All that has been said must apply equally well whether we consider the earth to have been in a gasiform state, or when by condensation and consequent increase of temperature it had been brought into a molten liquid condition. For up to that time it must have been a hollow sphere, and we must either consider it to be so still, or conceive that the opposite sides have continued to draw each other inwards till the hollow was closed up; in which case, the greatest density would not be at the centre, but at a distance therefrom corresponding to what has been called the plane of attraction of the pyramid. That the opposite sides have not yet met will be abundantly demonstrated by facts that will meet us, if we try to find out what is the greatest density of the earth at the region of greatest mass or attraction, wherever that may be.
Seeing that the foregoing reasoning forces us to look upon the earth as a hollow sphere, or shell, in which the whole of the matter composing it is divided into two equal parts, attracted outwards and inwards by each other to a common plane, or region of meeting, we shall divide its whole volume into two equal parts radially, that is, one comprising a half from the surface inwards, and the other a half from the centre outwards--that is to say, each one containing one-half of the whole volume of the earth. Referring now to our calculations, Table IV., we find that the actual half volume of the earth is comprised in very nearly 817 miles from the surface, where the diameter is 6284 miles, because the total volume at 7918 miles in diameter is 259,923,849,377 cubic miles. This being the case, we cannot avoid coming to the conclusion, after what has just been demonstrated by the pyramids that if one-half of the whole volume is comprehended in that distance from the surface, so also must be one-half of the mass.
But for further substantiation of this conclusion let us return to the table of calculations. There we find that from the surface to the depth of 817 miles--where the diameter would be 6284 miles--which comprehends one-half of the volume--the mass at the density of water is shown to be only 518,596,945,467 miles instead of 735,584,493,738 cubic miles, which is the half of the whole mass of the earth reduced to the density of water. That is, the outer half of the volume gives only 70·5 per cent. of half the mass, while the inner half of the volume gives not only one-half of the mass but 29·5 per cent. more; or, to put it more clearly, the mass of the inner half-volume is 1·84 times, nearly twice as great, as the mass of the outer half-volume. On the other hand, we have to notice that the line of division of the mass into two halves falls at 1163·25 miles from the surface, where the diameter is 5591·5 miles; so that on the outer half of the earth, measured by mass, 64·74 per cent. of the whole volume of the earth contains only one-half of the mass, whereas on the inner portion, measured in the same way, 35·26 per cent. of the same whole contains the other half. All these results must be looked upon as unsatisfactory, or we must believe that two volumes of cosmic matter which at one time were not far from equal, had been so acted upon by their mutual attractions that the one has come to be not far from double the mass of the other; that the vastly greater amount of cosmic matter at the outer part of a nebula has only one-half of the attractive force of the vastly inferior quantity at the centre. This we cannot believe if the original cosmic, or nebulous, matter was homogeneous; and if it was not homogeneous we have, in order to bring about such result, to conceive that the earth was built up, like any other mound of matter, under the direction of some superintendent who pointed out where the heavier and where the lighter matter was to be placed.
