The Solar System in the Light of Recent Discoveries
A SEW law of temperature, that was discovered by me on May 6, 1898, and announced in a lecture before the Lowell Institute in Boston on January 10, 1899, has thrown such an unexpected light upon the theories of creation as held by astronomers that it will not be inappropriate to summarize those conclusions from it which interest the lay reader. This new law may be assumed to regulate the temperature of every gaseous star in space, and is thus almost as general as the law of gravitation. Judging by the inferences already drawn from it, the law of temperature bids fair to do almost as much to explain the mysterious processes of celestial evolution as the law of Newton did to illuminate the older and more celebrated problem of the heavenly motions. The philosophic view thus opened to the astronomical investigator is one of the most attractive imaginable, nor has it less charm for the larger body of unprofessional readers who merely follow the achievements of physical science.
As it may be supposed that the account of this remarkable law now published will become historic, I must first relate how the law was discovered, and in conclusion I will give a sketch of the previous investigations bearing on the same problem. In this narrative it will appear that Lane, of Washington, came near reaching this law some thirty years ago, and that a German physicist by the name of Ritter actually found a similar result as early as 1881, but failed to recognize the significance of the discovery which was so near. It is proper to say that the details of this early history have just come to light, and are now chronicled for the first time.
I came upon this law of temperature while occupied with some researches on the heat of the sun, intended for the second volume of my Researches on the Evolution of the Stellar Systems ; the immediate cause of the inquiry being the necessity of explaining the contrast in brilliancy exhibited by the components of such systems as Sirius and Procyon, where a very bright star is associated physically with a very dark companion. Having lost all manuscript papers by a fire which on September 14, 1897, destroyed my library, I was fortunate enough to secure from Professor Eric Doolittle, of the Flower Observatory, Philadelphia, a set of notes which he took on a course of lectures on the sun’s heat given by me at Chicago in the summer of 1895; and in supplying the lost lectures I developed the theory of the heat produced by the condensation of a gaseous sphere of heterogeneous density. I then realized for the first time the full significance of some computations which Professor Doolittle had made in the summer of 1895. He showed that, in the condensation of the solar nebula from infinite expansion, very little energy had been developed by the contracting mass until it reached quite small dimensions. Thus, on the hypothesis of homogeneity it appeared that the heat generated before the solar nebula came within the orbit of Mercury was only one eighty-third part of the total heat produced up to the present time ; and as this indicated a rapid increase in the production of heat for a given shrinkage of radius, when the radius is small. I set for myself the problem to determine how the output of heat varies with the radius of the condensing mass. Following the method of Helmholtz, we can easily show that the increase in the total amount of heat generated by the mass in condensing from infinite expansion varies inversely as the square of the radius. When the radius is very small, the output of energy becomes extremely large. From this consideration, it was plain that the production of heat would become a maximum when the radius had attained the smallest value consistent with the laws of gaseous constitution.
The next step was to prove the law of temperature. It will be shown presently how it can be found by the consideration of the most elementary principles. The simplicity of the temperature law thus derived was so great as to excite astonishment even in the minds of cool and incredulous astronomers. On applying it to the heavens, I drew’ at once the body of the conclusions indicated below. The results were so startling that one might well hesitate to announce the law. Besides, it was deemed desirable to ascertain if any work on similar questions had been done by previous investigators. Accordingly, I referred the question of a law connecting the temperature of agaseous star with its radius to some fifteen of the most prominent astronomers in the United States, without getting much additional light on the subject; and on July 4, 1898, I sent a similar inquiry to an illustrious English friend who has spent his whole life in astro-physics, and who, therefore, of all men, would presumably know of such a law if any had been discovered by earlier workers. In his reply, dated August 12, 1898, this classic authority says : “The only investigation which I can remember which goes mathematically into similar questions — though whether such a law is definitely stated I do not recollect — is the series of papers, at some intervals, by Ritter, about ten years ago, in Wiedemann’s Annalen.”
