Recent Discoveries Respecting the Origin of the Universe
I.
THE origin of the heavenly bodies was one of the earliest philosophical subjects which engaged the attention of the Greeks. With their keen sense of the beautiful and the orderly, and their genuine admiration of surrounding nature and of all celestial phenomena, they were the first to realize that the processes of cosmical evolution, by which the existing order of things has come about, must ever be regarded as one of the ultimate problems of the inquiring mind. Whence and how came the beautiful cosmos ? was the question of the Ionian naturephilosophers of the seventh century. Yet with even so keen an interest in natural phenomena, the undeveloped state of the physical sciences in the pre-Socratic age permitted the acute reasoning of Anaximander and Anaxagoras, and also of Democritus and Plato at a later date, to reach only the general conclusion that the earth and other heavenly bodies had gradually arisen from the falling together of diffused atoms. After the decline of the ancient civilization and the advent of the less philosophical races and ideas which continued dominant till modern times, further advances in a purely speculative, not practical or moral question could hardly be expected ; and we meet with no important cosmogonic inquiry till the publication of Kant’s Natural History and Theory of the Heavens, in 1755. In this work we have a distinct advance, based upon the laws of mechanics and of gravitation discovered in the preceding age by Galileo, Huyghens, and Newton; and hence the work of Kant is to be regarded as the first speculation founded upon exact physical laws. But in that age the whole question of cosmogony was so completely unfathomed, and so little was known of the universe of fixed stars, that Kant not unnaturally limited his inquiries to the most simple phenomena, and gave little consideration to the manifold detail with which all nature abounds. His most important contribution to cosmogonic thought consisted in the assumption (at that time nearly incredible) that the universe had not been created in a day or a week, but was the outgrowth of indefinite ages, under the operation of natural mechanical laws. Important as was this conception, and suggestive as was his theory of the formation of the planets from an extensive nebula originally including the whole solar system, it could hardly be expected that such heterodox ideas would get much consideration in the circles of court philosophy dominating the middle of the eighteenth century. Accordingly, they gained little or no authority, or even notice, for many years.
In the meantime France had become the centre of the philosophic world, and the great geniuses who adorned the Academy of Sciences just before and after the French Revolution — that strong impetus to new ideas, even though some should not survive the turbulent times in which they arose — were destined to arouse and to fix philosophic attention on the sublime question of the formation of the heavenly bodies. Five celebrated geometers — Clairaut, Euler, d’Alembert, Lagrange, and Laplace — in the course of fifty years had well-nigh perfected the mathematical theory of gravitation ; and Laplace, who had solved the problems which all his illustrious predecessors and contemporaries had declared to be insoluble, became above all others the dominant power in the scientific world. He had explained all known anomalies in the motion of the planets and the moon by the simple law of gravitation, and now for the first time it was possible to assign the exact places of the heavenly bodies in the most remote ages, account being taken of their mutual gravitation according to the Newtonian law.
Lagrange and Laplace had proved, under certain conditions holding among the planets, that the solar system would never be destroyed by the mutual gravitation of its parts, and hence they found no difficulty in conceiving its existence during past millions of years. After his unrivaled career of discovery, Laplace formed the design of presenting in his Système du Monde (published in 1796) a concise and luminous popular account of the existing state of astronomy, which he had done so much to perfect; and as if to add one more laurel to his brow, he inserted at the end of this work a Seventh and Last Note. This was the celebrated nebular hypothesis, which from its origin at once commanded the attention of the age. In a short note of eleven pages the author of the Mécanique Céleste has condensed his theory of the formation of the planets and satellites. He conceives that at some remote epoch in the past the matter now constituting our system was expanded into a vast rotating fiery nebula extending beyond the limits of the outermost planet, and that as the heat radiated into surrounding space the mass gradually contracted, and by the law of the conservation of areas began to rotate more rapidly. As the mass accelerated its rotation by its gravitational condensation, the whole assumed the form of an oblate spheroid, a disk, or a double convex lens ; finally, at the periphery of the disk the centrifugal force became equal to the force of gravity, and as the contraction continued a ring of particles was left behind, revolving freely around the central mass. The condensation of this ring of matter would form the first planet, and so on for the other planets nearer the sun, as the nebula condensed. The planetary masses condensing and rotating in like manner would give birth to their satellites. This simple mechanical conception would account for the motion of all the planets in the same direction around the sun and nearly in the plane of its equator, and also for the rotations of the planets and satellites in the same direction in which they revolve in their orbits. The rings of Saturn were cited as a case of an uncondensed satellite, a model which had been left undisturbed to show us just how the system had formed.
