"At the beginning the universe consisted of a general chaos, of extreme tenuity, formed of all the elements of Chemistry more or less mixed and confounded together. These materials under the force of their mutual attractions were, from the beginning, endowed with diverse movements which brought about their separation into masses or clouds. These still retained their movements of rapid translation, and very gentle interior gyrations. These myriads of chaotic fragments have given birth, by means of progressive condensations, to the diverse worlds of the universe."
(2)So much for the formation of the universe, including, of course, the solar system, for which he acknowledges the necessity for the intervention of a creating power, because it is impossible to account for it simply by the laws of nature; and adds: It is unnecessary to say that the universe is an indefinite series of transformations, that what we see results logically from a previous condition, and thus necessary in the past as in the future; we cannot see how a previous condition could tend towards the immense diffusion of matter, to the chaos out of which the actual condition has arisen; and that it is, therefore, necessary to begin with a hypothesis, and postulate of God, as Descartes did, the disseminated matter and the forces which govern it.
(3)From dealing with the universe, M. Faye comes to the formation of an isolated star, and begins with an entirely ideal case, that of a spherical homogeneous mass, without interior movement of any kind, and concludes that the molecules would fall in straight lines towards the centre; that the mass would condense regularly without losing its homogeneity, and would end in producing an incandescent sphere perfectly immovable; and that that would be a star, but a star without satellites, without rotation, without proper movement. This not being what was wanted, he goes on to show how, previous to its separation and complete isolation from the universal chaos, such a mass would possess, and carry with it when separated, a considerable velocity of rotation, and would still retain the internal movements it had acquired from the attraction of the other masses with which it had been previously in contact; and how the molecules, drawn towards thecentre in obedience to gravitation, would not fall in straight lines but in concentric ellipses.
(4)From this state of affairs, two very different results might arise. One, that the molecules might resolve themselves into a multitude of small masses without the centre acquiring a preponderating increase. The other, that the central condensation might greatly exceed the others, and there would be formed a central star accompanied by a crowd of small dark bodies. M. Faye accepts the second result, in which case the ellipses described by the small bodies, now become satellites, would, as the central mass increased in preponderance, have one of their centres at the centre of the preponderating mass, and their times of revolution would vary from one to another in conformity to the third law of Kepler.
(5)For the formation of the solar system M. Faye finds that it is of little importance whether the movements of bodies around the sun be very eccentric or almost circular; the first cause is always the same. They arise from the eddies,tourbillonnements, they have brought with them from their rectilinear movements in the primitive chaos. But the circle is such a particular case of the ellipse, that we ought not to expect to see it realized in any system. It is therefore necessary that, among the initial conditions of the chaotic mass, one should be found which would prevent the gyrations, eddies, from degenerating into elliptical movements, and which has at first made right, and afterwards firmly preserved, the form, more or less circular, in all its changes.
(6)For the formation of circular rings he gives us the following conceptions: In order that a star should have companions, great or small, circulating round the centre of gravity of the system, it is necessary that the partial chaos from whence it proceeded should have possessed, from the beginning, a gentle eddying movement affecting a part of its materials. Besides, if the partial chaos has been really round and homogeneous, we shall see that these gyrations must have taken up, and to some extent preserved, the circular form. He then requests the reader not to lose sight of the feeble density of the medium, in which a succession of mechanical changes areto be brought about; and not to conclude that that density was such that a cubic miriamètre of the space occupied by it might not contain 3250 grammes of matter, as he stated in the preceding chapter (we think he said 5217 grammes), but that it might contain only 3 grammes or even less. And adds that in such a medium, the small agglomerations of matter which would be formed all through it, would move as if they were in an absolute vacuum, and any changes in them would be produced extremely slowly.
(7)Then he goes on to say that the gyrating movements belonging to the chaotic mass, would have very little difficulty in transforming a part of a motion of that kind into a veritable rotation, if this last were compatible with the law of the internal gravitation; that it is the nature of that kind of masses to only permit, to the bodies moving in them, revolutions, elliptic or circular, concentric and of the same duration; that therefore notable portions of the gyrating matter could take the form and movements of a flat ring, turning around the centre with the same angular velocity, exactly as if this nebulous ring were a solid body; that all the particles which have the proper velocity in the plane of the gyrations, will arrange themselves under the influence of gravitation in a flat ring with a veritable rotation around the centre; that any other parts having velocities too great or too small, will move in the same plane, describing ellipses concentric to the ring; that if the ellipses are very elongated the materials composing them will approach the centre, where they will produce a progressive condensation, communicating to the central globe formed there a rotation in the same plane with the primitive gyrations; and finishes off the whole scheme by specifying the first results to be: (1) The formation of concentric rings turning in one piece, in the manner of a solid body, around a centre almost empty (d'abord vide); and (2) A rotation in the same direction, communicated to the condensation which would be produced, little by little, by means of matter coming in, partly, from regions affected by the internal eddyings (tourbillonnements).