As the gentlemen consulted included several members of the distinguished board of editors of the Astro-Physical Journal, all of whom expressed surprise at the simplicity of the result obtained, further search for early work on the law of temperature was deemed useless. Meantime, my English friend, meditating on the announcement of July 4, that I had found a law connecting the temperature of a star with its radius, and that it had great significance for astro-physics, addressed a letter to one of the editors of the Astro-Physical Journal, suggesting that notice be made in that publication of this neglected work of Ritter. In preparing this review, one of the editors found and made known to me on December 7 (when I was visiting the Yerkes Observatory) that Ritter had stated in volume xiii. of Wiedemann’s Annalen a result similar to the one recently discovered and already announced to numerous astronomers. The theorem is there derived with a mass of other data, and expressed in words rather than in the usual mathematical symbols ; after which the author drops the matter of temperature, and proceeds with other inquiries relative to atmospheres. So far as can be learned, this result remained unknown to astronomers and astro-physicists ; and it will be seen from the above narrative that Ritter’s papers would have little chance of being known to-day but for my letter of July 4 to the illustrious British authority, which was the means of rescuing those writings from astronomical oblivion. These successive events disclose the origin of the interesting papers now appearing in the Astro - Physical Journal.
In 1869, Mr. J. Homer Lane, of Washington, discussed the theory of the heat of the sun in a mathematical paper which was read to the National Academy of Sciences, and published in the American Journal of Science for July, 1870; and though he implies that the temperature of a gaseous mass may rise by condensation, there is no formula given nor is there any specific statement of a law of temperature. This general result has gone into Young’s General Astronomy as Lane’s Law. It will be seen that the law of temperature given below is an exact formulation of what has passed as the somewhat indefinite conclusion of Lane.
In order to ascertain whether anything further could be determined regarding unpublished work of this profound but almost unknown author, I inquired recently of Professor Cleveland Abbe, of Washington, only to find that he had already made an unsuccessful search for Lane’s manuscripts some years ago. Consultation with Professor Newcomb elicited the information that he and Lane had discussed the heat of the sun in 1876, and that they agreed that the condensing mass could rise in temperature and grow hotter. Newcomb mentioned this matter to Lord Kelvin, in a conversation at the Smithsonian Institution the same year, and it seems that this illustrious physicist afterward recognized the correctness of the conclusions of Lane and Newcomb. It does not appear that any of these gentlemen published the law in a mathematical form, and, so far as can be ascertained, it took that form for the first time in a recent number of the Astronomical Journal. The true historical statement thus seems to be: —
(1.) In stating the great principle of the conservation of energy, in a popular address delivered at Konigsberg, February 7, 1854, Helmholtz discussed the contraction of the sun’s mass as the source of its heat (Philosophical Magazine, 1856).
(2.) In 1869 Lane went mathematically into the theory of the gaseous constitution of the sun, and implied in his discussion that the temperature may rise ; but he never published any law of temperature. Newcomb and Lane conferred about this point in 1876, and the result was made known to Lord Kelvin, who recognized the general conclusion reached by the American astronomers.
(3.) While engaged in researches on atmospheres, about 1881, Ritter obtained independently an exact formulation of the theorem, and published it in a physical journal, where it remained unknown to astronomers and astro-physicists.
(4.) On May 6, 1898, while occupied with the heat of the sun and with the cause of the darkness of the companions of Sirius and Procyon, I discovered the law independently, stated it generally as an exact formula, and derived from it conclusions of a far-reaching character. Sir William Huggins, with whom I communicated, was the means of rescuing Ritter’s work from oblivion, and the foregoing history of this remarkable law is at last brought to light. By scientific usage, he is recognized as the discoverer who finds, makes known, and renders useful and effective the products of his labors.
