Many years afterwards, the supposed liquid state of the interior of the earth was taken advantage of, to frame a theory that earthquakes and eruptions of volcanoes are caused by the attraction of the moon on the liquid interior producing tides, in the same manner as it produces tides in the sea, which in their turn act upon the crust, cracking and rending it to produce the one, and forcing the liquid matter out through the rents, or up through the vents of volcanoes to produce the other, in some way that it is more easy to imagine than to explain mechanically. Also when the effect of the attraction of the moon on the liquid internal matter came to be duly considered, it was concluded that the crust, with only 25 to 30 miles in thickness, could not be rigid enough to resist the pressure brought upon it by the movements of the interior tides; and it began to be thought that, owing to the pressure of the superincumbent strata, the density of the matter at that depth might be so great that it would become solid at a much higher temperature than it does at the surface; and some physicists went the length of supposing that the earth has a solid crust and solid nucleus with liquid matter between them. On the other hand Sir William Thomson, Lord Kelvin, looking more as it would appear to the effects of the moon's attraction on the crust than on the liquid interior, concluded that the earth must be a solid globe, contracting through gravitation in the interior, and cooling at the surface, because a crust so thin as 25 to 30 miles, or even 100 miles, would be continually rent and broken up by the tidal action of the moon; but Professor Clerk Maxwell and others have thought that the elasticity of the crust would be great enough to admit of its accommodating itself to all the changes of form that would be caused by the action of those tides. Notwithstanding that they agree with Lord Kelvin in the main, in his objections to the existence of a liquid interior, many scientific men suppose that, through the effects of pressure, the liquid interior of the earth may have been changed into a viscous state, as it went on contracting through gravitation, which would, according to the degree of viscosity, either annul, or almost annul, the tidal action on it of the moon. To which it may be added that that action would not raise such high waves in even perfectly liquid molten matter as it would upon water; because it would be easier for the moon to lift a cubic mile of water three or four feet high, than to lift a cubic mile of melted rock or metal to the same height.
Other parties look upon the earth as mainly solid to the centre, but with large reservoirs of liquid matter in various parts of it near the surface, which furnish all the material for volcanic eruptions and are the causes of earthquakes. There are others also who, believing the earth to be altogether solid, consider that when any part of the intensely heated and dense interior is relieved suddenly from pressure, as, for example, by the convulsive action of an earthquake, it will immediately assume the liquid state and become material for volcanic eruptions; a theory which they consider to be substantiated by the fact of these two phenomena generally accompanying each other. And Mr. Mallet seems to have demonstrated that earthquake-shocks proceed from centres not far from the surface, which would seem to point out that if a liquid interior did exist at 25 to 30 miles from the surface, it could have no part in causing earthquakes. There are others still who consider earthquakes and volcanic eruptions to be caused by water penetrating deeply into the interior, but it is difficult to understand how water could penetrate into the interior to a greater depth than where it would be converted into steam, that is to a greater depth than from three to four miles.
Many other notions about the interior state and conditions of the earth have been formed, more or less entertainable, more or less fanciful, to provide liquid matter for volcanic eruptions. One of these, referred to in "Nature" of December 12, 1889, takes for granted "that granite has consolidated from a state of igneo-aqueous fusion, and that the liquid magma from which all granitic intrusions have proceeded contains water-substance," and proceeds, "It is, therefore, only a further step to assume that this water-substance is an essential constituent of the liquid substratum (assumed by the author), and to suppose that it has been there since the consolidation of the earth." This mixture of water, fire, and molten granite is one that does not agree with what we have been taught of the nature of any of the three components, and we cannot accept it. Why we refer to it more particularly than to the other ideas we have cited, is because it so far comprehends some of them, and that we shall have to return to it hereafter, when we think it will be seen that it has not been properly thought out.
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 2½ 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 1½ 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 2½ 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 2½ 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 2½ miles of solid matter, we shall have 1·82 as the average density of the outer 4½ 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 2½ miles alone of solid matter to be 2·25 times that of water.
We shall now go down to 9 miles deep, because the diameter of 7918 miles we have adopted for the earth will there be reduced to 7900 miles, which will be convenient for our further operations. At that depth we shall have a superincumbent pressure at the very least as follows:—