# Popular Science Monthly/Volume 13/September 1878/The Astronomical History of Worlds

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* THE ASTRONOMICAL HISTORY OF WORLDS.
By Professor DANIEL VAUGHAN.
THE information which geologists derive from the evidences of organic remains does not wholly satisfy the keen appetite of educated minds for a knowledge of the mysteries of Nature and the revolutions of past times. The relics disentombed from our globe give no clew to its origin; and they throw but little light on the great physical events which transpired before life appeared on its surface. There are, however, reasonable hopes that the records which are wanting on this earth may be supplied from the heavens; and that some general cause, to which the numerous orbs of celestial space are indebted for their existence, may be revealed from the peculiar character of their movements, or from some of the mysterious phenomena which they occasionally exhibit. In associating his researches with those of the geologist, and in taking cognizance of the great events in the course of time, the astronomer may enhance the value of the inquiries which more commonly fall to his lot. A knowledge of the condition of the earth in past ages is calculated to give much insight into the state of similar orbs in remote space; and opinions of the habitability of other planets must be more valuable in proportion as geology and terrestrial physics show more definitely how our globe acquired and how long it can retain the conditions necessary for the maintenance of life.
The tendency to widen the range of its inquiries and to speculate on the origin of the celestial bodies cannot be considered as a new feature of astronomy. The sudden appearance of the new stars, in 1572 and 1604, led Tycho Brahe and Kepler to the belief that the cosmical vapor or exceedingly rarefied matter of space was occasionally condensed to form great stellar orbs. These crude notions of the quick growth and ephemeral life of great suns were gradually replaced by views less repugnant to reason and experience. In the succeeding age the faintly luminous spots which the telescope revealed in the heavens were regarded as primitive chaotic matter exceedingly rarefied by intense heat, and they were supposed to be undergoing a slow cooling and a gradual condensation which would ultimately convert them into suns or into planetary systems. This opinion, however, though ​held by many astronomers, was controverted by others who maintained that the light, supposed to come from primitive fire-mist or nebulous matter, was in reality emitted by extensive sidereal groups, or vast universes too distant to show their individual stars. But, after some time, the round and the oval forms of many of these faint objects were looked upon as marks of a concentration around a centre, and the rare matter seemed to be emerging from its original chaotic state. It was thus that Kant, guided chiefly by the observations of Maupertuis, obtained a basis for his nebular hypothesis, which he published in 1755, and which, in essential features, differs little from that which has been held during the present century. Yet the subject excited little attention until many years afterward, when Sir William Herschel made his extensive and careful observations on planetary nebulæ, and pronounced them incipient solar systems, while he looked on irregular nebulosity as indicative of the presence of distant collections of stars.
As the doctrine founded on these observations was generalized by Laplace and supported by him with additional evidence, it obtained for a while much currency in astronomical circles; but it was seriously shaken in 1845, when many of the supposed embryonic systems of Herschel were resolved into stars by the powerful telescope of Lord Rosse. Yet, after a decline for a few years, the nebular hypothesis was revived on this side of the Atlantic by the announcement of Kirkwood's analogy; and some time afterward it obtained more decided support from the authority of Kirchhoff, as, on the discovery of spectrum analysis, it seemed to furnish a good explanation of solar phenomena. When Huggins obtained positive proof of the gaseous constitution of many of the irresolvable nebulae, the tide of scientific opinion set more strongly in favor of the views of Herschel and Laplace; but it was soon checked when it was found that all the true nebulous objects had a uniformity of composition, and consisted entirely of hydrogen, nitrogen, and an unknown gas. It seems impossible that the vast diversity of material objects in future families of worlds could be afforded by the agency of three elements, one of which is noted for its reluctance to take part in chemical combinations. In addition to this difficulty, the periodical and the permanent changes, detected in certain nebulous objects by Hind and Holden, differ widely from a slow transition into a planetary system; and they are fatal to the idea that these cosmical clouds were in past ages impassive to physical influences and departed little from their primitive condition. But facts still more difficult of explanation, in regard to these celestial objects, have been made known by the recent observations on Nova Cygni; and the apparent metamorphosis which was witnessed, of a temporary star into a nebula, was so little expected that theory seems much at fault; and it is evident that many of the views on this obscure department of astronomy must be either considerably modified or entirely abandoned.
