In the second case, that is, looking upon the nebula as a hollow sphere—when it was of the dimensions we have just supposed it to be—we get rid of all the difficulties, and we may add impossibilities, that we encountered in the first case. In such a formation there could be no particle of matter in a state approaching to inertness, not one that could not work its way, through force of attraction and collisions, from the outer to the inner surface of the hollow shell, orvice versâ, or all through and round it and from pole to pole—if it had poles then; it might increase or decrease in density, according to the density of the particles with which it came into collision, as it moved from one place to another, but it would find no spot where it could stand still or be imprisoned. Even arrived at the region of greatest density, it could change places with its neighbours and move all over that region, if it were condemned to remain with one density once it had acquired it; if not, by acquiring or loosing a little density—i.e.by being compressed or allowed to expand a little—it could work its way outwards or inwards, as we have just said, and be as free as the law of attraction would admit of, and as active as that law would oblige it to be. It must be borne in mind that gravitation would act in two opposite directions depending on whether it was acting on the outside or inside of the region of greatest density. We do not go the length of supposing that it could escape altogether from the nebula were its progress outwards; because, as it approached the border, it would meet with plenty of other particles coming in, which would reduce its velocity and prevent its escape. Besides, the law of attraction would take good care to prevent it from passing over to a neighbour nebula or sun.
It may be argued that in the first case—i.e.condensation to the centre—the particles would have the same facilities for changing place, in so far as moving all round the interior of the nebula, or across it, on their way to quasi stagnation, astheir densities and the superincumbent weight concentrated and increased; but there could be no motion outwards because theattraction of gravitationwould not permit it; nothing couldfall upwards, all mustgravitateto the centre. Thus the power of motion in the particles would be limited to very much less than half what they would have in the case of the hollow sphere.
It will not do to argue that the increasing heat at the centre would create an upward current. It might create repulsion and prevent the farther-out particles from so soon reaching their final resting or vibrating place, but it could not create an upward convection current of any magnitude; because the colder particles falling down to replace those rising up—that is, if the warmer ones did rise up—being greater in number because occupying greater space, would soon cool down the centre and put an end to the upward current, that is, if it ever came to be set in motion. The greater weight of the greater number would be sure to keep the lesser number in their prison. If any one should say that those nearest the centre would be the heaviest, let him remember that the heaviest liquid or fluid does not rise to the surface. There could be no furnace at the centre to heat the cold particles as they came down to replace those that had just risen up; and if there was, it would be gradually cooled and extinguished. In fact, the centre region would become colder than that immediately outside of it, and so on until the greatest heat would be at the surface of the nebula. Should it be argued that the vastly greater number of particles in the outer regions would help those at the centre to rise up, we agree; but it would be because the attraction would be greater outwards than inwards, as we have shown all along, and not because the pressure forced them out—against itself. But, it must be added, this means that if there was still a plenum at the centre the particles that had once left the centre could never come back again, nor any others to replace them, and that no convection current could ever be formed for carrying heat or matter from the centre, or its immediate neighbourhood, outwards.
In view of the above comparison of the two cases—added as a complement to what we believe we have demonstrated in a former part of our work—we shall adopt the second as being most in harmony with the laws of attraction, and of nature in general, and shall endeavour to describe in some detail, the construction of the nebula out of the matter belonging to the domains of the sun, as we have marked them out.
We have already said that on account of being at the greatest distance from the main body, and at the same time nearer than all other parts of it, to the attractive force in the domains of the neighbouring stars or nebulæ—which attraction continues to be exerted upon the solar system up to the present day—the matter in the high peaks which we have shown would form part of the sun's domains, would come to be completely separated from the rest of the nebulous matter. We shall now assume this to have come about, the detached pieces, somewhat in the shape of cones, occupying positions distant from the main body, in some sort of proportion to their altitudes and masses. This separation would naturally make some alteration on the centre of gravity of the remaining mass. It would come to be nearer to the deep hollows, made in the mass by the attraction of the most powerful of the nearest neighbouring stars; and as we have seen that the hollows made by Sirius and α Centauri would be the deepest, and also for greater simplicity in description, we shall suppose that the centre of gravity would come to be nearer to these hollows than it had been before. Then, as the condensation and contraction proceeded, the tendency would be to fill up these hollows, and, as a consequence, the matter at the opposite side of the nebula would at the same time tend to lag behind in approaching the centre—for the same reasons we have given in the case of the peaks—and might easily come to be detached from the main body altogether, first in the form of shreds, then in larger masses, and afterwards in concave segments of hollow spheres, as contraction advanced; and the whole seen from a sufficient distance, would have the appearance of a nebula with crescents, perhaps almost rings, ofnebulous matter and detached masses on one side of it; all very much like what we know to be the figures presented by some nebulæ.