The nebular hypothesis as thus outlined by the profound dynamical judgment and imaginative genius of Laplace was supported by Sir William Herschel’s contemporary and independent discovery of all classes of celestial objects between the finished star and the embryo nebula, and this testimony to the truth of the nebular hypothesis was afterward confirmed by Sir John Herschel’s more critical survey of the nebulæ of the whole face of the heavens. But while both the mechanical speculations and the observations of the younger Herschel tended to support Laplace’s views, the huge reflector of Lord Rosse, erected about the middle of the century, began to turn the scale of evidence the other way. Under the power of Lord Rosse’s six-foot speculum some of the so-called nebulæ of Herschel were resolved into clusters, and the conclusion seemed imminent that under sufficient power perhaps all nebulæ might be resolved into discrete stars. Fortunately, the invention of the spectroscope about 1860, and Huggins’s application of it to the heavenly bodies, showed that many of the nebulæ are masses of glowing gas gradually condensing into stars, and so far as possible realized the postulates laid down by Laplace. The confirmation arising from the demonstrated existence of real nebulae in the sky was supplemented by Helmholtz’s proof that the heat of the sun is maintained by the contraction of its own mass, and that our central luminary is therefore the core of the nebula first conceived by Laplace in 1796. The theoretical possibility of Laplace’s assumption was further established by Lane’s investigation of the condensation of gaseous masses, wherein it was proved that a cold nebula or diffused body of gas condensing under its own gravitation would rise in temperature ; also by Lord Kelvin’s researches on the age of the sun and the duration of the sun’s heat; and by various researches into the actual conditions of the planets of the solar system.
But while all sound speculations since Joule’s discovery of the mechanical equivalent of heat have confirmed the essential parts of the nebular hypothesis, other recent investigations have introduced modifications of which Laplace took no account. It is particularly of these later discoveries, which throw an entirety new light upon the general problems of cosmogony, that we shall treat in this paper.
II.
Prior to the year 1875 the labors of astronomers and mathematicians had been devoted to the questions raised by Laplace over three quarters of a century before, and very little, if any, advance had been attempted on new lines, though many new researches and observations had been accumulating which confirmed the sagacity of the bold conceptions embodied in the Seventh and Last Note to the Système du Monde. About this time, the young mathematician G. H. Darwin, son of the illustrious naturalist, became occupied with certain tide-reductions undertaken by Lord Kelvin for determining the rigidity of the earth, and in the course of this work was led to develop the mathematical theory of the bodily tides which would arise in the earth on the supposition that it is not highly rigid as at present, but fluid, as, according to Laplace, it must have been at some past age. These researches were presented to the Royal Society between 1878 and 1882, and led to the conclusion that bodily tidal friction, as it is called, had played a prominent part in the cosmogonic history of the earth and the moon.
By tidal friction is meant the gravitational reaction arising from change of form due to tidal distortion of figure, with the resulting effects on the motions of bodies revolving around the tidally distorted mass ; for the attraction of a heavenly body depends upon its form as well as upon its mass and distance. Now, when the moon raises tides in the earth, the form of the latter (in case it were fluid throughout) would not be spheroidal, but ellipsoidal or egg-shaped, with one end of the ellipsoid pointed somewhere in advance of the moon in its orbit. This tidal apex in the earth exercises a disturbing force on the moon’s motion, and in fact tends to accelerate the velocity in the orbit, which results in an increase in the moon’s distance, and at the same time renders her orbit more eccentric, so that the earth is relatively nearer one end of her orbit the next time the moon goes round. This action is very minute, and, like the mills of God, grinds slowly, but in the course of immense ages, millions of years, the effects become very conspicuous and the whole character of the orbit is changed.
