdot 10^9\) years.

So small a number—small because it lies much closer to the lower of the boundaries indicated earlier than to the upper—may evidently be supported by the following considerations. The age of the sun determines the diminution of its mass as a consequence of radiation; in all radioactive processes known to us this diminution is measured, as is known, only in small fractions per mille.

We may confidently suppose that in the radioactive decay of elements higher than uranium (i.e. with an atomic number greater than 92), the matter concerns incomparably more powerful radioactive processes, which will undoubtedly cause a greater loss of mass. However, one must recognize as most probable that supposition which removes us least from the known facts; if we were to make our choice based exclusively on probability, then we would have to try to proceed from the assumption of a minimum of energy developed, so as not to depart, so to speak without necessity, from the known empirical facts. Thus, on the basis of these considerations as well, when choosing a value lying between both of the boundaries found above, the advantage belongs to a number near the lower boundary.

Let us now try to examine in more detail the development of a stationary star, attributing, in accordance with our guiding hypothesis, a radioactive origin to the energy developed in it.

We have seen that the energy of contraction developed as a consequence of the work of attraction, which since the time of Helmholtz had been considered as the chief factor, could cover the radiation of the sun (especially in earlier periods) only for less than a million years1; let us recall further that cooling of the mass of the sun would have had to occur in a very short time2, even if an improbably high specific heat were assigned to it; thus we arrive at an exceedingly simple energy balance: at every moment the heat radiated by a stationary star must be equal to the heat developed as a consequence of radioactive processes (or, perhaps, in some other way).

This law is nothing other than the law of conservation of energy as applied to stars, with attention being paid to the fact that, as

stores of energy, as well as the energy of attraction in the energy balance of a fixed star, are vanishing—even quite vanishing—small in comparison with the quantity of energy radiated by the star during its, as was shown above, extraordinarily long life.

It is surprising that in the new astrophysics this law has not yet been formulated—so simple and, it seems to me, quite indisputable, given the assumptions already made and, so far as I know, nowhere contested; all the more so because, as will soon be shown, it gives us entirely new and exceedingly important foundations for the theory of the evolution of fixed stars.

Let us denote by \(U\) the quantity of heat developed inside the star in one second, by \(r\) the radius of the star, and by \(T\) the absolute temperature on its surface (usually called the “effective temperature”). In that case we have:

\[ U = 4\pi r^{2}\sigma T^{4}, \ldots\ldots\ldots\ldots\ldots\ldots (1) \]

where \(\sigma\) is the radiation constant of the Stefan–Boltzmann law, which is equal to \(1.40\cdot 10^{-12}\), if we carry out the calculation with centimeters as the unit of length and gram-calories as the unit of heat \((1\ \text{g-cal.} = 4.18\cdot 10^{7}\ \text{erg})\).

The mean density \(\delta\) of a star of mass \(M\) is:

\[ \delta = \frac{M}{\frac{4}{3}\pi r^{3}} \ldots\ldots\ldots\ldots\ldots\ldots (2) \]

On the right-hand side of equation (1) there are two variables, namely \(r\) and \(T\); since the mass may be regarded as known and, in the sense of the preceding, constant, one may introduce instead of \(r\) and \(T\) the variables \(\delta\) and \(T\), which, generally speaking, will be more perspicuous. A complete theory of the evolution of a star must, of course, indicate in what relation \(\delta\) and \(T\) stand to one another for a given mass. As is known, Eddington\(^{1}\) attempted to give such a theory. However, in this question we cannot consider it satisfactory,\(^{2}\) since in Eddington’s calculations equation (1), which we here assume to be absolutely reliable, is not satisfied. Incidentally, in my opinion, the most important successes of Eddington’s theory—namely the conclusion that, owing to light pressure, which counteracts gravitation, first, there cannot exist stars possessing a mass many times greater than the mass of the sun, and, second, that the temperature inside a star can never rise significantly above several million degrees, a circumstance of especially great importance for our arguments—these successes of the theory are not affected by the objection stated above,

\(^{1}\) See especially Astrophys. Journ., 48, p. 205, 1918.