According to the crude opinions prevailing during the infancy of ​modern science, matter and motion were all required for calling a world into existence; but it was soon found that, unless, in the beginning, the materials which formed the solar system moved with a certain order and regularity, they could never have risen from the chaotic to the cosmical condition. As all the planets move around the sun in the same direction, Laplace was led to believe that in remote times all must have been connected together; and such a primitive connection might be afforded if the sun and his attendants were originally a vast fire-mist, their matter being so much attenuated by heat that it extended far beyond its boundaries of the solar domain. He supposed that such an immense rarefied mass, on being set in motion by some cause which he does not specify, would ultimately be compelled by its own friction and by gravity to rotate with a uniform angular velocity in all its parts and around a common centre. In accordance with the principles of physical astronomy, he concluded that this rotation would become rapid as the immense solar nebula cooled and contracted, until at last the centrifugal force became great enough to overpower gravity and to throw off matter from the equator of the whirling mass. Laplace considered that, under the most probable circumstances, the nebulous matter thus thrown off, or abandoned by the shrinking spheroid, would all collect together to form a planet; but that, in some unusual cases, it would assume the expanded figure of a vast solar ring; and that, under certain conditions, it might break up into a number of asteroids. The singular group of bodies revolving between Mars and Jupiter is supposed to have come into existence in consequence of some rare accident, which made the great solar ring a prey to many centres of aggregation, instead of allowing it to coalesce around a single one. In all other cases, the cooling and contraction are said to have been successful in giving birth to a great planet, whenever the centrifugal force became sufficient to separate the equatorial portions of the rotating solar nebula. According to the views of Laplace, Neptune must be regarded as the first-born world of those already known; while Uranus is next in age, and the other planets were launched into being in a succession depending on their distances from the sun; so that Mercury is the youngest member of the solar family. It has been also concluded that from the condition of its birth each planet must have commenced its career as a rotating nebula; and that many of the larger ones, by subsequent cooling and contraction, were at certain periods enabled to throw off their equatorial matter, which in all but two instances was converted into a satellite. Of these minor worlds or moons, Saturn has succeeded in obtaining eight, in addition to the double ring, which in the eyes of Laplace appeared as two embryonic satellites, and which has been so often appealed to for proof of the world-making doctrine under consideration.
Yet, when examined with care and impartiality, the evidence derived from the condition of the Saturnian girdle will be found unfavorable, if ​not fatal, to the views which it has been so frequently adduced to sustain. The superficial character of the examination which Laplace has given to this subject is betrayed by two statements which he makes in regard to it in two different parts of his writings. In setting forth the nebular hypothesis in his "Système du Monde," he asserts that the matter separated from a contracting nebula would take and maintain an annular figure, if there were a complete uniformity in its entire circuit and in its rate of cooling; but in the "Mécanique Céleste," in treating on Saturn's rings, he concludes that their preservation would be impossible without some decided irregularities in their structure. It is scarcely necessary to say that the annular appendage could not be of long duration if the conditions necessary for its existence or security in one age were fatal to it at another. On examining the alleged history of its birth, also, we feel at a loss for some cause of intermission in the work of detaching matter from the cooling nebula. It is difficult to imagine why, after the outer ring was completed, the separation of matter from Saturn, after a long continuance, should have ceased for a while; and why, after the completion of the inner ring, the centrifugal force again became weak, and that it has declined steadily until the present time, when, at the planet's equator, it is scarcely one-sixth of the force of gravity. Since the period when Saturn is supposed to have launched forth the zone of matter circulating nearest to him, his movements could be but little retarded by tidal action; and there seems to be no cause which could reduce his angular velocity of rotation during a contraction from the loss of primitive heat.
