[CHAPTER IX.]

Page
[165]Inquiry into the Interior Construction of the Earth—continued
[166]The earth gasiform at one period. Density including the moon may have been 1/10,000th
  that of air. Must have been a hollow body. Proofs given
[169]Division of the mass of the earth alone into two parts
[171]Division of the two masses at 817 miles from surface
[172]Reasons why the earth cannot be solid to the centre
[172]Gasiform matter condensing in a cone leaves apex empty
[173]Proportions of the matter in a cone
[174]Calculations of the densities of the outer half of the hollow
  shell of the earth. Remarks upon the condensation
[175]Calculations of inner half of the hollow shell
[177]Remarks upon position of inner surface of the shell
[179]Calculations of the same

The Interior of the Earth and its Density—continued.

When, according to the nebular hypothesis, the ring for the formation of the earth and moon had been thrown off by the nebula, and had broken up and formed itself into one isolated mass—rotating or not on an axis, as the case may have been—it must have been in a gasiform state. What was its density, more or less, may be so far deduced from [Table III]., where it will be seen that when it had condensed to about one-half of its volume, it must have had a density of only 1/9000th part of our atmosphere, and in which each grain of matter would have for its habitat 16 cubic feet of space, or a cube of 2·52 feet to the side. So that, with an average distance from its neighbours of 2½ feet, a grain of matter could not be looked upon as wedged-in in any way, and would be free to move anywhere. Now, supposing this earth-moon nebula to have been in the form of even an almost shapeless mass, and that it was nearly homogeneous—as it could hardly be otherwise after the tumbling about it had in condensing from a flat ring—its molecules would attract each other in all directions, and as the mass—without having arrived perhaps at the stage of having any well defined centre—would have an exterior as well as an interior, the individual molecules at the exterior would draw those of the interior out towards them, just as much as those at the interior would attract those of the exterior in towards them; but as the number of those at the exterior would—owing to the much greater space there, being able to contain an immensely greater number—be almost infinitely greater than of those nearer to the central part, the latter would be more effectually attracted, or drawn, outwards than the former would be inwards, and there would be none left at the interior after condensation had fairly begun. The mass would speedily become a hollow body, the hollow part gradually increasing in diameter. But let us go deeper into the matter.

Let us suppose that the whole mass had assumed nearly the form of a sphere. We have already shown that, although the general force of attraction would cause all the component particles of the sphere to mutually draw each other in towards the centre, yet the more powerful tendency of the particles at the exterior—due to their greatly superior number—would at first be to draw the particles near the centre outwards towards them, and that there would consequently be a void at the centre, for a time at least. Of course it is to be understood that each part of the exterior surface would draw out to it the particles on its own side of the centre, just in the same manner as the four masses we placed at the centre were shown to be drawn out by those at London, Calcutta, and their antipodes. Now we must try to find out what would be the ultimate result of this action; whether it would be to form a sphere solid to the centre, or whether the void at first established there would be permanent.

In order to show how the heat of the sun is maintained by the condensation and contraction of that luminary, Lord Kelvin—in his lecture delivered at the Royal Institution, on Friday, January 21, 1887—described an ideal churn which he supposed to be placed in a pit excavated in the body of the sun, with the dimension of one metre square at the surface, and tapering inwards to nothing at the centre. In imitation of him, we shall suppose a similar pit of the same dimensions to be dug in the spherical mass, out of which we have supposed the earth to have been formed; only we shall call it a pyramid instead of a pit. This we shall suppose to be filled with cosmic matter, and try to determine what form it would assume were it condensed into solid matter, in conformity with the law of attraction. The apex of our imaginary pyramid would, mathematically speaking, have no dimension at all, but we shall assume that it had space enough to contain one molecule of the cosmic matter of which the sphere was formed. This being so arranged, we have to imagine how many similar molecules would be contained in one layer at the base of the pyramid at the surface of the sphere, and we may be sure that when brought under the influence of attraction, the great multitude of them would have far more power to draw away the solitary molecule from the apex, than the single one there would have to draw the whole of those in the layer at the base in to the centre of the sphere. A molecule of the size of a cubic millimetre would be an enormously large one, nevertheless one of that size placed at the apex of the pyramid would give us one million for the first layer at the base, and shows us what chance there would be of the solitary one maintaining its place at the apex. At the distance of one-twentieth of the radius of the sphere from the centre, the dimension of the base of the pyramid would be one-twentieth of a square metre, and the proportion of preponderance of a layer of molecules there would be as 25 to 1, so that the molecule at the centre would be drawn out almost to touch those of that layer; at one-tenth of the radius from the centre, the preponderance of a layer over the solitary central molecule would be as 10,000 to 1; and so on progressively to 1,000,000 to 1, as we have already said.

Following up this fact, if we divide the pyramid into any number of frusta, the action of attraction will be the same in each of them; the molecules in the larger end of each will have more power to draw outwards those of the small end, than they will have to draw inwards those of the larger end; and then the condensed frusta will act upon each other in the same manner as the molecules did, the greater mass of those at the larger end, or base, drawing down, or out—whichever way it may seem best to express it—a greater number of the frusta at the smaller end of the pyramid, until, in the whole of it, a point would be reached where the number of molecules in the various frusta drawn down from the apex would be equal to those drawn up from the base, leaving a part of the pyramid void at each end, because we are dealing with attraction, not gravitation, and there would be no falling to the base or apex, but concurrence to the point, just hinted at, where the outwards and inwards attractions of the masses would balance each other. This point of meeting of the two equal portions of cosmic matter may be called the plane of attraction in the pyramid. The whole pyramid would thus be reduced to the frustum of a pyramid, whose height would be as much more than double the distance from the plane of attraction to its base, as would be required to make the upper part above the plane of attraction equal in volume, or rather in number of molecules, to the lower part. It would be impossible for us to explain how, in a pyramid such as the one we have before us, the action of attraction could condense, and at the same time cram, the whole of the molecules contained in it into the apex end.

We must not, however, forget that there are two sides to a sphere, as well as to a question, and that we must place on the opposite side to the one we are dealing with, another equal pyramid with apex at the centre and base at the surface, at a place diametrically opposite to the first one, and that the tendency of the whole of this new pyramid would be to draw the whole of the first one in towards the centre of the sphere. But in the second, the law of attraction would have the same action as in the first; the molecules of the matter contained in it near the base would far exceed, in attractive force, those near the apex, and would draw them outwards till the whole were concentrated in a frustum of a pyramid, exactly the same as the one in the first pyramid. And while the whole masses of matter in the two pyramids were attracting each other at an average distance, say, for simplicity's sake, of one-half the diameter of the sphere, the molecules in each of them would be attracting each other from an average distance of one-quarter the diameter of the sphere; their action would consequently be four times more active, and they would concentrate into the frusta as we have shown, before the two pyramids had time to draw each other in to the centre. There would be then two frusta of pyramids attracting each other towards the centre with an empty space between them. Here then we have two elements of a hollow sphere, one on each side of the centre, and if we suppose the whole sphere to have been composed of the requisite number of similar pyramids, set in pairs diametrically opposite to each other, we see that the whole mass of the matter out of which the earth was formed must have—by the mutual attractions of its molecules—formed itself into a hollow sphere.