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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]

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] 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]

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.

(1.) Between the greatest and least mean distances of the planetoids there is a space of 200 millions of miles; so that the whole of the Earth's orbit might be placed between the limits of the zone occupied, and leave 7 millions of miles on either side: add to which that the widest excursions of the planetoids occupy a zone of 270 millions of miles. Had the rings from which Mercury, Venus, and the Earth were formed been one-sixth of the smaller width or one-ninth of the greater, they would have united: there would have been no nebulous rings at all, but a continuous disk. Nay more, since one of the planetoids trenches upon the orbit of Mars, it follows that the nebulous ring out of which the planetoids were formed must have overlapped that out of which Mars was formed. How do these implications consist with the nebular hypothesis? (2.) The tacit assumption usually made is that the different parts of a nebulous ring have the same angular velocities. Though this assumption may not be strictly true, yet it seems scarcely likely that it is so widely untrue as it would be had the inner part of the ring an angular velocity nearly thrice that of the outer. Yet this is implied. While the period of Thule is 8.8 years, the period of Medusa is 3·1 years. (3.) The eccentricity of Jupiter's orbit is 0·04816, and the eccentricity of Mars' orbit is 0·09311. Estimated by groups of the first found and last found of the planetoids, the average eccentricity of the assemblage is about three times that of Jupiter and more than one and a half times that of Mars; and among the members of the assemblage themselves, some have an eccentricity thirty-five times that of others. How came this nebulous zone, out of which it is supposed the planetoids arose, to have originated eccentricities so divergent from one another as well as from those of the neighbouring planets? (4.) A like question may be asked respecting the inclinations of the orbits. The average inclination of the planetoid-orbits is four times the inclination of Mars' orbit and six times the inclination of Jupiter's orbit; and among the planetoid-orbits themselves the inclinations of some are fifty times those of others. How are all these differences to be accounted for on the hypothesis of genesis from a nebulous ring? (5.) Much greater becomes the difficulty on inquiring how these extremely unlike eccentricities and inclinations came to co-exist before the parts of the nebulous ring separated, and how they survived after the separation. Were all the great eccentricities displayed by the outermost members of the group, and the small by the innermost members, and were the inclinations so distributed that the orbits having much belonged to one part of the group, and those having little to another part of the group; the difficulty of explanation might not be insuperable. But the arrangement is by no means this. The orbits are, to use an expressive word, miscellaneously jumbled. Hence, if we go back to the nebulous ring, there presents itself the question—How came each planetoid-forming portion of nebulous matter, when it gathered itself together and separated, to have a motion round the Sun differing so much from the motions of its neighbours in eccentricity and inclination? And there presents itself the further question—How, during the time when it was concentrating into a planetoid, did it manage to jostle its way through all the differently-moving like masses of nebulous matter, and yet to preserve its individuality? Answers to these questions are, it seems to me, not even imaginable.