The derivation of the law is comparatively simple, but as numerous equations are out of place in The Atlantic Monthly, I shall state merely the result and the principles on which it depends. According to the kinetic theory of gases, a body of gaseous matter is made up of elastic molecules, which we may think of as small spheres flying hither and thither, colliding with one another and rebounding from the walls of the containing vessel. In the case of the sun and the gaseous stars, these molecules are subject to the attraction of the masses of which they are a part. The action of gravitation keeps such a body in a globular form, and no walls are needed to contain the vibrating spherules. Those molecules in the centre of the sun must sustain the pressure communicated to them by the gravity of other molecules on all sides. As the sun is a body of immense mass, this pressure is tremendous beyond all conceiving, and the result is an enormous density of the gas at the centre of the fiery globe. It is found by the investigations of mathematicians that the density decreases toward the surface according to a given law, and that the temperature also decreases correspondingly. Thus, on the supposition that the sun is gaseous throughout, Lane and Lord Kelvin agree in showing that the central density of the sun is something like thirtytwo times that of water, while at the solar surface the density is known to be less than that of the terrestrial atmosphere. Under the force of gravity there is a certain height above which a gaseous atmosphere will not rise, and this accordingly forms the surface of the gaseous globe.
Now, in deriving the law of temperature we consider the globe in equilibrium, so that the pressure of gravity exactly balances the expansive force due to internal heat. For if the internal heat were removed, so that the flying molecules were reduced to quiescence, the mass would collapse ; on the other hand, if gravity should suddenly cease to act, the energy of the molecules would cause the mass to explode and rapidly expand into a nebula of infinite extent. Taking the globe of gas to be in equilibrium, we consider how the surface of the condensing mass decreases as the volume diminishes, and how the force exerted upon this surface increases as the diameter shrinks, and compare with the forces tending to produce contraction those which tend to produce expansion. Molecular repulsion is the chief agency of expansion, and this augments rapidly with the increase of density in the shrinking mass. It will be noticed that in this procedure we assume nothing whatever but the operation of the ordinary law of gravitation, and the laws of gases as made known by terrestrial experiments. The basis upon which we proceed is thus the most certain and exact which physical science affords ; and if our reasoning is correct, no doubt can attach to our final conclusions. Now, it is found that, in order to keep the mass in equilibrium when it has contracted as here suggested, the temperature would have to rise by an amount proportional to the shrinkage of the sun’s radius. The resultinglaw of temperature is written thus : T =•K/R. T is the absolute temperature of the mass, K a certain constant different for each body, and R the radius of the condensing globe. This remarkable formula expresses one of the most fundamental of all the laws of nature.
AXIS OF TEMPURETURE T
Class I Sirian Stars
Class II Solar Stars
Class III Orange Stars
AXIS OF RADIUS R
Planetary Nebule
Diffused NEbule
T=K/R
LotV of Temperature for Gaseous Celestial Bodies Condensing under the Line of Gravitation..
T. J. J. SEE, Maij 6‡ tS9S,
It is one of the glories of modern science that the law of gravitation has been shown to apply alike to all bodies, gaseous, liquid, and solid, and whether intensely cold or heated to enormous temperatures ; the above law, of course, applies only to gaseous masses, but as the stars and nebulæ of space in the main are of a gaseous constitution, it has apparently the widest application in the actual universe. The new law regulating the temperature of gaseous bodies is illustrated by the accompanying diagram ; the curve which the temperature follows is what is described mathematically as the rectangular hyperbola referred to its asymptotes. Thus, when the radius is infinite the temperature is zero, and when the radius is zero the temperature is infinite. But as no physical body can ever have a radius infinitely small, it follows that for actual bodies the temperature is always finite. For after the star has attained a certain very great density, it ceases to act as a gas, becomes liquid or solid, and the law of temperature thenceforth ceases to hold true. Let us now consider the temperature of the diffused nebulæ which have interested philosophers for two hundred and fifty years.
