Essays: Scientific, Political, and Speculative, Volume I

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: —

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

⁄

of gravity, whereas in Mercury with no satellite and greatest density centrifugal force is but

⁄

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 - 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.]

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.

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.

If we thus distinguish between the two sources of heat accompanying nebular condensation – the heat due to proto-chemical combinations and that due to the contraction caused by gravitation (both of them, however, being interpretable as consequent on loss of motion), it may be inferred that they take different shares during the earlier and during the later stages of aggregation. It seems probable that while the diffusion is great and the force of mutual gravitation small, the chief source of heat is combination of units of matter, simpler than any known to us, into such units of matter as those we know; while, conversely, when there has been reached close aggregation, the chief source of heat is gravitation, with consequent pressure and gradual contraction. Supposing this to be so, let us ask what may be inferred. If at the time when the nebulous spheroid from which the Solar System resulted, filled the orbit of Neptune, it had reached such a degree of density as enabled those units of matter which compose the sodium molecules to enter into combination; and if, in conformity with the analogies above indicated, the heat evolved by this proto-chemical combination was great compared with the heats evolved by the chemical combinations known to us; the implication is that the nebulous spheroid, in the course of its contraction, would have to get rid of a much larger quantity of heat than it would, did it commence at any ordinary temperature and had only to lose the heat consequent on contraction. That is to say, in estimating the past period during which solar emission of heat has been going on at a high rate, much must depend on the initial temperature assumed; and this may have been rendered intense by the proto-chemical changes which took place in early stages.[21 - Of course there remains the question whether, before the stage here recognized, there had already been produced a high temperature by those collisions of celestial masses which reduced the matter to a nebulous form. As suggested in First Principles (§ 136 in the edition of 1862, and § 182 in subsequent editions), there must, after there have been effected all those minor dissolutions which follow evolutions, remain to be effected the dissolutions of the great bodies in and on which the minor evolutions and dissolutions have taken place; and it was argued that such dissolutions will be, at some time or other, effected by those immense transformations of molar motion into molecular motion, consequent on collisions: the argument being based on the statement of Sir John Herschel, that in clusters of stars collisions must inevitably occur. It may, however, be objected that though such a result may be reasonably looked for in closely aggregated assemblages of stars, it is difficult to conceive of its taking place throughout our Sidereal System at large, the members of which, and their intervals, may be roughly figured as pins-heads 50 miles apart. It would seem that something like an eternity must elapse before, by ethereal resistance or other cause, these can be brought into proximity great enough to make collisions probable.]

Respecting the future duration of the solar heat, there must also be differences between the estimates made according as we do or do not take into account the proto-chemical changes which possibly have still to take place. True as it may be that the quantity of heat to be emitted is measured by the quantity of motion to be lost, and that this must be the same whether the approximation of the molecules is effected by chemical unions, or by mutual gravitation, or by both; yet, evidently, everything must turn on the degree of condensation supposed to be eventually reached; and this must in large measure depend on the natures of the substances eventually formed. Though, by spectrum-analysis, platinum has recently been detected in the solar atmosphere, it seems clear that the metals of low molecular weights greatly predominate; and supposing the foregoing arguments to be valid, it may be inferred, as not improbable, that the compoundings and recompoundings by which the heavy-moleculed elements are produced, not hitherto possible in large measure, will hereafter take place; and that, as a result, the Sun's density will finally become very great in comparison with what it is now. I say "not hitherto possible in large measure", because it is a feasible supposition that they may be formed, and can continue to exist, only in certain outer parts of the Solar mass, where the pressure is sufficiently great while the heat is not too great. And if this be so, the implication is that the interior body of the Sun, higher in temperature than its peripheral layers, may consist wholly of the metals of low atomic weights, and that this may be a part cause of his low specific gravity; and a further implication is that when, in course of time, the internal temperature falls, the heavy-moleculed elements, as they severally become capable of existing in it, may arise: the formation of each having an evolution of heat as its concomitant.[22 - The two sentences which, in the text, precede the asterisk, I have introduced while these pages are standing in type: being led to do so by the perusal of some notes kindly lent to me by Prof. Dewar, containing the outline of a lecture he gave at the Royal Institution during the session of 1880. Discussing the conditions under which, if "our so-called elements are compounded of elemental matter", they may have been formed, Prof. Dewar, arguing from the known habitudes of compound substances, concludes that the formation is in each case a function of pressure, temperature, and nature of the environing gases.] If so, it would seem to follow that the amount of heat to be emitted by the Sun, and the length of the period during which the emission will go on, must be taken as much greater than if the Sun is supposed to be permanently constituted of the elements now predominating in him, and to be capable of only that degree of condensation which such composition permits.