\(^{2}\) I cannot fail to emphasize here that during this time Professor Westphal, in an oral report on Eddington’s work, also expressed a similar judgment.

so that Eddington’s theory must be recognized as a most important step forward in the field of astrophysical research.

Thus, theoretically, the relation between $\delta$ and $T$ has not yet been established. If our views are correct, then it cannot be established before we are able to form special conceptions of the nature of the radioactive transformations taking place inside a star; moreover, besides light pressure, one must take into account also thermal conductivity, which probably attains very large values inside a star, and, especially, must take into account the electrostatic forces caused by the separation of the positive nucleus and the numerous free negative electrons; thus for the time being we are compelled to seek, purely empirically, i.e. with the aid of stellar statistics, the relation between $\delta$ and $T$.

A more exact solution of this extremely important problem I must, of course, leave to specialist astronomers. With the aid of a table given by Eddington1, partly empirical and partly theoretical, and thanks to the friendly support of Guthnick and Bernewitz, to whom I owe deep gratitude for supplying me with experimental material, I arrived at the following, quite provisional table, which refers to stars with the mass of our Sun ($\delta$ is referred to water, taken as 1; consequently, $\delta$ for the Sun $=1.38$).

$\delta$	T	$U . 10^{-41}$
0.001	5000	57.6
0.035	8000	35.6
0.23	9500	29.3
0.33	9500	15.7
0.65	8500	6.42
1.00	7500	2.92
1.38	6300	1.20
1.50	6000	0.91
2.00	4000	0.15

Substituting for the Sun the directly found value:

\[ U_0 = 1.20 \cdot 10^{41}\ \text{ergs}, \]

we easily find from formulas (1) and (2) ($T_0=6300$, $\delta_0=1.38$):

\[ U = U_0 \frac{T^4}{T_0^4} \left(\frac{\delta_0}{\delta}\right)^{\frac{2}{3}} \]

the relation by means of which the values placed in the last column of the above table were obtained.

According to Russell1, stellar statistics show that giant stars possess a luminosity and, consequently, a thermal radiation \(U\), approximately independent of the stage of development; therefore a small extrapolation leads us to the initial value

\[ U_1 = 64 \cdot 10^{41}\ \text{ergs}. \]

The considerable decrease of \(U\), which, according to experiment, is noted in the table given above, we explain—in the spirit of our preceding arguments—by the radioactive expenditure of the active substance; in the absence of more precise information concerning this process, we shall make use of the ordinary law of radioactive decay, applicable, strictly speaking, only to a homogeneous substance, but giving, at least in general outline, an idea of the character of the phenomena also in the case of radioactive mixtures.

Let us put the period of decay (that is, the time during which half of the radioactive substance present undergoes transformation) equal to \(0.6 \cdot 10^9\) years; in that case \(3 \cdot 10^9\) years will be required for the radiation to fall from the initial value

\[ U_1 = 64 \cdot 10^{41}\ \text{erg} \]

to the value corresponding to the present state of the Sun,

\[ U_0 = 1.20 \cdot 10^{41}\ \text{erg}, \]

as indeed it should according to our definition of the age of the Earth.

Let us represent graphically the value of \(U\) as a function of time; on the basis of our table we can also represent the surface temperatures corresponding to the values of \(U\) as functions of time, and thus obtain a second curve. In the figure on page 184 the corresponding density values are not connected by a third curve, but are written at the side near the various points of the curve \(T\).

In this way we obtain a simple and extremely vivid diagram of the development of a stationary star with the mass of the Sun. It is self-evident that exactly the same procedure may be used for stars of another mass, only the determinations of times will be less reliable. In this case the most essential assumption, of course, is that \(U_1\) is proportional to the mass, i.e. that the stars are formed from identical mixtures of elements, although, however, other assumptions are also possible. In any case, it can hardly be doubted that, generally speaking, the development of a star proceeds the more slowly, the greater its mass, and that the maximum temperature of a star likewise increases with its mass, which, as is known, is in agreement with observations.