In this way, by a most profound analysis, Darwin showed that the moon was formerly much nearer the earth, and indeed a part of our globe, the whole probably rotating in about two hours and forty-one minutes ; that the moon, after parting from Mother Earth, had been gradually driven away to its present distance by the tidal action of the fluid globe working over a great space of time. He was enabled to explain all the essential features of the system of the earth and moon, and, encouraged by this novel and unexpected result, wherein tidal friction had modified the course of evolution as predicted by Laplace, he tried to extend his new theory to other parts of the solar system. But while he found that tidal friction had played some part in the other planets of our system and in the system as a whole, the effects in general were much less considerable than in the case of the earth and moon, where the satellite is relatively quite large, amounting to one eightieth of the planet’s mass ; elsewhere the satellites are very small compared to the planet, and all the planets are very small compared to the sun. Where the attendant bodies are so small compared to the central body, the effects of tidal friction are greatly diminished ; for, among other things, the effects depend on the mass and rotational velocity of the body in which the tides are raised. The mathematical methods which Darwin employed in his researches are extremely elegant, and in their line as appropriate as the proofs devised by his father in the Origin of Species, but it would be vain to attempt any popular account of them. It must suffice to say that we can trace our moon through the most remote ages by a simple process of computation.
After Darwin had developed the theory of bodily tides and applied it to the planets and satellites, he gave his attention to other researches on the figures of equilibrium of rotating masses of fluid, with a view to finding out exactly what process is involved in the birth of a satellite from a planet. Just prior to the publication of his paper a similar investigation was made in France by Poincaré. Both geometers had essentially the same object in view, namely, the testing of Laplace’s nebular hypothesis, and their results were identical in proving that a rotating mass (like the fluid earth when the moon was formed) would not break up into two extremely unequal parts, but that the two bodies would be fairly equal, or at least comparable, in size. Nor would the separation necessarily lead to the formation of a ring; the detached satellite might, and probably would, take instead the form of a lump or globular mass without the intervention of the annular form assumed by Laplace and previous investigators.
Comparing these results with the facts of the solar system, neither Darwin nor Poincaré could see that his profound researches had thrown much light upon the theories of cosmogony; for the satellites are quite small compared to their planets, and the planets are insignificant compared to the sun. I may remark here that the sun has a mass 1047 times larger than that of Jupiter, the largest planet, and 746 times the mass of all the planets combined. In the formation of our system, therefore, substantially all the matter has gone into the sun. Here the case rested in the year 1888, with no indication of further advance along either old or new lines. Indeed, such advance might be considered the more improbable as the problem had well-nigh baffled the efforts of two of the foremost mathematicians of the age, — one of them the successor of Newton, the other of Laplace.
III.
Apparently this was only the calm before a more decisive step than any which had yet been taken. Having always felt a deep interest in cosmogonic inquiries, and without knowledge of the results of Darwin and Poincareé I ventured to approach the general question of cosmogony from a new point of view. The first effort was elementary, of course, since it was made when I was still an undergraduate at the Missouri State University ; yet it contained the germ of the researches which have since occupied my attention. All previous investigators from the time of Laplace had fixed their eyes steadily upon the planets and satellites, and had given no attention to the universe of fixed stars. It seemed to me that something should be done to throw light upon the formation of the stellar systems, and therefore I set about the problem of explaining the formation of the double and multiple stars.
At first there were few results available for a careful study of the stellar systems, as the researches were scattered in all manner of publications, and no one had ever reduced the observations to a homogeneous form and sifted the wheat from the chaff. When this work had been hastily done, I found that the orbits are very eccentric, and in this respect totally unlike the nearly circular orbits of the planets and satellites. It was evident that it would not be possible to explain the formation of these systems if we could not account for the high eccentricities ; and it occurred to me as if by intuition that as the stars are melted fluid masses, not cold solid bodies like the earth, the mutual gravitation of two neighboring suns would raise enormous bodily tides, and the secular working of the tidal friction in the bodies of the stars would render the orbits eccentric. I had not then read or seen Darwin’s papers, and had only heard of them by popular reports which ignored their most important results. Before I got access to his works, I succeeded in proving that, under the conditions probably existing among the stars, the eccentricity of the orbits would steadily increase. To my surprise and to my delight, I afterwards found that Darwin had reached the same result ten years before, though it had attracted no attention, and was but little known. Indeed, no one had thought of the changes in the eccentricity except in connection with the orbit of the moon, and as this orbit is almost circular the matter was passed over in silence.