The constant K is always finite and moderately small, and hence we see from the law of temperature that when R is infinite, T is zero ; thus, the diffused nebulæ are near the inexpressibly cold temperature of space, the so-called absolute zero, —273° C., where the molecules are reduced to a state of quiescence. This may also be inferred from other considerations. If such diffused masses were appreciably heated, they would soon cool off ; and besides, molecules on the outskirts of these nebulæ, having sensible molecular velocities, would escape into interstellar space. How the light of such masses is maintained is not certainly known, but it is probably due to electric luminescence such as we observe in the tails of comets, which also shine at temperatures approaching the absolute zero. We may therefore suppose the diffused and irregular nebulæ, as well as the milky nebulosity so abundantly scattered over the sky, to be intensely cold. It is an impressive fact that hydrogen and nebulium are the only elements recognized in the nebulæ, and all other elements presumably present are wholly non-luminous.
In view of this conclusion, the theories traditionally handed down from the days of Laplace seem very strange. That great geometer assumed that our system originated from the condensation of a fiery nebula of immense extent which at one time stretched beyond the orbit of the outermost planet. This nebula was supposed to be a gaseous mass, heated to a high temperature, and to have been endowed originally with a slow rotatory motion. When the mass cooled and shrunk, and a certain velocity of rotation had been attained, so that the centrifugal force at its equator overcame gravity, a ring of particles on the periphery was left behind — thrown off, as it were — revolving freely about the contracting mass. This broad zone of heated vapor, it was held, condensed into a planet, which in turn formed satellites : and so on with the other planets nearer the sun. By this sublime mechanical process the great Laplace accounted for the extraordinary symmetry and orderly arrangement of the planetary system. As the finished nebular hypothesis was known to embody the conclusions of the immortal author of the Mécanique Céleste. formed after a profound study of all the phenomena of our system, it has always carried with it the prestige naturally associated with the name of the greatest interpreter of the physical universe since Newton. Brave and audacious, indeed, was the man who could assail or dissent from the theories of Laplace, who, by the majesty of his researches and the sublimity of his conceptions, towered like the Colossus of Rhodes over the other splendid geniuses gathered at Paris a century ago. Yet on a few points a gradual breaking away from the old views was inevitable, and in 1854 my venerated teacher at the University of Berlin, the illustrious Helmholtz, delivered his classic address at the Kant Commemoration, in which he showed that gravitational shrinkage alone fully accounted for all the energy radiated away by our sun, and thus indirectly implied that the falling together of cold matter could produce the solar system. Nevertheless, the old conception of fiery nebulæ seems to have remained in the minds of the main body of scientific and philosophic thinkers in both hemispheres, and indeed is still current. It has thus taken several efforts to upset traditions, and now for the first time we have genuine and incontestable proof that the nebulæ are cold.
The stars of the first spectral type are admitted to be at the highest temperatures known. This is inferred generally from the bluish-white color of the light which they emit, and in the particular case of Sirius is proved by the very great radiation of that body compared to that of our sun. Thus, while the mass of Sirius is only about twice that of our sun, its radiation is shown by measurement to be forty or fifty times the greater of the two bodies. Accordingly, it follows that the Sirian stars are intensely hot. By the above law of temperature, such heat can be developed and such radiation maintained only when the radius of the condensing mass is relatively small. The Sirian stars have therefore already shrunk to small volume, and the contention, hitherto current among astro-physicists, that the Sirian stars are greatly expanded and resemble nebulæ, must be relegated to the ever widening domain of abandoned hypotheses. It is evident that such tremendous radiation as we observe could not be kept up by the gravitational shrinkage of the mass, except when the radius is small and the force of gravity correspondingly enormous. As respects volume, therefore, as well as temperature, the Sirian stars are as far removed from the nebular condition as possible ; and any spectral parallel between these two classes of objects should be explained in some other way. The diffused nebulæ are cold, infinitely rare, and almost free from pressure ; the Sirian stars are intensely hot, dense, and subject to extraordinary gravitational pressure.
