Illustrations of Universal Progress: A Series of Discussions

Moreover, 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 analogies 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; 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 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 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 masses 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.

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. Uranus, 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 asserted that Venus has a satellite. Cassini, 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.¹³

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 matter 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 planete doit donc être, d'apres cette hypothèse, plus petite que la durée de la révolution du corps le plus voisin qui circule autour d'elle," says Laplace.¹⁴ 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.

But besides the existence of these rings, and their movements in the required manner, there is a highly suggestive circumstance 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 Uranus, who, for purposes of illumination, has far greater need of them. On the common hypothesis, we repeat, no reason can be assigned 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 passing into liquid, and the mass is about to assume 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 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 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 masses of diffused matter from which satellites and planets are believed to have originated. 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, is 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, will 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: —

Two seemingly insurmountable objections are presented by this series. The first is, that the progression is but a broken one. Neptune is as dense as Saturn, which, by the hypothesis, it ought not to be. Uranus is as dense as 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 not much above that of water. Instead of being far denser than the nearest planet, it is not one-fourth as dense. And a parallel relation holds between Jupiter and his smallest satellite.¹⁵

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. On the contrary, we believe that the facts admit of an interpretation quite consistent with the hypothesis of Laplace.

There are three possible causes of unlike specific gravities in the members of our Solar System: – 1. Differences between the kinds of matter or matters composing them. 2. Differences between the quantities of matter; for, other things equal, the mutual gravitation of atoms will make a large mass denser than a small one. 3. Differences between the structures: the masses being either solid or liquid throughout, or having central cavities filled with elastic aeriform substance. Of these three conceivable causes, that commonly assigned is the first, more or less modified by the second. The extremely low specific gravity of Saturn, which but little exceeds that of cork (and, on this hypothesis, must at his surface be considerably less than that of cork) is supposed to arise from the intrinsic lightness of his substance. That the Sun weighs not much more than an equal bulk of water, is taken as evidence that the matter he consists of is but little heavier than water; although, considering his enormous gravitative force, which at his surface is twenty-eight times the gravitative force at the surface of the Earth, and considering his enormous mass, which is 390,000 times that of the Earth, the matter he is made of can, in such case, have no analogy to the liquids or solids we know. However, spite of these difficulties, the current hypothesis is, that the Sun and planets, inclusive of the Earth, are either solid or liquid, or have solid crusts with liquid nuclei: their unlike specific gravities resulting from unlikenesses of substance. And indeed, at first sight, this would seem to be the only tenable supposition; seeing that, unless prevented by some immense resisting force, gravitation must obliterate any internal cavity by collapsing the surrounding liquid or solid matter.

Nevertheless, that the Earth, in common with other members of the Solar System, is solid, or else consists of a solid shell having a cavity entirely filled with molten matter, is not an established fact: it is nothing but a supposition. We must not let its familiarity and apparent feasibility delude us into an uncritical acceptance of it. If we find an alternative supposition which, physically considered, is equally possible, we are bound to consider it. And if it not only avoids the difficulties above pointed out, but many others hereafter to be mentioned, we must give it the preference.

Before proceeding to consider what the Nebular Hypothesis indicates respecting the internal structures of the Sun and planets, we may state that our reasonings, though of a kind not admitting of direct verification, are nothing more than deductions from the established principles of physics. We have submitted them to an authority not inferior to any that can be named; and while unprepared to commit himself to them, he yet sees nothing to object. Starting, then, with a rotating spheroid of aeriform matter, in the later stages of its concentration, but before it has begun to take a liquid or solid form, let us inquire what must be the actions going on in it. Mutual gravitation continually aggregates its atoms into a smaller and denser mass; and the aggregating force goes on increasing, as the common centre of gravity is approached. An obstacle to concentration, however, exists in the centrifugal force, which at this stage bears a far higher ratio to gravity than afterwards, and in a gaseous spheroid must produce a very oblate form. At the same time, the approximation of the atoms is resisted by a force which, in being overcome, is evolved as heat. This heat must be greatest where the atoms are subject to the highest pressure – namely, about the central parts. And as fast as it escapes into space, further approximation and further generation of heat must take place. But in a gaseous spheroid, having internal parts hotter than its external parts, there must be some circulation. The currents must set from the hottest region to the coolest by some particular route; and from the coolest to the hottest by some other route. In a very oblate spheroid, the coolest region must be that about the equator: the surface there bearing so large a ratio to the mass. Hence there will be currents from the centre to the equator, and others from the equator to the centre. What will be the special courses of these currents? Supposing an original state of rest, about to pass into motion in obedience to the disturbing forces, the currents commencing at the centre will follow the lines of most rapidly-decreasing density; seeing that the inertia will be least in those lines. That is to say, there will be a current from the centre towards each pole, along the axis of rotation; and the space thus continually left vacant will be filled by the collapse of matter coming in at right angles to the axis. The process cannot end here, however. If there are constant currents from the centre towards the poles, there must be a constant accumulation at the poles; the spheroid will be ever becoming more protuberant about the poles than the conditions of mechanical equilibrium permit. If, however, the mass at the poles is thus ever in excess, it must, by the forces acting on it, be constantly moved over the outer surface of the spheroid from the poles towards the equator: thus only can that form which rotation necessitates be maintained. And a further result of this transfer of matter from the centre, by way of the poles, to the equator, must be the establishment of counter-currents from the equator in diametrical lines, to the centre.

