Analysis of the Nebular Hypothesis—continued.

When Laplace elaborated his hypothesis, heat was considered to be an imponderable material substance, and continued to be thought of as such—though perhaps not altogether believed to be so—for somewhere about half a century afterwards; so that it cannot be wondered at that he thought the nebula could have been endowed with excessive heat, more especially as it was looked upon as imponderable, and could in no way have any effect on the mass of the nebula. He only accepted the idea that was common to almost all astronomers of his time, that nebulÆ were masses of cosmic matter of extreme tenuity but self-luminous, and consequently possessed of intense heat; they saw the sun gave light and felt its heat, and very naturally thought the nebula must be hot also. Without this idea he could not have formed the hypothesis at all, because he could not have conceived that the condensation of the nebula could only take place at its surface, or, as he terms it, "in the atmosphere of the sun," as most assuredly would be the case with an excessively hot body. And in order that there may be no doubt about this being his idea, we quote his own words as guaranteed by M. Faye in "L'Origine du Monde": "La considÉration des mouvements planÉtaires nous conduit donc À penser qu'en vertu d'une chaleur excessive l'atmosphÈre du soleil s'est primitivement Étendu au delÀ des orbes de toutes les planÈtes, et qu'elle s'est reserrÉe successivement jusqu'À ses limites actuelles." And again: "Mais comment l'atmosphÈre solaire a-t-elle dÉterminÉ les mouvements de rotation et de rÉvolution des planÈtes et des satellites? Si ces corps avaient pÉnÉtrÉ profondÉment dans cette atmosphÈre, sa rÉsistance les aurait fait tomber sur le soleil. On peut donc conjecturer que les planÈtes ont ÉtÉ formÉes À ses limites successives par la condensation des zones de vapeurs qu'elle À dÛ, en se refroidissant, abandonner dans le plan de son Équateur." Proceeding on these ideas Laplace was quite in order and logical in conceiving that successive rings could be abandoned by the hot nebula, through the centrifugal force of rotation, for the formation of planets, more or less just in the way we have separated them. Having obtained his end quite legitimately, as he thought, in this way, he had no occasion to look any deeper into the affair, and consequently was not under the necessity of taking any thought of what the interior construction of the nebula might be, any more than so many others have not done since his day.

That he should have conceived the nebula to have been endowed with intense heat was, as we have already said, a natural consequence of the mistaken notions of the nature of heat at that period; but that so many astronomers should, up to the present day, think that the nebula must have been intensely hot, even to the degree required to dissociate the meteorites of which they conceive it to have consisted, seems to us to be almost inconceivable. We believe we have shown abundantly plainly, that there could have been almost no heat in the primitive nebula, because there was hardly any cosmic matter to hold it in. We have given as proof of this the laws of gases recognised and accepted by every scientist, according to which a gas cannot contain a stated amount of heat except it be at a pressure corresponding to that temperature, that is, unless it is subjected to conditions foreign to its natural state. Therefore we must either persist in maintaining that there was almost no heat in the original nebula, or we must throw the laws of gases to the winds, for they all depend one upon another. There may be nebulÆ possessed of very high temperature, that of incandescence for example, but certainly the nebula out of which the solar system was made, could not have contained more heat than what we have shown it had at the various stages through which we have carried it. If there be nebulÆ at the temperature of incandescence, they must be possessed of densities, or pressures, corresponding to that temperature. A few pages back we have spoken of the impossibility of two grains of matter 90 feet apart, raising, by mutual collisions, their temperature and that of the space occupied by each to the temperature of incandescence, and if we now substitute for them meteorites of a pound weight each, the space occupied by each of them will be a cube of 1670 feet to the side, which does not help us in any way to believe that the spaces occupied by them could be heated up by their collisions, so as to shine with the temperature of incandescence. So we get no help from meteorites.

