Essays: Scientific, Political, and Speculative, Volume I

"As seen through colossal telescopes," says Humboldt, "the contemplation of these nebulous masses leads us into regions from whence a ray of light, according to an assumption not wholly improbable, requires millions of years to reach our earth – to distances for whose measurement the dimensions (the distance of Sirius, or the calculated distances of the binary stars in Cygnus and the Centaur) of our nearest stratum of fixed stars scarcely suffice."

In this confused sentence there is implied a belief, that the distances of the nebulæ from our galaxy of stars as much transcend the distances of our stars from one another, as these interstellar distances transcend the dimensions of our planetary system. Just as the diameter of the Earth's orbit, is a mere point when compared with the distance of our Sun from Sirius; so is the distance of our Sun from Sirius, a mere point when compared with the distance of our galaxy from those far-removed galaxies constituting nebulæ. Observe the consequences of this assumption.

If one of these supposed galaxies is so remote that its distance dwarfs our interstellar spaces into points, and therefore makes the dimensions of our whole sidereal system relatively insignificant; does it not inevitably follow that the telescopic power required to resolve this remote galaxy into stars, must be incomparably greater than the telescopic power required to resolve the whole of our own galaxy into stars? Is it not certain that an instrument which can just exhibit with clearness the most distant stars of our own cluster, must be utterly unable to separate one of these remote clusters into stars? What, then, are we to think when we find that the same instrument which decomposes hosts of nebulæ into stars, fails to resolve completely our own Milky Way? Take a homely comparison. Suppose a man who was surrounded by a swarm of bees, extending, as they sometimes do, so high in the air as to render some of the individual bees almost invisible, were to declare that a certain spot on the horizon was a swarm of bees; and that he knew it because he could see the bees as separate specks. Incredible as the assertion would be, it would not exceed in incredibility this which we are criticising. Reduce the dimensions to figures, and the absurdity becomes still more palpable. In round numbers, the distance of Sirius from the Earth is half a million times the distance of the Earth from the Sun; and, according to the hypothesis, the distance of a nebula is something like half a million times the distance of Sirius. Now, our own "starry island, or nebula," as Humboldt calls it, "forms a lens-shaped, flattened, and everywhere detached stratum, whose major axis is estimated at seven or eight hundred, and its minor axis at a hundred and fifty times the distance of Sirius from the Earth."[11 - Cosmos. (Seventh Edition.) Vol. i. pp. 79, 80.] And since it is concluded that the Solar System is near the centre of this aggregation, it follows that our distance from the remotest parts of it is some four hundred distances of Sirius. But the stars forming these remotest parts are not individually visible, even through telescopes of the highest power. How, then, can such telescopes make individually visible the stars of a nebula which is half a million times the distance of Sirius? The implication is, that a star rendered invisible by distance becomes visible if taken twelve hundred times further off! Shall we accept this implication? or shall we not rather conclude that the nebulæ are not remote galaxies? Shall we not infer that, be their nature what it may, they must be at least as near to us as the extremities of our own sidereal system?

Throughout the above argument, it is tacitly assumed that differences of apparent magnitude among the stars, result mainly from differences of distance. On this assumption the current doctrines respecting the nebulæ are founded; and this assumption is, for the nonce, admitted in each of the foregoing criticisms. From the time, however, when it was first made by Sir W. Herschel, this assumption has been purely gratuitous; and it now proves to be inadmissible. But, awkwardly enough, its truth and its untruth are alike fatal to the conclusions of those who argue after the manner of Humboldt. Note the alternatives.

On the one hand, what follows from the untruth of the assumption? If apparent largeness of stars is not due to comparative nearness, and their successively smaller sizes to their greater and greater degrees of remoteness, what becomes of the inferences respecting the dimensions of our sidereal system and the distances of nebulæ? If, as has lately been shown, the almost invisible star 61 Cygni has a greater parallax than [Greek: a] Cygni, though, according to an estimate based on Sir W. Herschel's assumption, it should be about twelve times more distant – if, as it turns out, there exist telescopic stars which are nearer to us than Sirius; of what worth is the conclusion that the nebulæ are very remote, because their component luminous masses are made visible only by high telescopic powers? Clearly, if the most brilliant star in the heavens and a star that cannot be seen by the naked eye, prove to be equidistant, relative distances cannot be in the least inferred from relative visibilities. And if so, nebulæ may be comparatively near, though the starlets of which they are made up appear extremely minute.

On the other hand, what follows if the truth of the assumption be granted? The arguments used to justify this assumption in the case of the stars, equally justify it in the case of the nebulæ. It cannot be contended that, on the average, the apparent sizes of the stars indicate their distances, without its being admitted that, on the average, the apparent sizes of the nebulæ indicate their distances – that, generally speaking, the larger are the nearer and the smaller are the more distant. Mark, now, the necessary inference respecting their resolvability. The largest or nearest nebulæ will be most easily resolved into stars; the successively smaller will be successively more difficult of resolution; and the irresolvable ones will be the smallest ones. This, however, is exactly the reverse of the fact. The largest nebulæ are either wholly irresolvable, or but partially resolvable under the highest telescopic powers; while large numbers of quite small nebulæ are easily resolved by far less powerful telescopes. An instrument through which the great nebula in Andromeda, two and a half degrees long and one degree broad, appears merely as a diffused light, decomposes a nebula of fifteen minutes diameter into twenty thousand starry points. At the same time that the individual stars of a nebula eight minutes in diameter are so clearly seen as to allow of their number being estimated, a nebula covering an area five hundred times as great shows no stars at all! What possible explanation of this can be given on the current hypothesis?

Yet a further difficulty remains – one which is, perhaps, still more obviously fatal than the foregoing. This difficulty is presented by the phenomena of the Magellanic clouds. Describing the larger of these, Sir John Herschel says: —

"The Nubecula Major, like the Minor, consists partly of large tracts and ill-defined patches of irresolvable nebula, and of nebulosity in every stage of resolution, up to perfectly resolved stars like the Milky Way, as also of regular and irregular nebulæ properly so called, of globular clusters in every stage of resolvability, and of clustering groups sufficiently insulated and condensed to come under the designation of 'clusters of stars.'" —Cape Observations, p. 146.