Mark now the changes of temperature that must occur in these currents. An aeriform mass ascending from the centre towards either pole, will expand as it approaches the surface, in consequence of the diminution of pressure. But expansion, involving an absorption of heat, will entail a diminished temperature; and the temperature will be further lowered by the greater freedom of radiation into space. This rarefied and cooled mass must be still more rarefied and cooled in its progress over the surface of the spheroid to the equator. Continually thrust further from the pole by the ceaseless accumulation there, it must acquire an ever-increasing rotatory motion and an ever-increasing centrifugal force: whence must follow expansion and absorption of heat. To the refrigeration thus caused must be added that resulting from radiation, which, at each advance towards the equator, will be less hindered. And when the mass we have thus followed arrives at the equator, it will have reached its maximum rarity and maximum coolness. Conversely, every portion of a current proceeding in a diametrical direction from the equator to the centre, must progressively rise in temperature; in virtue alike of the increasing pressure, the gradual arrest of motion, and the diminished rate of radiation. Note, lastly, that this circulation will go on, but slowly. As the matter proceeding from the equator towards the centre must have its rotatory motion destroyed, while that proceeding from the poles to the equator must have rotatory motion given to it, it follows that an enormous amount of inertia has to be overcome; and this must make the currents so slow as to prevent them from producing anything like an equality of temperature.

Such being the constitution of a concentrating spheroid of gaseous matter, where will the gaseous matter begin to condense into liquid? The usual assumption has been, that in a nebulous mass approaching towards the planetary form, the liquefaction will first occur at the centre. We believe this assumption is inconsistent with established physical principles.

Observe first that it is contrary to analogy. That the matter of the Earth was liquid before any of it became solid, is generally admitted. Where has it first solidified? Not at the centre, but at the surface. Now the general principles which apply to the condensation of liquid matter into solid, apply also to the condensation of gaseous matter into liquid. Hence if the once liquid substance of the Earth first solidified at the surface, the implication is that its once aeriform substance first liquified at the surface.

But we have no need to rest in analogy. On considering what must happen in a rotating gaseous spheroid having currents moving as above described, we shall see that external condensation is a corollary. A nebulous mass, when it has arrived at this stage, will consist of an aeriform mixture of various matters; the heavier and more condensible matters being contained in the rarer or less condensible, in the same way that water is contained in air. And the inference must be, that at a certain stage, some of these denser matters will be precipitated in the shape of a cloud.¹⁶

Now, what are the laws of precipitation from gases? If a gas through which some other substance is diffused in a gaseous state, expands in consequence of the removal of pressure, it will, when the rarefaction and consequent cooling reach a certain point, begin to let fall the suspended substance. Conversely, if, a gas, saturated even with some substance, is subject to increased pressure, and is allowed to retain the additional heat which that pressure generates; so far from letting fall what it contains, it will gain the power to take up more. See then, the inference respecting condensation in a nebulous spheroid. The currents proceeding from the equator to the centre, subject to increasing pressure, and acquiring the heat due both to this increasing pressure and to arrested motion, will have no tendency to deposit their suspended substances, but rather the reverse: a formation of liquid matter at the centre of the mass will be impossible. Contrariwise, the gaseous currents moving from the centre to the poles and thence to the equator, expanding as they go, first from diminished pressure and afterwards from increased centrifugal force; and losing heat, not only by expansion, but by more rapid radiation; will have less and less power to retain the matter diffused through them. The earliest precipitation will take place in the region of extremest rarefaction; namely, about the equator. An equatorial belt of cloud will be first formed, and widened into a zone, will by-and-by begin to condense into liquid.¹⁷ Gradually this liquid film will extend itself on each side the equator, and encroaching on the two hemispheres, will eventually close over at the poles: thus producing a thin hollow globe, or rather spheroid, filled with gaseous matter. We do not mean that this condensation will take place at the very outermost surface; for probably, round the denser gases forming the principal mass, there will extend strata of gases too rare and too cool to be entangled in these processes. It is the surface of this inner spheroid of denser gases to which our reasoning points as the place of earliest condensation.

The internal circulation we have described, continuing, as it must, after the formation of this liquid film, there will still go on the radiation of heat, and the progressive aggregation. The film will thicken at the expense of the internal gaseous substances precipitated on it. As it thickens, as the globe contracts, and as the gravitative force augments, the pressure will increase; and the evolution and radiation of heat will go on more rapidly. Eventually, however, when the liquid shell becomes very thick, and the internal cavity relatively small, the obstacle put to the escape of heat by this thick liquid shell, with its slowly-circulating currents, will turn the scale: the temperature of the outer surface will begin to diminish, and a solid crust will form while the internal cavity is yet unobliterated.

