Chapter VI: Preface (6)

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]

Mercury. 1/360
Venus. 1/253
Earth. 1/289 1 Satellite.
Mars. 1/127 2 Satellites.
Jupiter. 1/11·4 4 Satellites.
Saturn. 1/6·4 8 Satellites, and three rings.
Uranus. 1/10·9 4 Satellites.

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]

Respecting Saturn's rings it may be further remarked that the place of their occurrence is not without significance.

Rings detached early in the process of concentration, consisting of gaseous matter having extremely little power of cohesion, can have little ability to resist the disruptive forces due to imperfect balance; and, therefore, collapse into satellites. A ring of a denser kind, whether solid, liquid, or composed of small discrete masses (as Saturn's rings are now concluded to be), we can expect will be formed only near the body of a planet when it has reached so late a stage of concentration that its equatorial portions contain matters capable of easy precipitation into liquid and, finally, solid forms. Even then it can be produced only 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 leaving behind of rings when the mass has become dense. Only where the centrifugal force has all along been very great, and remains powerful to the last, as in Saturn, can we expect dense rings to be formed.

We find, then, that besides those most conspicuous peculiarities of the Solar System which first suggested the theory of its evolution, there are many minor ones pointing in the same direction. Were there no other evidence, these mechanical arrangements would, considered in their totality, go far to establish the Nebular Hypothesis.

* * * * *

From the mechanical arrangements of the Solar System, turn we now to its physical characters; and, first, let us consider the inferences deducible from relative specific gravities.

The fact that, speaking generally, the denser planets are the nearer to the Sun, has been by some considered as adding another to the many indications of nebular origin. Legitimately assuming that the outermost parts of a rotating nebulous spheroid, in its earlier stages of concentration, must be comparatively rare; and that the increasing density which the whole mass acquires as it contracts, must hold of the outermost parts as well as the rest; it is argued that the rings successively detached will be more and more dense, and will form planets of higher and higher specific gravities. But passing over other objections, this explanation is quite inadequate to account for the facts. Using the Earth as a standard of comparison, the relative densities run thus:--

Neptune. Uranus. Saturn. Jupiter. Mars. Earth. Venus. Mercury. Sun.
0·17 0·25 0·11 0·23 0·45 1·00 0·92 1·26 0·25

Two insurmountable objections are presented by this series. The first is, that the progression is but a broken one. Neptune is denser than Saturn, which, by the hypothesis, it ought not to be. Uranus is denser than Jupiter, which it ought not to be. Uranus is denser than Saturn, and the Earth is denser than Venus--facts which not only give no countenance to, but directly contradict, the alleged explanation. The second objection, still more manifestly fatal, is the low specific gravity of the Sun. If, when the matter of the Sun filled the orbit of Mercury, its state of aggregation was such that the detached ring formed a planet having a specific gravity equal to that of iron; then the Sun itself, now that it has concentrated, should have a specific gravity much greater than that of iron; whereas its specific gravity is only half as much again as that of water. Instead of being far denser than the nearest planet, it is but one-fifth as dense.

While these anomalies render untenable the position that the relative specific gravities of the planets are direct indications of nebular condensation; it by no means follows that they negative it. Several causes may be assigned for these unlikenesses:--1. Differences among the planets in respect of the elementary substances composing them; or in the proportions of such elementary substances, if they contain the same kinds. 2. Differences among them in respect of the quantities of matter they contain; for, other things equal, the mutual gravitation of molecules will make a larger mass denser than a smaller. 3. Differences of temperatures; for, other things equal, those having higher temperatures will have lower specific gravities. 4. Differences of physical states, as being gaseous, liquid, or solid; or, otherwise, differences in the relative amounts of the solid, liquid, and gaseous matter they contain.

It is quite possible, and we may indeed say probable, that all these causes come into play, and that they take various shares in the production of the several results. But difficulties stand in the way of definite conclusions. Nevertheless, if we revert to the hypothesis of nebular genesis, we are furnished with partial explanations if nothing more.