In his Outlines of Astronomy, Sir John Herschel, after repeating this description in other words, goes on to remark that —

"This combination of characters, rightly considered, is in a high degree instructive, affording an insight into the probable comparative distance of stars and nebulæ, and the real brightness of individual stars as compared with one another. Taking the apparent semidiameter of the nubecula major at three degrees, and regarding its solid form as, roughly speaking, spherical, its nearest and most remote parts differ in their distance from us by a little more than a tenth part of our distance from its center. The brightness of objects situated in its nearer portions, therefore, cannot be much exaggerated, nor that of its remoter much enfeebled, by their difference of distance; yet within this globular space, we have collected upwards of six hundred stars of the seventh, eighth, ninth, and tenth magnitudes, nearly three hundred nebulæ, and globular and other clusters, of all degrees of resolvability, and smaller scattered stars innumerable of every inferior magnitude, from the tenth to such as by their multitude and minuteness constitute irresolvable nebulosity, extending over tracts of many square degrees. Were there but one such object, it might be maintained without utter improbability that its apparent sphericity is only an effect of foreshortening, and that in reality a much greater proportional difference of distance between its nearer and more remote parts exists. But such an adjustment, improbable enough in one case, must be rejected as too much so for fair argument in two. It must, therefore, be taken as a demonstrated fact, that stars of the seventh or eighth magnitude and irresolvable nebula may co-exist within limits of distance not differing in proportion more than as nine to ten." —Outlines of Astronomy (10th Ed.), pp. 656-57.

This supplies yet another reductio ad absurdum of the doctrine we are combating. It gives us the choice of two incredibilities. If we are to believe that one of these included nebulæ is so remote that its hundred thousand stars look like a milky spot, invisible to the naked eye; we must also believe that there are single stars so enormous that though removed to this same distance they remain visible. If we accept the other alternative, and say that many nebulæ are no further off than our own stars of the eighth magnitude; then it is requisite to say that at a distance not greater than that at which a single star is still faintly visible to the naked eye, there may exist a group of a hundred thousand stars which is invisible to the naked eye. Neither of these suppositions can be entertained. What, then, is the conclusion that remains? This only: – that the nebulæ are not further from us than parts of our own sidereal system, of which they must be considered members; and that when they are resolvable into discrete masses, these masses cannot be considered as stars in anything like the ordinary sense of that word.[12 - Since the publication of this essay the late Mr. R. A. Proctor has given various further reasons for the conclusion that the nebulæ belong to our own sidereal system. The opposite conclusion, contested throughout the foregoing section, has now been tacitly abandoned.]

And now, having seen the untenability of this idea, rashly espoused by sundry astronomers, that the nebulæ are extremely remote galaxies; let us consider whether the various appearances they present are not reconcilable with the Nebular Hypothesis.

Given a rare and widely-diffused mass of nebulous matter, having a diameter, say, of one hundred times that of the Solar System,[13 - Any objection made to the extreme tenuity this involves, is met by the calculation of Newton, who proved that were a spherical inch of air removed four thousand miles from the Earth, it would expand into a sphere more than filling the orbit of Saturn.] what are the successive changes that may be expected to take place in it? Mutual gravitation will approximate its atoms or its molecules; but their approximation will be opposed by that atomic motion the resultant of which we recognize as repulsion, and the overcoming of which implies the evolution of heat. As fast as this heat partially escapes by radiation, further approximation will take place, attended by further evolution of heat, and so on continuously: the processes not occurring separately as here described, but simultaneously, uninterruptedly, and with increasing activity. When the nebulous mass has reached a particular stage of condensation – when its internally-situated atoms have approached to within certain distances, have generated a certain amount of heat, and are subject to a certain mutual pressure, combinations may be anticipated. Whether the molecules produced be of kinds such as we know, which is possible, or whether they be of kinds simpler than any we know, which is more probable, matters not to the argument. It suffices that molecular unions, either between atoms of the same kind or between atoms of different kinds, will finally take place. When they do take place, they will be accompanied by a sudden and great disengagement of heat; and until this excess of heat has escaped, the newly-formed molecules will remain uniformly diffused, or, as it were, dissolved in the pre-existing nebulous medium.