Turn we now to the alternative hypothesis. During revision of the foregoing essay, in preparation for that edition of the volume containing it which was published in 1883, there occurred the thought that some light on the origin of the planetoids ought to be obtained by study of their distributions and movements. If, as Olbers supposed, they resulted from the bursting of a planet once revolving in the region they occupy, the implications are:—first, that the fragments must be most abundant in the space immediately about the original orbit, and less abundant far away from it; second, that the large fragments must be relatively few, while of smaller fragments the numbers will increase as the sizes decrease; third, that as some among the smaller fragments will be propelled further than any of the larger, the widest deviations in mean distance from the mean distance of the original planet, will be presented by the smallest members of the assemblage; and fourth, that the orbits differing most from the rest in eccentricity and in inclination, will be among those of these smallest members. In the fourth edition of Chambers's Handbook of Descriptive and Practical Astronomy (the first volume of which has just been issued) there is a list of the elements (extracted and adapted from the Berliner Astronomisches Jahrbuch for 1890) of all the small planets (281 in number) which had been discovered up to the end of 1888. The apparent brightness, as expressed in equivalent star-magnitudes, is the only index we have to the probable comparative sizes of by far the largest number of the planetoids: the exceptions being among those first discovered. Thus much premised, let us take the above points in order. (1) There is a region lying between 2·50 and 2·80 (in terms of the Earth's mean distance from the Sun) where the planetoids are found in maximum abundance. The mean between these extremes, 2·65, is nearly the same as the average of the distances of the four largest and earliest-known of these bodies, which amounts to 2·64. May we not say that the thick clustering about this distance (which is, however, rather less than that assigned for the original planet by Bode's empirical law), in contrast with the wide scattering of the comparatively few whose distances are little more than 2 or exceed 3, is a fact in accordance with the hypothesis in question?[24] (2) Any table which gives the apparent magnitudes of the planetoids, shows at once how much the number of the smaller members of the assemblage exceeds that of those which are comparatively large; and every succeeding year has emphasized this contrast more strongly. Only one of them (Vesta) exceeds in brightness the seventh star-magnitude, while one other (Ceres) is between the seventh and eighth, and a third (Pallas) is above the eighth; but between the eighth and ninth there are six; between the ninth and tenth, twenty; between the tenth and eleventh, fifty-five; below the eleventh a much larger number is known, and the number existing is probably far greater—a conclusion we cannot doubt when the difficulty of finding the very faint members of the family, visible only in the largest telescopes, is considered. (3) Kindred evidence is furnished if we broadly contrast their mean distances. Out of the 13 largest planetoids whose apparent brightnesses exceed that of a star of the 9·5 magnitude, there is not one having a mean distance that exceeds 3. Of those having magnitudes at least 9·5 and smaller than 10, there are 15; and of these one only has a mean distance greater than 3. Of those between 10 and 10·5 there are 17; and of these also there is one exceeding 3 in mean distance. In the next group there are 37, and of these 5 have this great mean distance. The next group, 48, contains 12 such; the next, 47, contains 13 such. Of those of the twelfth magnitude and fainter, 72 planetoids have been discovered, and of those of them of which the orbits have been computed, no fewer than 23 have a mean distance exceeding 3 in terms of the Earth's. It is evident from this how comparatively erratic are the fainter members of the extensive family with which we are dealing. (4) To illustrate the next point, it may be noted that among the planetoids whose sizes have been approximately measured, the orbits of the two largest, Vesta and Ceres, have eccentricities falling between .05 and .10, whilst the orbits of the two smallest, Menippe and Eva, have eccentricities falling between .20 and .25, and between .30 and .35. And then among those more recently discovered, having diameters so small that measurement of them has not been practicable, come the extremely erratic ones—Hilda and Thule, which have mean distances of 3.97 and 4.25 respectively; Æthra, having an orbit so eccentric that it cuts the orbit of Mars; and Medusa, which has the smallest mean distance from the Sun of any. (5) If the average eccentricities of the orbits of the planetoids grouped according to their decreasing sizes are compared, no very definite results are disclosed, excepting this, that the eight Polyhymnia, Atalanta, Eurydice, Æthra, Eva, Andromache, Istria, and Eudora, which have the greatest eccentricities (falling between .30 and .38), are all among those of smallest star-magnitudes. Nor when we consider the inclinations of the orbits do we meet with obvious verifications; since the proportion of highly-inclined orbits among the smaller planetoids does not appear to be greater than among the others. But consideration shows that there are two ways in which these last comparisons are vitiated. One is that the inclinations are measured from the plane of the ecliptic, instead of being measured from the plane of the orbit of the hypothetical planet. The other, and more important one, is that the search for planetoids has naturally been carried on in that comparatively narrow zone within which most of their orbits fall; and that, consequently, those having the most highly-inclined orbits are the least likely to have been detected, especially if they are at the same time among the smallest. Moreover, considering the general relation between the inclination of planetoid orbits and their eccentricities, it is probable that among the orbits of these undetected planetoids are many of the most eccentric. But while recognizing the incompleteness of the evidence, it seems to me that it goes far to justify the hypothesis of Olbers, and is quite incongruous with that of Laplace. And as having the same meanings let me not omit the remarkable fact concerning the planetoids discovered by D'Arrest, that "if their orbits are figured under the form of material rings, these rings will be found so entangled, that it would be possible, by means of one among them taken at hazard, to lift up all the rest,"—a fact incongruous with Laplace's hypothesis, which implies an approximate concentricity, but quite congruous with the hypothesis of an exploded planet.

Next to be considered come phenomena, the bearings of which on the question before us are scarcely considered—I mean those presented by meteors and shooting stars. The natures and distributions of these harmonize with the hypothesis of an exploded planet, and I think with no other hypothesis. The theory of volcanic origin, joined with the remark that the Sun emits jets which might propel them with adequate velocities, seems quite untenable. Such meteoric bodies as have descended to us, forbid absolutely the supposition of solar origin. Nor can they rationally be ascribed to planetary volcanoes. Even were their mineral characters appropriate, which many of them are not (for volcanoes do not eject iron), no planetary volcanoes could propel them with anything like the implied velocity—could no more withstand the tremendous force to be assumed, than could a card-board gun the force behind a rifle bullet. But that their mineral characters, various as they are, harmonize with the supposition that they were derived from the crust of a planet is manifest; and that the bursting of a planet might give to them, and to shooting stars, the needful velocities, is a reasonable conclusion. Along with those larger fragments of the crust constituting the known planetoids, varying from some 200 miles in diameter to little over a dozen, there would be sent out still more multitudinous portions of the crust, decreasing in size as they increased in number. And while there would thus result such masses as occasionally fall through the Earth's atmosphere to its surface, there would, in an accompanying process, be an adequate cause for the myriads of far smaller masses which, as shooting stars, are dissipated in passing through the Earth's atmosphere. Let us figure to ourselves, as well as we may, the process of explosion.