Some people evidently seem to think that nebulÆ can be incandescent and give the spectrum of incandescent gas, without their density or pressure being increased to the corresponding degree. Sir Robert Ball seems to be one of them, though at the same time he appears to be not altogether sure of it. When discussing the self-luminosity of the nebula in Orion, in his "Story of the Heavens," Ed. 1890, p. 465, he says:

"We have, fortunately, one or two very interesting observations on this point. On a particularly fine night, when the speculum of the great six-foot telescope of Parsonstown was in its finest order, the skilled eye of the late Earl of Rosse and of his assistant, Mr. Stoney, detected in the densest part of the nebula myriads of minute stars, which had never before been recognised by human eye. Unquestionably the commingled rays of these stars contribute not a little to the brilliancy of the nebula, but there still remains the question as to whether the entire luminosity of the great nebula can be explained, or whether the light thereof may not partly arise from some other source. The question is one which must necessarily be forced on the attention of any observer who has ever enjoyed the privilege of viewing the great nebula through a telescope of power really adequate to render justice to its beauty. It seems impossible to believe that the bluish light of such delicately graduated shades has really arisen merely from stellar points. The object is so soft and so continuous—might we not almost say ghost-like?—that it is impossible not to believe that we are really looking at some gaseous matter."

Here we see that his own belief about the matter is not very firm. He admits that the stars contribute not a little to the brilliancy of the nebula, and the most he can say in favour of its shining with its own light is, that it seems impossible to believe that the light has arisen merely from stellar points. He then goes on to show how the self-luminosity may be explained, as follows:—

"But here a difficulty may be suggested. The nebula is a luminous body, but ordinary gas is invisible. We do not see the gases which surround us and form the atmosphere in which we live. How, then, if the nebula consisted merely of gaseous matter, would we see it shining on the far distant heavens? A well-known experiment will at once explain this difficulty. We take a tube containing a very small quantity of some gas: for example hydrogen; this gas is usually invisible; no one could tell that there is any gas in the tube, or still less could the kind of gas be known; but pour a stream of electricity through the tube, and instantly the gas begins to glow with a violet light. What has the electricity done for us in this experiment? Its sole effect has been to heat the gas. It is, indeed, merely a convenient means of heating the gas and making it glow. It is not the electricity which we see, it is rather the gas heated by the electricity. We infer, then, that if the gas be heated it becomes luminous. The gas does not burn in the ordinary sense of the word; no chemical change has taken place. The tube contains exactly the same amount of hydrogen after the experiment that it did before. It glows with the heat just as red-hot iron glows. If, then, we could believe that in the great nebula of Orion there were vast volumes of rarefied gas in the same physical condition as the gas in the tube while the electricity was passing, then we should expect to find that this gas would actually glow."

There is a great deal to be said about this explanation. We presume that a very small quantity of hydrogen gas means that it was considerably below atmospheric pressure. Even so we admit that by introducing sufficient heat into the tube by means of electricity or otherwise, the gas could be raised to the temperature of incandescence, but its pressure would, at the same time, be increased to the corresponding force measured in atmospheres; and we also admit that when the gas was allowed to cool down to its original temperature, the same quantity of hydrogen would be found in the tube; but how about the tube? When the gas came to be at the temperature of incandescence the tube would be the same, or very soon raised to it, and being made of glass would be sufficiently plastic to be distorted, or even burst by the pressure within, probably even before the gas reached the temperature of incandescence. We must not forget that the first appearance of incandescence begins with red heat whose temperature is not far from 500° in daylight, and that white heat rises to above 1000°. If the experiment was made in an almost capillary tube, sufficiently thick to prevent accidents, then it might appear to prove a foregone conclusion, but nothing else; it might keep the idea of pressure out of sight, but it could not prove that the gas inside was in a rarefied state when incandescent. That the gas glowed the same as a red-hot bar of iron has not been shown. The gas had to be shut up in a tube to make it glow, but the bar of iron could glow outside of the tube. Could a streak of hydrogen be put into a furnace along with a bar of iron and heated to incandescence by its side, there might be some fair comparison between them, as long as they were in the furnace together, but the moment they were taken out the glow would disappear from the gas, whereas the iron would glow for some time. On the other hand we might say that a stream of incandescent gas might be made to heat a bar of iron in an oven to its own temperature, but the moment the stream of gas and the iron bar were removed from the oven, the former would disappear at once and the latter would continue to glow, simply because it was dense enough to contain a very considerable supply of heat compared to what the gas could, or rather, because the pressure of the gas, even did it correspond to the temperature, would disappear at once and the heat with it. So it is not always safe to say things. But it is quite safe to say that no gas—or substance such as we are accustomed to look upon as gas—can abide in a state of incandescence, and merely glow, unless its pressure, or density, corresponds to the temperature of incandescence; which for red heat (in the dark) would be 370° = 2·35 atmospheres, and for white heat at 1000° = 4·65 atmospheres, above absolute zero of pressure in both cases. And also, that if the self-luminosity of a nebula arises from incandescent gas, the pressure in the gas of that nebula must be somewhere between 2 and 5 atmospheres above absolute zero of pressure. Now we have shown, at page 85, that the density and pressure in the solar nebula, at the stage there specified, could not have been more than the 403 millionth part of those of our atmosphere, and consequently were justified in asserting that in it there could be almost no heat whatever.