(8)It is unnecessary to go any farther, and take note of his method of the formation of planets and satellites from rings, as it is much the same as what we have seen described by others who have written on the same subject; only interpreted by him in a way to suit his own purposes, and in which interpretation he does not do full justice to Laplace, through not having paid sufficient attention to his explanation of how planets could be formed out of rings. Except in so far as to note that all along he has considered that rings were formed, and even those nearest to the centre condensed into globes, long before the central condensation had attained any magnitude of importance, or assumed any distinctive shape, and that afterwards all the disposable matter of the rings and also all the exterior matter that had not formed part of what was separated from the original universal chaos, had fallen in towards the small central mass, and so completed the formation of the sun last of all.
We shall now proceed to make a few remarks with respect to this condensation of M. Faye's cosmogony, which we think we have made without adding to or omitting anything of importance that we have met with in his work, for which purpose we have numbered the paragraphs containing it, in the last six pages, in order to do away with the necessity of repeating the parts to which we refer.
No. 1.All those who believe that "the solar system did originate somehow, by the condensation of a primitive nebula," agree with M. Faye in considering that the density of the nebulous matter must have been extremely low, and some of them seem almost to vie with each other in showing how great must have been the degree of its tenuity; but M. Faye is one of the few who, paying due respect to the law of the interdependence of temperature and pressure in a gas or vapour, maintain that it must have been almost devoid of temperature, and we have to acknowledge that he is in the right. Then we believe that his assumption, that the whole universe of stars, including the sun, was created, humanly speaking, about the same time, is shared by the great majority of those who have thought at all seriously on the subject. Also, we agree with him firmly in his statement that each star—and weadd planet, satellite, etc.—was originally supplied with an extremely limited quantity of heat, and that what it has expended and what it still retains has been derived entirely from the condensation of the original cosmic matter out of which it was made.
With regard to his theorem: we cannot follow him in his statement that the diverse movements caused by the mutual attractions of parts of the original universal mass of cosmic matter, have brought about its separation into myriads of fragments; nor how these fragments could carry with them a rapid movement of translation, unless the whole universal mass was endowed with a rapid movement of translation through space, in which case we think that such a motion would have had no greater particular effect in producing new forms of motion in the fragments, than if the whole had been created in a state of rest. Stray movements of translation might give rise to collisions among the multitude of fragments, and perhaps that was one of the modes of formation into suns through which they had to pass; but we cannot follow it out. Neither can we see clearly how translation could be effected of one mass into the space occupied by another mass—unless empty spaces were reserved for that purpose from the beginning. Without that, translation could not exist: it would be collision.
No. 2.We have nothing to object to what is said in this paragraph; except that a rotating sphere might have been postulated at once, in imitation of Laplace, instead of trying like Descartes to join fragments together, endowed with movements so adjusted that, among the whole of them, they would produce in the whole mass, when united, the kind of movement that was wanted.
No. 3.To the ideal case of the formation of an isolated sun from a homogeneous mass without interior movement of any kind, we cannot agree in any way. The molecules of matter would not, could not, fall in towards the centre in straight lines. Their mutual collisions would drive them generally in curved lines in all directions as they fell in, which would create new internal movements; and these movementswould prevent the possibility of the formation of an immovable incandescent sphere such as is described. There could be no immobility in the interior of a sun, as long as its temperature was sufficient to keep the surface incandescent. But we cannot give our reasons here for this assertion—to most people they will, we think, occur at once—because we have a long road to travel before we can do so.
When M. Faye abandons the isolated case, he leaves us without giving us any help, to conceive for ourselves how the mass would possess and carry with it a considerable velocity of rotation, and still retain the internal movements it had acquired from the attraction of the other masses—of the universal chaos—with which it had been in contact; and also how the molecules drawn towards the centre would not fall in straight lines but in concentric ellipses. And this last we have to do without his giving us any reason why the molecules should fall in towards the centre at all; or rather in spite of the fact that one of his principal ideas would lead us to expect exactly the contrary, as we shall see presently.
No. 4.Here he places before us again, two cases in one of which the molecules might resolve themselves into a multitude of small masses, without the centre acquiring any preponderating increase; and the other where the central condensation might greatly exceed the others, and there would be formed a central star accompanied by a crowd of small dark bodies, now become satellites, describing ellipses around the central preponderating mass. This second case he seems, for the time being, to accept as the most probable; but it is strangely at variance with what he sets forth afterwards. He does not give us the least hint as to why or how the satellites acquired their various times of revolution, but only assumes that they did so; and we are very sure that it was not the third law of Kepler that was the agent in the case, however much it might suit his purpose.