When contraction had continued till the hollows caused by Sirius and α Centauri were filled up, we might suppose that the nebula had come to be somewhat of a spherical form, although far from being very pronounced, and we have now to consider what its internal structure might be and most probably was.
In describing the construction of the earth-nebula we showed that particles of matter placed at different parts of its interior, even not very far from the surface, would be drawn out, in the first place by the greater number coming in from a greater distance from the centre, and that when they met they would all be drawn in towards the centre by the conjoint attraction of the whole mass; and now we can apply this fact to the larger solar nebula, and consider what might be the result. Let us fix upon a certain number of equidistant zones in a sphere of cosmic matter, extending from the centre atatob,c,dande, at the surface. We know that, according to our former reasoning on particles, and the law of attraction, part of the matter of the zone atawill be drawn outwards by that atb, while part of that atbwill be drawn inwards by that ata, and that the same will take place with all the other zones out to the surface ate; and thus there might come to be congested layers between these equidistant places, and there might even be formed hollow spheres within hollow spheres, independent of each other, all through the nebula from near the centre to the surface. This idea is by no means fanciful, as is witnessed by the accounts given in Chambers's "Handbook of Astronomy," already referred to, Vol. I., and the Figs. 215, 222 and 223, showing the form and appearance of the remarkable comets of 1874 and 1882. If different, almost concentric, zones or layers of cosmic matter can be constituted in the hemisphere forming the head of a comet, there is no reason why concentric layers of the same matter should not be formed in a nearly spherical nebula. In fact, we can appeal to what is seen in the heads of the two comets cited,Donati's also represented in the same work, Figs. 199-203, as convincing proof of the correctness of our contention and demonstration that all satellites, planets, suns, and stars are hollow bodies. Even the tails of comets, at least of the larger ones, are acknowledged to be hollow bodies.
When steadily looked into we find the notion that all fluid bodies are hollow to be much more common than is perhaps generally believed. Beginning with the smallest, we find what follows in the Rev. Dr. Samuel Kinn's work, entitled "Moses and Geology," Edition 1889, page 86:
"A mist, whether in the form of a cloud or fog, is composed of small bodies of water obeying the laws of universal gravitation by forming themselves into spherules, which Halley and other eminent philosophers thought to be hollow. As water is heavier than air, scientists were for a long time seeking for a good reason to account for clouds floating. It may be that Kratzenstein has somewhat solved the problem. He was examining in the sunshine some of the vesicles of steam through a magnifying glass when he observed upon their surface coloured rings like those of soap-bubbles, and some of the rays of light were reflected by the outside surface, others penetrated through and were reflected by the inner surface; he concluded, therefore, that the envelope of the sphere must be excessively thin to admit of this taking place. We may, therefore, suppose that these vesicles are filled in some way with rarefied air, and are so many little balloons whose height in the atmosphere varies in proportion to the density of the air they contain. How this enclosed air should become rarefied on the formation of the tiny globule is a problem still to be solved."
Dr. Kinn says nothing ofhowthe spherules of cloud or fog were formed by the laws of universal gravitation, norwhyHalley and the other eminent philosophers thought them to be hollow, and only states the fact that Kratzenstein found the vesicles of steam to be hollow; and only one cause can be assigned for such being the case, namely, the manner in which we have shown how hollow spheres can alone be formed. That the vesicles of steam examined in the sunshine werehollow it would seem there can be no doubt; and if so, there can be as little that Halley and the others were right in thinking the spherules of clouds to be hollow. The steam vesicles could not come into existence at once in the air, in form large enough to be examined through a magnifying glass, but must have been built up out of a multitude of the very smallest atoms of water turned into vapour; and would follow the same law as the atoms of cosmic matter and so form the little balloons. In their formation the hollow space would be filled with air, which would expand when heated and contract when cooled, and so regulate their height in the atmosphere. And thus the problem of the last sentence of the quotation is solved.