The subsequent investigation was based upon Darwin’s method, and consisted in showing that if two fluid stars were rotating about axes perpendicular to the plane of their orbital motion and in the same direction in which they revolve in their orbits, the tides raised in either star would react upon the other star, and by the action of tidal friction continued over great ages their orbits would be rendered more and more eccentric, so that they would finally resemble the elongated orbits of the periodic comets rather than the circular orbits of the planets and satellites. Now, continued investigation has proved that the orbits of the double stars are on the average twelve times as eccentric as those of the planets and satellites, and this is shown by my recent researches to be a fundamental law of nature, so far as we yet understand the visible universe. We reach, then, the remarkable result that tidal friction, working over millions of years, has elongated the orbits of the stars, and at the same time has expanded their dimensions, so that their paths are both larger and more eccentric than formerly. Going back in time, we reach an age when their orbits must have been smaller and rounder than at present, and at last when the two stars were parts of the same nebula. The agency of tidal friction, which Darwin showed to be of small importance in our system, except in the case of the moon, is thus shown to be of general application and of the vastest significance in the universe at large, because the bodies constituting the stellar systems are not solid, but fluid, not very unequal, but equal or comparable in mass, so that the tidal effects are enormously increased. The stellar systems are thus different from our system in two respects : —
(1.) The orbits are highly eccentric, on the average twelve times more elongated than those of the planets and satellites.
(2.) The components of the stellar systems are frequently equal and always comparable in mass, whereas our satellites are insignificant compared to their planets, and the planets are equally small compared to the sun.
I may add here that about ten thousand double stars have been discovered since the time of Sir William Herschel, and that of this number about five hundred objects are known to be in motion. In the course of the past century only about forty have shown sufficient motion to enable us to fix their orbits accurately, while about twenty more may be determined approximately. The longest-period binary star known with certainty is Sigma Coronæ Borealis, which completes its immense circuit in about three hundred and seventy years ; it has thus made but little more than one revolution since Columbus landed in America. Other systems have periods ranging from two hundred and thirty to eighty years; while others are still more rapid, completing their orbits in only twenty-five, eighteen, eleven, and five and a half years. This last is the period of a small star just visible to the naked eye, situated in the constellation Orion ; its rapid motion, detected by me during the present year, has now made it the most interesting of all double stars. It is known as Burnham 883, from the astronomer who first noticed its duplicity in 1879. Since that time it lias made more than three revolutions, yet so difficult is the object that it can be investigated only with very powerful telescopes. Our observations last year with the Lowell twenty-four-inch refractor were the first to furnish the key to its mysterious movement.
The known periods of the binary stars, therefore, vary from five and a half to about three hundred and seventy years. In other cases, yet to be investigated, it is certain that thousands of years are required for a single revolution, while some of the close and difficult stars now being discovered are likely to give periods even shorter than five years. The distances of some of the systems from the earth have been carefully measured, and we are thus enabled to compare them with our solar system. The companion of Sirius, for example, completes its period in about fifty years, and moves in an orbit somewhat larger than that of Uranus, the mean distance from the central star being twenty-one times the distance of the earth from the sun. In the case of 70 Ophiuchi the period is eightyeight years, and the mean distance about twenty - eight times the distance of the sun. This system is celebrated for the long period over which it has been observed, and the perturbation by which its motion is affected; there is some dark body or other cause disturbing the regularity of its elliptical motion, but heretofore all efforts to see it with the telescope have been unsuccessful. Alpha Centauri, the nearest of all the fixed stars, is removed from us 275,000 times farther than the sun ; the companion is found to revolve around the central star in an orbit with dimensions which are about a mean between those of Uranus and Neptune. Its period is eighty-one years, and each of the stars is just equal to our sun in mass. In the case of Sirius the mass is 3.47, and in that of 70 Ophiuchi it is 2.83 ; the combined mass of the sun and earth being unity. It is thus seen that the stellar systems are grand almost beyond conception, and the investigation of such glorious natural phenomena may well occupy our attention.