Assume that the diameter of the missing planet was 20,000 miles; that its solid crust was a thousand miles thick; that under this came a shell of molten metallic matter which was another thousand miles thick; and that the space, 16,000 miles in diameter, within this, was occupied by the equally dense mass of gases above the "critical point", which, entering into a proto-chemical combination, caused the destroying explosion. The primary fissures in the crust must have been far apart—probably averaging distances between them as great as the thickness of the crust. Supposing them approximately equidistant, there would, in the equatorial periphery, be between 60 and 70 fissures. By the time the primary fragments thus separated had been heaved a mile outwards, the fissures formed would severally have, at the surface, a width of 170 odd yards. Of course these great masses, as soon as they moved, would themselves begin to fall in pieces; especially at their bounding surfaces. But passing over the resulting complications, we see that when the masses had been propelled 10 miles outwards, the fissures between them would be each a mile wide. Notwithstanding the enormous forces at work, an appreciable interval would elapse before these vast portions of the crust could be put in motion with any considerable velocities. Perhaps the estimate will be under the mark if we assume that it took 10 seconds to propel them through the first mile, and that, by implication, at the end of 20 seconds they had travelled 4 miles, and at the end of 30 seconds 9 miles. Supposing this granted, let us ask what would be taking place in each intervening fissure a thousand miles deep, which, in the space of half a minute, had opened out to nearly a mile wide, and in the subsequent half minute to a chasm approaching 3 miles in width. There would first be propelled through it enormous jets of the molten metals composing the internal liquid shell; and these would part into relatively small masses as they were shot into space. Presently, as the chasm opened to some miles in width, the molten metals would begin to be followed by the equally dense gaseous matter behind, and the two would rush out together. Soon the gases, predominating, would carry with them the portions of the liquid shell continually collapsing; until the blast became one filled with millions of small masses, billions of smaller masses, and trillions of drops. These would be driven into space in a stream, the emission of which would continue for many seconds or even several minutes. Remembering the rate of motion of the jets emitted from the solar surface, and supposing that the blasts produced by this explosion reached only one-tenth of that rate, these myriads of small masses and drops would be propelled with planetary velocities, and in approximately the same direction. I say approximately, because they would be made to deviate somewhat by the friction and irregularities of the chasm passed through, and also by the rotation of the planet. Observe, however, that though they would all have immense velocities, their velocities would not be equal. During its earlier stages the blast would be considerably retarded by the resistance which the sides of its channel offered. When this became relatively small the velocity of the blast would reach its maximum; from which it would decline when the space for emission became very wide, and the pressure behind consequently less. Hence these almost infinitely numerous particles of planet-spray, as we might call it, as well as those formed by the condensation of the metallic vapours accompanying them, would forthwith begin to part company: some going rapidly in advance, and others falling behind; until the stream of them, perpetually elongating, formed an orbit round the Sun, or rather an assemblage of innumerable orbits, separating widely at aphelion and perihelion, but approximating midway, where they might fall within a space of, say, some two millions of miles, as do the orbits of the November meteors. At a later stage of the explosion, when the large masses, having moved far outwards, had also fallen to pieces of every size, from that of Vesta to that of an aerolite, and when the channels just described had ceased to exist, the contents of the planet would disperse themselves with lower velocities and without any unity of direction. Hence we see causes alike for the streams of shooting stars, for the solitary shooting stars visible to the naked eye, and for the telescopic shooting stars a score times more numerous.

Further significant evidence is furnished by the comets of short periods. Of the thirteen constituting this group, twelve have orbits falling between those of Mars and Jupiter: one only having its aphelion beyond the orbit of Jupiter. That is to say, nearly all of them frequent the same region as the planetoids. By implication, they are similarly associated in respect of their periods. The periods of the planetoids range from 3.1 to 8.8 years; and all these twelve comets have periods falling between these extremes: the least being 3.29 and the greatest 8.86. Once more this family of comets, like the planetoids in the zone they occupy and like them in their periods, are like them also in the respect that, as Mr. Lynn has pointed out, their motions are all direct. How happens this close kinship—how happens there to be this family of comets so much like the planetoids and so much like one another, but so unlike comets at large? The obvious suggestion is that they are among the products of the explosion which originated the planetoids, the aerolites, and the streams of meteors; and consideration of the probable circumstances shows us that such products might be expected. If the hypothetical planet was like its neighbour Jupiter in having an atmosphere, or like its neighbour Mars in having water on its surface, or like both in these respects; then these superficial masses of liquid, of vapour, and of gas, blown into space along with the solid matters, would yield the materials for comets. There would result, too, comets unlike one another in constitution. If a fissure opened beneath one of the seas, the molten metals and metallic gases rushing through it as above described, would decompose part of the water carried with them; and the oxygen and hydrogen liberated would be mingled with undecomposed vapour. In other cases, portions of the atmosphere might be propelled, probably with portions of vapour; and in yet other cases masses of water alone. Severally subject to great heat at perihelion, these would behave more or less differently. Once more, it would ordinarily happen that detached swarms of meteors projected as implied, would carry with them masses of vapours and gases; whence would result the cometic constitution now insisted on. And sometimes there would be like accompaniments to meteoric streams.