We shall now go to the opposite extreme of matter, and see what Mr. Proctor says when treating of the formation of a Stellar System; but we must state that it is not very clear to us, whether he is exposing Mädler's ideas or his own, although we think they are his own or, at least, adopted. He says in "The Universe of Stars" at page 112:
"He (Mädler) argues that if a galaxy has a centre within the range of the visible stars, a certain peculiarity must mark the motions of the stars which lie nearer to the centre than our sun does. As has already been mentioned, the neighbourhood of the centre of a stellar system is a scene of comparative rest. In the solar system we see the planets travelling faster and faster, the nearer they are to the great ruling centre of the scheme; and the reason is obvious.a.The nearer a body is to a great centre of attraction like the sun, the greater is the attraction to which it is subject, and the more rapid must its motion be to enable it to maintain itself, so to speak, against the increased attraction; but in a vast scheme of stars tolerably uniform in magnitude and distribution,the outside of the scheme is the region of greatest attraction, for there the mass of all the stars is operative in one general direction. (The italics are ours.) As we leave the outskirts of the scheme, the attraction towards the centre becomes counterbalanced by the attractions towards the circumference; and at the centre there is a perfect balance of force, so that a body placed therewould remain in absolute rest. It is clear, then, that the nearer a body is to the centre, the more slowly will it move."
(Compare this last sentence with the one beginning ataabove.)
Here we have recognised, the principle that in a star system the immensely greater number of stars at the outside of the scheme would produce a perfect balance of force, and that a body placed at the centre would remain in absolute rest. This agrees wonderfully well with what we have been arguing, a few pages back, with respect to a sun solid to the centre. Matter at the centre would be at absolute rest,dead, that nearest to it would be nearest to dead, and so on through a sun or planet, gradually coming to life as it came nearer to the surface; exactly as we have shown it would be, having in it little more than rotary motion. When once acknowledging the immense superiority of attractive force of the stars at the outskirts of the system, over the very few there could be at its centre, Mr. Proctor seems to have stopped short with the idea and to have contented himself with one body at the centre in absolute rest. Had he gone one step further he must have seen that one, or even a very few, could not maintain themselves near the centre with such an immense number pulling them away in every direction. There could be no perfect balance of force. And had he applied the same idea to the earth, and followed it out to the end, he could not have written as he has done, in "The Poetry of Astronomy," at page 354, "that the frame of the earth is demonstrably not the hollow shell formerly imagined, but even denser at its core than near the surface." He would have found some difficulty in fixing his first dead particle at the centre, when there were such infinite hosts of near and far-off neighbours endeavouring to annex it. He would have found that the absolute rest was neither more nor less than absolute vacuum. It is utterly impossible to show how any body could be built up out of a nebula of cosmic matter, or even meteorites, from a solid centre, under the law of attraction. We repeat that any foundation laid there would be in a state of unstable equilibrium, and would be hauled away out of its place neverto return; unless the cosmic matter around it were so perfectly arranged on all sides that its attraction on the foundation would be absolutely equal in all directions; a condition which cannot be imagined by any one who takes the trouble to think of it. And we think we may add, that no body could be established at the centre of a system of any kind unless it were of sufficient magnitude to control the whole matter within range of it, exactly as we see in the solar system; and that the central body could be no other than a hollow sphere. Thus we have either to look upon the sun with his planets and their satellites as hollow bodies or to conclude that the solar system was not formed out of a nebula.
Coming back to our nebula after the hollows in it, caused by the attraction of Sirius and α Centauri, were filled up, and when we showed that it might have had the interior form of a series of hollow spheres one within the other, and also might be accompanied by crescents and shreds of cosmic matter on the opposite side to the hollows—a supposition we put forward more in explanation of what is to be seen in some nebulæ and comets, than as in any way necessary for our purposes—then, even although it had been separated interiorly into different layers or concentric shells of spheres, these layers continuing to attract each other, would finally come to form one hollow sphere with its greatest density at the region where the inwards and outwards attractions came to balance each other. Long previous to this stage—even from the very beginning—the atoms gradually coalescing into larger bodies, would be attracting, colliding with, repelling and revolving around each other, sometimes increasing in dimensions, at others knocking each other to atoms again; but there would be a tendency in them to combine into larger masses as they approached the region of greater density, where the attraction was greatest.
Now, if the collisions and encounters amongst the masses, great and small, always exactly balanced each other, the whole mass of the nebula would gradually contract towards the region of greatest density, and the whole would ever remain without any other kind of motion in it than what can be seen in a mity cheese—a kind of congeries of particles heaving in every,and at the same time in no, direction. But as an absolute balance of collisions could not be maintained for ever, especially where they would be constantly varying in force and direction, a time would come when movements of translation, as well as of collision, would be instituted on a large scale, in many directions, which, if they also did not manage to balance each other—an affair equally as impossible as in the other case—would ultimately resolve themselves into motion in one predominating direction through the whole nebula.