But now what may be expected by and by to happen? When radiation has adequately lowered the temperature, these molecules will precipitate; and, having precipitated, they will not remain uniformly diffused, but will aggregate into flocculi; just as water, precipitated from air, collects into clouds. Concluding, thus, that a nebulous mass will, in course of time, resolve itself into flocculi of precipitated denser matter, floating in the rarer medium from which they were precipitated, let us inquire what are the mechanical results to be inferred. Of clustered bodies in empty space, each will move along a line which is the resultant of the tractive forces exercised by all the rest, modified from moment to moment by the acquired motion; and the aggregation of such clustered bodies, if it eventually results at all, can result only from collision, dissipation, and the formation of a resisting medium. But with clustered bodies already immersed in a resisting medium, and especially if such bodies are of small densities, such as those we are considering, the process of concentration will begin forthwith: two factors conspiring to produce it. The flocculi described, irregular in their shapes and presenting, as they must in nearly all cases, unsymmetrical faces to their lines of motion, will be deflected from those courses which mutual gravitation, if uninterfered with, would produce among them; and this will militate against that balancing of movements which permanence of the cluster pre-supposes. If it be said, as it may truly be said, that this is too trifling a cause of derangement to produce much effect, then there comes the more important cause with which it co-operates. The medium from which the flocculi have been precipitated, and through which they are moving, must, by gravitation, be rendered denser in its central parts than in its peripheral parts. Hence the flocculi, none of them moving in straight lines to the common centre of gravity, but having courses made to diverge to one or other side of it (in small degrees by the cause just assigned, and in much greater degrees by the tractive forces of other flocculi) will, in moving towards the central region, meet with greater resistances on their inner sides than on their outer sides; and will be thus made to diverge outwardly from their courses more than they would otherwise do. Hence a tendency which, apart from other tendencies, will cause them severally to go on one or other side of the centre of gravity, and, approaching it, to get motions more and more tangential. Observe, however, that their respective motions will be deflected, not towards one side of the common centre of gravity, but towards various sides. How then can there result a movement common to them all? Very simply. Each flocculus, in describing its course, must give motion to the medium through which it is moving. But the probabilities are infinity to one against all the respective motions thus impressed on this medium, exactly balancing one another. And if they do not balance one another the result must be rotation of the whole mass of the medium in one direction. But preponderating momentum in one direction, having caused rotation of the medium in that direction, the rotating medium must in its turn gradually arrest such flocculi as are moving in opposition, and impress its own motion upon them; and thus there will ultimately be formed a rotating medium with suspended flocculi partaking of its motion, while they move in converging spirals towards the common centre of gravity.[14 - A reference may fitly be made here to a reason given by Mons. Babinet for rejection of the Nebular Hypothesis. He has calculated that taking the existing Sun, with its observed angular velocity, its substance, if expanded so as to fill the orbit of Neptune, would have nothing approaching the angular velocity which the time of revolution of that planet implies. The assumption he makes is inadmissible. He supposes that all parts of the nebulous spheroid when it filled Neptune's orbit, had the same angular velocities. But the process of nebular condensation as indicated above, implies that the remoter flocculi of nebulous matter, later in reaching the central mass, and forming its peripheral portions, will acquire, during their longer journeys towards it, greater velocities. An inspection of one of the spiral nebulæ, as 51st or 99th Messier, at once shows that the outlying portions when they reach the nucleus, will form an equatorial belt moving round the common centre more rapidly than the rest. Thus the central parts will have small angular velocities, while there will be increasing angular velocities of parts increasingly remote from the centre. And while the density of the spheroid continues small, fluid friction will scarcely at all change these differences.A like criticism may, I think, be passed on an opinion expressed by Prof. Newcomb. He says: – "When the contraction [of the nebulous spheroid] had gone so far that the centrifugal and attracting forces nearly balanced each other at the outer equatorial limit of the mass, the result would have been that contraction in the direction of the equator would cease entirely, and be confined to the polar regions, each particle dropping, not towards the sun, but towards the plane of the solar equator. Thus, we should have a constant flattening of the spheroidal atmosphere until it was reduced to a thin flat disk. This disk might then separate itself into rings, which would form planets in much the same way that Laplace supposed. But there would probably be no marked difference in the age of the planets." (Popular Astronomy, p. 512.) Now this conclusion assumes, like that of M. Babinet, that all parts of the nebulous spheroid had equal angular velocities. If, as above contended, it is inferable from the process by which a nebulous spheroid was formed, that its outer portions revolved with greater angular velocities than its inner; then the inference which Prof. Newcomb draws is not necessitated.]

Before comparing these conclusions with facts, let us pursue the reasoning a little further, and observe certain subordinate actions. The respective flocculi must be drawn not towards their common centre of gravity only, but also towards neighbouring flocculi. Hence the whole assemblage of flocculi will break up into groups: each group concentrating towards its local centre of gravity, and in so doing acquiring a vortical movement like that subsequently acquired by the whole nebula. According to circumstances, and chiefly according to the size of the original nebulous mass, this process of local aggregation will produce various results. If the whole nebula is but small, the local groups of flocculi may be drawn into the common centre of gravity before their constituent masses have coalesced with one another. In a larger nebula, these local aggregations may have concentrated into rotating spheroids of vapour, while yet they have made but little approach towards the general focus of the system. In a still larger nebula, where the local aggregations are both greater and more remote from the common centre of gravity, they may have condensed into masses of molten matter before the general distribution of them has greatly altered. In short, as the conditions in each case determine, the discrete masses produced may vary indefinitely in number, in size, in density, in motion, in distribution.

And now let us return to the visible characters of nebulæ, as observed through modern telescopes. Take first the description of those nebulæ which, by the hypothesis, must be in an early stage of evolution.

Among the "irregular nebulæ," says Sir John Herschel, "may be comprehended all which, to a want of complete and in most instances even of partial resolvability by the power of the 20-feet reflector, unite such a deviation from the circular or elliptic form, or such a want of symmetry (with that form) as preclude their being placed in class 1, or that of Regular Nebulæ. This second class comprises many of the most remarkable and interesting objects in the heavens, as well as the most extensive in respect of the area they occupy."

And, referring to this same order of objects, M. Arago says: – "The forms of very large diffuse nebulæ do not appear to admit of definition; they have no regular outline."

This coexistence of largeness, irregularity, and indefiniteness of outline, with irresolvability, is extremely significant. The fact that the largest nebulæ are either irresolvable or very difficult to resolve, might have been inferred a priori; seeing that irresolvability, implying that the aggregation of precipitated matter has gone on to but a small extent, will be found in nebulæ of wide diffusion. Again, the irregularity of these large, irresolvable nebulæ, might also have been expected; seeing that their outlines, compared by Arago with "the fantastic figures which characterize clouds carried away and tossed about by violent and often contrary winds," are similarly characteristic of a mass not yet gathered together by the mutual attraction of its parts. And once more, the fact that these large, irregular, irresolvable nebulæ have indefinite outlines – outlines that fade off insensibly into surrounding darkness – is one of like meaning.

Speaking generally (and of course differences of distance negative anything beyond average statements), the spiral nebulæ are smaller than the irregular nebulæ, and more resolvable; at the same time that they are not so small as the regular nebulæ, and not so resolvable. This is as, according to the hypothesis, it should be. The degree of condensation causing spiral movement, is a degree of condensation also implying masses of flocculi that are larger, and therefore more visible, than those existing in an earlier stage. Moreover, the forms of these spiral nebulæ are quite in harmony with the explanation given. The curves of luminous matter which they exhibit, are not such as would be described by discrete masses starting from a state of rest, and moving through a resisting medium to a common centre of gravity; but they are such as would be described by masses having their movements modified by the rotation of the medium.