We have just been speaking of a streak of gas and a bar of iron being heated in an oven to a red or white heat side by side, but everybody knows that this could not be done; but everybody has not thought of why it could not be done, otherwise Sir Robert Ball would not have favoured us with his laboratory experiment of a streak, or remnant, of hydrogen in a glass tube. We know that a plate, or bar, of iron can be heated up to the temperature of incandescence in an oven, but it has never occurred to anyone, who has seen the thing done, that the gas, air, or vapour which heats them must be at a pressure corresponding to that temperature. Multitudes of people may have thought of how the thing is done, but apparently very few have thought that it is not the gaseous part of the current of heated matter introduced into the oven, that heats it and the metal in it, but the solid part which is the distinctive and most important part of the constituents of the current. The solid part of the matter—let it be gas or any other element—is heated to incandescence in some furnace and carried along by the gaseous part—that is the stuff that fills the empty spaces between the solid molecules—to give it out to the oven and iron. We are not sure that the gaseous part even glows. We see plainly enough that the walls of the oven glow, but with respect to the gas, or carrying agent, we are inclined to think that it rather dims the glow of the oven and iron than otherwise. In passing, we say it is not unreasonable to suppose that the solid matter which contained the heat till it was given out, consisted of the elements which were put into the furnace to raise the heat, and of those which were drawn in by the draught—in a word, the elements of combustion—but about the carrying constituent there is a great deal to be said after we know more about it. It seems to us from all this that the hydrogen gas in Sir Robert Ball's tube was not made to glow by heating up to the temperature of incandescence, but somehow by the electricity passing through it, if it did pass. We, therefore, come to the conclusion that the light of nebulÆ does not come from gas—or what we call gas—heated up to be incandescent merely to make it glow, and that it might be as cold as the light that comes from the aurora, or as that of a glow-worm. Sir Robert Ball refers to stellar points seen through the nebula, and acknowledges that part of the glow may be due to them, which shows that the nebula must have been excessively tenuous; for we know how thin a cloud will hide Sirius from us, and we think that nobody will assert that two grains of matter dispersed in 1,426,445 cubic feet of space, as we have seen at page 86, would hide Sirius from us. Therefore, we must acknowledge that the glow of nebula in Orion, observed by Sir Robert Ball, was caused either by the stellar points, or by some other thing that most assuredly could not be gas heated to the temperature of incandescence, or in part from both. For we believe that the glowing of nebulÆ, fluorescence, phosphorescence, Will-o'-the-wisp, auroras, fire-flies, fire-on-the-wave, etc., etc., all, all proceed from the same cause.