We do not forget that we are dealing with the shell of a hollow sphere, not with a ring, or section of a cylinder, and we can conceive that there would be, from the first, partial motions of translation in multitudes of directions, radial, angular, transverse, etc. etc., constantly changing, even being sometimes reversed, but also constantly combining with each other, and gradually leading on to decided, though partial, uniformity in one direction. As a matter of course this motion of translation would be controlled by its own constituent parts attracting each other to some extent, and thus a rotary motion would be established in the interior of the nebula in the region of greatest density. We can also conceive that when the motions of translation had become nearly uniform, the plane of that uniform motion might be in any direction through the whole mass of the nebula, and might be continually varying until final uniformity was attained, when the greater part of the mass was moving in combination, and the rotation was thereby firmly established in one direction, though still not embracing the whole.
We have to take into account also that when the rotary movement had settled down into one plane, it would be most active at the distance of the region of greatest density of the nebula from its centre; in fact it would be instituted at that region and be, therefore, most active there; and then the most active part of the matter would be in the form of a rotating ring, still surrounded by an immense mass of nebulous matter, both inwards and outwards, to which it would gradually communicate its own motion, until the whole mass would rotate, in one direction, on an axis. But it is evident that inthe whole rotating mass there would be different degrees of velocity of rotation at different places, decreasing from the supposed ring inwards towards the centre, and outwards to the surface at what would thus become the equatorial region; and also decreasing from the equatorial plane to the poles. Following up this idea, we have a more reasonable manner of accounting for the different velocities of rotation observed on the surface of the sun, between the equator and the poles, than we have seen suggested in any speculations on the cause that have come under our observation. Until rotation was fully instituted, the areolar law could have no power over the multitudinous movements going on in the nebula, but from that time it would begin to act, and condensation would increase it at the region where it began; and as all increase had to be propagated from there, inwards, outwards, and in all directions, the differences in velocity of rotation throughout the sun must endure as long as he continues to contract. In this we find an immense field for producing heat in the sun, from the eternal churning which must be going on in the interior.
A rotary motion produced in this way might have two different results: in one case the rotation might be continued until the matter at the polar regions had all fallen in towards the centre, and had been thrown out afterwards by centrifugal force and the whole mass converted into a nebular ring, in the form of the annular nebula in Lyra. In the other case we could conceive that, in a smaller nebula, the centrifugal force of rotation caused zones to be abandoned at the equatorial surface, in the manner set forth by Laplace in his hypothesis, and that the matter from the polar regions fell in more or less rapidly for the formation of the different members of a system like the sun's; and that the dimensions of the planets would be determined by the rapidity with which the matter fell in as the process went on. Such a conception would help to account for the outer planets of the solar system being so much larger than the inner ones, because there would be more matter falling in; and make us think that the nebula in Lyra is destined to form a system of multiple stars.
Some years after this mode of instituting rotary motionin a nebula was thought and written out, and also an extension of it to which we may refer later on, we came upon a kind of confirmation of the correctness of our views in an article in "Science Gossip" of January 1890, on the nebular hypothesis, where it is said:
"We have established, then, the existence of irregular nebulæ which are variable—that is, the various parts of which are in motion.... Now, with the parts of the nebula in motion, whether the motion is in the form of currents determined hither and thither according to local circumstances, or in any other conceivable way, such motions bearing some reference to a common centre, unless the currents exactly balanced each other—a supposition against which the chances are as infinity to one—one set must eventually prevail over the other, and the mass must at last inevitably assume the form peculiar to rotating bodies in which the particles move freely upon each other. It must have become an oblate spheroid flattened at the poles and bulging at the equator, rotating faster and faster as it contracted. In some such manner has our solar system acquired its definite rotation from west to east."
The writer in "Science Gossip" has taken the irregular motions in the nebula as made to his hand, and has come to the same conclusion as we have, namely, that they would all resolve themselves into motion in one direction only, always subject to the general attraction towards the centre of gravity of the nebula, which means motion round a centre, perhaps not necessarily rotary motion. However, the only difference between his ideas and ours is that we deal with a hollow nebular shell, in which, it will be acknowledged, it would be much more easy for the law of attraction to produce marked and distinct motions of any kind, and which would lead to one motion in one direction throughout, than in a nebula homogeneous, or nearly so, from the surface to the centre. Whether it would lead to the formation of an oblate spheroid is another question, as that might depend on a variety of circumstances, one or more of which we shall have to touch later on; in fact, we have already shown how the very reverse might be the case.