In the centre of a spiral nebula is seen a mass both more luminous and more resolvable than the rest. Assume that, in process of time, all the spiral streaks of luminous matter which converge to this centre are drawn into it, as they must be; assume further, that the flocculi, or other discrete portions constituting these luminous streaks, aggregate into larger masses at the same time that they approach the central group, and that the masses forming this central group also aggregate into larger masses; and there will finally result a cluster of such larger masses, which will be resolvable with comparative ease. And, as the coalescence and concentration go on, the constituent masses will gradually become fewer, larger, brighter, and more densely collected around the common centre of gravity. See now how completely this inference agrees with observation. "The circular form is that which most commonly characterises resolvable nebulæ," writes Arago. Resolvable nebulæ, says Sir John Herschel, "are almost universally round or oval." Moreover, the centre of each group habitually displays a closer clustering of the constituent masses than the outer parts; and it is shown that, under the law of gravitation, which we now know extends to the stars, this distribution is not one of equilibrium, but implies progressing concentration. While, just as we inferred that, according to circumstances, the extent to which aggregation has been carried must vary; so we find that, in fact, there are regular nebulæ of all degrees of resolvability, from those consisting of innumerable minute masses, to those in which their numbers are smaller and the sizes greater, and to those in which there are a few large bodies worthy to be called stars.

On the one hand, then, we see that the notion, of late years uncritically received, that the nebulæ are extremely remote galaxies of stars like those which make up our own Milky Way, is totally irreconcilable with the facts – involves us in sundry absurdities. On the other hand, we see that the hypothesis of nebular condensation harmonizes with the most recent results of stellar astronomy: nay more – that it supplies us with an explanation of various appearances which in its absence would be incomprehensible.

Descending now to the Solar System, let us consider first a class of phenomena in some sort transitional – those offered by comets. In them, or at least in those most numerous of them which lie far out of the plane of the Solar System, and are not to be counted among its members, we have, still existing, a kind of matter like that out of which, according to the Nebular Hypothesis, the Solar System was evolved. Hence, for the explanation of them, we must go back to the time when the substances forming the sun and planets were yet unconcentrated.

When diffused matter, precipitated from a rarer medium, is aggregating, there are certain to be here and there produced small flocculi, which long remain detached; as do, for instance, minute shreds of cloud in a summer sky. In a concentrating nebula these will, in the majority of cases, eventually coalesce with the larger flocculi near to them. But it is tolerably evident that some of those formed at the outermost parts of the nebula, will not coalesce with the larger internal masses, but will slowly follow without overtaking them. The relatively greater resistance of the medium necessitates this. As a single feather falling to the ground will be rapidly left behind by a pillow-full of feathers; so, in their progress to the common centre of gravity, will the outermost shreds of vapour be left behind by the great masses of vapour internally situated. But we are not dependent merely on reasoning for this belief. Observation shows us that the less concentrated external parts of nebulæ, are left behind by the more concentrated internal parts. Examined through high powers, all nebulæ, even when they have assumed regular forms, are seen to be surrounded by luminous streaks, of which the directions show that they are being drawn into the general mass. Still higher powers bring into view still smaller, fainter, and more widely-dispersed streaks. And it cannot be doubted that the minute fragments which no telescopic aid makes visible, are yet more numerous and widely dispersed. Thus far, then, inference and observation are at one.

Granting that the great majority of these outlying portions of nebulous matter will be drawn into the central mass long before it reaches a definite form, the presumption is that some of the very small, far-removed portions will not be so; but that before they arrive near it, the central mass will have contracted into a comparatively moderate bulk. What now will be the characters of these late-arriving portions?

In the first place, they will have either extremely eccentric orbits or non-elliptic paths. Left behind at a time when they were moving towards the centre of gravity in slightly-deflected lines, and therefore having but very small angular velocities, they will approach the central mass in greatly elongated curves; and rushing round it, will go off again into space. That is, they will behave just as we see the majority of comets do; the orbits of which are either so eccentric as to be indistinguishable from parabolas, or else are not orbits at all, but are paths which are distinctly either parabolic or hyperbolic.

In the second place, they will come from all parts of the heavens. Our supposition implies that they were left behind at a time when the nebulous mass was of irregular shape, and had not acquired a definite rotation; and as the separation of them would not be from any one surface of the nebulous mass more than another, the conclusion must be that they will come to the central body from various directions in space. This, too, is exactly what happens. Unlike planets, whose orbits approximate to one plane, comets have orbits that show no relation to one another; but cut the plane of the ecliptic at all angles, and have axes inclined to it at all angles.

In the third place, these remotest flocculi of nebulous matter will, at the outset, be deflected from their direct courses to the common centre of gravity, not all on one side, but each on such side as its form, or its original proper motion, determines. And being left behind before the rotation of the nebula is set up, they will severally retain their different individual motions. Hence, following the concentrated mass, they will eventually go round it on all sides; and as often from right to left as from left to right. Here again the inference perfectly corresponds with the facts. While all the planets go round the sun from west to east, comets as often go round the sun from east to west as from west to east. Of 262 comets recorded since 1680, 130 are direct, and 132 are retrograde. This equality is what the law of probabilities would indicate.

Then, in the fourth place, the physical constitution of comets accords with the hypothesis.[15 - It is true that since this essay was written reasons have been given for concluding that comets consist of swarms of meteors enveloped in aeriform matter. Very possibly this is the constitution of the periodic comets which, approximating their orbits to the plane of the Solar System, form established parts of the System, and which, as will be hereafter indicated, have probably a quite different origin.] The ability of nebulous matter to concentrate into a concrete form, depends on its mass. To bring its ultimate atoms into that proximity requisite for chemical union – requisite, that is, for the production of denser matter – their repulsion must be overcome. The only force antagonistic to their repulsion, is their mutual gravitation. That their mutual gravitation may generate a pressure and temperature of sufficient intensity, there must be an enormous accumulation of them; and even then the approximation can slowly go on only as fast as the evolved heat escapes. But where the quantity of atoms is small, and therefore the force of mutual gravitation small, there will be nothing to coerce the atoms into union. Whence we infer that these detached fragments of nebulous matter will continue in their original state. Non-periodic comets seem to do so.

