Illustrations of Universal Progress Part 13

When diffused matter, precipitated from a rarer medium, is aggregating, there are certain to be here and there produced small flocculi, which, either in consequence of local currents or the conflicting attractions of adjacent ma.s.ses, remain detached; as do, for instance, minute shreds of cloud in a summer sky. In a concentrating nebula these will, in the great majority of cases, eventually coalesce with the larger flocculi near to them. But it is tolerably evident that some of the remotest of these small flocculi, formed at the outermost parts of the nebula, will _not_ coalesce with the larger internal ma.s.ses, 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 ma.s.ses 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 nebulae, _are_ left behind by the more concentrated, internal parts. Examined through high powers, all nebulae, even when they have a.s.sumed regular forms, are seen to be surrounded by luminous streaks, of which the directions show that they are being drawn into the general ma.s.s. 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 ma.s.s 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 ma.s.s 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 extremely eccentric orbits. 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 ma.s.s in greatly elongated ellipses; and rus.h.i.+ng round it will go off again into s.p.a.ce. That is, they will behave just as we see comets do; whose orbits are usually so eccentric as to be indistinguishable from parabolas.

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 ma.s.s was of irregular shape, and had not acquired a definite rotary motion; and as the separation of them would not be from any one surface of the nebulous ma.s.s more than another, the conclusion must be that they will come to the central body from various directions in s.p.a.ce. This, too, is exactly what happens. Unlike planets, whose orbits approximate to one plane, comets have orbits that show no relation to each other; but cut the plane of the ecliptic at all angles.

In the third place, applying the reasoning already used, these remotest flocculi of nebulous matter will, at the outset, be deflected from their straight courses to the common centre of gravity, not all on one side, but each on such side as its form 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 concentrating ma.s.s, 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. Out of 210 comets known in 1855, 104 are direct, and 106 are retrograde. This equality is what the law of probabilities would indicate.

Then, in the fourth place, the physical const.i.tution of comets completely accords with the hypothesis. The ability of nebulous matter to concentrate into a concrete form, depends on its ma.s.s. 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 acc.u.mulation of them; and even then the approximation can slowly go on only as fast as the evolved heat escapes. But where the quant.i.ty 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. We find that they do so.

Comets consist of an extremely rare medium, which, as shown by the description already quoted from Sir John Herschel, has characters like those we concluded would belong to partially-condensed nebulous matter.

Yet another very significant fact is seen in the distribution of comets.

Though they come from all parts of the heavens, they by no means come in equal abundance from all parts of the heavens; but are far more numerous about the poles of the ecliptic than about its plane. Speaking generally, comets having orbit-planes that are highly inclined to the ecliptic, are comets having orbits of which the major axes are highly inclined to the ecliptic--comets that come from high lat.i.tudes. This is not a necessary connexion; for the planes of the orbits _might_ be highly inclined to the ecliptic while the major axes were inclined to it very little. But in the absence of any habitually-observed relation of this kind, it may safely be concluded that, _on the average_, highly-inclined cometary orbits are cometary orbits with highly-inclined major axes; and that thus, a predominance of cometary orbits cutting the plane of the ecliptic at great angles, implies a predominance of cometary orbits having major axes that cut the ecliptic at great angles. Now the predominance of highly inclined cometary orbits, may be gathered from the following table, compiled by M.

Arago, to which we have added a column giving the results up to a date two years later.

------------------------------------------------------------------------- Inclinations. Number of Comets Number of Comets Number of Comets in 1831. in 1853. in 1855. ------------------------------------------------------------------------- Deg. to Deg. From 0 to 10 9 19 19 " 10 " 20 13 18 19 " 20 " 30 10 13 14 " 30 " 40 17 22 22 " 40 " 50 14 35 36 " 50 " 60 23 27 29 " 60 " 70 17 23 25 " 70 " 80 19 26 27 " 80 " 90 15 18 19 ------------------------------------------------------------------------- Total 137 201 210 -------------------------------------------------------------------------

At first sight this table seems not to warrant our statement. a.s.suming the alleged general relation between the inclinations of cometary orbits, and the directions in s.p.a.ce from which the comets come, the table may be thought to show that the frequency of comets increases as we progress from the plane of the ecliptic up to 45, and then decreases up to 90. But this apparent diminution arises from the fact that the successive zones of s.p.a.ce rapidly diminish in their areas on approaching the poles. If we allow for this, we shall find that the excess of comets continues to increase up to the highest angles of inclination. In the table below, which, for convenience, is arranged in inverted order, we have taken as standards of comparison the area of the zone round the pole, and the number of comets it contains; and having ascertained the areas of the other zones, and the numbers of comets they should contain were comets equally distributed, we have shown how great becomes the deficiency in descending from the poles of the ecliptic to its plane.