We may now proceed to say a few words about the separation of the rings for the planets, brought about by the rotation of the nebula on its axis, and the centrifugal force produced throughout it thereby. We have shown, at page 88, that a ring could not be detached from the nebula at once in one large annular mass, as it seems to have been the common notion was the mode of separation; and we shall now try to show with some detail what the process must have been, notwithstanding that it has been in a general way described by others; because, like everything else, there is something to be learnt from it. For this purpose we shall select what we have called the Jovian nebula, because we can suppose, for the present, it must have been more nearly in the form of a sphere than either the original or any of the exterior nebulÆ, which may not have been properly licked into shape, as it were; and also because we have found that the thickness and mass of the ring for his, Jupiter's, system were vastly greater than those for any other one of the planets. We have made the Jovian nebula to have been 1,370,800,000 miles in diameter, and the greatest thickness of the ring detatched from it to have been 1,406,771 miles. Now in a circle of that diameter, a chord of the length of that thickness would subtend an arc of very little more than 7 minutes, one half of which we shall suppose to be measured on each side of the equatorial diameter of the nebula at right angles to the diameter; then, the middle ordinate of a chord of 1,406,771 miles long, would be 359 miles long. This length would be a very small fraction of the radius of the circle which would be 685,400,000 miles long, but in a rotating sphere of the same dimension, we must acknowledge that the centrifugal force at the middle of the arc would be greater—however small the difference—than at its ends, and would sooner come to balance the force of gravitation; therefore we must admit that the process of separation would begin there by abandoning a thin layer of matter, convex on the outer side and in a measure concave on the inner side, for the reason just given, much the same as a layer that could be peeled off from the equator of an orange—the poles and equator of an orange are easily distinguished. As the velocity of rotation increased another layer would be abandoned following the first, so far curved on both sides, i.e. convex and concave, and the same process would continue on and on, according as the centrifugal force continued to balance that of gravitation, till the whole of the matter for all the attendants of the sun was abandoned; so that in the process itself no such division of rings as we have been following could have taken place, but one continuous sheet, as it were, would be formed from first to last. Whether the thickness of the ring for Jupiter's system, or any other system or planet, was limited to the length of the chord we have been dealing with, or came to be many times greater or even less, makes no difference on our explanation. After being abandoned in a sheet, as we have shown it would be, the centrifugal force they had acquired would, for a time at least, keep the particles of the sheet near the radial positions they then occupied, and their mutual attraction would go on diminishing its thickness, till finally the radial attractions among the particles divided the sheet into entirely separate rings after the manner of those of Saturn; which would in due course break up and form themselves into the smaller nebulÆ from which the planets were supposed to have been made.

M. Faye has made it a great point against the nebula hypothesis that when these rings broke up, the rotary motions of the planets resulting from them would be retrograde, because the outer parts of them would be travelling at a slower rate than the inner ones, and has taken the trouble to construct a diagram to show how this would be the case; but he himself has told us, in "L'Origine du Monde," that Laplace had duly considered this point, and had shown how the friction of the particles of the flat rings among themselves would, through course of time, retard and accelerate each other, so that a ring would come to revolve as if it were one solid piece, and consequently that the outer edge of the ring would come to be travelling faster than the inner one, which according to his (M. Faye's) own showing would produce, on breaking up, a planet with direct motion of rotation. Laplace's words, as cited by him, are:—

"Le frottement mutuel des molÉcules de chaque anneau a dÛ accÉlÉrer les unes et retarder les autres jusqu'À ce qu'elles aient acquis une mÊme mouvement angulaire. Ainsi les vitesses rÉelles des molÉcules ÉloignÉes du centre de l'astre out ÉtÉ plus grandes. La cause suivante a dÛ contribuer encore À cette diffÉrence de vitesse: les molÉcules les plus distantes du soleil et qui, par les effets du refroidissement et de la condensation, s'en sont rapprochÉes pour former la partie supÉrieure de l'anneau out toujours dÉcrit les aires proportionnelles aux temps, puisque la force centrale dont elles Étaient animÉes a ÉtÉ constamment dirigÉe vers cet astre; or cette constance des airs exige un accroissement de vitesse À mesure qu'elles s'en sont rapprochÉes. On voit que la mÊme cause a dÛ diminuer la vitesse des molÉcules qui se sont ÉlevÉes vers l'anneau pour former sa partie infÉrieure."