We have already seen that this view of the origin of comets harmonizes with the characters of their orbits; but the evidence hence derived is much stronger than was indicated. The great majority of cometary orbits are classed as parabolic; and it is ordinarily inferred that they are visitors from remote space, and will never return. But are they rightly classed as parabolic? Observations on a comet moving in an extremely eccentric ellipse, which are possible only when it is comparatively near perihelion, must fail to distinguish its orbit from a parabola. Evidently, then, it is not safe to class it as a parabola because of inability to detect the elements of an ellipse. But if extreme eccentricity of an orbit necessitates such inability, it seems quite possible that comets have no other orbits than elliptic ones. Though five or six are said to be hyperbolic, yet, as I learn from one who has paid special attention to comets, "no such orbit has, I believe, been computed for a well-observed comet." Hence the probability that all the orbits are ellipses is overwhelming. Ellipses and hyperbolas have countless varieties of forms, but there is only one form of parabola; or, to speak literally, all parabolas are similar, while there are infinitely numerous dissimilar ellipses and dissimilar hyperbolas. Consequently, anything coming to the Sun from a great distance must have one exact amount of proper motion to produce a parabola: all other amounts would give hyperbolas or ellipses. And if there are no hyperbolic orbits, then it is infinity to one that all the orbits are elliptical. This is just what they would be if comets had the genesis above supposed.

And now, leaving these erratic bodies, let us turn to the more familiar and important members of the Solar System. It was the remarkable harmony among their movements which first made Laplace conceive that the Sun, planets, and satellites had resulted from a common genetic process. As Sir William Herschel, by his observations on the nebulæ, was led to the conclusion that stars resulted from the aggregation of diffused matter; so Laplace, by his observations on the structure of the Solar System, was led to the conclusion that only by the rotation of aggregating matter were its peculiarities to be explained. In his Exposition du Système du Monde, he enumerates as the leading evidences: – 1. The movements of the planets in the same direction and in orbits approaching to the same plane; 2. The movements of the satellites in the same direction as those of the planets; 3. The movements of rotation of these various bodies and of the sun in the same direction as the orbital motions, and mostly in planes little different; 4. The small eccentricities of the orbits of the planets and satellites, as contrasted with the great eccentricities of the cometary orbits. And the probability that these harmonious movements had a common cause, he calculates as two hundred thousand billions to one.

This immense preponderance of probability does not point to a common cause under the form ordinarily conceived – an Invisible Power working after the method of "a Great Artificer;" but to an Invisible Power working after the method of evolution. For though the supporters of the common hypothesis may argue that it was necessary for the sake of stability that the planets should go round the Sun in the same direction and nearly in one plane, they cannot thus account for the direction of the axial motions.[16 - Though this rule fails at the periphery of the Solar System, yet it fails only where the axis of rotation, instead of being almost perpendicular to the orbit-plane, is very little inclined to it; and where, therefore, the forces tending to produce the congruity of motions were but little operative.] The mechanical equilibrium would not have been interfered with, had the Sun been without any rotatory movement; or had he revolved on his axis in a direction opposite to that in which the planets go round him; or in a direction at right angles to the average plane of their orbits. With equal safety the motion of the Moon round the Earth might have been the reverse of the Earth's motion round its axis; or the motions of Jupiter's satellites might similarly have been at variance with his axial motion; or those of Saturn's satellites with his. As, however, none of these alternatives have been followed, the uniformity must be considered, in this case as in all others, evidence of subordination to some general law – implies what we call natural causation, as distinguished from arbitrary arrangement.

Hence the hypothesis of evolution would be the only probable one, even in the absence of any clue to the particular mode of evolution. But when we have, propounded by a mathematician of the highest authority, a theory of this evolution based on established mechanical principles, which accounts for these various peculiarities, as well as for many minor ones, the conclusion that the Solar System was evolved becomes almost irresistible.

The general nature of Laplace's theory scarcely needs stating. Books of popular astronomy have familiarized most readers with his conceptions; – namely, that the matter now condensed into the Solar System, once formed a vast rotating spheroid of extreme rarity extending beyond the orbit of the outermost planet; that as this spheroid contracted, its rate of rotation necessarily increased; that by augmenting centrifugal force its equatorial zone was from time to time prevented from following any further the concentrating mass, and so remained behind as a revolving ring; that each of the revolving rings thus periodically detached, eventually became ruptured at its weakest point, and, contracting on itself, gradually aggregated into a rotating mass; that this, like the parent mass, increased in rapidity of rotation as it decreased in size, and, where the centrifugal force was sufficient, similarly left behind rings, which finally collapsed into rotating spheroids; and that thus, out of these primary and secondary rings, there arose planets and their satellites, while from the central mass there resulted the Sun. Moreover, it is tolerably well known that this a priori reasoning harmonizes with the results of experiment. Dr. Plateau has shown that when a mass of fluid is, as far may be, protected from the action of external forces, it will, if made to rotate with adequate velocity, form detached rings; and that these rings will break up into spheroids which turn on their axes in the same direction with the central mass. Thus, given the original nebula, which, acquiring a vortical motion in the way indicated, has at length concentrated into a vast spheroid of aeriform matter moving round its axis – given this, and mechanical principles explain the rest. The genesis of a Solar System displaying movements like those observed, may be predicted; and the reasoning on which the prediction is based is countenanced by experiment.[17 - It is true that, as expressed by him, these propositions of Laplace are not all beyond dispute. An astronomer of the highest authority, who has favoured me with some criticisms on this essay, alleges that instead of a nebulous ring rupturing at one point, and collapsing into a single mass, "all probability would be in favour of its breaking up into many masses." This alternative result certainly seems the more likely. But granting that a nebulous ring would break up into many masses, it may still be contended that, since the chances are infinity to one against these being of equal sizes and equidistant, they could not remain evenly distributed round their orbit. This annular chain of gaseous masses would break up into groups of masses; these groups would eventually aggregate into larger groups; and the final result would be the formation of a single mass. I have put the question to an astronomer scarcely second in authority to the one above referred to, and he agrees that this would probably be the process.]