We find it somewhat difficult to understand just what is the nature of matter under such tremendous pressure and at such enormous temperature. The heat is so terrific that the elements cannot form into any fixed liquids or solids of a complex molecular nature ; and the radiation must be kept up by currents which renew the heat of the external glowing surface as it tends to cool. Thus, the circulation of the mass also retards liquefaction and solidification. In view of the circulation required to maintain the intense heat of the white-hot surface, we may suppose that the mass is very mobile, and that the convective currents are little obstructed by friction ; the molecular consistency probably resembles that of quicksilver, and in many cases the glowing incandescent fluid is no doubt equally dense. Unless the surface heat were renewed with the utmost ease, the rapidity of the radiation would cause the outer layers to cool, and the body would fall in temperature. Though we are much in the dark as to the nature of the convective currents, the constancy of the radiation shows that the machinery of circulation works without the least clog or friction.
When we come to consider stars of the second class, of which our sun is an example, we find them at lower temperatures than those of the first class, and the question naturally arises whether their temperatures are rising or falling. The Sirian stars are surrounded by dense hydrogen atmospheres, which produce the heavy absorption observed in their spectra. Now, investigation of the expansive force of gases rising against gravity, by which we determine the theoretical heights of atmospheres, shows that the heights to which gases of different molecular weights ascend under any given condition vary inversely as the molecular weights of the elements. Thus, hydrogen, the lightest of all the elements, ascends sixteen times as high as oxygen ; and helium, with a molecular weight of only four, rises four times as high as oxygen, and one fourth as high as hydrogen. From these considerations, we see that when a star is far condensed, so that gravity tends to stratify the atmosphere in layers of different heights, the hydrogen appears on the outside as the uppermost layer. This is what we have in the whitehot stars of the first class, and the great width of the hydrogen lines in the spectra of such stars indicates that the gas is under high pressure. If the radius of the star is large, so that gravity is relatively weak, there is little tendency to stratify the elements of the atmosphere, and all the vapors, the heaviest as well as the lightest, mix freely, and the spectrum shows lines of all the elements present. This is what we have in the stars of the second class, of which the sun and Capella are typical examples ; the circumstance that hydrogen is not yet uppermost in their atmospheres may be taken to mean that the radius is still relatively large, and gravity correspondingly weak. This inference is confirmed by the lower temperature of these yellow stars, and in the case of our sun it admits of direct verification. The prominences are found to contain hydrogen and calcium, about equally mixed, while in the chromosphere vapors of heavy elements, like sodium and iron, float nearly on a level with those of helium. The facts that the elements in our sun are so little stratified, and that its globe has no overlying atmosphere of hydrogen (such as we should expect if it had already been a star of the first class), show that yellow stars of the second class are not cooling, but are yet to become bluish-white objects like Sirius and Vega. The lower temperatures of the solar stars thus indicate an earlier stage of development than that met with in the Sirian stars.
If this view be correct, it follows that the stars of the third class, which usually present an orange or reddish color, are at a still earlier stage of development than the solar stars. Their spectra are characterized by bands as well as by a great number of lines, and the indications point to an atmosphere of slight pressure and comparatively low temperature. There is a very strong suspicion that these stars are the youngest of celestial bodies. It is well known that many of these reddish stars are variable, and this fact doubtless has deep significance ; but before we can be certain of its meaning the whole subject of stellar classification must be examined anew. As the orange stars are the coolest, and presumably the most bulky, the solar stars the next in order of rising temperature and of diminution of bulk, while the Sirian stars are the most condensed and the hottest, we may suppose the color to pass from orange to yellow, and from yellow to white and even blue.
Our sun is now a yellow star similar to Capella, and hence it will eventually become bluish-white like Sirius and Vega. The secular shrinkage of the sun’s radius will cause a steady rise in its temperature, and when the body has reached the stage of Sirius, where the temperature is perhaps doubled, the light emitted will become intensely blue. The temperature may be expected to go on rising till a small radius is attained, and finally, when the dense mass, intensely hot, becomes incapable of further shrinkage, on account of increase in the molecular forces resisting condensation, a cooling will gradually ensue, after which the body will liquefy, and then rapidly decline in splendor. The sun will thenceforth be wrapped in everlasting darkness, and the chill of death will overtake the planetary system. A condition of darkness thus follows close upon a period of intense brilliancy, and hence the obscurity of such bodies as the companions of Sirius, Procyon, and Algol. The most obscure satellites are associated with some of the brightest and most intensely luminous stars in our sky; and here the smaller of the two masses, as in the case of the planets of the solar system, have developed most rapidly.