Kant, who regarded the rings as composed of aëriform matter separated from Saturn, was led to the natural inference that the time in which the planet turns once on his axis must be equal to that which the nearest annular zone requires to make a circuit around him. From such considerations, the eminent savant was induced to assign for the rotation of the planet the period of six hours, twenty-three minutes, and fifty-three seconds. But this theoretical or predicted length of Saturn's day is only about three-fifths of the actual value which was first revealed by the observations of Sir William Herschel, and lately determined with more precision by Prof. A. Hall. From the difficulties which the facts present in this case, Laplace endeavors to extricate his doctrine of planetary evolution by maintaining that it requires only that Saturn's day should be shorter than the period of revolution due to the inner ring, supposed to be one unbroken solid mass. But the basis on which this conclusion is founded has been exploded by modern researches, which show the impossibility of the existence of such vast solid annular structures; and Prof. Kirkwood, though long a supporter of the views of the great French astronomer, has lately pronounced the evidence obtained from the Saturnian system and from the inner moon of Mars as adverse to the nebular hypothesis.
While all scientific researches are exposed to uncertainty in ​proportion as they aim to penetrate very far into space and time, the ordinary means for avoiding error are wanting, and mathematical investigation is unavailable, in dealing with the supposed primitive fire-mist to which the birth of worlds has been ascribed. It would be hazardous to attempt to calculate or to trace the precise effects of gravity, motion, and friction, on matter more than 100,000,000 times more rarefied than the air we breathe, and diffused over a spheroidal space more than 6,000,000,000 miles in extent. It may seem easy to suppose all its parts rotating with regularity in the same direction around a common axis; but it would be very difficult to determine how many millions of years or centuries must elapse before such a regular rotation of the entire mass would be produced by an impulse at any locality. Inquiries respecting the arrangement of matter in the primitive solar nebula may seem to come within the scope of physical science; yet they have been hitherto unproductive of the evidence expected from them. Reasoning from the principles of hydrostatics, Kant regarded the great density of the planets near the sun and the rarity of Saturn as a proof of their nebulous origin; and he ventured to predict that, on future discoveries, the most remote members of the solar system would be found to resemble comets, in being composed of very light matter and deviating widely from circular paths in their revolutions. Yet time has shown the fallacy of his predictions, and of the proof on which he placed so much reliance. The evidence which late writers have endeavored to deduce from the large size of Jupiter and Saturn is equally weak and unsatisfactory; for the most distant planets are not the largest, and there is no definite law calling for an increased size of worlds in proportion as they are distant from the solar orb. According to the most generally received theory of its variability, the star Algol presents the case of a remote sun with a planet nearly as large as himself, yet confined to so small an orbit that the period of revolution is less than three days. But the defects and the utter inadequacy of the hypothesis are rendered most apparent when it is called on to furnish an account of the origin of binary systems, and to show the cause of the great eccentricities of the ellipses which pairs of distant suns describe around a common centre of gravity.
In modern times the doctrine of the nebular origin of worlds has been much modified by new speculations and inquiries; and it has been extended far beyond the state in which it was left by Herschel and Laplace. More than twenty years ago Helmholtz advanced the hypothesis that the sun's heat and light are produced by the contraction of his mass; and that, in concentrating from primitive nebulous diffusion and shrinking to its present dimensions, the solar orb has derived from the same cause the calorific energy which enlivened the ancient world. When the views of Mayer, who regarded falling meteors as the solar fuel, were exploded, chiefly through the discoveries by the spectroscope, the contraction theory of Helmholtz gained many votaries; and it ​became more attractive as it held out the hopes of giving a means of definitely measuring vast periods of time. It was calculated that the concentration from a widely-diffused nebula to its present size would produce as much heat as the sun would lose in 20,000,000 years, according to the present rate of radiation. This period was accordingly fixed as the age of the sun and the duration of solar light. Another step was soon taken in this direction by fixing a limit to the age of worlds. It was concluded, with much confidence, that less than 20,000,000 years have elapsed since the earth became a planet, and that previously it must have formed a part of the solar atmosphere. In Prof. Tait's "Recent Advances in Science," the estimate obtained in this way for the age of our globe is placed between 15,000,000 and 20,000,000 years; and geologists are given to understand that they must recognize the infallibility of mathematical authority and abstain from their usual extravagance in making exceedingly large drafts on the limited fund of time.