No. 5.Although this part of his exposition is dedicated to the formation of the solar system, all that M. Faye says is that it is of little importance whether the movements of bodies around the sun be very eccentric or almost circular;and that among the initial conditions of the chaotic mass, all that we require is that one should be found which would prevent the gyrations from degenerating into elliptic movements, and which had first put right and afterwards firmly preserved the form, more or less circular, in all its changes. But he does not make any attempt to show what that one condition is, and allows us to find it out for ourselves.
No. 6.What M. Faye says about the formation of circular rings is more or less a repetition of what he has adduced, to explain all the other movements which he has derived from the universal chaos; and which he seems to think sufficient to account for such movements being nearly circular. For our part we do not think they are sufficient, and he does not show us how they influence each other to bring about the final movements he wants to present to us.
We duly take note of the tenuity of the cosmic matter on which he operates, which at 3 grammes in weight to 1 cubic miriamètre would correspond to one grain in weight to 771,947,719,300 cubic feet of space, or 1 grain to a cube of 9173 feet—more than 3000 yards—to the side. We do this in order to remind him of what he says at page 151 of his work, when dealing with the rotation of the Kant-Laplace nebula—namely, that it is impossible to comprehend how an immense chaos, of almost inconceivable tenuity, could possess such a rotation from the beginning, and that for want of that inadmissible supposition nothing remains to fall back upon but themouvements tourbillonnairesof Descartes. Thus he wants us to believe that histourbillonscould move in straight or curved lines, have motions of translation, could attract, restrain, and drive each other into all sorts of movements with the tenuity he has indicated; but that Laplace's nebula, with a density of 1 grain to a cube of 90 feet—or at most 150 feet—to the side, could not be conceived to have the single movement of rotation. And lastly, we repeat that if the centre of the chaos was almost empty, we do not see what induced the cosmic matter to fall into it in elliptic orbits.
Nos. 7 & 8.In these paragraphs, the main features are repetitions of the simple assertions made in all the others,that certain movements possessed by matter in one state would produce other movements in another state, without attempting to show how they all came to so far coincide with each other and form one harmonious whole, with movements in almost one single direction. It is clear that one side of the separated chaos might have acquired motion in one direction from the universal chaos with which it had been in contact, and that the opposite side might have acquired motion in exactly the opposite direction from the original chaos with which it had been in contact; and we are left to find out how these came to agree with each other in the end. And, going back to the beginning, we are left to find out where the mass, out of which he constructs his solar system, was stowed away, after it was separated from the original universal chaos. We can conceive of its being separated by condensation, in obedience to the law of attraction, from the surrounding chaos, in which case it might fall towards a centre, or that some parts of it might come to revolve round each other, and that finally the whole of these parts might come to rotate about a common centre; but that is evidently very different from the mode of formation of the solar system which M. Faye has advocated. It comes to be by far too like the nebula which Laplace supposed to be endowed with rotary motion from the beginning, probably because he did not see, or did not take the trouble to see, how such a motion could be produced. In any case, Laplace did not consider that the primary motion of rotation was the most important part of his hypothesis; neither was it, as it seems to have been in the case we have been considering. And he did not go much further than M. Faye in postulating primary motion, only he did it in a more effectual and business-like manner. He drew on the bank at once for all the funds he required, instead of having to draw afresh every time he found himself in difficulties, as has been the lot of his critic and successor.
Finally, M. Faye tries to show that after all his rings, flat or otherwise, converted or not converted into globes, had been formed according to his ideas, the greater mass by far of the chaos had fallen into the centre, and had formed the sun therelast of all. Now, if the preponderating mass of the chaos had been outside of the field of his operations, up to the period when all his planets, satellites, etc. were formed, or at least laid out, it is more natural to suppose that the matter inside of his structure, if there was any, would be drawn outwards by the attraction of the greatly preponderating mass outside, than that any portion of it should have fallen in, in elongated ellipses, towards the insignificant mass that he supposes to have been inside his structure. This, of course, would be nearly exactly the reverse of the mode of formation he was trying to demonstrate, and clearly shows that he was working on unsound principles from the beginning to the end of his cosmogony. It had never occurred to him that matter could be attracted outwards as well as inwards, most probably because it would seem to him ridiculous to imagine that anything in the universe couldgravitateupwards.
There are other theories of the formation of the solar system from meteorites and meteors, giving us the idea of its being made out of manufactured articles instead of originally created raw material, which does not in any way simplify the process. In some of them, the inrush of meteor swarms is invoked as the cause of gyratory motion, which places them in much the same category as impact theories. We know that broadcloth is made out of woollen yarn, but we also know how the yarn is made out of wool, and how it is woven into the cloth, whereas we are not told by what process, or even out of what the meteors and meteorites are made, although some of them are said to have thumb-marks upon them.