Beforegoing any farther it will be convenient to try to find out whether the solar system could have been constructed from a hollow nebula such as we have been describing gradually contracting as the matter for the formation of one planet after another was abandoned until—as we have put it—the nebula could abandon no more matter, and finally resolved itself into the sun. For this purpose we may suppose it to have been condensed and contracted until its extreme diameter was 6,600,000,000 miles; the same as we supposedit to have been, when we began the analysis of the nebular hypothesis. We will not now, however, suppose it then to have contained the whole of the cosmic matter out of which the system was formed, as we did before; because we have seen as we have come along that a very considerable part of that matter must have been left behind, almost from the moment that contraction commenced. We have already given the reasons for this in describing the domains of the sun; and, leaving the peaks out of account altogether for the present, we will only deal with the regions of what we have called the main body.
Although we have fixed a limit beyond which the neighbouring stars could not draw off any cosmic matter from the domains of the sun, that does not mean to say that their attractive powers would cease at that limit; because we have had to acknowledge that each one of them continues, even now, to exert its attractive power up to the very centre of the sun. They would still have power to counteract, in some measure, the sun's attraction of the matter of the nebula towards his centre, and the result would follow that there would be one or more, even many, fragments of the main body which would be left more or less behind, and in varied forms, when the more central part had contracted to the dimensions to which we have now reduced the nebula—all much the same as we have already said a few pages back.
When the nebula was 6,600,000,000 miles in diameter its volume would be 150,53324cubic miles—as we have seen atpage 87—the half of which is 75,26624cubic miles, corresponding to a diameter of 5,238,332,000 miles, or radius of 2,619,166,000 miles. Now, according to our theory, it would be at this distance from the centre that the greatest density and activity of the nebulous matter would be, where we have just been showing how a movement of rotation could be generated, and where, in consequence, its motive power, so to speak, originated and existed. Here we find by dividing 5,238,332,000 by 6,600,000,000 that the region of greatest density in such a nebula would be at 0·7937 of its diameter. In our calculations about the earth, as it is, the proportionwas found to be 0·7939, but the densities of the outer layers were empirically arranged by us; and, besides, almost the whole of the mass was supposed to be solid matter, so that no accurate result could be expected from that operation. There also we found that the inner surface of the hollow shell was at 0·5479 of the whole diameter, which we may adopt for the nebula we are about to deal with, as that dimension may be varied considerably—so may the other also—without in any way vitiating our theory.
Having found these proportions, which can only be considered as distantly approximate, let us go back to the 9 nebulæ—excluding the final solar one—into which we supposed the original nebula to have been divided—in the analysis just alluded to—and see how the regions of greatest density in them would correspond to the orbits of the planets formed out of them. This examination requires a good deal of calculation and accompanying description, which it might be found tiresome to follow, and would really answer no good end were it written out; so we shall suppose it to be made and the results obtained from the calculations to be represented in the form ofTable IX., where they can be seen at a glance almost, and compared without much trouble. This arrangement will also furnish a readier means of reference for the remarks we shall have to make on, and the information obtained from, the examination. And we have still to add that the extreme diameters of the 9 nebulæ are the same as those we used for the analysis; as also, that we make use of only the first of the proportions just cited, viz., 0·7937, it being the only one required for determining the positions of the regions of greatest density in the nebulæ.
TABLE IX..—Dimensions of the nine Nebulæ, with their Diameters and Regions of greatest Density compared with the Diameters of the Orbits of the Planets formed from them.
From the table we see that the region of greatest density of our original nebula was at 6·26 per cent.withinthe distance of Neptune's orbit from the sun, a state of matters which precludes the idea of condensation during, at least, a great part of the act of abandoning the ring for the formation of that planet. But it will be remembered that we gave it the diameter of 6,600,000,000 miles without assigning any adequate reason for doing so, and, we can say with truth, with the idea, more than anything else, of not increasing the almost unimaginable tenuity of the matter composing the nebula; and the position of Neptune in the system is so peculiar compared with the other planets, that it cannot be properly used as a standard for any kind of inquiry. The result obtained above can therefore be of no use for the investigation we have undertaken. Not only so, but the almost similar result in the case of Uranus is also rendered useless from the same cause, in which we find that the region of greatest density of the nebula is only 1·92 per cent. beyond the orbit of the planet. If the mean distance from the sun of Neptune's orbit had been what was used by Leverrier in the calculations which led to his discovery, namely, 36·152 radii of the earth's orbit, the region of greatest density of the Uranian nebula would have been 14·48 per cent. beyond his orbit, as may be seen from the addition toTable IX., in finding which we have used the same system as in all our work.