But the conditions on which this surrender of geological belief has been demanded are far more liberal than any which the eminent mathematician is legitimately authorized to offer. The estimate on which he relies has been made for an homogeneous nebula supposed to be equally dense at its borders and in its central regions, whereas there must be a preponderating density near the centre, according to the necessary inferences from the doctrines of Laplace. This early central condensation must be adopted to account for the great mass of the sun compared with that of the planets. In an able investigation on the subject, in this point of view, published in Silliman's Journal in 1864, Prof. Trowbridge concludes that, even in the earliest stage of planetary development, there must have been a very great concentration of matter around the central nucleus of our solar nebula. If we adopt the law which he deduces for the rapid increase of density toward the centre, it may be found that the amount of heat due to contraction since the supposed birth of our world would not be enough to compensate for the calorific waste which the sun sustains in 1,000,000 years.
To obtain information of the age of the earth's crust from the increase of subterranean temperature with the depth, according to the method devised by Fourier, is an object to which much labor has been devoted, and from which valuable fruits may be expected. On this principle, the time since the permanent solidification of the surface of our globe has been estimated by Sir William Thomson at about 100,000,000 years. But this estimate, which is obtained by taking 7,000° Fahr. as the highest limit of internal temperature, will appear too low when we consider the vast amount of heat arising from the primitive concentration of terrestrial materials, and the obstacles which central density or igneous fusion may present to its escape. Instead, however, of controverting the peculiar views of the eminent scientist on physical geology, I will only trace the consequences to which they lead. He maintains ​that, in a molten globe, the rocks which became solid should sink into the fiery menstruum; that permanent solidification must have accordingly commenced at the centre and ended at the surface, leaving some internal lakes or pockets of lava to keep up volcanic action. Now, such reservoirs of molten rock should have a small size in order to receive a roof in opposition to the laws of hydrostatics; and, if much of the original fluidity of their contents is still preserved, notwithstanding their immense losses of heat, especially during volcanic eruptions, we are compelled to make a very high estimate of the time required for the solidification of a fused globe 8,000 miles in diameter; and we must conclude that the time since the earth was covered by a permanent crust is but a very small part of that which has elapsed since terrestrial matter began its career in a gaseous or in a molten condition.
Though deprived by recent investigations of much of the support first claimed for it by Hopkins, the doctrine of the almost total solidity of the internal earth is still held by many; and, in the hands of Thomson and Tait, it is made to contribute to the evidences of the youth of our planet. They consider that, with such a solid and inflexible constitution, the terrestrial structure must have retained almost immutably, to the present day, the exact shape impressed on it in the beginning. As the figure which it now bears differs little from that of equilibrium, and as the polar compression is nearly the same as that which the present diurnal movement would occasion in a molten world, it has been concluded that, during geological history, the length of our day has changed little, though it would be increased by tidal friction one per cent, in the course of 20,000,000 years. From such considerations, the period since our earth assumed its terraqueous character has been estimated at not more than 10,000,000 years. Yet, in the vague use of this round number for marking the career of our globe, there is shown a wish rather to fix a limit to geological time than to adhere to strict mathematical precision. So little does the earth deviate from a figure of equilibrium, and so imperfect are the means for ascertaining the exact amount of the deviation, that it would be hazardous to say whether the age obtained by this course for the terrestrial crust is nearer to 1,000,000 or to 10,000,000 years.