Our diagram admits of a simple verification. The number of stars at various stages of development—for simplicity we shall distinguish only

giant stars, white, denser stars, yellow dwarf stars, and red dwarf stars—must be proportional to the duration of the corresponding stage. From our diagram one can directly derive the following conclusions (in order):

There are very few giant stars, very many denser white stars, rather many yellow dwarfs, and very many red dwarf stars.

If one disregards the last conclusion, which can scarcely be verified, since red dwarf stars, owing to their extremely diminished radiation, soon become invisible, then our diagram reproduces the most important result of stellar statistics. If, instead of drawing the \(U\) curve in accordance with the law of radioactive decay, we draw a straight line from the initial value to the present value for the Sun, then a quite impossible temperature curve is obtained; this is undoubtedly a sign of experimental confirmation of the above-derived law.

From the dotted energy curve, whose course is determined uniquely by means of the law of radioactive decay, one obtains, on the basis of the numbers on page 182, just as uniquely the temperature curve; of course, owing to the inaccuracy of the available data, the curve is valid only in its general features, so that no significance should be attached to the small bend visible in it. The density curve is not plotted, but near the corresponding temperatures the values of \(\delta\) are indicated.

Knowing the total energy of radiation, we can easily derive the loss of mass which the Sun has experienced since the moment of its formation as a result of radiation; it comes out to \(6.0 \cdot 10^{30}\) grams, i.e. \(0.31\%\) of the Sun’s mass. A higher value would, as has already been pointed out, be difficult to explain from the physical point of view at the present level of knowledge. Of course, it is entirely compatible with this that in reality, in addition, there is constantly some increase of mass due to the absorption of meteorites. Thus one can scarcely count on expla-

some change in the time of the Earth’s revolution as a check on the preceding results.

As regards the reliability of the determination of time, it can hardly be said that the computed intervals could be considerably smaller: larger values are not excluded, but are scarcely very probable. It would, of course, be of the greatest importance if it were possible to confirm the diagram under consideration by some other method. To a certain extent this can be done in the following way.

1. From our diagram we can easily estimate how long ago the temperature conditions on the Earth permitted organic life. Solar radiation \(0.6 \cdot 10^9\) years ago was twice as intense as now; the same must also be said of the radioactive store, which is distributed both in the Sun and in the Earth. A doubling of the amount of heat delivered to the Earth raises the absolute temperature of its surface, according to formula (1) (see p. 181), by a factor of \(\sqrt[4]{2}\), i.e. by 19% or \(53^\circ\) Celsius. Such a rise in temperature, for example near the poles, may still be regarded as tolerable. Geological methods of determination speak of 400 million years (instead of 600 million). Thus here there is a satisfactory agreement. Conversely, we can predict that organic life on Earth will be able to exist for approximately another 400 million years, at least near the equator.

2. Nebulae, as is usually assumed, are formed near the Milky Way. They have little proper motion, and their existence proceeds almost in the immediate neighborhood of the Milky Way. The circumstance that they do not have time to mix with other stars shows that the stage of development of giant stars ends relatively quickly. Our diagram in fact allots to it only about 400 million years1. Perhaps from this more qualitative agreement one may proceed to a quantitative determination of the duration of the stage of giant stars.

In conclusion, let us briefly touch upon the important question of whether it may be asserted, as has repeatedly been done in recent times, that, with respect to the distribution of positions and proper velocities of individual stars, the system of the Milky Way should be regarded as being in statistical equilibrium (like a mass of gas). Suppose that the path which stars can traverse is equal to 40,000 light-years—in reality we should take it to be still larger, for it is obvious that, in the sense of such a conception, stars may in principle, like comets, move far away from the system of the Milky Way; taking the mean proper motion of a star to be 10 kilometers per second—even if it were in reality sometimes even in-

many times greater, but at the turning points the star would, over a long period of time, have much smaller proper velocities; thus, for traversing the entire “free path” the star would require a time equal to

\[ \frac{40000 \cdot 3 \cdot 10^{10}}{10^{6}} = 1.2 \cdot 10^{9}\ \text{years}. \]

Let us further suppose that, in order for the aforementioned kinetic-statistical equilibrium to be established, the star must leave behind it at least a tenfold free path—a requirement certainly moderate; in that case this will require \(12 \cdot 10^{9}\) years, i.e., an interval of time during which the star, according to the preceding, will have time to become invisible to us.