------------------------------------------------------------------------- Number of Actual Relative Between Area of Comets, if Number of Deficiency. Abundance. Zone. equally Comets. distributed. ------------------------------------------------------------------------- Deg. Deg. 90 and 80 1 19 19 0 11.5 80 " 70 2.98 56.6 27 29.6 5.5 70 " 60 4.85 92 25 67 3.12 60 " 50 6.6 125 29 96 2.66 50 " 40 8.13 154 36 118 2.68 40 " 30 9.42 179 22 157 1.4 30 " 20 10.42 198 14 184 0.8 20 " 10 11.1 210 19 191 1.04 10 " 0 11.5 218 19 199 1 -------------------------------------------------------------------------

In strictness, the calculation should be made with reference, not to the plane of the ecliptic, but to the plane of the sun's equator; and this might or might not render the progression more regular. Probably, too, the progression would be made somewhat different were the calculation based, as it should be, not on the inclinations of orbit-planes, but on the inclinations of major axes. But even as it is, the result is sufficiently significant: since, though the conclusion that comets are 115 times more abundant about the poles of the ecliptic than about its plane, can be but a rough approximation to the truth, yet no correction of it is likely very much to change this strong contrast.

What, then, is the meaning of this fact? It has several meanings. It negatives the supposition, favoured by Laplace among others, that comets are bodies that were wandering in s.p.a.ce, or have come from other systems; for the probabilities are infinity to one against the orbits of such wandering bodies showing any definite relation to the plane of the Solar System. For the like reason, it negatives the hypothesis of Lagrange, otherwise objectionable, that comets have resulted from planetary catastrophes a.n.a.logous to that which is supposed to have produced the asteroids. It clearly shows that, instead of comets being _accidental_ members of the Solar System, they are _necessary_ members of it--have as distinct a structural relation to it as the planets themselves. That comets are abundant round the axis of the Solar System, and grow rarer as we approach its plane, implies that the genesis of comets has followed some _law_--a law in some way concerned with the genesis of the Solar System.

If we ask for any so-called final cause of this arrangement, none can be a.s.signed: until a probable use for comets has been shown, no reason can be given why they should be thus distributed. But when we consider the question as one of physical science, we see that comets are ant.i.thetical to planets, not only in their great rarity, in their motions as indifferently direct or retrograde, in their eccentric orbits, and in the varied directions of those orbits; but we see the ant.i.thesis further marked in this, that while planets have some relation to the plane of nebular rotation, comets have some relation to the axis of nebular rotation.[K] And without attempting to explain the nature of this relation, the mere fact that such a relation exists, indicates that comets have resulted from a process of evolution--points to a past time when the matter now forming the Solar System extended to those distant regions of s.p.a.ce which comets visit.

[K] It is alike remarkable and suggestive, that a parallel relation exists between the distribution of nebulae and the axis of our galaxy. Just as comets are abundant around the poles of our Solar System, and rare in the neighbourhood of its plane: so are nebulae abundant around the poles of our sidereal system, and rare in the neighbourhood of its plane.

See, then, how differently this cla.s.s of phenomena bears on the antagonistic hypotheses. To the hypothesis commonly received, comets are stumbling-blocks: why there should be hundreds (or probably thousands) of extremely rare aeriform ma.s.ses rus.h.i.+ng to and fro round the sun, it cannot say; any more than it can explain their physical const.i.tutions, their various and eccentric movements, or their distribution. The hypothesis of evolution, on the other hand, not only allows of the general answer, that they are minor results of the genetic process; but also furnishes us with something like explanations of their several peculiarities.

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 subsisting 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 nebulae, 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 Systeme du Monde," he enumerates as the leading evidences of evolution:--1.

The movements of the planets in the same direction and almost in the same plane; 2. The movements of the satellites in the same direction as those of the planets; 3. The movement of rotation of these various bodies and of the sun in the same direction as the orbitual motions, and in planes little different; 4. The small eccentricity of the orbits of the planets and satellites, as contrasted with the great eccentricity of the cometary orbits. And the probability that these harmonious movements had a common cause, he calculates as two hundred thousand billions to one.