All these theories and cosmogonies may be very appropriately classified as variations of the nebula hypothesis, and like variations in another science, may be very brilliant, scientific, imaginative, grand, but after all the flights of fancy exhibited by them are set before us, we feel in a measure relieved when a return is made to the original air. They all assume original motion, varied, accidental, opportune, more dependent upon the will of the cosmogonist than on the laws of nature, which tend to confound rather than enlighten any one who tries to understand and bring them, mentally, intoactual operation. Laplace assumed rotary motion for the whole of his nebula, and was thus able to account at once for the relation which exists among the planets in respect of distance from, and period of revolution around the sun—arising from the original rotation of the whole mass in one piece—a result which, in any impact theory, has to be accounted for separately, and, in plain truth, empirically in each case, and at each step.
Seeing, then, that we have not been able to find any cosmogony, or speculation, that gives us a more plausible idea of how the solar system has been formed, we shall try whether from the original nebula as imagined by Laplace, it is possible to separate the various members, and form the system in the manner described in his celebrated hypothesis. In other words, we shall endeavour to analyse the hypothesis.
Itmay be thought that there is little benefit to be derived from analysing an hypothesis which has been declared, by very eminent authorities in the matter treated of, to be erroneous in some points of very serious importance; but hypotheses are somewhat of the nature of inventions, and we know that it has often happened that many parties, aiming at the same invention, have altogether failed, while some other person using almost exactly the same means as his predecessors, has been entirely successful in his pursuit. How many times has it been pointed out to us, that if such a person had only gone one step further in the process he was following, or had only studied more deeply the matter he had in hand, he would have anticipated by many years one of the greatest discoveries of the age! In some cases the failure to take that one step was occasioned through want of knowledge acquired long years afterwards; whereas we think that in the case we have in hand, it can be shown that the want of knowledge acquired many years after he had formulated his hypothesis, or ifotherwise, the want of faith in what he knew, enabled Laplace to construct an edifice which otherwise he could hardly have convinced himself could be built up in a practical form. We think also that if he had made the proper use of the knowledge he must have had of the law of attraction, he would have seen that no nebula could ever have existed such as the one he assumed, extending far beyond the orbit of the remotest planet. Furthermore, we think it can be shown that if he had thoroughly considered what must have been the interior construction of his nebula, he would have found one that would have suited his hypothesis in the main point, viz. condensation at the surface, at least equally as well as endowing it with excessive heat. But to be able to show these things our first step must be to analyse the hypothesis, to examine into it as minutely and deeply as lies in our power.
For this purpose it will be necessary to define what the hypothesis is. Many definitions have been given, more or less clear, and it would be only a waste of time to try to set forth Laplace's own exposition of it, with all its details, which he had no doubt studied very carefully. But in those definitions that have come under our observation, several of the conditions he has specified are wanting, or not made sufficiently prominent; so instead of adopting any one of them we will make a sort of condensation of the whole, adding the conditions that have been left out; because the want of them, has been the cause of mistaken conceptions of the evolution of the system having been formed by very eminent astronomers. Our definition will therefore be as follows:—
(1)It is supposed that before the solar system was formed the portion of space in which its planets and other bodies now perform their revolutions and other movements, was occupied by an immense nebula of cosmic matter in its most simple condition—of molecules or atoms—somewhat of a spherical form, extending far beyond its present utmost limits, and that it was endowed with excessive heat and a slow rotary motion round its centre; which means that while it made one revolution at the circumference it also made one at the centre. The excessive heat, by counteracting in a certain measure theforce of gravitation, kept the molecules of matter apart from each other; but as the heat was gradually radiated into space, gravitation became more effective, and then began to condense and contract more rapidly, by which process its rotary motion was, in accordance with the areolar law, gradually increased at the surface,in the atmosphere of the sun, where the cooling took place, and condensation was most active; and the increase of rotation was propagated from there towards the centre.
(2)As the contraction and rotation increased a time or times arrived, when the centrifugal force produced by the rotation came to balance the force of gravitation, and a series of zones or rings were separated from the nebula, each one of them continuing to rotate—revolve now—around the central mass, with the same velocities they had at the times of their separation; until at last the nebula became so contracted that it could not abandon any more rings, and what of it remained condensed and contracted into a central mass which ultimately assumed the form of the actual sun.