In the cooling of celestial bodies several factors are concerned. The first and simplest is the one illustrated at every fire-side by the rapid blackening of little cinders which fall into the ashes, in contrast with the long-continued redness of big lumps. This factor is the relation between increase of surface and increase of content: surfaces, in similar bodies, increasing as the squares of the dimensions while contents increase as their cubes. Hence, on comparing the Earth with Jupiter, whose diameter is about eleven times that of the Earth, it results that while his surface is 125 times as great, his content is 1390 times as great. Now even (supposing we assume like temperatures and like densities) if the only effect were that through a given area of surface eleven times more matter had to be cooled in the one case than in the other, there would be a vast difference between the times occupied in concentration. But, in virtue of a second factor, the difference would be much greater than that consequent on these geometrical relations. The escape of heat from a cooling mass is effected by conduction, or by convection, or by both. In a solid it is wholly by conduction; in a liquid or gas the chief part is played by convection--by circulating currents which continually transpose the hotter and cooler parts. Now in fluid spheroids--gaseous, or liquid, or mixed--increasing size entails an increasing obstacle to cooling, consequent on the increasing distances to be travelled by the circulating currents. Of course the relation is not a simple one: the velocities of the currents will be unlike. It is manifest, however, that in a sphere of eleven times the diameter, the transit of matter from centre to surface and back from surface to centre, will take a much longer time; even if its movement is unrestrained. But its movement is, in such cases as we are considering, greatly restrained. In a rotating spheroid there come into play retarding forces augmenting with the velocity of rotation. In such a spheroid the respective portions of matter (supposing them equal in their angular velocities round the axis, which they will tend more and more to become as the density increases), must vary in their absolute velocities according to their distances from the axis; and each portion cannot have its distance from the axis changed by circulating currents, which it must continually be, without loss or gain in its quantity of motion: through the medium of fluid friction, force must be expended, now in increasing its motion and now in retarding its motion. Hence, when the larger spheroid has also a higher velocity of rotation, the relative slowness of the circulating currents, and the consequent retardation of cooling, must be much greater than is implied by the extra distances to be travelled.

And now observe the correspondence between inference and fact. In the first place, if we compare the group of the great planets, Jupiter, Saturn, and Uranus, with the group of the small planets, Mars, Earth, Venus, and Mercury, we see that low density goes along with great size and great velocity of rotation, and that high density goes along with small size and small velocity of rotation. In the second place, we are shown this relation still more clearly if we compare the extreme instances--Saturn and Mercury. The special contrast of these two, like the general contrast of the groups, points to the truth that low density, like the satellite-forming tendency, is associated with the ratio borne by centrifugal force to gravity; for in the case of Saturn with his many satellites and least density, centrifugal force at the equator is nearly 1/6th of gravity, whereas in Mercury with no satellite and greatest density centrifugal force is but 1/360th of gravity.

There are, however, certain factors which, working in an opposite way, qualify and complicate these effects. Other things equal, mutual gravitation among the parts of a large mass will cause a greater evolution of heat than is similarly caused in a small mass; and the resulting difference of temperature will tend to produce more rapid dissipation of heat. To this must be added the greater velocity of the circulating currents which the intenser forces at work in larger spheroids will produce--a contrast made still greater by the relatively smaller retardation by friction to which the more voluminous currents are exposed. In these causes, joined with causes previously indicated, we may recognize a probable explanation of the otherwise anomalous fact that the Sun, though having a thousand times the mass of Jupiter, has yet reached as advanced a stage of concentration. For the force of gravity in the Sun, which at his surface is some ten times that at the surface of Jupiter, must expose his central parts to a pressure relatively very intense; producing, during contraction, a relatively rapid genesis of heat. And it is further to be remarked that, though the circulating currents in the Sun have far greater distances to travel, yet since his rotation is relatively so slow that the angular velocity of his substance is but about one-sixtieth of that of Jupiter's substance, the resulting obstacle to circulating currents is relatively small, and the escape of heat far less retarded. Here, too, we may note that in the co-operation of these factors, there seems a reason for the greater concentration reached by Jupiter than by Saturn, though Saturn is the elder as well as the smaller of the two; for at the same time that the gravitative force in Jupiter is more than twice as great as in Saturn, his velocity of rotation is very little greater, so that the opposition of the centrifugal force to the centripetal is not much more than half.

