A good deal has been written about planets or other bodies existing between Mercury and the sun, especially about Vulcan whose existence seemed to be so certain, that his distance from the sun and period of revolution were calculated to be about 13,000,000 miles and 20 days respectively. Now, with what we have seen about the rate of acceleration of planets as their orbits approach the sun, we may endeavour to form some notion of where any within the orbit of Mercury may be found. If we take the same rate of acceleration we have found between Venus and Mercury—that is 2·5543, which may be looked upon as almost the general rate for all the planets—we find that there might be a planet revolving round the sun in 34·4436 days; but here we must stop, because, though we could make no objection to the existence of a planet with the period of revolution just shown, were we to take another equal step towards the centre of the nebula, the same acceleration of rotation would give us a planet, or ring for a planet, revolving round the sun in 13·4454 days; not much more than one-half the average of his rotation round his axis at the present day, which would knock on the head most completely the theory that each planet was detached from the nebula at the time that it was rotating with the velocity of the planet's orbit, or we should have to conclude that the nebula had passed, by a long way, its power to abandon matter through centrifugal force. No one could suppose that a ring for a planet could be formed within the body of the nebula and abandoned, or thrown out, afterwards, because centrifugal force could not throw out the ring and at the same time retain the surrounding matter.
Turning our thoughts now to the supposed planet Vulcan, which was calculated to revolve round the sun in about 20 days, we have either to conclude that it was formed in the body of the nebula and come to the same breakdown of the nebular hypothesis, or we have to acknowledge that the sun is now rotating much more slowly on its axis than the nebula did at the time the ring for Vulcan was abandoned.
If we now direct our attention to the densities of the several planets, we shall find some suggestive matter in their study. A general look shows us at once that there are four periods of rise and fall in their densities. There is one rise and fall (referring to our register) from Neptune to Uranus and on to Saturn; then another rise to Jupiter and fall to, we suppose, the asteroids, because we are told that the quantity of matter in the region where the asteroids travel is less than in any other zone of the solar system, and the general density must in consequence have been less there than anywhere else; still another rise from the Asteroids to the Earth, and fall to Venus; and then a final rise to Mercury accompanied, without doubt, by a fall after the planet was abandoned, because the centrifugal force of the rotating nebula must have been decreasing, at the least, preparatory to its ceasing to have the power to throw off more matter. The first rise and fall would seem to indicate that there had been a much closer mutual relation in the births of Neptune, Uranus and Saturn than is indicated in any way in the nebular hypothesis. We could imagine that at one time they formed one flat ring, which afterwards divided itself into three, following the same law as we see dividing the rings of Saturn at the present day. With respect to Jupiter, his enormous size is sufficient to entitle us to believe that his ring was separated from the nebula independently of any of the others, and to account for there having been the rise and fall in the density that we have noted between Saturn and the Asteroids. Then the rise and fall from Mars to Venus, or further on towards Mercury as it would be, may indicate one ring divided into three in the same manner as we have supposed for the three outer planets. And the final rise to Mercury and subsequent fall to the sun or to the solar nebula might be either due to one operation or to complication with other unknown bodies that may be travelling between Mercury and the sun.
In support of the foregoing ideas, we may also refer to our having said on a previous occasion, that the whole of the matter separated from the nebula in the form of thin hoop-shaped rings, would condense into one continuous sheet, perhaps even up to the time when centrifugal force could not throw off any more matter against the force of gravitation. In that case we can conceive that the radial attraction, outwards and inwards, of the particles of the matter forming the sheet would gradually establish lines of separation, dividing off the matter into distinctly separate rings, preparatory to their transformation into planets; but we cannot explain how these separate rings came to be more dense in one place than another. We must leave that for future discovery. Meanwhile the idea of one continuous sheet of matter extending from the sun out to Neptune, suggests the possibility of all the rings having been in existence as rings, more or less advanced in their evolution, at the same time; and if not so much as that, makes it more easy for us to see how the four inner planets, being made out of more condensed cosmic matter, and being of so much smaller volume, have arrived at a much more advanced stage of their being than the four outer ones. Going a little further, we can see how the cosmic matter of the rings condensing from both sides in the direction of their thickness, and falling in impeded, so to speak, the tendency to contract in length, or circularly, until they arrived at a certain stage of density, when they began to contract in their orbital direction, to break up into pieces, each one of which would form itself into a small, probably shapeless, nebula with a tendency to direct rotation, as explained and shown by M. Faye in "L'Origine du Monde," chapter xiii., page 267, entitled "Formation de l'Universe et du Monde Solaire"—an explanation which must have occurred to everyone who has taken the trouble to think seriously, of how nebulous spheres could be formed out of a flat nebulous ring endowed with a motion of revolution.
We have seen at [page 127] that when the nebula was condensed to a little over 4,000,000 miles in diameter, its average temperature might have been 2740°, provided no heat had been radiated into space. In like manner, we can see that the sun being now condensed to 1·413 times the density of water, or 1093 times the density of air, in other words, that number of atmospheres, its present average temperature might be about 300,000°—as each atmosphere corresponds to 274°—provided no radiation of heat into space had been going on. But this way of estimating could not in any way apply to the nebula after it had ceased to throw off planetary matter; because from that time, or at all events from the time when it came to be of a density equal to one atmosphere and temperature of 0°, or freezing point of water, that would be accumulated within it, owing to the difficulty of carrying to the surface, to be radiated into space, what was produced by condensation in the interior, as we have shown before. Both heat and pressure would increase from the surface towards the centre, the former rising, in spite of surface radiation, to something far beyond what we have stated above that it might be, aided by the increase of pressure which near the centre must be enormously greater than the average of 1093 atmospheres, seeing that the pressure at the surface of the sun is estimated to be not far from 28 atmospheres. The first cause of the increase of pressure would be the condensation produced by gravitation, which according to the areolar law would increase the rotary velocity of the nebula in proportion as the centre was approached; and as this would begin long before it had given up abandoning rings, or rather from the very beginning of its rotation; from that time, there would be different rates of rotation at different distances between the surface and the centre, which would cause friction among the particles of its matter, in other words a churning of the matter shut up in the interior of the nebula, and thus produce heat over and above that produced by the condensation of gravitation alone. If two particles of matter would produce a given quantity of heat, in falling from the surface of the nebula to any point nearer to the centre, they would surely produce more if they were rubbed against each other by churning action during their fall.
Reflecting on what we have written up till now, we see that the analysis of the nebular hypothesis we have made, which at first may have appeared to be unnecessary or even useless, has shown us and made us think over many details, of which we had only a vague notion previously. It has shown us that without condensation at or near the surface of the nebula—which we have pointed out must have been caused by its greatest mass being near that region, and which Laplace procured by endowing it with excessive heat—the various members of the solar system could not have been evolved from it in terms of the hypothesis. From it we have been able to learn, by means of the register of the acceleration of revolution from one planet to another, when, and for what reason, the nebula ceased to be able to throw off any planet nearer to the sun than the supposed Vulcan, or almost even so near. Finally, and not to go into greater detail, it has so far given us some ideas, that we had not before, of the internal structure of the sun, and has made us believe that a great deal may be learnt by attempting to find out what that structure really is. For this purpose, it appears to us that a careful examination into, and study of, the interior of the earth might be a great help, and to this we shall appeal, as we cannot think of any other process by which our object can be attained. This, therefore, we shall endeavour to do in the following chapters.