See, then, the contrast between the two hypotheses. That of Laplace, looking probable while there were only four planetoids, but decreasing in apparent likelihood as the planetoids increase in number, until, as they pass through the hundreds on their way to the thousands, it becomes obviously improbable, is, at the same time, otherwise objectionable. It pre-supposes a nebulous ring of a width so enormous that it would have overlapped the ring of Mars. This ring would have had differences between the angular velocities of its parts quite inconsistent with the Nebular Hypothesis. The average eccentricities of the orbits of its parts must have differed greatly from those of adjacent orbits; and the average inclinations of the orbits of its parts must similarly have differed greatly from those of adjacent orbits. Once more, the orbits of its parts, confusedly interspersed, must have had varieties of eccentricity and inclination unaccountable in portions of the same nebulous ring; and, during concentration into planetoids, each must have had to maintain its course while struggling through the assemblage of other small nebulous masses, severally moving in ways unlike its own. On the other hand, the hypothesis of an exploded planet is supported by every increase in the number of planetoids discovered; by the greater numbers of the smaller sizes; by the thicker clustering near the inferred place of the missing planet; by the occurrence of the greatest mean distances among the smallest members of the assemblage; by the occurrence of the greatest eccentricities in the orbits of these smallest members; and by the entanglement of all the orbits. Further support for the hypothesis is yielded by aerolites, so various in their kinds, but all suggestive of a planet's crust; by the streams of shooting stars having their radiant points variously placed in the heavens; and also by the solitary shooting stars visible to the naked eye, and the more numerous ones visible through telescopes. Once more, it harmonizes with the discovery of a family of comets, twelve out of thirteen of which have mean distances falling within the zone of the planetoids, have similarly associated periods, have all the same direct motions, and are connected with swarms of meteors and with meteoric streams. May we not, indeed, say, that if there once existed a planet between Mars and Jupiter which burst, the explosion must have produced just such clusters of bodies and classes of phenomena as we actually find?

And what is the objection? Merely that if such an explosion occurred it must have occurred many millions of years ago—an objection which is in fact no objection; for the supposition that the explosion occurred many millions of years ago is just as reasonable as the supposition that it occurred recently.

It is, indeed, further objected that some of the resulting fragments ought to have retrograde motions. It turns out on calculation, however, that this is not the case. Assuming as true the velocity which Lagrange estimated would have sufficed to give the four chief planetoids the positions they occupy, it results that such a velocity, given to the fragments which were propelled backwards by the explosion, would not have given them retrograde motions, but would simply have reduced their direct motions from something over 11 miles per second to about 6 miles per second. It is, however, manifest that this reduction of velocity would have necessitated the formation of highly-elliptic orbits—more elliptic than any of those at present known. This seems to me the most serious difficulty which has presented itself. Still, considering that there remain probably an immense number of planetoids to be discovered, it is quite possible that among these there may be some having orbits answering to the requirement.

Note V. Shortly before I commenced the revision of the foregoing essay, friends on two occasions named to me some remarkable photographs of nebulæ recently obtained by Mr. Isaac Roberts, and exhibited at the Royal Astronomical Society: saying that they presented appearances such as might have been sketched by Laplace in illustration of his hypothesis. Mr. Roberts has been kind enough to send me copies of the photographs in question and sundry others illustrative of stellar evolution. Those representing the Great Nebulæ in Andromeda and Canum Venaticorum as well as 81 Messier are at once impressive and instructive—illustrating as they do the genesis of nebulous rings round a central mass.

I may remark, however, that they seem to suggest the need for some modification of the current conception; since they make it tolerably clear that the process is a much less uniform one than is supposed. The usual idea is that a vast rotating nebulous spheroid arises before there are produced any of the planet-forming rings. But both of these photographs apparently imply that, in some cases at any rate, the portions of nebulous matter composing the rings take shape before they reach the central mass. It looks as though these partially-formed annuli must be prevented by their acquired motions from approaching even very near to the still-irregular body they surround.

Be this as it may, however, and be the dimensions of the incipient systems what they may (and it would seem to be a necessary implication that they are vastly larger than our Solar System), the process remains essentially the same. Practically demonstrated as this process now is, we may say that the doctrine of nebular genesis passes from the region of hypothesis into the region of established truth.