But now let us inquire whether, besides these most conspicuous structural and dynamic peculiarities of the Solar System, sundry minor ones are not similarly explicable.

Take first the relation between the planes of the planetary orbits and the plane of the Sun's equator. If, when the nebulous spheroid extended beyond the orbit of Neptune, all parts of it had been revolving exactly in the same plane, or rather in parallel planes – if all its parts had had one axis; then the planes of the successive rings would have been coincident with each other and with that of the Sun's rotation. But it needs only to go back to the earlier stages of concentration, to see that there could exist no such complete uniformity of motion. The flocculi, already described as precipitated from an irregular and widely-diffused nebula, and as starting from all points to their common centre of gravity, must move not in one plane but in innumerable planes, cutting each other at all angles. The gradual establishment of a vortical motion such as we at present see indicated in the spiral nebulæ, is the gradual approach towards motion in one plane. But this plane can but slowly become decided. Flocculi not moving in this plane, but entering into the aggregation at various inclinations, will tend to perform their revolutions round its centre in their own planes; and only in course of time will their motions be partly destroyed by conflicting ones, and partly resolved into the general motion. Especially will the outermost portions of the rotating mass retain for a long time their more or less independent directions. Hence the probabilities are, that the planes of the rings first detached will differ considerably from the average plane of the mass; while the planes of those detached latest will differ from it less.

Here, again, inference to a considerable extent agrees with observation. Though the progression is irregular, yet, on the average, the inclinations decrease on approaching the Sun; and this is all we can expect. For as the portions of the nebulous spheroid must have arrived with miscellaneous inclinations, its strata must have had planes of rotation diverging from the average plane in degrees not always proportionate to their distances from the centre.

Consider next the movements of the planets on their axes. Laplace alleged as one among other evidences of a common genetic cause, that the planets rotate in a direction the same as that in which they go round the Sun, and on axes approximately perpendicular to their orbits. Since he wrote, an exception to this general rule has been discovered in the case of Uranus, and another still more recently in the case of Neptune – judging, at least, from the motions of their respective satellites. This anomaly has been thought to throw considerable doubt on his speculation; and at first sight it does so. But a little reflection shows that the anomaly is not inexplicable, and that Laplace simply went too far in putting down as a certain result of nebular genesis, what is, in some instances, only a probable result. The cause he pointed out as determining the direction of rotation, is the greater absolute velocity of the outer part of the detached ring. But there are conditions under which this difference of velocity may be too insignificant, even if it exists. If a mass of nebulous matter approaching spirally to the central spheroid, and eventually joining it tangentially, is made up of parts having the same absolute velocities; then, after joining the equatorial periphery of the spheroid and being made to rotate with it, the angular velocity of its outer parts will be smaller than the angular velocity of its inner parts. Hence, if, when the angular velocities of the outer and inner parts of a detached ring are the same, there results a tendency to rotation in the same direction with the orbital motion, it may be inferred that when the outer parts of the ring have a smaller angular velocity than the inner parts, a tendency to retrograde rotation will be the consequence.

Again, the sectional form of the ring is a circumstance of moment; and this form must have differed more or less in every case. To make this clear, some illustration will be necessary. Suppose we take an orange, and, assuming the marks of the stalk and the calyx to represent the poles, cut off round the line of the equator a strip of peel. This strip of peel, if placed on the table with its ends meeting, will make a ring shaped like the hoop of a barrel – a ring of which the thickness in the line of its diameter is very small, but of which the width in a direction perpendicular to its diameter is considerable. Suppose, now, that in place of an orange, which is a spheroid of very slight oblateness, we take a spheroid of very great oblateness, shaped somewhat like a lens of small convexity. If from the edge or equator of this lens-shaped spheroid, a ring of moderate size were cut off, it would be unlike the previous ring in this respect, that its greatest thickness would be in the line of its diameter, and not in a line at right angles to its diameter: it would be a ring shaped somewhat like a quoit, only far more slender. That is to say, according to the oblateness of a rotating spheroid, the detached ring may be either a hoop-shaped ring or a quoit-shaped ring.

One further implication must be noted. In a much-flattened or lens-shaped spheroid, the form of the ring will vary with its bulk. A very slender ring, taking off just the equatorial surface, will be hoop-shaped; while a tolerably massive ring, trenching appreciably on the diameter of the spheroid, will be quoit-shaped. Thus, then, according to the oblateness of the spheroid and the bulkiness of the detached ring, will the greatest thickness of that ring be in the direction of its plane, or in a direction perpendicular to its plane. But this circumstance must greatly affect the rotation of the resulting planet. In a decidedly hoop-shaped nebulous ring, the differences of velocity between the inner and outer surfaces will be small; and such a ring, aggregating into a mass of which the greatest diameter is at right angles to the plane of the orbit, will almost certainly give to this mass a predominant tendency to rotate in a direction at right angles to the plane of the orbit. Where the ring is but little hoop-shaped, and the difference between the inner and outer velocities greater, as it must be, the opposing tendencies – one to produce rotation in the plane of the orbit, and the other, rotation perpendicular to it – will both be influential; and an intermediate plane of rotation will be taken up. While, if the nebulous ring is decidedly quoit-shaped, and therefore aggregates into a mass whose greatest dimension lies in the plane of the orbit, both tendencies will conspire to produce rotation in that plane.