In view of this approaching extinction of the sun’s activity, it becomes a matter of interest to inquire how long its heat will sustain life upon the earth. Though it is difficult to submit the subject to accurate computation, it is easy to see that the exhaustion of the sun’s light and heat certainly will not occur for several hundred thousand years, and perhaps not for several million. The ultimate doom of our system need occasion no anxiety among those now living, but the result is philosophically interesting to those who look several million years into the future.
As experiment has shown that the sun’s vertical rays falling continuously upon terrestrial ice would melt a layer three centimetres in thickness per day, it follows that a similar shell of ice would form over the earth in case the sun’s light and heat were cut off : thus, in a month the whole earth would be frozen like the polar regions, and only the deeper bodies of water, containing a great amount of heat, would remain in a liquid state. The oceans themselves would freeze over within a few years at the latest, and the winds and even the tides would cease to agitate the terrestrial globe, which would thenceforth spin in its orbit as a rigid, lifeless mass.
Our sun is an ordinary star, and probably of about the same size as the average of the thousands of stellar objects which stud the firmament. It is well known that it has much the same luminosity as neighboring fixed stars, a similar spectrum, and a proper motion in space, and that it is attended by a system of smaller bodies which we call planets. Its amazing brilliancy is due to its closeness to the earth ; measurement shows that if it were removed to the distance of Alpha Centauri, it would shine as a star of the second magnitude. We therefore take the sun as a model star, and, from our better knowledge of it, infer the nature of objects too remote ever to admit of close examination with the optical means known to science. Thus, we are enabled to penetrate the mysteries of stellar temperatures and relative ages, and get a new light upon the problems of cosmical evolution.
After the foundation of the modern theory of the sun’s heat had been laid by Helmholtz, a number of astronomers developed or perfected the general theory. From these investigations, it appears that the sun has not radiated at its present rate for more than about twenty million years ; but taking account of the heterogeneity of its mass, I have shown that the duration might perhaps be lengthened to thirty million years as a maximum limit.
Though the foregoing law shows that the sun’s temperature will steadily rise as its radius shrinks, the area of its disc will diminish in more than corresponding degree. Now, the amount of heat received by a given square metre on the earth’s surface depends upon the size of the sun’s disc as well as upon its temperature ; and since the size of the disc is proportional to the square of the sun’s radius, while the temperature is inversely as the radius, it follows that the heat received by the earth will experience a secular diminution proportional to the contraction of the sun’s radius. Thus, in geological times the earth was warmer than it is now, which in general accords with known phenomena. May not this conclusion tend to elucidate the cause of the carboniferous era, and of those periods of considerable heat which followed it?
If we adopt the effective temperature of the sun experimentally determined by Wilson and Gray (Philosophical Transactions, 1894), which is about 8000° C., we see that when the sun’s diameter was twice as great as at present, the effective temperature, by the above law, was about 4000° C. ; and when the diameter of the disc was eight times as large as at present, the temperature was only 1000 C-, which would not, fuse the more refractory metals. The following table shows the effective temperatures of the solar nebula when it extended to the several planets:—
| Extent of solar mass. | Absolute temperature. | Below zero. |
|---|---|---|
| Present globe of the sun | 8000° C. | — |
| Orbit of Mercury | 92° | 181° C. |
| Orbit of Venus | 54° | 219° |
| Orbit of the Earth | 40° | 233° |
| Orbit of Mars | 24° | 239° |
| Orbit of Jupiter | 7° | 266° |
| Orbit of Saturn | 4° | 269° |
| Orbit of Uranus | 2° | 271° |
| Orbit of Neptune | 1° | 272° |
It is worthy of remark that as the present density of the sun is about 1.4. a contraction to one half its present radius, which would give a temperature of 16,000° C.. if the mass still remains gaseous, would make the density about 11.2. It is difficult to see how much further shrinkage under gaseous conditions could take place ; and hence, if the highest temperature of our sun is equal to that of the Sirian stars, it is probable that the temperature of the hottest stars is from 10.000° C. to 20,000° C.