In full agreement with this calculation, not only nebulae but also denser white stars deviate far from the distribution corresponding to probability\(^1\). Thus it must be admitted that, if in this region one operates with the laws of statistical mechanics, then we find ourselves on very uncertain ground.

Uranium as an explosive substance. Of the power of the action that would be produced by the instantaneous transformation of uranium, one can easily form an idea from the following considerations. The force of an explosive substance is the greater, the more densely it is packed and the more intense the development of heat connected with the transformation. Hence it may readily be concluded that uranium, upon its instantaneous transformation into uranium lead and helium, would produce an effect millions of times greater than the best of our explosives. And that such a transformation at an extraordinarily high temperature will occur instantaneously and likewise spread instantaneously, we may quite rightly expect by analogy with ordinary explosives, all the more since uranium occupies no fundamentally exceptional place among the elements.

The energy of the sun’s radiation. If the sun consisted entirely of uranium, then half the energy it radiates would be covered by the heat developed by uranium. One gram of uranium in the stationary state (that is, in “radioactive equilibrium” with all its decay products) gives \(2.5 \cdot 10^{8}\) cal per second\(^2\). A mass of uranium equal to the sun would give per second \(1.9 \cdot 10^{33}\) times \(2.5 \cdot 10^{8}\) calories, that is, \(0.48 \cdot 10^{26}\) calories per second; in reality the sun now radiates approximately \(10^{26}\) calories per second, and in earlier periods possessed more than fivefold radiation.

\(^1\) On this question, as well as on many others connected with it, see the considerations and numerical data in Arrhenius (S. Arrhenius, Lebenslauf der Planeten, Leipzig, 1921).

\(^2\) Cf. the work by St. Meyer and E. Schweidler mentioned on p. 178.

Thus, with the radioactive elements known to us we shall not escape the difficulty; but in any case it is very significant that, at least as regards the order of magnitude, the possibility of covering the energy is revealed. This strengthens the conviction that, although the heat of the stars is of radioactive origin, in any case it is due to the presence of radioactive elements of higher atomic number, which are still unknown to us, or perhaps to radioactive isotopes of known elements.

Chemical composition of meteorites. Privatdozent Dr. Eggert kindly undertook the task of reviewing the literature on the indicated question; he communicated to me the following:

“In his very detailed critical review of the literature on meteorites, Cohen (Meteoritenkunde, Stuttgart, 1894, 1903, 1905) establishes the undoubted presence of the following elements:

Fe	Ni	Co	Cu	C	P	S	Cr	Cl	Gi
60–95	5–10	1	10⁻²	10⁻²	0.25	10⁻²	10⁻²	10⁻²	10⁻¹, 10⁻² %

“In addition, in stony meteorites, apart from the indicated substances, there occur embedded fragments of rocks (for example, olivine with the composition: SiO: 46; FeO: 2; CaO: 3; MgO: 49%; and, according to Moissan, also grains of diamond), so that in these meteorites there are also the elements:

Ca	Mg	Al	K	Na	Si
1	2	2	10⁻¹	10⁻¹	3

as well as resinous organic substances (1–70%).