How, then, did the double stars originate ? By the breaking up of a Laplacean ring ? Certainly not. It had always been a favorite objection of those who did not accept the process of separation outlined by Laplace to say that there are only a few ring nebulæ in the heavens, and that what few exist are by no means so regular as the rings of Saturn ; but at this point the objectors ceased. In my earliest essay, before I was acquainted with the researches of Darwin and Poincaré on rotating masses of fluid, I suspected that the double stars arose from double nebulæ by a division into two nearly equal masses. As soon as I ascertained from the papers of Darwin and Poincare that such a division was theoretically possible, I no longer hesitated to affirm that if their results were inapplicable in the solar system, they were of the widest application among the stars ; and this conviction was made a certainty when I found from the drawings of Sir John Herschel that double nebulae exactly resembling the figures computed by the mathematicians actually exist in the heavens. These admirable sketches of Hersehel had been published in the Philosophical Transactions of the Royal Society for 1833, and were now almost forgotten. Darwin and Poincaré had looked for applications of their results in the solar system, but it was only among the stars and nebulæ of remote space, with the details of which neither was acquainted, that the real discovery was to be made ; and it was possible only to one who held in mind the results of mathematical analysis on the one hand and those of Herschel’s observations on the other. We may conclude, then, that the annular process by which Saturn’s rings were separated, while a theoretical possibility, is not generally realized in the actual universe, but that the nebulæ divide into two nearly equal parts by a process externally resembling “fission" among the protozoa. When the rotating mass has thus divided into two nearly equal parts, each part will begin to rotate on its own axis, and the tides raised in either mass by the attraction of the other will cause the orbit to grow gradually larger as well as more eccentric, and in the course of some millions of years we shall have a double star such as Alpha Centauri or 70 Ophiuchi.
It may be pointed out here that notwithstanding all the labors of astronomers on double and multiple stars since the time of Sir William Herschel, they have not yet recognized in all the immensity of the heavens a single system in any way resembling our own. The obstacle to seeing such insignificant bodies as our planets at the distance of the fixed stars is at present insurmountable even with our largest telescope; and henee we must not conclude that systems like our own — a star with a large number of small dark planets — do not exist in the heavens, but only that all such bodies would be invisible even if the power of our telescopes were increased a hundredfold, and consequently no such systems are known.
On the contrary, we do know of several thousands of stellar systems of a radically different type; indeed, I myself have augmented by several hundred the number of such systems during the past year, in the course of a survey of the southern heavens undertaken by the Lowell Observatory. These systems are composed of two or more self-luminous suns moving under the law of gravitation, and subject to the tidal effects described above. It is very singular that no visible system yet discerned has any resemblance to the orderly and beautiful system in which we live; and one is thus led to think that probably our system is unique in its character. At least it is unique among all known systems. Our observations during 1896-97 have certainly disclosed stars more difficult than any which astronomers had seen before. Among these obscure objects about half a dozen are truly wonderful, in that they seem to be dark, almost black in color, and apparently are shining by a dull reflected light. It is unlikely that they will prove to be self-luminous. If they should turn out dark bodies in fact, shining only by the reflected light of the stars around which they revolve, we should have the first case of planets — dark bodies — noticed among the fixed stars. The difficulties of seeing these objects may be imagined when we recall that they are visible only in the blackest and clearest sky, when the atmosphere is so still that the definition of the great telescope is perfect; even then they are recognized by none but the trained observer.