On referring to the facts, we find them, as far as can be judged, in harmony with this view. Considering the enormous circumference of Uranus's orbit, and his comparatively small mass, we may conclude that the ring from which he resulted was a comparatively slender, and therefore a hoop-shaped one: especially as the nebulous mass must have been at that time less oblate than afterwards. Hence, a plane of rotation nearly perpendicular to his orbit, and a direction of rotation having no reference to his orbital movement. Saturn has a mass seven times as great, and an orbit of less than half the diameter; whence it follows that his genetic ring, having less than half the circumference, and less than half the vertical thickness (the spheroid being then certainly as oblate, and indeed more oblate), must have had a much greater width – must have been less hoop-shaped, and more approaching to the quoit-shaped: notwithstanding difference of density, it must have been at least two or three times as broad in the line of its plane. Consequently, Saturn has a rotatory movement in the same direction as the movement of translation, and in a plane differing from it by thirty degrees only. In the case of Jupiter, again, whose mass is three and a half times that of Saturn, and whose orbit is little more than half the size, the genetic ring must, for the like reasons, have been still broader – decidedly quoit-shaped, we may say; and there hence resulted a planet whose plane of rotation differs from that of his orbit by scarcely more than three degrees. Once more, considering the comparative insignificance of Mars, Earth, Venus, and Mercury, it follows that, the diminishing circumferences of the rings not sufficing to account for the smallness of the resulting masses, the rings must have been slender ones – must have again approximated to the hoop-shaped; and thus it happens that the planes of rotation again diverge more or less widely from those of the orbits. Taking into account the increasing oblateness of the original spheroid in the successive stages of its concentration, and the different proportions of the detached rings, it may fairly be held that the respective rotatory motions are not at variance with the hypothesis but contrariwise tend to confirm it.

Not only the directions, but also the velocities of rotation seem thus explicable. It might naturally be supposed that the large planets would revolve on their axes more slowly than the small ones: our terrestrial experiences of big and little bodies incline us to expect this. It is a corollary from the Nebular Hypothesis, however, more especially when interpreted as above, that while large planets will rotate rapidly, small ones will rotate slowly; and we find that in fact they do so. Other things equal, a concentrating nebulous mass which is diffused through a wide space, and whose outer parts have, therefore, to travel from great distances to the common centre of gravity, will acquire a high axial velocity in course of its aggregation; and conversely with a small mass. Still more marked will be the difference where the form of the genetic ring conspires to increase the rate of rotation. Other things equal, a genetic ring which is broadest in the direction of its plane will produce a mass rotating faster than one which is broadest at right angles to its plane; and if the ring is absolutely as well as relatively broad, the rotation will be very rapid. These conditions were, as we saw, fulfilled in the case of Jupiter; and Jupiter turns round his axis in less than ten hours. Saturn, in whose case, as above explained, the conditions were less favourable to rapid rotation, takes nearly ten hours and a half. While Mars, Earth, Venus, and Mercury, whose rings must have been slender, take more than double that time: the smallest taking the longest.

From the planets let us now pass to the satellites. Here, beyond the conspicuous facts commonly adverted to, that they go round their primaries in the directions in which these turn on their axes, in planes diverging but little from their equators, and in orbits nearly circular, there are several significant traits which must not be passed over.

One of them is that each set of satellites repeats in miniature the relations of the planets to the Sun, both in certain respects above named and in the order of their sizes. On progressing from the outside of the Solar System to its centre, we see that there are four large external planets, and four internal ones which are comparatively small. A like contrast holds between the outer and inner satellites in every case. Among the four satellites of Jupiter, the parallel is maintained as well as the comparative smallness of the number allows: the two outer ones are the largest, and the two inner ones the smallest. According to the most recent observations made by Mr. Lassell, the like is true of the four satellites of Uranus. In the case of Saturn, who has eight secondary planets revolving round him, the likeness is still more close in arrangement as in number: the three outer satellites are large, the inner ones small; and the contrasts of size are here much greater between the largest, which is nearly as big as Mars, and the smallest, which is with difficulty discovered even by the best telescopes. But the analogy does not end here. Just as with the planets, there is at first a general increase of size on travelling inwards from Neptune and Uranus, which do not differ very widely, to Saturn, which is much larger, and to Jupiter, which is the largest; so of the eight satellites of Saturn, the largest is not the outermost, but the outermost save two; so of Jupiter's four secondaries, the largest is the most remote but one. Now these parallelisms are inexplicable by the theory of final causes. For purposes of lighting, if this be the presumed object of these attendant bodies, it would have been far better had the larger been the nearer: at present, their remoteness renders them of less service than the smallest. To the Nebular Hypothesis, however, these analogies give further support. They show the action of a common physical cause. They imply a law of genesis, holding in the secondary systems as in the primary system.

Still more instructive shall we find the distribution of the satellites – their absence in some instances, and their presence in other instances, in smaller or greater numbers. The argument from design fails to account for this distribution. Supposing it be granted that planets nearer the Sun than ourselves, have no need of moons (though, considering that their nights are as dark, and, relatively to their brilliant days, even darker than ours, the need seems quite as great) – supposing this to be granted; how are we to explain the fact that Uranus has but half as many moons as Saturn, though he is at double the distance? While, however, the current presumption is untenable, the Nebular Hypothesis furnishes us with an explanation. It enables us to predict where satellites will be abundant and where they will be absent. The reasoning is as follows.