“In these statistics a strong predominance of elements with low atomic weight is striking; the upper limit is represented by iron, above which Mallet, only as an isolated exception, established in the Staunton meteorite the presence of 0.02% tin, to which special attention was drawn; furthermore, this metal was also found by Rammelsberg in the Klein-Wenden meteorite, 3.49%, although all authors (Smith, Cohen) emphasize its exceptional rarity. Cohen considers altogether doubtful the presence of As, Sb, and Zn, which had been accidentally established but were not confirmed by his own analysis. In any case, it is evident that high-atomic elements occur in meteorites in quantities too small to be discovered by ordinary analytical methods.”

It would obviously be of the highest interest to pay special attention to small traces of elements with high atomic numbers. One might think that, if radioactive processes had been taking place over an enormous interval of time, they could have been reflected in the structure of meteorites. However, against this it may be objected that meteorites, on their paths through world space—

in space, like comets, may more than once pass near very hot stars; the melting processes connected with this would, of course, have destroyed such a structure. It is self-evident that all such difficulties fall away if meteorites simply represent fragments of our solar system; it would be extremely important to resolve this question. The circumstance that on the sun, just as on the earth and in meteorites, iron appears to be the principal constituent part would mean, from our point of view, that this element possesses an especially great duration of life and therefore represents, as it were, a point of rest in the radioactive transformation of the elements.

The zero energy of the ether. A study published by me in 19161 makes it probable that the luminiferous ether contains an enormous quantity of energy in the form of zero energy, organized in a manner unknown to us, perhaps in the form of vibrational energy. Quite recently, and entirely independently, Wiechert2 (E. Wiechert) has arrived at the same conclusion. Whereas I gave, for the lower limit of this zero energy, \(0.36 \cdot 10^{16}\) gram-calories per cubic centimeter, Wiechert estimates it, at least, at \(7 \cdot 10^{20}\) ergs per cubic centimeter, i.e. \(0.9 \cdot 10^{22}\) gram-calories per cubic centimeter. How it is explained that this enormous energy entirely eludes direct observation is set forth in detail by me in the study mentioned.

The so-called Hess radiation. If, as is at present most probable, this radiation really is very hard cosmic Röntgen radiation filling world space or, at least, the system of the Milky Way, then it is, of course, of extremely great interest for astrophysics. (See the excellent textbook of radioactivity by St. Meyer and E. Schweidler (1916) and especially the new investigations of R. Seeliger (Münch. Ber. 1, 1918.) Of course, before reaching the earth, this radiation is greatly weakened by the large mass of atmosphere through which it must penetrate; therefore more precise investigations are best carried out on high mountains. Under these conditions one can also decide the fundamental question whether it is uniformly distributed in space or increases more strongly toward the Milky Way. The circumstance that the sun, which, according to our calculations, must still contain significant quantities of extremely powerful radioactive substances, does not send to the earth any noticeable \(\gamma\)-radiation is explained, of course, simply by the fact that the high-atomic elements under consideration are located chiefly within the sun, which, moreover, is in complete agreement with the facts about

which will be discussed in the following note. Therefore one also cannot expect that younger stars, and hence stars richer in radioactive substances, can send us appreciable quantities of γ-rays.

If a considerable quantity of “primary matter” were concentrated, as we have repeatedly assumed, in the Milky Way, then the latter might in any case be a place of stronger radiation, and it would be of great interest to prove this experimentally. At present, however, the most important thing is, of course, to decide whether Hess’s radiation is indeed of cosmic origin; if it were proved that the Milky Way (or perhaps nebulous clusters) is the place where it predominantly originates, then the question would, of course, be answered in the affirmative. But if the entire world ether as a whole is the source of this radiation, which would be in the spirit of the considerations on page 36, then the radiation could have a cosmic origin, even if, for example, the Milky Way did not occupy any special position in this respect. On this point we can only wish for precise measurements.

The formation of planets and binary stars. Since at present the determination of stellar masses is possible only for binary stars, it is only binary stars that provide the material necessary for compiling tables similar to the table on page 182, concerning stars with masses close to the mass of the Sun. As Prof. Guthnick informed me orally, here there arises the natural question whether binary stars may be regarded as typical stars, and whether their path of development is not essentially different from the path of development of other stars, for example, the Sun.