(3)In the meantime, or following afterwards, each one of the rings which were abandoned by the nebula, acquired, through the friction of its molecules with each other, an equal movement of revolution throughout its entire mass, so that the real velocities of the molecules furthest removed from the centre of the nebula were greater than those of the molecules nearest to its centre, and the ring revolved as if it were in one solid piece. Arrived at this stage the rings broke up and formed themselves into smaller nebulæ, each of which condensed into a globe or planet, and continued to revolve around the central mass in the same time as its mass had done when in the form of a ring. And some of these sub-nebulæ, imitating the example of their common parent more perfectly than others, abandoned in space in their turn smaller rings which in the same manner condensed, broke up, and formed themselves into smaller globes or satellites; all, as far as we know, except the rings of Saturn, which have not as yet been converted into satellites.
TABLE I.
Elements and other Data of the Solar System Employedin this Analysis.
Part I.—Sun and Planets.
Part II.—Satellites of Planets.
Part III.—Rings of Saturn.
(4)All of these bodies, planets, satellites, and rings were supposed to revolve around their primaries, and to rotate on their axes, in the same direction viz., from right to left, in the opposite direction to the hands of a watch.
In addition to the above definition it is necessary to give some sort of description of the various parts of the machine or system which has to be made out of the nebula, with their positions, dimensions, and details. This we believe will be made plain enough, in the simplest manner, byTable No. I., taken and calculated from the elements of the solar system given in almost all astronomical works, from which we have selected what we believe to be the most modern data.
The construction of this table requires some explanation on account of its being made to show complete results from incomplete data. There has been no difficulty with the sun, the major planets, and the satellites of the earth and Jupiter, but for the minor planets, the satellites of the three outer planets, and the rings of Saturn, we have been obliged to exercise our judgment as best we could.
There being almost no data whatever of the dimensions and densities of the minor planets, to be found, we have been driven in order to assign some mass to them, to imagine the existence of one planet to represent the whole of them (in fact Olbers's planet before it exploded), which we have supposed to be placed at the mean distance of 260,300,000 miles from the centre of the sun; and we have given to it a mass equal to one-fourth of the mass of the earth, that being, in the opinion of some astronomers, the greatest mass which the whole of them put together could have. This assumption we shall explain more fully at a more suitable time.
In the case of Saturn the diameters of two of the satellites are wanting which we have assumed to be the same as those of the smallest of those nearest to them, and thus have been able to compute the volumes of the whole of them; but we have not been able to find any statement anywhere of their densities, and to get over this difficulty we have reasoned in the following manner.
The density of the moon is very little over two-thirds of that of the earth, while that of the satellites of Jupiter varies from a little more than the same to a little more than twice as much as the density of their primary. Why this difference? To account for it we appeal to the very general opinion of astronomers, that the four inner planets are in a more advanced stage of their development, or existence, than the four outer ones. In this way it is easy to conceive that the earth has arrived at the stage of being more dense than its satellite; while in the case of Jupiter, his satellites being of so very much less volume than their primary, have already arrived at a higher degree of development. Carrying this motion forward to Saturn, we have supposed that from his being considerably less dense than any other of the outer planets—quite possibly from having been formed out of material comparatively (perhaps not actually) less dense than the others—his satellites may not have condensed to a greater degree than his own mass, and we have, therefore assumed their density, that is the density of the volume of the whole of them, to be the same as that of their primary.
To determine some mass for the rings of Saturn, is a much more intricate matter than for his satellites, and presents to us some ideas—facts rather—which had never before crossed our imagination. The most natural way to look upon these rings is to suppose that they are destined to become satellites at some future time. All the modern cosmogonies that have come under our notice are founded upon the idea that rings are the seed, as it were, of planets and satellites, and if those of Saturn have been left, as it has been said, to show how the solar system has been evolved, it cannot be said that the supposition is not well founded. In this way we are led to speculate upon how many satellites are to be made out of the rings before us. Considering, then, that the nearest satellite is 120,800 miles from the centre of Saturn, leaving only 83,500 miles between his surface and that of Mimas, and also that the distances between satellites diminish rapidly as they come to be nearer to their primaries, there is not room to stow away a great number of satellites. On the other hand, seeing that there are at least three distinct rings, we cannot reasonably doless than conclude that three satellites are intended to be made out of them. But let the number be what it may, all that we have to do with them for our present purpose is to assign some mass to them. With this view, we have given, arbitrarily, to each one of the three we have supposed, a volume equal to that of one of the satellites of 500 miles in diameter, that is, about 65,000,000 cubic miles, and we have supposed their density to be the same as that of water, instead of that of the planet. Thus, in the table, we have assigned to the three a mass of 195,000,000 cubic miles at density of water, which would be more than sufficient to make four other satellites for the system of 500 miles in diameter each, and of the same density as the planet.