But now, not judging more than roughly of the effects of these several factors, co-operating in various ways and degrees, some to aid concentration and others to resist it, it is sufficiently manifest that, other things equal, the larger nebulous spheroids, longer in losing their heat, will more slowly reach high specific gravities; and that where the contrasts in size are so immense as those between the greater and the smaller planets, the smaller may have reached relatively high specific gravities when the greater have reached but relatively low ones. Further, it appears that such qualification of the process as results from the more rapid genesis of heat in the larger masses, will be countervailed where high velocity of rotation greatly impedes the circulating currents. Thus interpreted then, the various specific gravities of the planets may be held to furnish further evidences supporting the Nebular Hypothesis.

* * * * *

Increase of density and escape of heat are correlated phenomena, and hence in the foregoing section, treating of the respective densities of the celestial bodies in connexion with nebular condensation, much has been said and implied respecting the accompanying genesis and dissipation of heat. Quite apart, however, from the foregoing arguments and inferences, there is to be noted the fact that in the present temperatures of the celestial bodies at large we find additional supports to the hypothesis; and these, too, of the most substantial character. For if, as is implied above, heat must inevitably be generated by the aggregation of diffused matter, we ought to find in all the heavenly bodies, either present high temperatures or marks of past high temperatures. This we do, in the places and in the degrees which the hypothesis requires.

Observations showing that as we descend below the Earth's surface there is a progressive increase of heat, joined with the conspicuous evidence furnished by volcanoes, necessitate the conclusion that the temperature is very high at great depths. Whether, as some believe, the interior of the Earth is still molten, or whether, as Sir William Thomson contends, it must be solid; there is agreement in the inference that its heat is intense. And it has been further shown that the rate at which the temperature increases on descending below the surface, is such as would be found in a mass which had been cooling for an indefinite period. The Moon, too, shows us, by its corrugations and its conspicuous extinct volcanoes, that in it there has been a process of refrigeration and contraction, like that which has gone on in the Earth. There is no teleological explanation of these facts. The frequent destructions of life by earthquakes and volcanoes, imply, rather, that it would have been better had the Earth been created with a low internal temperature. But if we contemplate the facts in connexion with the Nebular Hypothesis, we see that this still-continued high internal heat is one of its corollaries. The Earth must have passed through the gaseous and the molten conditions before it became solid, and must for an almost infinite period by its internal heat continue to bear evidence of this origin.

The group of giant planets furnishes remarkable evidence. The _a priori_ inference drawn above, that great size joined with relatively high ratio of centrifugal force to gravity must greatly retard aggregation, and must thus, by checking the genesis and dissipation of heat, make the process of cooling a slow one, has of late years received verifications from inferences drawn _a posteriori_; so that now the current conclusion among astronomers is that in physical condition the great planets are in stages midway between that of the Earth and that of the Sun. The fact that the centre of Jupiter's disc is twice or thrice as bright as his periphery, joined with the facts that he seems to radiate more light than is accounted for by reflection of the Sun's rays, and that his spectrum shows the "red-star line", are taken as evidences of luminosity; while the immense and rapid perturbations in his atmosphere, far greater than could be caused by heat received from the Sun, as well as the formation of spots analogous to those of the Sun, which also, like those of the Sun, show a higher rate of rotation near the equator than further from it, are held to imply high internal temperature. Thus in Jupiter, as also in Saturn, we find states which, not admitting of any teleological explanations (for they manifestly exclude the possibility of life), admit of explanations derived from the Nebular Hypothesis.