From a new, very valuable critical review by Bernewitz1 it follows, however, that (with the exception of 85 Pegasi) the brighter star is always the one with the greater mass. This circumstance makes it almost certain (apart from very rare exceptions) that binary stars have arisen as a result of the splitting of a central mass.

If we further assume that the mean chemical composition of both systems remains unchanged during the splitting, then for the radiated quantities of energy \(U'\) and \(U''\) we could put:

\[ U' : U'' = m' : m'', \]

where \(m'\) and \(m''\) denote the masses of the two systems; and from this one could further conclude (with a known approximation) that the ratio of luminosities should be equal to the ratio of masses.

This, however, is in no case confirmed; the smaller star almost without exception possesses a much lower luminosity than would be required—

will be the preceding proportion; thus, for example, the smaller companion of Sirius (2.4 times lighter) is, in round numbers, 10 stellar magnitudes fainter than the principal star. Thus, as applied to our ideas, stellar statistics show that, when splitting off, the smaller companion proves to be considerably less rich in radioactive impurities than the principal star.

This circumstance, however, from the physical point of view, is almost self-evident. Indeed, elements with very great atomic weight, among which, according to our previous arguments, radioactive elements should be sought exclusively, will, according to the barometric formula—which, at least qualitatively, is applicable to the gaseous sphere—be concentrated chiefly inside the star. When a companion separates from the central mass, as we have pictured it since the time of Laplace, its mass will consist chiefly of the surface layers and therefore will be considerably poorer in radioactive substances than the central body.

Obviously these considerations open up a new point of view for the statistics of double stars. We shall note here only the most important conclusions from our mode of consideration:

1. For double stars with approximately equal masses, if only their temperatures are not very different, the star with the mass having the mean value may serve as the typical star.

2. In double stars with markedly different masses, only the principal star can serve for that same purpose (with the observance of certain small corrections, readily following from our reasoning).

3. For double stars deviating from the norm, such as 85 Pegasi, for which it is assumed that they arose independently of one another, one must use both companions.

Incidentally, from a comparison of the Sun and the Earth one can easily calculate that, in full agreement with the preceding considerations, the Earth contains relatively far fewer radioactive substances than the Sun; since the Sun radiates \(1.20 \cdot 10^{41}\) ergs per year, the Earth, with its mass 329,000 times smaller, should radiate \(3.64 \cdot 10^{35}\) ergs. If one takes the mean temperature of its surface to be \(280^\circ\) (on the absolute scale), then, according to the law of radiation (the application of which in the highly simplified form required here must, of course, be regarded only as approximate), the Earth emits about

\[ 5.74 \cdot 10^{5} \cdot 280^{4} \cdot 5.09 \cdot 10^{8} = 18.0 \cdot 10^{23} \]

ergs per second, or

\[ 5.40 \cdot 10^{31}\ \text{ergs per year}, \]

that is, in reality far less than follows from the above law. If we take into account, moreover, that the Earth receives a greater quantity of energy from the Sun, much greater than

then the amount of heat which, as a result of radioactive processes in stars, flows from the inner layers of the Earth to its surface is so great that the difference must increase still further. Thus, in exactly the same way as in the analogous case of binary stars, we must ascribe to the mass of the Earth a far smaller radioactivity than to the mass of the Sun.

Thus observation, whether it is carried out on the Earth or on binary stars, shows, even quantitatively, that, as is to be expected from the physical point of view, the share of radioactivity which the central body gives up to the satellites splitting off from it increases with the mass of the satellite; moreover, those parts which come from the deeper layers of the central body always take from it a larger share of radioactivity.

Translated by G. Landeberg.

1. E. Bernewitz, Astr. Nachrichten, No. 5089, Vol. 213, March 1921. ↩↩↩↩↩↩↩↩↩↩↩↩↩

2. Der Aether im Weltbild der Physik; Berlin: Weidmannsche Buchhandlung, 1921. ↩↩↩↩