In his method of bringing all the molecules of matter in a ring, to revolve round the centre as if they formed one sole piece, Laplace does not appeal to any accommodating force among them except friction, while he might have called in that of the collisions of the molecules amongst themselves. It is not to be supposed that each molecule would remain fixed in the position it occupied when separated from the nebulÆ, and only went on rubbing against—and creating friction with—its neighbours, and only creeping closer to the centre or farther from it, as it was acted upon by the attraction of the other parts of the ring. The molecules would be rushing against each other in all directions, in spite of, although in the main obedient to, the law of attraction; and we could conceive the possibility of molecules gradually working their way from the extreme outer edge to the extreme inner edge of a ring, or vice versÂ, which would be a much more effectual means of bringing about one period of revolution throughout the whole ring, than the simple force of rubbing against each other. When physicists get a gas shut up in a close vessel, they grant to its molecules the power of committing exactly the same kind of freaks; and a planetary ring is, to all intents and purposes, a closed vessel to our molecules; because they have been placed in it by the laws of attraction and centrifugal force, and there is no other force acting upon them sufficiently powerful to liberate them from it. Therefore there is no reason why a molecule in a ring should be always wedged up in one place, especially after we have shown that each molecule of matter, in any of the rings we have been dealing with, must have had a much greater free path to move about in, than a molecule of gas shut up in any of the vessels used by physicists.

We have no reason to look upon the rings of Saturn otherwise than as in process of being converted into one or more satellites, most probably more than one; because if the matter they are composed of has been separated from the planet in the form of a sheet, the same as we have seen must have been the case with the matter separated from the original nebula for the planets, the sheet has been already divided into at least three distinct parts, and surely that cannot have been done without some object. If these rings have been left, as has been said, in order to show us how the solar system has been formed, that does not authorise us to conclude that they will always remain in the form they have. There is no reason why the lesson should not be carried out to the very end, through the breaking up of the rings, formation of spherical nebiculÆ, and finally satellites. It would be rash to assert that the matter of which any one of them is composed—be it atoms, molecules, meteorites, or brickbats—cannot, through friction and collisions of its particles among themselves, come to revolve around Saturn as if it were one solid piece. But should anyone do so, and adopt M. Faye's condemnation of Laplace's mode of forming rings, he must confess that when Saturn's rings are converted into satellites, their rotations must be retrograde; and it might be, for him, an interesting inquiry to find out whether the rotations of the existing satellites are direct or retrograde.

Astronomers have learnt the lesson as far as it has gone, have noted and registered the state of affairs as it is at present, and their successors will no doubt do the same as changes succeed each other. The day may be inconceivably remote, but it will inevitably come for the rings to be changed into satellites, unless they are disposed of in some other way. It has been said that were the rings to break up, in consequence of their being in a state of unstable equilibrium, they would fall back upon the planet, but that would depend on circumstances. If the motion of their revolution were stopped altogether, they would certainly fall back upon the planet; but if it were not stopped then each molecule would retain its centrifugal force, and would revolve around the primary on its own account, just as, according to very general opinion, it does at present. We do not see why, or for what purpose, these rings could have been separated from Saturn merely to fall back upon him again. It would be rather a strange way of giving a lesson if it were stopped, by a cataclysm of some kind, just when the most interesting part of it was in a fair way of being exhibited. Such a proceeding would assuredly not suit the ideas of those who believe that the solar system has been self-formed by a simple process of evolution.

During the whole process of separation of rings from the original nebula, the nebulous matter would be abandoned in what we may call the form of thin hoop-shaped rings, so that the equatorial region of the nebula would be flat—as we have shown at p. 115—and when the nebula came to be so much reduced that it could abandon no more matter through centrifugal force, its form would be, in some measure, like that of a rotating cylinder terminating at each end in a cap in the form of a segment of a sphere. When explaining the formation of planetary rings, we have seen that in the Jovian nebula the length of the flat part would have come very soon to be nearly 1,500,000 miles, and that it would increase rapidly. But, remembering that the flattening of the equatorial part must have begun on the original nebula, we see that the flat part must have increased vastly in length before it reached Jupiter, and that by the time the residuary, or solar, nebula was reached—which we made to be only a little over 63,000,000 miles in diameter—the cylindrical part of it would bear no small proportion to that diameter. Taking this form of the nebula into consideration, and also the fact that the separation of matter from it by centrifugal force could not always be absolutely equal all around it, the swaying in its rotary motion produced by the all but inevitable inequality of mass, at the two ends of the cylindrical part, and at the sides of the segmental caps, may have been the cause of the differences in the inclinations of the orbits of the planets to the ecliptic; and especially of why the difference came to be so much greater in the case of Mercury than in any of the others.