In the next four nebulæ of the table—including the one we introduced to represent the Asteroids—we see that their regions of greatest density are respectively 19·58, 12·47, 13·56 and 12·63 per cent. farther out from the centre of the sun than the orbits of the planets formed from them. Here, then, we see a very apparent approach of uniformity, and can say with much reason that planets could certainly be formed out of the matter abandoned, through centrifugal force, by hollow nebulæ similar in construction to what we have demonstrated that of the original nebula to have been; each of them occupying the position corresponding to its orbit.
Following these come the Earth and Venus nebulæ. In the former, the region of greatest density almost coincides with the orbit of the planet, being only 0·15 per cent. beyond it, instead of something like 12 per cent. as it ought to be to conform with the four preceding cases; and in the latter it is 5·25 per cent. within the orbit of the planet to be made from it. But in this case we have to note that the orbit of Venus is 3·33 per cent. beyond the position pointed out for it by Bode's law, and that it is the only one of the whole number of planets whose orbit is farther removed from the sun than thedistance assigned to it by that law. Also we see from our reversal of Bode's law, that the rates of acceleration of rotation for these two planets are 1·880 for the earth and 1·626 for Venus, instead of the average of 2·5896 of the four preceding planets; that the density of Venus is less than that of the Earth, instead of being greater as it is successively in all the other planets from Saturn inwards; and we may add that the diameters are nearly equal. All showing that influences had been at work in the formation of these two planets, different to those in the preceding four; and that until we know what these influences have been, we cannot account for any anomalies produced by them. Neither are we called upon to consider that our theory is destroyed by these anomalies, any more than it can be by the anomaly in the case of Neptune's position.
Lastly, we have in Mercury the region of greatest density of his nebula at 13·55 per cent. beyond his orbit, and the rate of acceleration of revolution over Venus 2·5543 times, both of which conform fairly well with the same noted facts; in relation to Mars, the Asteroids, Jupiter, Saturn, and, we may add, Uranus. But, in justice, we must not omit to add that there may be some error in the excess of 13·55 per cent. in the distance from the sun beyond his (Mercury's) orbit, arising from the fact that there may have been some difference from what we made it to be, in the line of separation between his nebula and that of Venus; and also that we had to guess at the line of separation between his and the residuary nebula. Moreover, it has to be taken into account that his orbit is 3·22 per cent. within the position assigned to it by Bode's law.
From theTable IX., and an examination of it, we learn that out of the 9 nebulæ into which we divided the original one, in the analysis of the nebular hypothesis, we have five—four of which are consecutive—which may have been almost of the same construction, and not far from the same proportions; that the original nebula cannot, for reasons assigned, be looked upon as either similar, or the reverse, to the five just classed; that one, the Uranian, is practically similar to the five, and might be exactly similar could the anomaly inthe position of Neptune be explained; and that the remaining two, the Earth and Venus nebulæ, seem to show that they have been abandoned in a manner different from the others. Perhaps we may be able, later on, and in a different way, to give a reasonable explanation of the anomalies in the positions occupied by Neptune, the Earth, and Venus, and also of the peculiarities of their dimensions. So far, we believe we are justified in concluding that out of the 9 nebulæ, 6 may really be considered as supporting our theory, and the remaining 3 as, in all probability, capable of being shown to be, at least, not opposed to it. To this we may add that on several occasions we have stated our opinion, that the divisions between the nebulæ we have established, could not have taken place at the half-distance between the orbits of any two planets, but much nearer to the outer one. It is evident, then, that if we had made the divisions at any distance farther out, say at three-fourths of that distance from the inner orbit, the extreme diameter of each one of the nebulæ would have been just so much greater, the region of greatest density farther out from the centre of the sun, and even that of Neptune would have been beyond his orbit. All this could be done, yet but it would serve no good purpose, as will be seen presently; and we might be accused of cooking our data in order to produce a result favourable to our theory.