"But what," it may be asked, "will become of this gaseous nucleus when exposed to the enormous gravitative pressure of a shell some thousands of miles thick? How can aeriform matter withstand such a pressure?" Very readily. It has been proved that even when the heat generated by compression is allowed to escape, some gases remain uncondensible by any force we can produce. An unsuccessful attempt lately made at Vienna to liquify oxygen, clearly shows this enormous resistance. The steel piston employed was literally shortened by the pressure used: and yet the gas remained unliquified! If, then, the expansive force is thus immense when the heat evolved is dissipated, what must it be when that heat is in great measure detained; as in the case we are considering? Indeed, the experiments of M. Cagniard de Latour have shown that gases may, under pressure, acquire the density of liquids while retaining the aeriform state; provided the temperature continues extremely high. In such a case, every addition to the heat is an addition to the repulsive power of the atoms: the increased pressure itself generates an increased ability to resist; and this remains true to whatever extent the compression is carried. Indeed, it is a corollary from the persistence of force, that if, under increasing pressure, a gas retains all the heat evolved, its resisting force is absolutely unlimited. Hence, the internal planetary structure we have described, is as physically stable a one as that commonly assumed.

And now let us see how this hypothesis tallies with the facts. One inference from it must be, that large masses will progress towards final consolidation more slowly than small masses. Though a large concentrating spheroid will, from its superior aggregative force, generate heat more rapidly than a small one; yet, having, relatively to its surface, a much greater quantity of heat to get rid of, it will be longer than a small one in going through the changes we have described. Consequently, at a time when the smaller members of our Solar System have arrived at so advanced a stage of aggregation as almost to have obliterated their central cavities, and so reached high specific gravities; the larger members will still be at that stage in which the central cavities bear great ratios to the surrounding shells, and will therefore have low specific gravities. This contrast is just what we find. The small planets Mercury, Venus, the Earth, and Mars, differing from each other comparatively little in density as in size, are about four times as dense as Jupiter and Uranus, and seven times as dense as Saturn and Neptune – planets exceeding them in size as oranges exceed peas; and they are four times as dense as the Sun, which in mass is nearly 5,000,000 times greater than the smallest of them. The obvious objection that this hypothesis does not explain the minor differences, serves but to introduce a further confirmation. It may be urged that Jupiter is of greater specific gravity than Saturn, though, considering his superior mass, his specific gravity should be less; and that still more anomalous is the case of the Sun, which, though containing a thousand times the matter that Jupiter does, is nearly of the same specific gravity. The solution of these difficulties lies in the modifying effects of centrifugal force. Had the various masses to be compared been all along in a state of rest, then the larger should have been uniformly the less dense. But during the concentrating process they have been rotating with various velocities. The consequent centrifugal force has in each case been in antagonism with gravitation; and, according to its amount, has hindered the concentration to a greater or less degree. The efficient aggregative force has in each case been the excess of the centripetal tendency over the centrifugal. Whence we may infer that wherever this excess has been the least, the consolidation must have been the most hindered, and the specific gravity will be the smallest. This, too, we find to be the fact. Saturn, at whose equator the centrifugal force is even now almost one-sixth of gravity, and who, by his numerous satellites, shows us how strong an antagonist to concentration it was in earlier stages of his evolution, is little more than half as dense as Jupiter, whose concentration has been hindered by a centrifugal force bearing a much smaller ratio to the centripetal.

On the other hand, the Sun, whose latter stages of aggregation have met with comparatively little of this opposition, and whose atoms tend towards their common centre with a force ten times as great as that which Jupiter's atoms are subject to, has, notwithstanding his immense bulk, reached a specific gravity as great as that of Jupiter; and he has done this partly for the reason assigned, and partly because the process of consolidation has been, and still is, actively going on, while that of Jupiter has long since almost ceased.

Before pointing out further harmonies let us meet an objection. Laplace, taking for data Jupiter's mass, diameter, and rate of rotation, calculated the degrees of compression at the poles which his centrifugal force should produce, supposing his substance to be homogeneous; and finding that the calculated amount of oblateness was greater than the actual amount, inferred that his substance must be denser towards the centre. The inference seems unavoidable; is diametrically opposed to the hypothesis of a shell of denser matter with a gaseous nucleus; and we confess that on first meeting with this fact we were inclined to think it fatal. But there is a consideration, apt to be overlooked, which completely disposes of it. A compressed elastic medium tends ever with great energy to give a spherical figure to the chamber in which it is confined. This truth is alike mathematically demonstrable, and recognized in practice by every engineer. In the case before us, the expansive power of the gaseous nucleus is such as to balance the gravitation of the shell of the planet; and this power perpetually strives to make the planet a perfect sphere. Thus the tendency of the centrifugal force to produce oblateness, is opposed not only by the force of gravity but by another force of great intensity; and hence the degree of oblateness produced is relatively small.