For the table referred to we have calculated the areas of the three rings to be 152,110,800,172 square miles, and we have assumed the thickness as 90 miles, that is about two-thirds of that estimated by Chambers in his handbook of Astronomy, but almost the same as that given by Edmund Dubois; nevertheless their total volume comes up to 1,369,062,060,480 cubic miles, which reduces their average density to 0·0001425 that of water, to make up the mass of 195,000,000 cubic miles at the density of water, which we have adopted for the three. This density corresponds to very nearly one-tenth of that of air, which, however strange it may appear to us, may be considered to be a very full allowance, seeing that we shall find, later on, that the planet itself was formed out of matter whose density could not have been more than one twenty-six millionth part of that of air. All the same, it is hardly matter that we could liken to brickbats. After being driven to this low estimate of density, which startled us, we referred to an article in "Nature" of Nov. 26, 1886, on Ten Years' Progress in Astronomy, where we find what follows:—"He (Newcomb) finds the mass of Titan to be about 1/12,000 that of Saturn. It may be noted, too, that Hall's observations of the motions of Mimas and Enceladus indicate for the rings a mass less than 1/10 that deduced by Bessel; instead of being 1/100 as large as the planet, they cannot be more than 1/1000, and are probably less than 1/10,000."(We make them 1/791514). Thinking over the numbers herein given we cannot help being surprised by them. If Titan be 1/12500 of the mass of Saturn, we cannot conceive how the mass of his rings can be so much greater than that of Titan. We cannot pretend to fit even one satellite of that size, mechanically, into a space of 83,500 miles wide, while Titan revels in an ample domain with a width of 332,000 miles. But we shall not pursue this part of our speculations any further. Astronomers may be able to demonstrate that the rings are of a totally different nature to those out of which the planets and their satellites are supposed to have been made, or that the nebular hypothesis or anything resembling it is no better than a foolish dream. All that we have pretended to do has been to give them their due place in the hypothesis we are attempting to analyze, and to look upon them in a practical and mechanical light, as an unfinished part of the solar system.
To determine masses for the satellites of the two outer planets, we have to be more empirical even than we have yet been. A little trouble will show that the whole mass of all the satellites and rings of Saturn put together is about 1/7820th of the mass of the planet, and we shall avail ourselves of this proportion to assign masses for the satellites of the remaining planets, the numbers and names of which are the only data we have been able to find. Considering then, that Uranus has only four satellites and no rings, we think if we give them 1/15,000th of the mass of their primary, it will be a very fair allowance; and with the same empiricism we have adopted for the solitary satellite of Neptune 1/40,000th of the mass of its primary.
However rude and crude these approximations may be, we have the satisfaction of thinking that the masses obtained by their means, can have no appreciable effect upon the operations into which they are to be introduced, whilst they enable us to deal with a complete system or machine. But for these we have another Table No. II. to present, arésuméof the foregoing one, for greater facility of reference.
TABLE II.
Volumes of the Various Members of the Solar Systemat the Density of Water.
Dividing 482,169,000,000,000,000 by 691,966,535,445,840 makes the mass of the whole of the members to be 1/696·86th part of the mass of the sun, instead of 1/700th as generally stated by astronomers.
Wemay now proceed to take the original nebula to pieces, by separating from it all the members of the solar system, in performing which operation we shall suppose the divisions between the nebula and each successive ring to have taken place at a little more or less than the half distances between the orbits of two neighbouring planets, because we have no other data to guide us in determining the proper places. These divisions have manifestly been brought about in obedience to some law, as is proved in great measure by what is calledBode's Law; although no one has as yet been able to explain the action of that law. It is no doubt certain that a division must have taken place much nearer to the outer than the inner planet in each case, if we think of what would be the limit to the sphere of attraction between the nebula and a ring just detached from it—for the attraction of the abandoned ring, and even of all those that were outside of it, would have very little influence in determining the line where gravitation and centrifugal force came to balance each other—but the data necessary for calculating what these would be are wanting. Even if they existed the calculations would become too complicated for our powers as the number of rings increased; and for our purpose it is really of very little importance where the divisions took place. The breadths of the rings would be practically the same, whether they were divided at the half distances between, or much nearer to, the outermost of two neighbouring planets; and although the extreme diameters of the consecutive residuary nebulæ would be somewhat greater, their densities and temperatures would not materially differ from those we shall find for them as we proceed in our operations. Their masses would be the same in all cases, which is the principal thing in which we are interested.
This premised, we shall first examine into the excessive heat attributed to the nebula, that being the first condition mentioned in our definition of the hypothesis.