In connection with this very reasonable conclusion as to the form of the nebula almost from the beginning, we may add that, when it ceased to throw off rings, it would be very much in the same condition as Saturn is at the present day. Therefore we may conclude with very great safety, that the present form of Saturn is that of a cylinder with segments of spheres forming the ends; and in this manner can account for his square-shouldered appearance, which has puzzled more than one astronomer.

The idea has been very general that in condensing and contracting, the nebula would gradually come to assume the form of a lens of a very pronounced character, from the circumference of which the rings would be abandoned one after the other; but when thoroughly looked into, it is difficult to see how this could be the case. In a sphere of cosmic matter contracting equally all round towards the centre through the force of attraction, it is more natural to suppose that the separation of matter from its equator through centrifugal force, would have a tendency to diminish the equatorial more rapidly than the polar diameter, as we have been trying to show above, more especially as the attraction of the matter in the rings as they were abandoned one after the other would, in a constantly increasing degree, assist the centrifugal force in facilitating the separation by drawing the matter outwards. Matter falling in from the polar regions would afterwards require to have its motion turned off at right angles before it could be sent off by centrifugal force to the equator, an operation which would be more easily effected in the equatorial regions, where the gravitating motion had only to be retarded; and as very unequal amounts of density could not be created in the interior parts of such a sphere by gravitation, so as to cause pressure outwards, it is difficult to show how the polar diameter could be more rapidly reduced than the equatorial diameter, which was being continually shorn of its length. It may be said that all that we have been writing in the last few pages is absurd, because we have been proceeding on the supposition that the condensation of the nebula was effected at or near its surface. Laplace procured this condition by piling up imponderable heat in his nebula, but he might have got it otherwise. Given a nebula such as the one we are dealing with of 6,600,000,000 miles in diameter, where would condensation be most active? Most undoubtedly where there was the greatest mass of matter. Compare, then, the mass of 1,000,000 miles in diameter at the surface with the mass of the same diameter at the centre, and we cannot hesitate for a moment in concluding that the most active condensation would not be very far from the surface. Not only so, but the same would continue to be the case, at least until the last ring was abandoned. Thus by working upon what may have appeared to be an absurd foundation, i.e. condensation at the surface due to the intense heat of the nebula, we have been able to acquire more correct ideas than we had before, of how the solar system was elaborated. But we shall have much more to say on the same subject hereafter.

There has been a great outcry raised about the rotation of the planets Neptune and Uranus being retrograde, as is correctly concluded to be the case from the revolution of their satellites being retrograde, but we do not see that there has been any good reason for it. Laplace, no doubt, concluded, wrongly, that the motions of all the bodies of the solar system—as known to him—were direct, and therefore used that conclusion in showing that there were 4000 milliards against 1 in favour of his hypothesis being right; but at the same time it cannot be concluded that he thought that it would be destroyed by the motion of rotation of one or even several of the forty-three bodies turning out to be retrograde; because, when discussing the hypothesis of Buffon, he states, most distinctly, that it is not necessary that the rotation of a planet should be in the same sense as that of its revolution, and that the earth might revolve from east to west, and at the same time the absolute movement of each of its molecules might be directed from west to east. His words as cited by M. Faye in "L'Origine du Monde," at page 158, are:

