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