The diameter of the sun being 867,000 miles, his volume is 341,238,000,000,000,000 cubic miles, and his density being 1·413 times that of water, his volume reduced to the density of water would be 482,169,000,000,000,000 cubic miles. Now, astronomers tell us that the whole of the planets, with their satellites and rings, do not form a mass of more than 1/700th part of the mass of the sun. If, then, we add 1/700th part to the above volume, we get a total volume, for the whole of the system, of 482,857,590,478,000,000 cubic miles at the density of water, which corresponds to a sphere of about 973,360 miles in diameter. On the other hand, the diameter of the orbit of Neptune being 5,588,000,000 miles, if we increase that diameter to 6,600,000,000 miles, so that the extreme boundaryof the supposed nebula may be as far beyond his orbit, as half the distance between him and Uranus is within it, we shall still be far within the limit at which the process of separation from the nebula, of the matter out of which Neptune was made, must have begun. From these data we can form a very correct calculation of what the density—tenuity rather—of the nebula must have been. For, as the volumes of spheres are to each other as the cubes of their diameters, the cube 973,630 is easily found to be to the cube of 6,600,000,000, as 1 is to 311,754,100,720, or in other words, the density of the nebula turns out to have been 1/311,754,100,720th part of density of the whole solar system reduced to that of water.
Carrying the comparison a little further, we find that as water is 773·395 times more dense than air, and 11,173·184 times more dense than hydrogen, the density of the nebula could not have been more than 1/403,000,000th part that of air, and 1/27,894,734th that of hydrogen. But, confining the comparison to air, as it suits our purpose better, we see that it would take 403,000,000 cubic feet of the nebula to be equal in mass to 1 cubic foot of air at atmospheric pressure; and that were we to expand this cubic foot of air to this number of times its volume, the space occupied by it would be as nearly in the state of absolute vacuum as could be imagined, far beyond what could be produced by any human means. Now, were heat a material, imponderable substance, as it was at one time supposed to be, we could conceive of its being piled up in any place in space in any desired quantity; but it has been demonstrated not only not to be a substance at all, but that its very existence cannot be detected or made manifest, unless it is introduced by some known means—friction, hammering, combustion—into a real material substance. Therefore, we must conclude that if it existed at all in the nebula, it must have been in a degree corresponding to the tenuity of the medium, and the air thermometer will tell us what the temperature must have been if we only choose to apply it.
Applying, then, this theory of the air thermometer, if we divide[B]274° by 403,000,000—the number of times the density of the nebula was less than that of air—we get 0·00000068°, as the absolute temperature of the nebula, something very different to excessive heat, incandescence, firemist, or any other name that has been given to its supposed state. Furthermore, as a cubic foot of air weighs 565·04 grains, 403,000,000 divided by 565·04, which is equal to 713,223, would be the number of cubic feet of the space occupied by the nebula, corresponding to each grain of matter in the whole solar system, which would be equal to a cube of very nearly 90 feet to the side. And as the only means by which the nebula could acquire heat would be by collision with each other of the particles of matter of which it was composed; to conceive that two particles weighing 1 grain each, butting each other from an average distance of 90 feet, could not only bring themselves, but all the space corresponding to both of them—which would be 1,426,446 cubic feet,of what?—up to the heat of incandescence, or excessive heat of any kind, is a thing which passes the wit of man. Consequently, neither by primitive piling up, nor by collisions among the particles, could there be any heat in the nebula at the dimensions we have specified, beyond what we have measured above.
Some people believe, at least they seem to say so, that meteors or meteorites colliding would knock gas out of each other, sufficient to fill up the empty space around them, and become incandescent, and so pile up heat in nebulæ sufficient to supply suns for any number of millions of years of expenditure. But they forget that gas is not anothing. It possesses substance, matter, of some kind, however tenuous. Therefore, if the meteors knock matter out of each other in the form of gas, they must end by becoming gas themselves, and we come back to what we have said above;we have two grains, in weight, of gas abutting each other at an average distance of 30 yards, instead of two grains of granite or anything else, and things are not much improved thereby. And if we compare 30 yards with M. Faye's 3000, where are we?
The next thing to deal with is the formation of the planets.
When the nebula was 6,600,000,000 miles in diameter its volume would be 150,532,847,22218[C]cubic miles, and we have just seen that its density must have been 311,754,100,720 times less than that of water, or 403,000,000 less than air, and its temperature 0·00000068° above absolute zero. On the other hand, we find fromTable II. that the volume of Neptune and his satellite is 29,107,964,680,925 cubic miles at the density of water. Multiplying, therefore, this volume by 311,754,100,720 we get 9,074,53018cubic miles as the volume of the ring for the formation of Neptune's system at the same density as the nebula. Then, subtracting this volume from 150,532,847,22218, there remain 150,523,772,69218cubic miles as the volume to which the nebula was reduced by the abandonment of the ring out of which Neptune and his satellite were formed.