Far more satisfactory would be the issue in dealing with a case like the hypothetical one which Prof. Tait introduces for illustration. Alluding to the ancient world he says: "Suppose, for instance, that it had not consolidated at less than 1,000,000,000 years ago. Calculation shows that at that time, at a moderate computation, it must have been rotating twice as fast as it now rotates; that is to say, the day must have been twelve hours instead of twenty-four. Now, if that had been the case, and the earth still fluid throughout or even pasty, the double rate of rotation would have produced four times as great centrifugal force; and the flattening of the earth's poles and the bulging out of the equator would have been much greater than we find them to be." ​There is, indeed, no doubt that, under such circumstances, the flattening would be about four times as great as it is now, so that the difference between the equatorial and polar diameters would be about a hundred miles; and then the age of our world might be found as accurately as its distance from the sun. Now, the neighboring zone of the solar system presents an actual case very similar to the extreme one under consideration. The difference between the equatorial and polar diameters of Mars is at least three times as great as that which could be expected from his present rotation if he were in a fluid condition. On taking even the lowest values which observers give for his compression, it must be concluded that, since changing his primitive fluid state and becoming solid and inflexible, the planet must have lost about forty per cent, of its diurnal motion. It evidently follows, according to Prof. Tait's rule, that about 800,000,000 years elapsed since the solidification took place, supposing the length of the day of Mars increased at the same rate as that of our globe. But the same great number will seem scarcely adequate to express the centuries since the event, when we consider that the rotation of our planetary neighbor is checked, not by strong tidal friction, but by the more feeble impediment from the resisting medium of space.
In two publications, during 1856 and 1858, I discussed the geological consequences of the slow reduction in the earth's diurnal motion; and many reasons led me to the conclusion that the long-continued decline of centrifugal force would make our planet undergo a change of form, by the gradual retirement of water to the poles, and, after long ages, by the upheaval of the bottoms of the polar oceans. I also maintained that such upheavals of circumpolar lands would be prevented by the strength of the crust of a small planet, and that Mars would be able to preserve for an exceedingly long period the form impressed on him in the very early term of his existence. The earth's internal fluidity, which I regarded as playing a very important part in such rare paroxysmal events, has been long a favorite doctrine with geologists, and has been often invoked as a means of accounting for the oft-repeated cases of elevation and submergence in the ancient world. But, on a globe entirely solid and inflexible, there would seem to be no scope or even possibility of the vast changes recorded in geological history; and speculative astronomy, in curtailing the time and restricting the means of great physical revolutions, makes the information from organic remains difficult to be understood and deficient in value. Since the authority of Hopkins gave currency to the doctrine of the internal solidity of our globe, much scientific talent has been expended in attempting to account for the great geological changes; but the causes which have been appealed to would require millions of centuries to produce the results ascribed to them. It seems very difficult to set aside the opinion which has been formed of the high antiquity of the physical world, not only from the marks in the terrestrial crust of repeated ​elevations and depressions, but also from a knowledge of the insignificant alterations in the outline of continents during the last 3,000 years.
In the imaginary systems of celestial architecture which Aristotle and Ptolemy gave to mankind, there was a very narrow limit assigned to the extent of the heavens; the entire stellar host was supposed to be confined to a very scanty domain, and the human mind was prevented by these erroneous dogmas from rising to a knowledge of the magnitude or the riches of the universe. If science, in former ages, had been crippled by being restricted to too narrow a region of space, it cannot avoid suffering, at the present day, from being subjected to similar restrictions with respect to the range of time which its researches should embrace. On grounds as uncertain as those which sustained many of the exploded doctrines of antiquity, it has been too hastily concluded that the past career of the earth and the duration of solar light must have been comprised within the course of a few millions of years. It is even supposed that, within a like circumscribed period of change and activity, the myriads of solar systems in the wide domains of space around us came into existence from chaotic fire-mist which filled the entire universe. The transitory character which modern speculation would thus assign to many important cosmical arrangements will appear more surprising if contrasted with the long endurance of others, as revealed by the older and the ripe fruits of physical astronomy. From the planetary theories of Lagrange and Laplace it would appear that the future life of the solar family, if not absolutely eternal, must be many thousand or even a few million times as long as the period into which certain modern scientific writers are endeavoring to squeeze geological history. According to Proctor, 20,000,000,000,000 years must elapse before even Mercury can meet a natural death by incorporating with the sun; and this estimate, which I believe to be somewhat too high, is introduced here to give an idea of the opinions prevailing on the subject in astronomical circles. It may, however, be safely asserted that the future age of the earth cannot be much less than a million times as long as the period during which the sun's contraction could supply heat and light, at the equable rate which the purposes of life require; and there is no reason to admire a course of creation which makes worlds outlive so long their term of utility, and condemns solar systems in coming time to endure an interminable reign of darkness.