But the argument from temperature does not end here. There remains to be noticed a more conspicuous and still more significant fact. If the Solar System was produced by the concentration of diffused matter, which evolved heat while gravitating into its present dense form; then there is an obvious implication. Other things equal, the latest-formed mass will be the latest in cooling--will, for an almost infinite time, possess a greater heat than the earlier-formed ones. Other things equal, the largest mass will, because of its superior aggregative force, become hotter than the others, and radiate more intensely. Other things equal, the largest mass, notwithstanding the higher temperature it reaches, will, in consequence of its relatively small surface, be the slowest in losing its evolved heat. And hence, if there is one mass which was not only formed after the rest, but exceeds them enormously in size, it follows that this one will reach an intensity of incandescence far beyond that reached by the rest; and will continue in a state of intense incandescence long after the rest have cooled. Such a mass we have in the Sun. It is a corollary from the Nebular Hypothesis, that the matter forming the Sun assumed its present integrated shape at a period much more recent than that at which the planets became definite bodies. The quantity of matter contained in the Sun is nearly five million times that contained in the smallest planet, and above a thousand times that contained in the largest. And while, from the enormous gravitative force of his parts to their common centre, the evolution of heat has been intense, the facilities of radiation have been relatively small. Hence the still-continued high temperature. Just that condition of the central body which is a necessary inference from the Nebular Hypothesis, we find actually existing in the Sun.

[The paragraph which here follows, though it contains some questionable propositions, I reproduce just as it stood when first published in 1858, for reasons which will presently be apparent.]

It may be well to consider more closely, what is the probable condition of the Sun's surface. Round the globe of incandescent molten substances, thus conceived to form the visible body of the Sun [which in conformity with the argument in a previous section, now transferred to the Addenda, was inferred to be hollow and filled with gaseous matter at high tension] there is known to exist a voluminous atmosphere: the inferior brilliancy of the Sun's border, and the appearances during a total eclipse, alike show this. What now must be the constitution of this atmosphere? At a temperature approaching a thousand times that of molten iron, which is the calculated temperature of the solar surface, very many, if not all, of the substances we know as solid, would become gaseous; and though the Sun's enormous attractive force must be a powerful check on this tendency to assume the form of vapour, yet it cannot be questioned that if the body of the Sun consists of molten substances, some of them must be constantly undergoing evaporation. That the dense gases thus continually being generated will form the entire mass of the solar atmosphere, is not probable. If anything is to be inferred, either from the Nebular Hypothesis, or from the analogies supplied by the planets, it must be concluded that the outermost part of the solar atmosphere consists of what are called permanent gases--gases that are not condensible into fluid even at low temperatures. If we consider what must have been the state of things here, when the surface of the Earth was molten, we shall see that round the still molten surface of the Sun, there probably exists a stratum of dense aeriform matter, made up of sublimed metals and metallic compounds, and above this a stratum of comparatively rare medium analogous to air. What now will happen with these two strata? Did they both consist of permanent gases, they could not remain separate: according to a well-known law, they would eventually form a homogeneous mixture. But this will by no means happen when the lower stratum consists of matters that are gaseous only at excessively high temperatures. Given off from a molten surface, ascending, expanding, and cooling, these will presently reach a limit of elevation above which they cannot exist as vapour, but must condense and precipitate. Meanwhile the upper stratum, habitually charged with its quantum of these denser matters, as our air with its quantum of water, and ready to deposit them on any depression of temperature, must be habitually unable to take up any more of the lower stratum; and therefore this lower stratum will remain quite distinct from it.[20]