As the terrestrial mass was very cold (—233 C.) when separated from the sun, it follows that what heat we observe in the interior of the globe must have arisen from the shrinkage of its original volume. Unfortunately, we do not know the dimensions of the nebular earth, but it will be reasonable to assume that they did not exceed the dimensions of the lunar orbit; and with this rough approximation, it is difficult to see how the internal temperature of the earth can have exceeded something like 1000° C. Moreover, it probably does not increase after a certain depth has been reached, but then remains essentially uniform throughout the interior of the globe. Contrary as it may seem to old theories like those of Laplace and Poisson, who assigned to the primitive mass a temperature of millions of degrees, there is no evidence that the temperature of the earth ever surpassed the melting point of lava and of the more refractory rocks. The retention of the terrestrial atmosphere is direct evidence that the primitive heat was quite moderate. For if the heat had been very great, the kinetic theory of gases shows that the molecules of our atmosphere would have been driven off into space.
As experiments upon the secular shrinkage of world - masses cannot be made in our laboratories, it is fortunate that the solar system offers to our observation large as well as small planets of approximately the same absolute age. We find the smaller planets, such as Earth, Venus, Mars, and Mercury, already solid, while the large planets, Jupiter, Saturn, Uranus, and Neptune, are apparently still gaseous, if not actually rising in temperature. The law of temperature shows that if bodies like Jupiter and Saturn are now gaseous, they have not been hot in the past, but may become so hereafter. There is some spectral indication of inherent luminosity in Uranus, and hence it is not improbable that all the large planets are still rising in temperature. As the temperatures of these masses were originally near the absolute zero of space, we are not to think of them as cooling, but rather as having slowly heated up ever since their separation from the solar nebula. The inferences of Kant, Zöllner, and Proctor, as well as the original assumption of Laplace, that the planets were originally very hot, must be wholly abandoned. It is possible, and perhaps even probable, that some of the large planets, especially Jupiter, may eventually become selfluminous.
The excessively low temperatures recorded in the foregoing table show that the matter which formed the planets must have been essentially solid when these bodies were separated from the solar nebula. If, on the one hand, these considerations indicate how little is known of the real process involved in the formation of our planetary system, they point the way, on the other, to lines of inquiry which future investigators should follow.
It is somewhat remarkable that while the law of gravitation causes bodies to describe conic sections, the law of temperature for every gaseous body is represented by a rectangular hyperbola referred to its asymptotes, and thus by a particular curve of the same general species. The law T = K/R certainly has the widest significance, and must be taken account of in all future researches on the temperatures and relative ages of the stars. The interpretation of spectral phenomena should at least conform to the more fundamental laws of gravitation and of temperature. In view of the undoubtedly high temperatures of the Sirian stars, it is not possible to deny that they are shrunk to small volume. Nothing could be more unwarranted than to connect such hot objects with the cold nebulæ which shine by some process of electric luminescence. The temperature curve indicates that the declining stage of a star’s life is probably very short, approximately the time required for such a hot globe to cool, when the source of heat is removed and the mass is allowed to radiate without shrinking, — which is to be reckoned at most in decades or centuries rather than in millions of years.
This remarkable law of temperature directs us as safely as the reappearing star does the mariner when wandering through the fogs of the unknown ocean, and vigorous prosecution of the lines of research suggested by it will assuredly open new vistas in the majestic drama of creation. Proceeding upon certain and exact principles that have been shown to be fundamental laws of the universe, and guided by the same consecration to truth which inspired the mighty investigators of old, it seems probable that at last we may not only penetrate the august processes of world-formation and world - decay, but even throw light upon the problem of the arrangement of the stars in space, and grasp the significance of the stupendous milky arch which spans the heavens as a perpetual inspiration to the mind of man.
T. J. J. See.