It is agreed by all, I think, that tidal action has been responsible for at least a part of the separation of the Earth and Moon, for at least a part of the gradual separation of the components of double stars, and for at least a part of the eccentricity of their orbits. See's investigations of 25 years ago led him to the conclusion that this force is sufficient to account for all the observed separation of the components of double stars, and for the well-known high eccentricities of their orbits. In recent years Moulton and Russell have seriously questioned the sufficiency of this force to account for the major part of the separation and eccentricity in the double star systems. I think, however, that if the tidal force is not competent to account for the observed facts as described, some other separating force or forces must be found to supply the deficiency.
THE FORMATION OF THE EARTH
Does the condition of the Earth's interior give evidence on the question of its origin? There are certain important facts which bear upon the problem.
1. The evidence supplied by the volcanoes, by the hot springs, and by the rise in temperature as we go down in all deep mines, is unmistakably to the effect that there is an immense quantity of heat in the Earth's interior. Near the surface the temperature increases at the average of 1 degrees Centigrade for every 30 meters of depth. If this rate were maintained we should at 60 km. in depth arrive at a temperature high enough to melt platinum, the most refractory of the known metals. What the law of temperature-increase at great depths is we do not know, but the temperature of the Earth's deep interior must be very high.
2. The pressures in the Earth increase from zero at the surface to the order of 3,000,000 atmospheric pressures at the center. We know that rock structure, or iron or other metals, can be slightly compressed by pressure, but the experiments at very high pressures, notably those conducted by Bridgman, give no indications that matter under such pressures breaks down and obeys different or unknown laws. It should be said, however, that laboratory pressure-effects alone are not a safe guide as to conditions within the Earth, where high pressures are accompanied by high temperature. Unfortunately it has not been found possible to combine the high-temperature factor with the high-pressure factor in the laboratory experiments. It is well known that the melting points of metals, including rocks, increase with increase of pressure; and although the temperatures in the Earth's interior are very high, it is easy to conceive that the materials of the Earth's interior are nevertheless in the solid state, or that they act like solids, because of the high pressures to which they are subjected.
3. The specific gravity of the entire Earth is 5.5 on the scale of water as one, whereas the density of the stratified rocks averages only 2.75; that is, the stratified rocks have but one half the density of the Earth as a whole. The basaltic rocks underlying the stratified attain occasionally the density 3.1, and perhaps a little higher. It follows absolutely that the density of the materials of the Earth's interior must be considerably in excess of 5.5. If the interior is composed chiefly of substances which are plentiful in the Earth's surface strata, our choice of materials which principally compose the interior is reduced to a few elements, notably the denser ones.
4. The observed phenomena of terrestrial precession can not be explained on the basis of an Earth with a thin solid surface shell and a liquid interior, for the attractions of the Moon and Sun upon the Earth's equatorial protuberance would cause the surface shell to shift over the fluid interior, instead of swinging the entire Earth.
5. If the Earth consisted of a thin solid shell upon a liquid interior there would be tides in the liquid interior, the crust would yield to these tides almost as if it were composed of rubber, and the ocean tides would be only an insignificant amount larger than the land tides. As a result we should not see the ocean tides; their visibility depends upon the contrast between the ocean tides and the land tides. If the Earth were absolutely unyielding from surface to center the ocean tides would be relatively 50 per cent. higher than we now see them. The conclusion from these facts is that the Earth yields to the tidal forces a little less than if it were a solid ball of steel, supposing that the well-known rigidity and density existed from surface to center of the ball. This result is established by Darwin's and Schweydar's studies of ocean tides, by studies of the tides in the Earth's surface strata made by Hecker, Paschwitz and others, and by Michelson's recent extremely accurate comparison of land and water tides. Michelson's results establish further that the Earth is highly elastic: though distortion is resisted, there is yielding, but the original form is recovered quickly, almost as quickly as a perfectly elastic body would recover.
6. Some 25 years ago it was discovered by Kustner that the latitudes of points on the Earth's surface are changing slowly. Chandler proved that these variations pass through their principal cycle in a period of 427 days. The entire Earth oscillates slightly in this period. The earlier researches of Euler had shown that the Earth would have a natural oscillation period of 305 days provided it were an absolutely rigid body. Newcomb showed that the period of oscillation would be 441 days if the Earth had the rigidity of steel. As the observed oscillation requires 427 days, Newcomb concluded that the Earth is slightly more rigid than steel.
7. The first waves from a very distant earthquake come to us directly through the Earth. The observed speeds of transmission are the greater, in general, the more nearly the earthquake origin is exactly on the opposite side of the Earth from the observer; that is, the speeds of transmission are greater the nearer the center of the Earth the waves pass. Now, we know that the speeds are functions of the rigidity and density of the materials traversed. The observed speeds require for their explanation, so far as we can now see, that the rigidity of the Earth's central volume be much greater than that of steel, and the rigidity of the Earth's outer strata considerably less than that of steel. Wiechert has shown that a core of radius 4,900 km. whose rigidity is somewhat greater than that of steel and whose average density is 8.3, overlaid by an outer stony shell of thickness 1,500 km. and average density 3.2, would satisfy the observed facts as to the average density of the Earth, as to the speeds of earthquake waves, as to the flattening of the Earth,—assuming the concentric strata to be homogeneous in themselves,—and as to the relative strengths of gravity at the Poles and at the Equator. The dividing line, 1,500 km. below the surface—1,600 km. would be just one fourth of the way from the surface to the center—places a little over half the volume in the outer shell and a little less than half in the core. Wiechert did not mean that there must be a sudden change of density at the depth of 1,500 km., with uniform density 8.3 below that surface and uniform density 3.2 above that surface. The change of density is probably fairly continuous. It was necessary in such a preliminary investigation to simplify the assumptions. The observational data are not yet sufficiently accurate to let us say what the law of increase in density and rigidity is as we pass from the surface to the center.