* * * * *

Considered in their _ensemble_, the several groups of evidences assigned amount almost to proof. We have seen that, when critically examined, the speculations of late years current respecting the nature of the nebulæ, commit their promulgators to sundry absurdities; while, on the other hand, we see that the various appearances these nebulæ present, are explicable as different stages in the precipitation and aggregation of diffused matter. We find that the immense majority of comets (_i.e._ omitting the periodic ones), by their physical constitution, their immensely-extended and variously-directed paths, the distribution of those paths, and their manifest structural relation to the Solar System, bear testimony to the past existence of that system in a nebulous form. Not only do those obvious peculiarities in the motions of the planets which first suggested the Nebular Hypothesis, supply proofs of it, but on closer examination we discover, in the slightly-diverging inclinations of their orbits, in their various rates of rotation, and their differently-directed axes of rotation, that the planets yield us yet further testimony; while the satellites, by sundry traits, and especially by their occurrence in greater or less abundance where the hypothesis implies greater or less abundance, confirm this testimony. By tracing out the process of planetary condensation, we are led to conclusions respecting the physical states of planets which explain their anomalous specific gravities. Once more, it turns out that what is inferable from the Nebular Hypothesis respecting the temperatures of celestial bodies, is just what observation establishes; and that both the absolute and the relative temperatures of the Sun and planets are thus accounted for. When we contemplate these various evidences in their totality--when we observe that, by the Nebular Hypothesis, the leading phenomena of the Solar System, and the heavens in general, are explicable; and when, on the other hand, we consider that the current cosmogony is not only without a single fact to stand on, but is at variance with all our positive knowledge of Nature, we see that the proof becomes overwhelming.

It remains only to point out that while the genesis of the Solar System, and of countless other systems like it, is thus rendered comprehensible, the ultimate mystery continues as great as ever. The problem of existence is not solved: it is simply removed further back. The Nebular Hypothesis throws no light on the origin of diffused matter; and diffused matter as much needs accounting for as concrete matter. The genesis of an atom is not easier to conceive than the genesis of a planet. Nay, indeed, so far from making the Universe less a mystery than before, it makes it a greater mystery. Creation by manufacture is a much lower thing than creation by evolution. A man can put together a machine; but he cannot make a machine develop itself. That our harmonious universe once existed potentially as formless diffused matter, and has slowly grown into its present organized state, is a far more astonishing fact than would have been its formation after the artificial method vulgarly supposed. Those who hold it legitimate to argue from phenomena to noumena, may rightly contend that the Nebular Hypothesis implies a First Cause as much transcending "the mechanical God of Paley," as this does the fetish of the savage.

FOOTNOTES:

[Footnote 11: _Cosmos._ (Seventh Edition.) Vol. i. pp. 79, 80.]

[Footnote 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.]

[Footnote 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.]

[Footnote 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.]

[Footnote 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.]

[Footnote 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.]

[Footnote 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.]

[Footnote 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:--

Mercury. 1/362
Venus. 1/282
Earth. 1/289 1 Satellite.
Mars. 1/326
Jupiter. 1/14 4 Satellites.
Saturn. 1/6·2 8 Satellites, and three rings.
Uranus. 1/9 4 (or 6 according to Herschel).

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.]

[Footnote 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.]

[Footnote 20: I was about to suppress part of the above paragraph, written before the science of solar physics had taken shape, because of certain physical difficulties which stand in the way of its argument, when, on looking into recent astronomical works, I found that the hypothesis it sets forth respecting the Sun's structure has kinships to the several hypotheses since set forth by Zöllner, Faye, and Young. I have therefore decided to let it stand as it originally did.

The contemplated partial suppression just named, was prompted by recognition of the truth that to effect mechanical stability the gaseous interior of the Sun must have a density at least equal to that of the molten shell (greater, indeed, at the centre); and this seems to imply a specific gravity higher than that which he possesses. It may, indeed, be that the unknown elements which spectrum analysis shows to exist in the Sun, are metals of very low specific gravities, and that, existing in large proportion with other of the lighter metals, they may form a molten shell not denser than is implied by the facts. But this can be regarded as nothing more than a possibility.

