Bearing in mind all these ideas we have cited, and working with the data we have considered as actual facts, we may now proceed with our inquiry.
The belief that the earth is a mass of matter increasing, whether liquid or solid, or part of both, in density from the surface to the centre is so general that we shall look at it in that light first, and endeavour to find out what must be its density at any place between its surface and its centre.
Astronomers and geologists concur in telling us that the mean density of the earth is very near to 5·66 times that of water: knowledge that has been acquired by measuring the attraction of high and precipitous mountains for plummets; by the attraction of masses of metals for each other, measured by the torsion balance; and by the acceleration or retardation of the vibrations of pendulums, as observed in the depths of mines and on the tops of mountains, compared with each other. They also tell us that the average density of the matter and rocks of which the crust is composed is about 2-1/2 times that of water; and then, in a general way, that the average density of the crust, taking into consideration that so much of its surface is covered by the sea, is not much more than 1-1/2 times that of water. This estimate is manifestly incorrect, for it implies that the whole of the crust of twenty-five to thirty miles is affected by the presence of water, when we know that the depth of the sea at any place does not exceed one-fourth of that thickness. Therefore, we shall endeavour to obtain some more accurate computation, as it is the only datum we have to go upon, and has a greater effect upon the result, and upon all things relating to the interior, than might at first sight be supposed.
We find in "Nature," of January 19, 1888, that Mr. John Murray has calculated that if the whole solid land of the earth were reduced to one level under the sea, its surface would be covered by an ocean with a uniform depth of about 2 miles. Here we have a very good beginning for our calculations.
Without taking into consideration the increase of density in water at 2 miles deep, at that depth we may suppose we have come to solid matter, the specific gravity of which could not be less than twice that of water, on account of the pressure of that depth of water upon it. If we now go down 2-1/2 miles further we shall have the solid matter subjected to a pressure proportioned to that depth; and if we take its weight per cubic foot at an average between granite (at 163 lb.) and earth (at 77 lb.), or 120 lb., the pressure at 2-1/2 miles deep of solid matter alone will be about 700 tons per square foot, or just about the crushing strain of our strongest granites, and therefore, the density of the matter under it must be equal to that of granite, or 2·5 times that of water. We do not add the pressure of the water, at present, because that may be looked upon by some people as of the same nature as of the atmosphere upon a human body, which neither increases the pressure upon it nor adds to its weight; but we see that at that depth the solid matter must have a density equal to the average between water on its surface and 2·5--that of granite; and if we choose to take the average between 2 miles of water and 2-1/2 miles of solid matter, we shall have 1·82 as the average density of the outer 4-1/2 miles in thickness of the crust of the earth. For our purposes, however, and for obvious reasons, we shall consider the average density of the 2-1/2 miles alone of solid matter to be 2·25 times that of water.