These reflections, as well as investigations on the perturbation of certain stellar systems, lead us to suppose that there are many dark bodies in the heavens ; but not even such bodies furnish us evidence of any other system similar to our own, as respects complexity and orderly arrangement. It must therefore strike every thoughtful person as astonishing that all the previous cosmogonic investigations should be based upon facts derived from the planetary system, which is now shown to be absolutely unique among the thousands of known systems, and in the present state of our knowledge appears to be an exceptional formation. In like manner it cannot fail to surprise us to recall the historical fact that it took two centuries after Newton detected the cause of the oceanic tides upon the earth’s surface for any one to conceive the existence of bodily tides; and after Darwin had developed his theory of tidal friction, it still apparently had little place in philosophic thought till it was extended and applied to the stellar systems observed in the immensity of space. Aside from this delay, it is alike gratifying and honorable to the human mind to recall that the tidal oscillations first noticed by the navigators of our seas are at last found to be but a special case of cosmic phenomena as universal and almost as important as gravitation itself, and that by the known laws of these phenomena we are enabled to interpret the development of the universe, — a great mystery extending over millions of years, and therefore forever sealed to mortal vision.
These recent cosmogonic investigations have also enabled us to realize for the first time that the visible universe is composed mainly of fluid bodies, selfluminous stars and nebulæ, and that some day celestial mechanics will become a science of the equilibrium and motions of fluids. To the theory of the mutual action of solid bodies according to the old theories must be added secular tidal friction, which by its cumulative effects may in time enormously modify the figures and motions of the heavenly bodies.
It may not be inappropriate to add that these recent researches among the stars have thrown a new light upon the formation of the planets and satellites. If the nebulæ as a class do not shed rings which form into stars, but divide into globular masses, as mentioned above, may it not be that the planets and satellites also were separated in the form of lumpy masses ? It is now known, by investigations made since the time of Laplace, that such a separation is a mathematical possibility; and as this avoids the necessity of explaining how a regular ring would condense, — a thing not easy to understand, — and as the planets now have a globular form, it is the most acceptable explanation that can be made. The objection has frequently been raised by mathematicians that a great outspread ring, such as Laplace imagined, would rapidly cool off, and become a swarm of small particles like those now constituting Saturn’s rings, and that such particles could never get together to form a single large body. To me this reasoning appears valid, and hence I take it that rings such as Laplace supposed never existed in the solar system, except in the case of Saturn’s rings and possibly the asteroidal zone between Mars and Jupiter.
It follows from the researches of Darwin and Poincaré that if the rotating nebula be extremely heterogeneous, very dense in the centre and very rare at the surface, the portion detached would be much smaller than in case the mass were homogeneous. Hence if in the beginning the solar nebula were very heterogeneous, it might detach small masses such as the planets and satellites; and on this view the formation of our system would be exceptional only as regards the primitive condition of the solar nebula. Since we find that the number of the asteroids is unlimited, and that they are scattered over a very wide belt, it seems fairly certain that by whatever process they were formed, the matter was originally diffused over the whole zone now occupied by them. A ring such as Laplace conceived would probably condense into just such a multitude of small masses. In the case of Saturn’s rings another cause comes into play, and prevents them from ever forming one or more large bodies. This is the tidal action of the planet upon bodies near its surface, — or within a certain distance called Roche’s limit,— and it happens that the rings of Saturn are actually within this critical distance. Even if the particles of the rings were to get together within this region, the tidal action of Saturn upon the resulting mass would tear it to pieces, and the particles would again be diffused into rings such as we now find about the planet. The rings of Saturn will therefore never form a satellite.
For the same reason satellites or planets could not exist too near the surface of Jupiter or the sun. All the known satellites are without this limit for their respective planets, but Jupiter’s fifth satellite, discovered by Barnard in 1892, is perilously near the danger - line within which it would be disintegrated by the tidal action of Jupiter.
It will be clear from the foregoing that the principal hope of cosmogony lies in the study of the systems of the universe at large rather than that of our own unique system, though the correct explanation of the planetary cosmogony will always be a desideratum of science. What is needed is a profound investigation of the stellar systems, of the double nebulæ, and of certain branches of celestial mechanics, particularly the theories of the figures of equilibrium and of the bodily tides of gases and liquid masses and their secular effects under conditions such as exist in the heavens. The time has now come when it is no longer sufficient to be able to predict the motions of the heavenly bodies in the most remote centuries; we must essay to trace the systems of the universe back through cosmical ages, and to investigate from laws and causes known to be at work in the heavens just how the present order of things has come about. The solution of this sublime problem, even if it takes centuries for its full realization, will be an achievement not unworthy of the past history of physical astronomy.
T. J. J. See.