No need, however, has arisen for either relinquishing or holding but loosely the associated conclusions respecting the constitution of the photosphere and its envelope. Widely speculative as seemed these suggested corollaries from the Nebular Hypothesis when set forth in 1858, and quite at variance with the beliefs then current, they proved to be not ill-founded. At the close of 1859, there came the discoveries of Kirchhoff, proving the existence of various metallic vapours in the Sun's atmosphere.]

ADDENDA.

Speculative as is much of the foregoing essay, it appears undesirable to include in it anything still more speculative. For this reason I have decided to set forth separately some views concerning the genesis of the so-called elements during nebular condensation, and concerning the accompanying physical effects. At the same time it has seemed best to detach from the essay some of the more debatable conclusions originally contained in it; so that its general argument may not be needlessly implicated with them. These new portions, together with the old portions which re-appear more or less modified, I here append in a series of notes.

NOTE I. For the belief that the so-called elements are compound there are both special reasons and general reasons. Among the special may be named the parallelism between allotropy and isomerism; the numerous lines in the spectrum of each element; and the cyclical law of Newlands and Mendeljeff. Of the more general reasons, which, as distinguished from these chemical or chemico-physical ones, may fitly be called cosmical, the following are the chief.

The general law of evolution, if it does not actually involve the conclusion that the so-called elements are compounds, yet affords _a priori_ ground for suspecting that they are such. The implication is that, while the matter composing the Solar System has progressed physically from that relatively-homogeneous state which it had as a nebula to that relatively-heterogeneous state presented by Sun, planets, and satellites, it has also progressed chemically, from the relatively-homogeneous state in which it was composed of one or a few types of matter, to that relatively-heterogeneous state in which it is composed of many types of matter very diverse in their properties. This deduction from the law which holds throughout the cosmos as now known to us, would have much weight even were it unsupported by induction; but a survey of chemical phenomena at large discloses several groups of inductive evidences supporting it.

The first is that since the cooling of the Earth reached an advanced stage, the components of its crust have been ever increasing in heterogeneity. When the so-called elements, originally existing in a dissociated state, united into oxides, acids, and other binary compounds, the total number of different substances was immensely augmented, the new substances were more complex than the old, and their properties were more varied. That is, the assemblage became more heterogeneous in its kinds, in the composition of each kind, and in the range of chemical characters. When, at a later period, there arose salts and other compounds of similar degrees of complexity, there was again an increase of heterogeneity, alike in the aggregate and in its members. And when, still later, matters classed as organic became possible, the multiformity was yet further augmented in kindred ways. If, then, chemical evolution, so far as we can trace it, has been from the homogeneous to the heterogeneous, may we not fairly suppose that it has been so from the beginning? If, from late stages in the Earth's history, we run back, and find the lines of chemical evolution continually converging, until they bring us to bodies which we cannot decompose, may we not suspect that, could we run back these lines still further, we should come to still decreasing heterogeneity in the number and nature of the substances, until we reached something like homogeneity?

A parallel argument may be derived from consideration of the affinities and stabilities of chemical compounds. Beginning with the complex nitrogenous bodies out of which living things are formed, and which, in the history of the Earth, are the most modern, at the same time that they are the most heterogeneous, we see that the affinities and stabilities of these are extremely small. Their molecules do not enter bodily into union with those of other substances so as to form more complex compounds still, and their components often fail to hold together under ordinary conditions. A stage lower in degree of composition we come to the vast assemblage of oxy-hydro-carbons, numbers of which show many and decided affinities, and are stable at common temperatures. Passing to the inorganic group, we are shown by the salts &c. strong affinities between their components and unions which are, in many cases, not very easily broken. And then when we come to the oxides, acids, and other binary compounds, we see that in many cases the elements of which they are formed, when brought into the presence of one another under favourable conditions, unite with violence; and that many of their unions cannot be dissolved by heat alone. If, then, as we go back from the most modern and most complex substances to the most ancient and simplest substances, we see, on the average, a great increase in affinity and stability, it results that if the same law holds with the simplest substances known to us, the components of these, if they are compound, may be assumed to have united with affinities far more intense than any we have experience of, and to cling together with tenacities far exceeding the tenacities with which chemistry acquaints us. Hence the existence of a class of substances which are undecomposable and therefore seem simple, appears to be an implication; and the corollary is that these were formed during early stages of terrestrial concentration, under conditions of heat and pressure which we cannot now parallel.