"A la veritÉ, le mouvement absolu des molÉcules d'une planÈte doit Être alors dirigÉ dans le sens du mouvement de son centre de gravitÉ, mais il ne s'ensuit point que le mouvement de rotation de la planÈte soit dirigÉ dans le mÊme sens; ainsi la Terre pouvait tourner d'orient en occident, et cependant le mouvement absolu de chacune de ses molÉcules serait dirigÉ d'occident en orient, ce qui doit s'appliquer au mouvement de rÉvolution des satellites, dont la direction, dans l'hypothÈse dont il s'agit, n'est pas nÉcessairement la mÊme que celle de la projection des planÈtes." He seems to say, "This would suit Buffon's hypothesis, but I do not require it for mine." Even were this not so, it would not be very difficult to account for the retrograde rotation of these two planets, but we are not yet prepared to show, in a convincing manner, how these motions were produced. We have to show first how the nebula itself was brought to the dimensions at which we took it up, and there is a great deal to be done before we can show that.

Should our belief in being able to explain how the retrograde rotations of Uranus and Neptune were brought about turn out to be unacceptable, we would not condemn the nebular hypothesis, because, as M. Faye himself says, if we add the asteroids to Laplace's 43 we should have somewhere about 500 bodies, all with direct motion, agreeing with the hypothesis, against 4 that do not, that is about 125 to 1 instead of 43 to 1, which was all Laplace could claim. Moreover, we have not been able to see that M. Faye's objections to it are well founded, rather the contrary; nor can we agree with him when he says that when one point in a hypothesis is found to be erroneous it ought to be abandoned altogether, and something better sought for. Is his something any better? All acquired knowledge has been built up from ideas collected from all sides, and from errors reformed. What would a grammarian say were we to return to him his grammar as useless, because we had found one exception to one of his rules against 125 cases in which we had found it to be right? Perhaps it would put him in mind of the name of a tree. And grammar is not the only case in which we say that the exception confirms the rule.

In taking the nebula to pieces, we have taken no notice of the satellites of Mars, not only because they are so small that they would have had no sensible effect on our calculations, but because we cannot conceive that they could have been abandoned by the planet, when in a nebulous state, in the same manner as the planetary rings are supposed to have been by the parent nebula; and we might simply refer to the dimensions, especially the thinness, we have found for the ring out of which Mercury was formed, for proof of our assertion; but for more satisfactory corroboration, we will go a little deeper into the affair. Let us take the diameters of Mars and of the orbits of his satellites, as they are stated in text-books of astronomy; that is 2957, 11,640 and 29,200 miles respectively, and suppose the diameters of what—in the method we have applied to the planets—we would call the Deimos and Phobos nebulÆ to have been 40,000 and 20,420 miles also, respectively; then these two diameters would make the breadth of the ring for the formation of Deimos to have been 9790 miles. With these data, if we go through a series of calculations with respect to this outer satellite, in all respects similar to those we have made for each of the rings of the planets, we shall find that the ring for Deimos would have been only 5·64 inches thick, without taking into account its condensation during the process of separation. This, of course, points out at once the impossibility of any such operation going on in Nature. We can imagine the possibility of a ring of even millions of miles broad, and of very great tenuity, holding together provided it be hundreds of thousands of miles thick, but to think of one 10,000 miles broad and less than 6 inches thick holding together is another affair altogether. With respect to Phobos, it is only necessary to say that he revolves round Mars in considerably less than one-third of the time that he ought to, and is therefore not a legitimate production of the nebular hypothesis any more than Deimos can be. Here, then, we have come upon two bodies, one of which has not been formed in the way, and the other has not the proper motion, prescribed in the hypothesis; but we do not think ourselves justified in declaring it to be worthy of condemnation on that account, seeing that we have found no other difficulty in working out the solar system from it.

Moreover, it is not impossible, nor do we think it at all improbable, that through the course of time astronomers may discover that Phobos is a captured asteroid—perhaps Deimos also—gradually working its way into final annexation. And who can tell how many of these erratic bodies Jupiter and Mars may have captured already? In the dark as it were, for they may have been too small to be noticed when they were being run in. Neither of these two worthies has ever been very much celebrated in song or history for respect for his neighbour's property. Jupiter is credited with sorting out the asteroids and arranging them in bands, and perhaps he has been human enough to exact a commission for his labour; and it might be more in his line, and certainly much more easy for Mars, to take forcible possession of as many of them as came within his reach.