In proceeding to trace the course of the great cosmical events throughout the universe, it seems necessary to begin with a careful study of the permanent alteration in the movements of the earth and many of the celestial bodies. During the prevalence of the ancient doctrine of the immutability of the heavens, the occurrence of such unperiodical changes was denied. Even in modern times they were long ignored, as they proceed so slowly that it is only in a few cases that they can be revealed by the most refined methods of theory and observation. During the last century the doctrine of the uniformity ​of Nature held such a sway over scientific opinion that even slight accession of foreign matter to the earth by falling meteors would not be admitted. As, even at the present day, the origin of meteoric stones and shooting-stars cannot be said to be entirely free from doubt, I shall not introduce them for evidence in this stage of my inquiry, as items of the greatest certainty must claim the first attention. There is, indeed, no doubt that, if the mass of the sun were increased by falling meteors, his greater attractive power would make the planets describe smaller ellipses and occupy less time in their revolutions. Were the large worlds also to have their attraction increased by similar accessions of meteoric matter, they would reduce the orbits and quicken the speed of their satellites. Analogous results should be indirectly occasioned to both classes of planets by the resistance of the medium supposed to pervade space. But tidal friction is the best known impediment to planetary motion, and the changes which it slowly occasions in the condition and the career of the celestial bodies come more decidedly within the range of the investigations of modern science.
This retarding influence has been studied much in modern times, in so far as it affects the rotation of the earth, and even the movements of the moon. More than a hundred years ago Kant maintained that the tide-wave, in rolling from east to west, would reduce the earth's diurnal motion; but no positive proof of this conclusion could be given for a long time, in consequence of the peculiar difficulties of the inquiry and the imperfect condition of the tidal theory. Laplace, in dealing with the problem, concluded that within the last 2,000 years the length of the day has not been perceptibly affected by the alternate rise and fall of our oceans. But about thirty years ago, when science was enriched by the development of the doctrines respecting the conservation and the transformation of energy, the question of the effects of tidal friction was again opened for discussion, and Mayer was able to reproduce and to maintain on new grounds the almost forgotten doctrine of Kant. The evidence on which Mayer based his convictions was subsequently strengthened by a discovery which Prof. Adams made, of an error in the investigations of Laplace; and soon afterward Delaunay, in taking up the inquiry and repeating the previous operations with great care, found that the earth's diurnal motion is reduced on a scale corresponding to the waste of power involved in tidal movements. Although the amount of energy thus wasted has been estimated as over two thousand times greater than that of the united labor of the entire human population, yet so great is the stock of working force embodied in terrestrial rotation that 20,000,000 years must elapse before the length of our day is increased one per cent, by tidal friction.
The alteration which the moon occasions in terrestrial gravity is too small to be detected by the most delicate experiment; and it might remain forever unknown if our watery domain were not so sensitive to ​extraneous disturbance. A tidal force more than a thousand times greater prevails on the majority of the known secondary planets. If our globe, while keeping its present rotation, could exchange orbits with Jupiter's first satellite, our oceans would feel a periodical disturbance more than 20,000 times as powerful as that which now affects them; and perhaps few mountains would be high enough to escape being covered by the daily swelling of the waters. But by such a violent oceanic movement the earth's rotation should rapidly change until it kept pace with the revolution and then the destructive tides would come to a close, as our planet, having the same hemisphere ever turned to Jupiter, would ever elongate in the same direction, and our oceans would be elevated in the same localities. Now, all the secondary planets, so far as observation has been able to decide, have their movements so adjusted as to keep the same ever turned to the primary. This arrangement, so necessary for security against excessive tides in a terraqueous satellite, would be the inevitable result of tidal friction during past ages. Even in the absence of a liquid envelope, the same result would be produced by the deformation which a solid satellite would experience from the enormous tidal force, if it turned at such a rate as to present its different sides alternately to the primary.