Yet another support for the belief that the so-called elements are compounds, is derived from a comparison of them, considered as an aggregate ascending in their molecular weights, with the aggregate of bodies known to be compound, similarly considered in their ascending molecular weights. Contrast the binary compounds as a class with the quaternary compounds as a class. The molecules constituting oxides (whether alkaline or acid or neutral) chlorides, sulphurets, &c. are relatively small; and, combining with great avidity, form stable compounds. On the other hand, the molecules constituting nitrogenous bodies are relatively vast and are chemically inert; and such combinations as their simpler types enter into, cannot withstand disturbing forces. Now a like difference is seen if we contrast with one another the so-called elements. Those of relatively-low molecular weights--oxygen, hydrogen, potassium, sodium, &c.,--show great readiness to unite among themselves; and, indeed, many of them cannot be prevented from uniting under ordinary conditions. Contrariwise, under ordinary conditions the substances of high molecular weights--the "noble metals"--are indifferent to other substances; and such compounds as they do form under conditions specially adjusted, are easily destroyed. Thus as, among the bodies we know to be compound, increasing molecular weight is associated with the appearance of certain characters, and as, among the bodies we class as simple, increasing molecular weight is associated with the appearance of similar characters, the composite nature of the elements is in another way pointed to.

There has to be added one further class of phenomena, congruous with those above named, which here specially concerns us. Looking generally at chemical unions, we see that the heat evolved usually decreases as the degree of composition, and consequent massiveness, of the molecules, increases. In the first place, we have the fact that during the formation of simple compounds the heat evolved is much greater than that which is evolved during the formation of complex compounds: the elements, when uniting with one another, usually give out much heat; while, when the compounds they form are recompounded, but little heat is given out; and, as shown by the experiments of Prof. Andrews, the heat given out during the union of acids and bases is habitually smaller where the molecular weight of the base is greater. Then, in the second place, we see that among the elements themselves, the unions of those having low molecular weights result in far more heat than do the unions of those having high molecular weights. If we proceed on the supposition that the so-called elements are compounds, and if this law, if not universal, holds of undecomposable substances as of decomposable, then there are two implications. The one is that those compoundings and recompoundings by which the elements were formed, must have been accompanied by degrees of heat exceeding any degrees of heat known to us. The other is that among these compoundings and recompoundings themselves, those by which the small-moleculed elements were formed produced more intense heat than those by which the large-moleculed elements were formed: the elements formed by the final recompoundings being necessarily later in origin, and at the same time less stable, than the earlier-formed ones.

NOTE II. May we from these propositions, and especially from the last, draw any conclusions respecting the evolution of heat during nebular condensation? And do such conclusions affect in any way the conclusions now current?

In the first place, it seems inferable from physico-chemical facts at large, that only through the instrumentality of those combinations which formed the elements, did the concentration of diffused nebulous matter into concrete masses become possible. If we remember that hydrogen and oxygen in their uncombined states oppose, the one an insuperable and the other an almost insuperable, resistance to liquefaction, while when combined the compound assumes the liquid state with facility, we may suspect that in like manner the simpler types of matter out of which the elements were formed, could not have been reduced even to such degrees of density as the known gases show us, without what we may call proto-chemical unions: the implication being that after the heat resulting from each of such proto-chemical unions had escaped, mutual gravitation of the parts was able to produce further condensation of the nebulous mass.