In a rotating nebulous spheroid which is concentrating into a planet, there are at work two antagonist mechanical tendencies – the centripetal and the centrifugal. While the force of gravitation draws all the atoms of the spheroid together, their tangential momentum is resolvable into two parts, of which one resists gravitation. The ratio which this centrifugal force bears to gravitation, varies, other things equal, as the square of the velocity. Hence, the aggregation of a rotating nebulous spheroid will be more or less hindered by this resisting force, according as the rate of rotation is high or low: the opposition, in equal spheroids, being four times as great when the rotation is twice as rapid; nine times as great when it is three times as rapid; and so on. Now the detachment of a ring from a planet-forming body of nebulous matter, implies that at its equatorial zone the increasing centrifugal force consequent on concentration has become so great as to balance gravity. Whence it is tolerably obvious that the detachment of rings will be most frequent from those masses in which the centrifugal tendency bears the greatest ratio to the gravitative tendency. Though it is not possible to calculate what ratio these two tendencies had to each other in the genetic spheroid which produced each planet, it is possible to calculate where each was the greatest and where the least. While it is true that the ratio which centrifugal force now bears to gravity at the equator of each planet, differs widely from that which it bore during the earlier stages of concentration; and while it is true that this change in the ratio, depending on the degree of contraction each planet has undergone, has in no two cases been the same; yet we may fairly conclude that where the ratio is still the greatest, it has been the greatest from the beginning. The satellite-forming tendency which each planet had, will be approximately indicated by the proportion now existing in it between the aggregating power, and the power that has opposed aggregation. On making the requisite calculations, a remarkable harmony with this inference comes out. The following table shows what fraction the centrifugal force is of the centripetal force in every case; and the relation which that fraction bears to the number of satellites.[18 - The comparative statement here given differs, slightly in most cases and in one case largely, from the statement included in this essay as originally published in 1858. As then given the table ran thus: —The calculations ending with these figures were made while the Sun's distance was still estimated at 95 millions of miles. Of course the reduction afterwards established in the estimated distance, entailing, as it did, changes in the factors which entered into the calculations, affected the results; and, though it was unlikely that the relations stated would be materially changed, it was needful to have the calculations made afresh. Mr. Lynn has been good enough to undertake this task, and the figures given in the text are his. In the case of Mars a large error in my calculation had arisen from accepting Arago's statement of his density (0·95), which proves to be something like double what it should be. Here a curious incident may be named. When, in 1877, it was discovered that Mars has two satellites, though, according to my hypothesis, it seemed that he should have none, my faith in it received a shock; and since that time I have occasionally considered whether the fact is in any way reconcilable with the hypothesis. But now the proof afforded by Mr. Lynn that my calculation contained a wrong factor, disposes of the difficulty – nay, changes the objection to a verification. It turns out that, according to the hypothesis, Mars ought to have satellites; and, further, that he ought to have a number intermediate between 1 and 4.]

Thus taking as our standard of comparison the Earth with its one moon, we see that Mercury, in which the centrifugal force is relatively less, has no moon. Mars, in which it is relatively much greater, has two moons. Jupiter, in which it is far greater, has four moons. Uranus, in which it is greater still, has certainly four, and more if Herschel was right. Saturn, in which it is the greatest, being nearly one-sixth of gravity, has, including his rings, eleven attendants. The only instance in which there is nonconformity with observation, is that of Venus. Here it appears that the centrifugal force is relatively greater than in the Earth; and, according to the hypothesis, Venus ought to have a satellite. Respecting this anomaly several remarks are to be made. Without putting any faith in the alleged discovery of a satellite of Venus (repeated at intervals by five different observers), it may yet be contended that as the satellites of Mars eluded observation up to 1877, a satellite of Venus may have eluded observation up to the present time. Merely naming this as possible, but not probable, a consideration of more weight is that the period of rotation of Venus is but indefinitely fixed, and that a small diminution in the estimated angular velocity of her equator would bring the result into congruity with the hypothesis. Further, it may be remarked that not exact, but only general, congruity is to be expected; since the process of condensation of each planet from nebulous matter can scarcely be expected to have gone on with absolute uniformity: the angular velocities of the superposed strata of nebulous matter probably differed from one another in degrees unlike in each case; and such differences would affect the satellite-forming tendency. But without making much of these possible explanations of the discrepancy, the correspondence between inference and fact which we find in so many planets, may be held to afford strong support to the Nebular Hypothesis.

Certain more special peculiarities of the satellites must be mentioned as suggestive. One of them is the relation between the period of revolution and that of rotation. No discoverable purpose is served by making the Moon go round its axis in the same time that it goes round the Earth: for our convenience, a more rapid axial motion would have been equally good; and for any possible inhabitants of the Moon, much better. Against the alternative supposition, that the equality occurred by accident, the probabilities are, as Laplace says, infinity to one. But to this arrangement, which is explicable neither as the result of design nor of chance, the Nebular Hypothesis furnishes a clue. In his Exposition du Système du Monde, Laplace shows, by reasoning too detailed to be here repeated, that under the circumstances such a relation of movements would be likely to establish itself.

Among Jupiter's satellites, which severally display these same synchronous movements, there also exists a still more remarkable relation. "If the mean angular velocity of the first satellite be added to twice that of the third, the sum will be equal to three times that of the second;" and "from this it results that the situations of any two of them being given, that of the third can be found." Now here, as before, no conceivable advantage results. Neither in this case can the connexion have been accidental: the probabilities are infinity to one to the contrary. But again, according to Laplace, the Nebular Hypothesis supplies a solution. Are not these significant facts?

Most significant fact of all, however, is that presented by the rings of Saturn. As Laplace remarks, they are, as it were, still extant witnesses of the genetic process he propounded. Here we have, continuing permanently, forms of aggregation like those through which each planet and satellite once passed; and their movements are just what, in conformity with the hypothesis, they should be. "La durée de la rotation d'une planète doit donc être, d'après cette hypothèse, plus petite que la durée de la révolution du corps le plus voisin qui circule autour d'elle," says Laplace. And he then points out that the time of Saturn's rotation is to that of his rings as 427 to 438 – an amount of difference such as was to be expected.[19 - Since this paragraph was first published, the discovery that Mars has two satellites revolving round him in periods shorter than that of his rotation, has shown that the implication on which Laplace here insists is general only, and not absolute. Were it a necessary assumption that all parts of a concentrating nebulous spheroid revolve with the same angular velocities, the exception would appear an inexplicable one; but if, as suggested in a preceding section, it is inferable from the process of formation of a nebulous spheroid, that its outer strata will move round the general axis with higher angular velocities than the inner ones, there follows a possible interpretation. Though, during the earlier stages of concentration, while the nebulous matter, and especially its peripheral portions, are very rare, the effects of fluid-friction will be too small to change greatly such differences of angular velocities as exist; yet, when concentration has reached its last stages, and the matter is passing from the gaseous into the liquid and solid states, and when also the convection-currents have become common to the whole mass (which they probably at first are not), the angular velocity of the peripheral portion will gradually be assimilated to that of the interior; and it becomes comprehensible that in the case of Mars the peripheral portion, more and more dragged back by the internal mass, lost part of its velocity during the interval between the formation of the innermost satellite and the arrival at the final form.]