Then the mean diameter of the orbit of Neptune being 5,588,000,000 miles, its circumference or length will be 17,555,261,000 miles, and if we divide the volume of his system as stated above, by this length, we get 516,912,620,000,000 square miles as the area of the cross section of the ring, which is equal to the area of a square of 22,735,123 miles to the side. Again, if we divide the circumference of the orbit by this length of side, we find that it is 1/772·165th part of it, and therefore about 28 minutes of arc. Also if we divide the diameter of the orbit by an arc of 22,735,123 miles in length, we find that it bears the proportion of 1 to 246 to the diameter of the orbit. Thus the cross section of the ring would bear the same ratio to its diameter that a ring of 1 foot square wouldbear to a globe of 246 feet in diameter. Here we find it difficult to believe that by rotating a ball of 246 feet in diameter of cosmic matter, meteorites, or brickbats, we could detach from it, mechanically, by centrifugal force a ring of 1 foot square, and the same difficulty presents itself to us with respect to the nebula. We cannot conceive how a ring of that form could be separated by centrifugal force from a rotating nebula, and have therefore to suppose it to have had some different form, and to apply for that to the example of Saturn's rings—just the same as Laplace no doubt did. We cannot tell how the idea originated that the ring should be of the form we were looking for—perhaps it was naturally—but it seems to have been very general, and in some cases to have led to misconceptions. It is not difficult to show how a Saturnian or flat ring could be formed, but we shall have a better opportunity hereafter of doing so. We must try, nevertheless, to form some notion, however crude it may be, of what might be the thickness of a flat ring of the cross section and volume we have found for Neptune.
Let us suppose that the final separation of the ring took place somewhere near the half-distance between his orbit and that of Uranus, say, 2,290,000,000 miles from the centre of the nebula, the breadth of the ring would be the difference between the radius of the original nebula, i.e. 33,000,000,000 miles and the above sum, which is 1,010,000,000 miles. Then if we divide the area of the cross section of the ring by this breadth, that is, 516,912,620,000,000 by 1,010,000,000, we find that the thickness would be 511,794 miles; provided the ring did not contract from its outer edge inwards during the process of separation. This could not, of course, be the case, but, as we have no means of finding how much it would contract in that direction, we cannot assign any other breadth for it; and we shall proceed in the same manner in calculating the thicknesses of the rings for all the other planets as we go along. We can, however, make one small approach to greater accuracy. We shall see presently that the density of the ring would be increased threefold at its inner edge as compared with the outer during the process of separation, which would reduce itsaverage thickness to somewhere about 341,196 miles at density of water, of course. The nebula remaining after Neptune's ring we may now call
The volume of the nebula after abandoning the ring for the system of Neptune was found to be 150,523,772,69218cubic miles at its original density, but during the separation it has been condensed into a sphere of 4,580,000,000 miles in diameter, whose volume would be 50,303,255,81418cubic miles; so that if we divide the larger of these two volumes by the smaller, we find that the density of the Uranian nebula would be increased 2·9923 times, and therefore it would then be 311,754,100,720 divided by 2·9923, equal to 104,184,535,721 times less dense than water. Furthermore, if we compare it to the density of air, which we can do by dividing this last quantity by 773·395, we find it to have been 134,710,620 times less than that density; and if we apply the air thermometer to it, we shall find that its absolute temperature must have been 274 divided by 134,710,620 = 0·000002034° or -273·9999796.°
We can now separate the ring for the system of Uranus from the Uranian nebula, reduced as we have seen to 4,580,000,000 miles in diameter, volume of 50,303,255,81418cubic miles, and density of 104,184,535,721 times less than water. Referring toTable II., we find the volume of the whole system of Uranus to have been 25,876,388,977,690 cubic miles at the density of water, but we have to multiply this volume by the new density of 104,184,535,721 times less than water in order to bring it to the same density as the nebula, which will make the volume of his system to be 2,695,918,85115cubic miles at that density. Then, subtracting this volume from 50,303,255,81418, we find that the nebula has been reduced to 50,300,559,895,14915cubic miles in volume.
Then the diameter of the orbit of Uranus being 3,566,766,000 miles, its circumference will be 11,205,352,065 miles, so that dividing the volume 2,695,918,85115of his system by this length of circumference, the area of the cross sectionof the ring would be 240,592,061,166,666 square miles. If we now suppose the diameter of the nebula, after abandoning the ring for the whole system of Uranus, to have been 2,672,000,000 miles—dimension derived from nearly the half-distance between the orbits of Uranus and Saturn—we find that the breadth of the ring would be 954,000,000 miles, which would be the difference between the radii of the Uranian and Saturnian nebulæ, respectively 2,290,000,000 miles, and 1,336,000,000 miles; so that if we divide the area of cross section of Uranus' ring or 240,592,070,232,288 square miles by this breadth we find the thickness of the ring to have been 252,193 miles. But the density of the inner edge of the ring would be 5·036 times more dense than the outer edge, for the same reason as in the case of the Neptunian ring, which would make the average thickness to have been about 100,553 miles.