Thus we have arrived at two measures of force which would compress to zero the rocks that are known upon the earth. One where rocks are looked upon as in a molten, liquid state, and analogous to water, where the force is equal to that exerted by a column of the material 51 miles high; and the other where the column requires to be 447 miles high. In either case the same method of calculation will show that columns one-half of these heights, will compress the material into at least one-half of its volume--that is half-way between what it is at the surface and would be at the specified depths--and consequently into double its density. So we find in the one case that the density of the earth ought to be about 5·66 times that of water at a depth of 25-1/2 miles; and, in the other, at somewhere less than 225 miles deep. But, before proceeding to use and reason upon these depths, we must recall to mind that the calculations from which we have derived them, in the second case, have been made in violation of the theory that was adduced for the purpose, and that in consequence the latter depth must be excessive. For, were we to erect a structure of any kind, calculating the stresses it would have to bear, under the same violation of the theory, we should inevitably find that the structure would give way under the strains that would be brought upon it; that is the columns 25-1/2 and 225 miles high would compress the same kind of matter composing them into very far below one-half of its volume.
This premised, let us go back to our layers of 25 miles thick with their respective volumes. Nine of them counted from the diameter of 7900 miles inwards, will be equal to 225 miles and will bring us to 234 miles deep, which at the same time that it leaves us the same volume and mass that we have always retained for the first 9 miles in depth, will facilitate our calculations considerably without making any appreciable difference in them. We shall then have to find for the 9 layers 9 corresponding densities increasing from 3 to 5·66, and if we multiply these together respectively, and add the numbers of the volumes and masses of the outer 9 miles in depth, we shall get, at the diameter of 7450 miles, a simple volume of 43,418,587,327 cubic miles, and mass volume of 195,312,523,450 cubic miles. Deducting this latter sum from 735,584,493,738 cubic miles, which represents the half mass of the earth at the density of water, we have a remainder of 540,271,970,288 cubic miles. On the other hand we find that the simple volume of the earth comprehended between the diameters of 7450 and 6284·5 miles is 86,543,337,361 cubic miles; so that if we divide 540,272,970,288 by this sum, we find that a density of 6·24 times that of water over the whole intervening space--between the two diameters just cited--will make up the whole half-volume, at the density of water, from the surface of the earth to the diameter of 6284·5 miles. Then, for the inner half-mass:--If we multiply the simple volume between the diameters of 6284·5 miles, and 3150 miles, which is 113,596,348,539 cubic miles by 6·24, we get 708,841,214,870 cubic miles at density of water; and if from there we run down the density to 3 at 2700 miles in diameter we get 27,400,652,354 cubic miles, which added to the last mentioned amount gives 736,241,867,224 cubic miles, somewhat in excess of the inner half-mass of the earth at density of water. Thus we see that in order that the average density of the earth of 5·66 may be made up, there is no necessity for appealing to matter of any kind with a density of more than 6·24 times of water. And there is still something else of importance to be taken into consideration before we can bind ourselves to a density even so great as that.