Observe that 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. The mechanical equilibrium would not have been at all 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 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 motion of Jupiter's satellites might similarly have been at variance with his axial motion; or that 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 whose authority is second to none, a definite theory of this evolution based on established mechanical laws, 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 Neptune; 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 ma.s.s, 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 ma.s.s; that this, like the parent ma.s.s, increased in rapidity of rotation as it decreased in size, and, where the centrifugal force was sufficient, similarly threw off 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 ma.s.s 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 ma.s.s 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 ma.s.s. Thus, given the original nebula, which, acquiring a vortical motion in the way we have explained, 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.[L]

[L] 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 ma.s.s, "all probability would be in favour of its breaking up into many ma.s.ses." This alternative result certainly seems to be more likely. But granting that a nebulous ring would break up into many ma.s.ses, 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 ma.s.ses would break up into groups of ma.s.ses; these groups would eventually aggregate into larger groups; and the final result would be the formation of a single ma.s.s. 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 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 saw must eventually arise, and such as we at present see indicated in the spiral nebulae, is the gradual approach toward motion in one plane--the plane of greatest momentum. But this plane can only 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 ma.s.s retain for long time their more or less independent directions; seeing that neither by friction nor by the central forces will they be so much restrained. Hence the probabilities are, that the planes of the rings first detached will differ considerably from the average plane of the ma.s.s; 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.

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 Ura.n.u.s, 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 will, we believe, show that the anomaly is by no means an insoluble one; 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 relatively insignificant, even if it exists: and others in which, though existing to a considerable extent, it will not suffice to determine the direction of rotation.

Note, in the first place, that in virtue of their origin, the different strata of a concentrating nebulous spheroid, will be very unlikely to move with equal angular velocities: only by friction continued for an indefinite time will their angular velocities be made uniform; and especially will the outermost strata, for reasons just now a.s.signed, maintain for the longest time their differences of movement. Hence, it is possible that in the rings first detached the outer rims may not have greater absolute velocities; and thus the resulting planets may have retrograde rotations. Again, the sectional form of the ring is a circ.u.mstance of moment; and this form must have differed more or less in every case. To make this clear, some ill.u.s.tration will be necessary. Suppose we take an orange, and a.s.suming 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 whose thickness in the line of its diameter is very small, but whose 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 fact 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 ma.s.sive 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 circ.u.mstance 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 very small; and such a ring, aggregating into a ma.s.s whose greatest diameter is at right angles to the plane of the orbit, will almost certainly give to this ma.s.s 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 of the inner and outer velocities also 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 ma.s.s 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 circ.u.mference of Ura.n.u.s's...o...b..t, and his comparatively small ma.s.s, we may conclude that the ring from which he resulted was a comparatively slender, and therefore a hoop-shaped one: especially if the nebulous ma.s.s was at that time less oblate than afterwards, which it must have been. Hence, a plane of rotation nearly perpendicular to his...o...b..t, and a direction of rotation having no reference to his...o...b..tual movement. Saturn has a ma.s.s 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 circ.u.mference, and less than half the vertical thickness (the spheroid being then certainly _as_ oblate, and indeed _more_ oblate), must have had considerably 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 ma.s.s 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...o...b..t by scarcely more than three degrees. Once more, considering the comparative insignificance of Mars, Earth, Venus, and Mercury, it follows that the diminis.h.i.+ng circ.u.mferences of the rings not sufficing to account for the smallness of the resulting ma.s.ses, 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 seems to us that the respective rotatory motions are not at variance with the hypothesis.

Not only the directions, but also the velocities of rotation are 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 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 ma.s.s that is diffused through a wide s.p.a.ce, 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 ma.s.s. 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 that is broadest in the direction of its plane will produce a ma.s.s rotating faster than one that 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 goes round his axis in less than ten hours. Saturn, in whose case, as above explained, the conditions were less favourable to rapid rotation, takes ten hours and a half. While Mars, Earth, Venus, and Mercury, whose rings must have been slender, take more than double the time: the smallest taking the longest.

From the planets, let us now pa.s.s to the satellites. Here, beyond the conspicuous facts commonly adverted to, that they go round their primaries in the same directions that 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 pa.s.sed over.

One of them is, that each set of satellites repeats in miniature the relations of the planets to the sun, both in the respects just named, and in the order of the 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. La.s.sell, the like is true of the four satellites of Ura.n.u.s. 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.

Moreover, the a.n.a.logy does not end here. Just as with the planets, there is at first a general increase of size on travelling inwards from Neptune and Ura.n.u.s, 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 a.n.a.logies 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 a.n.a.logies 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; what is to be said of Mars, which, placed half as far again from the Sun as we are, has yet no moon? Or again, how are we to explain the fact that Ura.n.u.s 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 actually enables us to predict, by a not very complex calculation, where satellites will be abundant and where they will be absent. The reasoning is as follows.