We have made the foregoing examination because, when we began our work, the general idea was that, according to the nebular hypothesis, the material for the formation of each planet was abandoned by the ideal nebula in a distinct and separate mass from any other—we are not at all sure, however, that this was Laplace's idea. This, we found out, could not be the case when we attempted to give some sort of separate or distinct form to the matter out of which Neptune was supposed to have been formed; and when we became convinced that all the matter abandoned by the nebula, from first to last, must have been thrown off in one continuous and, most probably, uninterrupted sheet. This, of course, makes us think of how the division of the sheet into separate rings was brought about, for there must have been absolute separationbetween them, otherwise separate planets could not have been made out of the sheet; and the only explanation that can be given is, that it must have depended on the quantity of matter that was abandoned, in nearly equal times, at different periods of the operation; for the areolar law precludes the idea of there having been very rapid changes in the rate of rotation of the nebula, and certainly of its decrease at any period as long as condensation and contraction went on. Whereas, although the sheet thrown off may have been continuous, we have no reason to suppose that it was of constant volume or density from beginning to end of the operation; in fact, we have already seen that its density was constantly increasing, and have suggested, in the reversal of Bode's law, that the differences in dimensions and densities of the planets have arisen, from irregularity in the quantities of matter abandoned from time to time. This irregularity could only arise from the mode of construction of the nebula, and from the forms it assumed during condensation, as we shall attempt to show in due time. Meanwhile we can conclude that the region of greatest density in any of our nebulæ had no influence whatever on the position of the orbit of the planet that was formed out of it.
We have shown, very clearly we believe, atpage 109, from quotations—at second hand—from his own exposition of his hypothesis, that Laplace considered that condensation could only take place at the surface, or in the atmosphere as he called it, of his nebula, on account of its being possible only after radiation into space of part of its excessive heat; and that consequently there could be no acceleration of rotation in the nebula, due to the areolar law, except where there was condensation. On the other hand, in our cold hollow-sphere nebula, condensation could only take place at the region of greatest density, or greatest mass, which must be always very much nearer to the surface than to the centre; so that in both cases, equally, the abandoning of matter under the influence of centrifugal force would be virtually the same, and no further remarks are called for, on our part, on that head.
Neither is it necessary for us to show how planets could be formed out of the rings abandoned by their respective nebulæ, for everybody seems to agree that when they broke up, the fragments could not do otherwise than form themselves into small nebulæ, which in the course of time condensed into planets. M. Faye's explanations are good for that.
With respect to their motions of rotation being direct or retrograde, we have seen, atpage 116, and following, that Laplace's description of how the former motion could be brought about is mechanically correct; and, atpage 121, that he did not consider that the direction of revolution of a ring necessarily demands that the rotation of a planet formed from it should be in the same direction. As already said, he has shown how direct rotation could be produced, and we have no doubt that he could have shown how retrograde rotation could also be produced, had he found it to be at all necessary. Be that as it may, however, it is a very simple matter to show how, following our method of construction of the primitive nebula, the retrograde rotation of Uranus and Neptune could, or rather must, have been determined.
It will be remembered that when we were "getting up" the original nebula in the domains of the sun, whose form we described as well as our limited means would admit of, we said that when the cosmic matter contained in them began to contract, not only the parts contained in the peaks and promontories would soon be left behind, and come in at a slower rate, but also large masses of the outer part of the main body, especially of what was on the sides opposite to the deep hollows made in the domains by the most powerful of the sun's neighbours, in the form of fragments, crescents, and parts of hollow segments. Let us now, then, suppose the operation of planet-making to have advanced so far that the whole nebula was rotating on its axis, and abandoning matter through centrifugal force, from its equatorial regions in a continuous sheet, as we have said several times that it must have done, and that the matter destined for Neptune and Uranus has not only been abandoned, but divided into twodistinct rings—a supposition made in this case only for facility of description. Then some of the matter which had been left behind, but still being gradually drawn in, would be almost totally intercepted in the equatorial regions of the nebula by these two rings, and would fall in greater quantity upon their outer edges than anywhere else, more especially in the case of the outer one. These adventitious additions would come in without any angular, or tangential, movement whatever, because rotary motion was not yet established in them, and would retard the revolutionary movement of the rings—in decreasing degree from their outer to their inner edges—while acquiring angular motion themselves; and would also intensify the original difference in revolutionary motion already existing at these edges. At the same time these additions of extraneous matter would seriously impede the contraction of the rings in the radial direction on account of their volume, but would have little or no effect on contraction in the circumferential direction; the consequence of which would be that they would break up before friction, and the mutual collisions of their particles, had time to produce a uniform revolving motion throughout their whole breadth; that is, while their inner edges would be still revolving with more rapid velocities than the outer ones; and the rotary motions of the planets derived from them would be retrograde, according to M. Faye's demonstration—or that of any other who has taken the trouble to think over the matter. And we may add that this mode of reasoning, applied with a little more detail, will very fully account for the rotation of Neptune being more decidedly retrograde than that of Uranus, because the quantity of matter so deposited on the outer flat ring in this process would unquestionably be greater than on the inner one, and consequently the difference of velocity between the outer and inner edges of the two rings also greatest on the outer one.