Note III. Are the internal structures of celestial bodies all the same, or do they differ? And if they differ, can we, from the process of nebular condensation, infer the conditions under which they assume one or other character? In the foregoing essay as originally published, these questions were discussed; and though the conclusions reached cannot be sustained in the form given to them, they foreshadow conclusions which may, perhaps, be sustained. Referring to the conceivable causes of unlike specific gravities in the members of the solar system, it was said that these might be —

"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 aëriform substance. Of these three conceivable causes, that commonly assigned is the first, more or less modified by the second."

Written as this was before spectrum-analysis had made its disclosures, no notice could of course be taken of the way in which these conflict with the first of the foregoing suppositions; but after pointing out other objections to it the argument continued thus: —

"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."[23 - At the date of this passage the established teleology made it seem needful to assume that all the planets are habitable, and that even beneath the photosphere of the Sun there exists a dark body which may be the scene of life; but since then, the influence of teleology has so far diminished that this hypothesis can no longer be called the current one.]

After saying that the familiarity of this hypothesis must not delude us into uncritical acceptance of it, but that if any other hypothesis is physically possible it may reasonably be entertained, it was argued that by tracing out the process of condensation in a nebulous spheroid, we are led to infer the eventual formation of a molten shell with a nucleus consisting of gaseous matter at high tension. The paragraph which then follows runs thus: —

"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 in 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 experiences 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."

Had this paragraph, and the subsequent paragraphs, been written five years later, when Prof. Andrews had published an account of his researches, the propositions they contain, while rendered more specific and at the same time more defensible, would perhaps have been freed from the erroneous implication that the internal structure indicated is an universal one. Let us, while guided by Prof. Andrews' results, consider what would probably be the successive changes in a condensing nebulous spheroid.

Prof. Andrews has shown that for each kind of gaseous matter there is a temperature above which no amount of pressure can cause liquefaction. The remark, made a priori in the above extract, "that if, under increasing pressure, a gas retains all the heat evolved, its resisting force is absolutely unlimited", harmonizes with the inductively-reached result that if the temperature is not lowered to its "critical point" a gas does not liquify, however great the force applied. At the same time Prof. Andrews' experiments imply that, supposing the temperature to be lowered to the point at which liquefaction becomes possible, then liquefaction will take place where there is first reached the required pressure. What are the corollaries in relation to concentrating nebulous spheroids?

Assume a spheroid of such size as will form one of the inferior planets, and consisting externally of a voluminous, cloudy atmosphere composed of the less condensible elements, and internally of metallic gases: such internal gases being kept by convection-currents at temperatures not very widely differing. And assume that continuous radiation has brought the internal mass of metallic gases down to the critical point of the most condensible. May we not say that there is a size of the spheroid such that the pressure will not be great enough to produce liquefaction at any other place than the centre? or, in other words, that in the process of decreasing temperature and increasing pressure, the centre will be the place at which the combined conditions of pressure and temperature will be first reached? If so, liquefaction, commencing at the centre, will spread thence to the periphery; and, in virtue of the law that solids have higher melting points under pressure than when free, it may be that solidification will similarly, at a later stage, begin at the centre and progress outwards: eventually producing, in that case, a state such as Sir William Thomson alleges exists in the Earth. But now suppose that instead of such a spheroid, we assume one of, say, twenty or thirty times the mass; what will then happen? Notwithstanding convection-currents, the temperature at the centre must always be higher than elsewhere; and in the process of cooling the "critical point" of temperature will sooner be reached in the outer parts. Though the requisite pressure will not exist near the surface, there is evidently, in a large spheroid, a depth below the surface at which the pressure will be great enough, if the temperature is sufficiently low. Hence it is inferable that somewhere between centre and surface in the supposed larger spheroid, there will arise that state described by Prof. Andrews, in which "flickering striæ" of liquid float in gaseous matter of equal density. And it may be inferred that gradually, as the process goes on, these striæ will become more abundant while the gaseous interspaces diminish; until, eventually, the liquid becomes continuous. Thus there will result a molten shell containing a gaseous nucleus equally dense with itself at their surface of contact and more dense at the centre – a molten shell which will slowly thicken by additions to both exterior and interior.