In a rotating nebulous spheroid that 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 strongly opposed by this outward impetus of its particles, according as its 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 centrifugal force produced by 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 ma.s.ses in which the centrifugal tendency bears the greatest ratio to the gravitative tendency. Though it is not possible to calculate what proportions 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.

Mercury. Venus. Earth. Mars. Jupiter. Saturn. Ura.n.u.s.

1 1 1 1 1 1 1 --- --- --- --- --- --- --- 362 282 289 326 14 6.2 9

1 4 8 4 (or 6 Satellite. Satellites. Satellites according and three to rings. Herschel.)

Thus, taking as our standard of comparison the Earth with its one moon, we see that Mercury and Mars, in which the centrifugal force is relatively less, have no moons. Jupiter, in which it is far greater, has four moons.

Ura.n.u.s, in which it is greater still, has certainly four, and probably more than four. 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 imperfect conformity with observation is that of Venus. Here it appears that the centrifugal force is relatively a very little greater than in the Earth; and according to the hypothesis, Venus ought, therefore, to have a satellite. Of this seeming anomaly there are two explanations.

Not a few astronomers have a.s.serted that Venus _has_ a satellite. Ca.s.sini, Short, Montaigne of Limoges, Roedkier, and Montbarron, professed to have seen it; and Lambert calculated its elements. Granting, however, that they were mistaken, there is still the fact that the diameter of Venus is variously estimated; and that a very small change in the data would make the fraction less instead of greater than that of the Earth. But admitting the discrepancy, we think that this correspondence, even as it now stands, is one of the strongest confirmations of the Nebular Hypothesis.[M]

[M] Since this essay was published, the data of the above calculations have been changed by the discovery that the Sun's distance is three millions of miles less than was supposed. Hence results a diminution in his estimated ma.s.s, and in the ma.s.ses of the planets (except the Earth and Moon). No revised estimate of the ma.s.ses having yet been published, the table is re-printed in its original form. The diminution of the ma.s.ses to the alleged extent of about one-tenth, does not essentially alter the relations above pointed out.

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 Systeme du Monde," Laplace shows, by reasoning too detailed to be here repeated, that under the circ.u.mstances 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 matter like those through which each planet and satellite once pa.s.sed; and their movements are just what, in conformity with the hypothesis, they should be. "La duree de la rotation d'une planete doit donc etre, d'apres cette hypothese, plus pet.i.te que la duree de la revolution du corps le plus voisin qui circule autour d'elle," says Laplace.[N] 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.

[N] "Mecanique Celeste," p. 346.

But besides the existence of these rings, and their movements in the required manner, there is a highly suggestive circ.u.mstance which Laplace has not remarked--namely, the place of their occurrence. If the Solar System was produced after the manner popularly supposed, then there is no reason why the rings of Saturn should not have encircled him at a comparatively great distance. Or, instead of being given to Saturn, who in their absence would still have had eight satellites, such rings might have been given to Mars, by way of compensation for a moon. Or they might have been given to Ura.n.u.s, who, for purposes of illumination, has far greater need of them. On the common hypothesis, we repeat, no reason can be a.s.signed for their existence in the place where we find them. But on the hypothesis of evolution, the arrangement, so far from offering a difficulty, offers another confirmation. These rings are found where alone they could have been produced--close to the body of a planet whose centrifugal force bears a great proportion to his gravitative force. That permanent rings should exist at any great distance from a planet's body, is, on the Nebular Hypothesis, manifestly impossible. Rings detached early in the process of concentration, and therefore consisting of gaseous matter having extremely little power of cohesion, can have no ability to resist the disrupting forces due to imperfect balance; and must, therefore, collapse into satellites. A liquid ring is the only one admitting of permanence. But a liquid ring can be produced only when the aggregation is approaching its extreme--only when gaseous matter is pa.s.sing into liquid, and the ma.s.s is about to a.s.sume the planetary form. And even then it cannot be produced save under special conditions. Gaining a rapidly-increasing preponderance, as the gravitative force does during the closing stages of concentration, the centrifugal force cannot in ordinary cases cause the detachment of rings when the ma.s.s has become dense. Only where the centrifugal force has all along been very great, and remains powerful to the last, as in Saturn, can liquid rings be formed. Thus the Nebular Hypothesis shows us why such appendages surround Saturn, but exist nowhere else.

And then, let us not forget the fact, discovered within these few years, that Saturn possesses a _nebulous_ ring, through which his body is seen as through a thick veil. In a position where alone such a thing seems preservable--suspended, as it were, between the denser rings and the planet--there still continues one of these annular ma.s.ses of diffused matter from which satellites and planets are believed to have originated.