We take it to be unnecessary even to say that, the revolution of the satellites of these two planets being retrograde and anomalous, the rotation of their principals must be retrograde and anomalous also.
Before going any farther we have something to say about the anomalous position of the orbit of Neptune, which is certainly not the position sought for by M. Leverrier; in fact, the elements employed by him in his calculations to discover a perturbing planet—whose existence may be said to have been known—are so different from the elements of the one actually discovered, that there would be nothing out of reason in saying that Neptune is not the perturber that was sought for, but only an instalment of the perturbing force. It may raise a storm in some quarters to say so, but the fact remains the same, or it must be confessed that mathematics is a more elastic science than it professes to be. He has not the power of attraction required to produce the perturbations in the movements of Uranus which gave rise to the search for an outer planet. M. Leverrier made his calculations under the belief that a planet of 1/9300th part of the mass of the sun was required to produce the perturbations that had been observed in the orbital motion of Uranus; whereas the planet discovered has only 1/20,000th of that mass—not one-half of what was required. On the other hand, the semi-axis major of the orbit of the planet discovered is found to be 30·037 instead of 36·154 (Bode's law measures) used for the search; which greater proximity to the sun, it is true, increases its power of attraction 1·449 times, but as its mass is only 0·465 per cent. of what was expected, the attractive force would amount to less than 0·68 per cent. of what was required. Then the question comes to be, Where did the wanting 0·32 per cent. of attractive force come from? And the answer is that some astronomers have been searching for another planet to make up the weight, with more or less diligence, ever since the deficiency came to be recognised. But all that we want to have to do with the question is to suggest a very plausible reason for the anomalous position of the orbit of Neptune.
If there is another planet beyond Neptune, the ring (perhaps the rings) out of which he and the others were made, must have been much greater in breadth than what we have assigned to it atpage 88, viz. 1,010,000,000 miles; perhaps even one-half more, as may be deduced from the additionmade toTable IX., and what we have said in connection with the semi-axis major adopted for the sought-for planet, by M. Leverrier in his calculations. Now, that a ring of such enormous breadth should have held together in one piece, until it finally broke up through condensation and contraction, requires an extraordinary effort of imagination, after seeing what has taken place with the rings of Saturn; even the breadth of 954,000,000 miles appropriated to the Uranian ring (see page 90) demands an elastic imagination to conceive its holding together; so that the outer ring of the system may very well have been divided into two, as we have said atpage 134, and two not very unequal planets made out of it—one into Neptune, and the other into one as far beyond M. Leverrier's adopted distance of 36·154, and of such mass as would make up the missing 0·32 per cent. of deficient attractive power. No doubt the outer ring may have broken up into several planets, or even into a swarm of asteroids, but we prefer to think of only two planets; because it seems to us that to draw Uranus into the position he occupied when Neptune was discovered, the two planets must have been operating in conjunction; an idea that is not so easily entertained when there are several planets, or a host of asteroids, to be taken into account.
We have already discussed, atpage 115, the mode of formation of the sheet of matter abandoned by the nebula, its posterior division into separate rings, and how the part of these rings from Saturn inwards could revolve themselves into planets having direct motion, so it is not necessary to go over the same ground again, merely because we are dealing with a hollow nebula instead of one full of cosmic matter to the centre.
We have also shown, atpage 119, that the nebula must have been somewhat in the form of a cylinder terminated at each end by what may be looked upon as a segment of a sphere, although it would more probably be an almost shapeless mass of cosmic matter, because the greater part of it would be very slowly brought under the influence of centrifugal force as it fell in from the polar directions; and again, afew pages back, that almost all the matter coming in from its equatorial regions—even what might be called its tropical regions—would be intercepted before it could reach the Saturnian nebula. Likewise, atpage 137, when examining Bode's law reversed, we have seen a limit set to the acceleration of the movement of revolution in the planets of the system as they approached the centre, because any acceleration beyond a certain limit, clearly marked out, would of necessity be within the nebula itself, and the rate of revolution would be less than that of the sun on its axis at the present day. This may be used as an argument against the nebular hypothesis, but we think we have shown in the sameChapter VII. that this is not the case. But we have still to try to account for the repeated rises and falls in density in the planets from Neptune to Mercury, or even farther; which operation causes us to bring forward, first of all, a new idea as to what the form of the nebula would come to be.