That a solid crust will eventually form on this molten shell may be reasonably concluded. To the demurrer that solidification cannot commence at the surface, because the solids formed would sink, there are two replies. The first is that various metals expand while solidifying, and therefore would float. The second is that since the envelope of the supposed spheroid would consist of the gases and non-metallic elements, compounds of these with the metals and with one another would continually accumulate on the molten shell; and the crust, consisting of oxides, chlorides, sulphurets, and the rest, having much less specific gravity than the molten shell, would be readily supported by it.

Clearly a planet thus constituted would be in an unstable state. Always it would remain liable to a catastrophe resulting from change in its gaseous nucleus. If, under some condition of pressure and temperature eventually reached, the components of this suddenly entered into one of those proto-chemical combinations forming a new element, there might result an explosion capable of shattering the entire planet, and propelling its fragments in all directions with high velocities. If the hypothetical planet between Jupiter and Mars was intermediate in size as in position, it would apparently fulfil the conditions under which such a catastrophe might occur.

Note IV. The argument set forth in the foregoing note, is in part designed to introduce a question which seems to require re-consideration – the origin of the minor planets or planetoids. The hypothesis of Olbers, as propounded by him, implied that the disruption of the assumed planet between Mars and Jupiter had taken place at no very remote period in the past; and this implication was shown to be inadmissible by the discovery that there exists no such point of intersection of the orbits of the planetoids as the hypothesis requires. The inquiry whether, in the past, there was any nearer approach to a point of intersection than at present, having resulted in a negative, it is held that the hypothesis must be abandoned. It is, however, admitted that the mutual perturbations of the planetoids themselves would suffice, in the course of some millions of years, to destroy all traces of a place of intersection of their orbits, if it once existed. But if this be admitted why need the hypothesis be abandoned? Given such duration of the Solar System as is currently assumed, there seems no reason why lapse of a few millions of years should present any difficulty. The explosion may as well have taken place ten million years ago as at any more recent period. And whoever grants this must grant that the probability of the hypothesis has to be estimated from other data.

As a preliminary to closer consideration, let us ask what may be inferred from the rate of discovery of the planetoids, and from the sizes of those most recently discovered. In 1878, Prof. Newcomb, arguing that "the preponderance of evidence is on the side of the number and magnitude being limited", says that "the newly discovered ones" "do not seem, on the average, to be materially smaller than those which were discovered ten years ago"; and further that "the new ones will probably be found to grow decidedly rare before another hundred are discovered". Now, inspection of the tables contained in the just-published fourth edition of Chambers' Descriptive Astronomy (vol. I) shows that whereas the planetoids discovered in 1868 (the year Prof. Newcomb singles out for comparison) have an average magnitude of 11∙56 those discovered last year (1888) have an average magnitude of 12∙43. Further, it is observable that though more than ninety have been discovered since Prof. Newcomb wrote, they have by no means become rare: the year 1888 having added ten to the list, and having therefore maintained the average rate of the preceding ten years. If, then, the indications Prof. Newcomb names, had they arisen, would have implied a limitation of the number, these opposite indications imply that the number is unlimited. The reasonable conclusion appears to be that these minor planets are to be counted not by hundreds but by thousands; that more powerful telescopes will go on revealing still smaller ones; and that additions to the list will cease only when the smallness ends in invisibility.

Commencing now to scrutinize the two hypotheses respecting the genesis of these multitudinous bodies, I may first remark concerning that of Laplace, that he might possibly not have propounded it had he known that instead of four such bodies there are hundreds, if not thousands. The supposition that they resulted from the breaking up of a nebulous ring into numerous small portions, instead of its collapse into one mass, might not, in such case, have seemed to him so probable. It would have appeared still less probable had he been aware of all that has since been discovered concerning the wide differences of the orbits in size, their various and often great eccentricities, and their various and often great inclinations. Let us look at these and other incongruous traits of them.