The sorting-out theory is one of these notions that occur to humanity and are accepted at once, without consideration of what the consequences may be. If it is made to account for the four inferior planets being so much more dense, and of coming so much sooner to maturity—so to speak—than the four superior ones, it is hard to understand why the sun up to the present day almost ranks in low density with the large planets. If that theory holds good, it would be most natural to suppose that the mean density of the sun should be very much greater than that of Mercury. But it appears to be only carried as far as it suits the theorist, and to be there dropped, or rather ignored.
Having been defeated in our attempt to build up or construct an earth solid to the centre by appealing to the metals to make up the weight or density required for the foundation layers, and that even to somewhere about three-fourths of the diameter of the whole structure, we are forced to fall back upon our known rocks, earths, etc., in order to compound out of them the dense material we require, and of course we feel that we have in hand a more hopeless task than we had with the metals. How are we to compress the everlasting hills into one-fourth or one-fifth of their volume? Some solution of the difficulty, or mystery, must be found somewhere; but at the same time the mountains of gold, silver, and less precious metals required have shown us how absurd, even laughable, it is to appeal to them.
Let us suppose that we have a cubic foot of matter of any kind of 13¾ times the density of water, and that we place it in one of the scales of a balance at the centre of the earth; we shall find that it does not depress the scale one hair-breadth, for the very good reason that it has nowhere to depress it to; it would be already at what may be called the end of gravitation or tendency to fall lower. As it could not get any lower it would have a tendency to fly off anywhere—provided it was free to do so—and drag the scale and balance along with it, in obedience to its own attractive power and the attraction of all the matter of the earth surrounding it, except that the attraction might be so equally distributed all around it that it would not move in any direction. It would, however, be in a state of very unstable equilibrium, and if by some means the attraction were increased a little on one side more than the others, and it were at liberty to do so, it would abandon the centre and fly off in that direction never to return. Now, this being the case, we are forced to consider how a cubic foot of matter, such as the one we are dealing with, could ever have found its way to the centre of the earth; and the law of gravitation, or rather of attraction, does not in any way help us out of the difficulty. We know that we put our cubic foot of extremely dense matter there for an experiment, but we do not know of any process of nature that could place there any equal mass of matter of that density.
Gravitation and attraction are generally used as synonymous terms, more especially gravitation—somewhat after the manner of the likeness between the two negroes, Cæsar and Pompey, the latter being most especial in the likeness—but there is a very appreciable distinction between them, if we want to use each of them in its proper and strict sense. Gravitation implies the conception of a weight of some kind falling to a fixed centre, while attraction gives the idea of two weights, or masses, drawing each other to a common centre, which when properly looked at is a different thing; because the centre may be anywhere between the two, depending entirely on the difference, if any, in the weights of the masses. The confounding of the two, or rather the almost universal adoption of the less correct term, name, expression—whichever it may be called—has been the cause of wrong conceptions being formed of the construction of almost all—probably all—celestial bodies, and of that most absurd expression, attraction of gravitation, used by all our most eminent physicists. The gravitation of attraction might be excused, but putting cause for effect is hardly scientific. A name is nothing as long as what is meant by it is understood and taken into consideration, but that is not always the case, as we shall proceed to show.
The term gravitation may be applied with almost, but not absolutely, perfect strictness to the attraction between the sun and the planets, because the common centres of their attractions and the centre of the sun are so near each other that they may be looked upon as one and the same thing, or point; but it is not so with the attractions of the planets for each other where there is no common fixed centre, or if there is something approaching to it in a far off way, it is constantly varying, so that the term gravitation cannot be strictly applied to them, nor even to the sun, to speak truly. Planets sometimes gravitate away from each other and from the sun, otherwise Adams and Leverrier could not have discovered Neptune from the perturbations of Uranus. Neither can it be properly applied to the different masses of matter in the sun or in the earth—although it was no doubt notions connected with the earth that gave rise to the term, from all ponderable matter falling upon it—because per se they could have no tendency to fall to the centre, for at the centre there is no sufficient attractive force to draw them towards it. Gravitation was a known term long before the days of Newton, who had the glory of enlightening the world by showing that attraction was the cause of it; and, perhaps unfortunately, the name was continued to represent what it in reality does not.
Let us suppose that we have an empty earth to fill up; if we place one mass of matter at London and another at Calcutta, they could have no tendency of themselves to fall to the centre, but if left alone would go for each other in a straight line and meet half-way between the two, provided they were equal in mass, and attraction, not gravitation, would be the proper term to apply to them. But supposing that two equal masses were placed at their antipodes and the four were left to themselves, they would gravitate towards and meet at the centre in the usual meaning of the word, but the force that drew them there would be really that of attraction. We could, however, place four similar and equal masses at the centre, and give the outer ones just and good reason for gravitating or falling down to it, because those at the centre being equally attracted in the four directions might remain stationary there, but would be in a state of unstable equilibrium. We may now suppose that when the masses had just left London and Calcutta to meet the others, a goodly number of other equal masses were added to those at these two places and began to attract the two bound towards the centre, they would prevent the two from proceeding, or at least retard them on their journey inwards. Moreover, the larger numbers at these two places would attract the four masses at the centre with more force than would the two at the antipodes, and would draw the whole of the four away from the centre and outwards towards themselves; but we might also suppose that at the same moment an equal number of equal masses were added to those at the antipodes, which would again equalize the attractions at the four outer posts, and things would continue as they were at the first; with this difference, that the four at the centre would not be able to balance the attractions at the four outer posts, and the consequence would be—seeing that the forces at the four outer stations were equal to each other, and far superior to the four at the centre—that each one of the four at the centre would be drawn away from it towards one of the outer stations—provided the law of attraction acted impartially—and so the centre would be left without any of the masses at it, that is empty. No doubt when the four outgoing masses met the larger ones coming in, they would all then move towards the centre; but the four places where they met would be immensely nearer the places occupied at first by the outer masses than half-way between them and the centre—proportioned, in exact conformance with the law of attraction, to the excess of the numbers of the masses at the outer stations over those at the centre—and they would be moving, all of them together, to a remote and void space. We may now increase the four outer stations to thousands or millions, with the security that the mode of proceeding would be the same with the whole of them; that is, that the first tendency of the masses at each one of the millions of stations would be to draw away the filling we were pouring into the hollow earth—provided we did it equally and impartially all over the hollow—from the centre, and to leave a void there.
We are accustomed to look upon the earth as a solid body in which there are no acting and counteracting forces, no movements of matter from one place to another, similar to those we have been calling into play, and as if there was only one force acting upon its whole mass and driving it to the centre; we have, in our ideas, got the whole mass so compressed and wedged in that it cannot move, and never has been able to move in any direction except towards the centre, and this is no doubt the case at the present day. We never stop to think with sufficient care how this compression and wedging-in were brought about, and we only accept what we have been accustomed to believe to be facts, and trouble ourselves no more about it; but there must have been a time, according to any cosmogony we may choose to adopt—even to the vague one that the solar system was somehow made out of a nebula of some kind—when the matter of the earth was neither compressed nor wedged in, nor prevented from moving in any direction towards which it was most powerfully attracted—before superincumbent matter came, so to speak, to have any wedging-in force—and we must go back to that period and study it deeply, if we want to acquire an accurate knowledge of the construction of the earth.
[TABLE IV].— Calculations of the Volumes and Densities
of the Earth between the Diameter specified,
reduced to the Density of Water.