Yet, notwithstanding this arrangement, a satellite would experience tidal oscillation, though on a lower scale, if its path deviated much from a true circle. If a watery envelope had been given to the moon in the same proportion as it has been to our globe, there would be tides occasioned by the periodical change of distance between the two bodies, the lunar waters pressing during nearly fourteen days to the points nearest and most distant from the earth, and then retiring to other localities. The friction in such tidal movements would have the effect of making the moon describe an ellipse somewhat smaller and nearer to a circle in form, but the alterations which it could produce in the lunar distance could not exceed two or three miles in the course of a million years. Yet the agency of permanent changes, so feeble in the supposed case, may in the vicinity of great central orbs, and in the absence of great periodical disturbances, become potent enough to impress peculiar features on the paths of secondary planets. To the tides which rose on their surfaces in past times, as well as to oscillations in their solid matter, the first and second satellites of Jupiter seem mainly indebted for their peculiarity in revolving in true circles; while in the orbit of the third moon there is a slight and in that of the fourth a considerable deviation from a circular figure.
I shall now proceed to the examination of cases in which the cause under consideration becomes far more potent, and under the required conditions makes its effects recognizable by observation, and admitting of no doubt. The powerful tidal action which a great central orb is capable of exerting in its immediate vicinity would render it impossible for satellites to hold their parts together if revolving close to its ​surface. In a somewhat wider zone, the planetary structure could be only preserved under the form of an ellipsoid, which would deviate widely from a sphere, not so much on account of its rotation as from the effects of the unequal attraction which its different parts receive from the primary. The accompanying diagram shows the equilibrium form of a satellite moving in a circle around a large sphere, both bodies
being equally dense and separated by small distances. In a somewhat greater proximity to the primary, the satellite would be reduced to a state of instability; and its matter, if not kept together by a great cohesive power, would scatter into independent orbits, and ultimately form a ring. There are, perhaps, in our solar domain too few cases to show how excessive tidal action can produce its definite results in its various degrees of power. If the nearest satellite of Mars bore to its primary such relations of size and density as subsist between the earth and the moon, it would, no doubt, surpass all known planets in deviating from a true sphere, even though its materials were not of the most yielding character. If similar relations existed between Saturn and his closest secondary, the latter would show a greater deviation than the primary does from a spherical form.
​In the limited number of cases which one system is capable of affording, we cannot expect to see the last struggles of a satellite to maintain its planetary structure when moving in a very close proximity to its primary. But the wonderful annular girdle around Saturn shows evidence not only of a great conflict for planetary existence in past times, but even of lesser ones, on an extensive scale, at the present day. From the investigations which I have published on the subject in the Philosophical Magazine, it appears that in the zone of the outer ring a satellite as dense as Saturn could not hold its parts together, and that one twice as dense could not move in safety in the central zone of the inner ring. If, in treating on stability in small orbits, I have generally supposed the satellite fluid in my papers on the subject, it was because they were chiefly intended to decide whether or not it was possible for the matter of the rings to unite and form two secondary planets.
The long-cherished idea that the rings are two integral solid masses is now generally abandoned. For such a constitution the nearer ring would require to be composed of materials over 200 times as strong as wrought-iron, in order to escape rupture; but even this condition could not avert destruction from other dangers to which it is exposed. From the estimates and observations of Bond, as well as from the theoretical researches of Pierce and Maxwell, it appears certain that the innumerable parts of Saturn's ring cannot be all connected together, in a rigid or permanent manner, but must move independently around the great planet. But, while affording much valuable negative information on the subject, the investigations of these eminent mathematicians do not show how the floating matter eternally circulating in these extensive zones is kept from concentrating into two satellites by the impulse of gravity. The cause which prevents this aggregation is to be found in the proximity of Saturn, whose tidal action either annuls gravity or reduces it so much in two directions as to render a planetary structure unstable; and though an incipient satellite may constantly grow by appropriating the floating matter around it, yet it must fall to pieces before it has attained any considerable magnitude. The state of the rings thus depends not on accidental but on inevitable circumstances; and, with this basis for our inquiries on the subject, we may arrive at very important information in regard to the past and the future condition of worlds.