Illustrations of the Huttonian Theory of the Earth

by John Playfair

It is then clear, that every particle taken away by attrition from the parts above the level of the sea, and deposited under the surface of it, makes the general figure more compact, bringing the remoter parts nearer to the centre of gravity of the whole; so that, in time, if the body is homogeneous, all the points of the surface will become equally distant from that centre. Thus the actual figure changes continually, and approaches nearer to the statical.

While this change is going forward in the actual figure, there is another produced on the statical, that tends very much to accelerate the final coincidence, of the two.

The effect of the inequalities of the land, that rise above the horizontal surface, is, by their attraction, to render the parts of that surface immediately under them, more convex, cæteris paribus, than the rest. Again, where there are parts of extraordinary depth in the sea, that is, where the solid and denser parts are far removed from the surface of the ocean, the curvature of the superficies of the sea is thereby diminished, and that superficies is rendered less convex than it would be if the sea were shallower. These propositions are both capable of strict mathematical demonstration. Hence the taking away of any particle of matter from the top of a mountain tends to diminish the curvature of the horizontal surface under the mountain, where it is greatest; and the deposition of the same particle at the bottom of the sea, tends to increase the curvature of this superficies where it is least. The general tendency, therefore, being to increase the curvature where it is least, and to diminish it where it is greatest, must be to bring about an uniform curvature throughout, that is, a spherical figure. Thus, by the waste and subsequent stratification of the land, the direction of gravity is continually altered; it is more and more concentrated, and the figure brought nearer to that which a fluid would assume.

439. If now we suppose the body to revolve on its axis, all other things remaining as before, the surface bounding the sea will become different from what it was in the former case, and will be more swelled out toward the middle or equatorial regions. The land above the level of the sea will still, as before, be worn down and deposited in the bottom of the sea, so as to form strata nearly parallel to its surface: the tendency, therefore, is to render the real figure of the planet nearer to the statical. At the same time the statical figure is changed, as explained above; so that the two figures mutually approach, and the limit, or ultimate figure to which they tend, is one over which the ocean might be diffused every where to the same depth, for then the causes of change would entirely cease. But this figure is no other than the spheroid of equilibrium, which, therefore, is the effect which the waste and reconsolidation of the land would necessarily produce, if the process were continued indefinitely, without interruption. In this, as in many other instances, when a body is subject to the action of causes by which its form is gradually changed, the figure best adapted to resist those changes, is the figure which the changes themselves ultimately produce.

Also, whatever be the irregularities of density, the tendency to a change of figure will not cease till the body is moulded into that particular spheroid which admits of being covered with water every where to the same depth.[232] Thus it appears, that a solid of an irregular figure, and of irregular density, provided it be in part covered with water; and be at the same time subject to waste above the surface of the sea, and reconsolidation under it, has a tendency to acquire, in time, the same figure that it would have acquired had it been entirely fluid.

[232] In the same manner as a transition is thus made from an irregular figure to a spheroid of equilibrium, so, if the actual figure were at first more simple than the spheroid, it would still be changed into this last by degrees.

Let us conceive, for instance, that the earth is at rest, and is a perfect sphere of solid matter, surrounded by an ocean every where of equal depth, for example, of one mile. Then, if a rotatory motion be communicated to it, so that it shall revolve on its axis in twenty-four hours, in consequence of the centrifugal force, the water circumfused about the sphere will immediately rise up under the equator, and will become part of a spheroidal surface, (not elliptical, but nearly so,) the equatorial diameter of which is greater than the polar axis, in the ratio of 588 to 577 By this means the water will be accumulated at the equator to the depth of nearly 2.5 miles, and form a zone surrounding the earth, and extending about 37° on each side of the equator. The remainder of the surface will be left dry, forming two vast circumpolar continents, that reach 53° on every side of the poles, and that are elevated in the middle more than four miles above the level of the sea.

Such would be the state of our globe, on the hypothesis above laid down; and, if there were no waste or destruction of the land, this order of things would be permanent, and neither the solid nor fluid part of the mass could ever acquire any other figure than that which has been described. But, if the same laws be supposed to regulate the action of the atmosphere in those circumstances, that do actually regulate it according to the present constitution of the globe, the vapours raised up from the surface of the sea, would be carried by the winds over the land, where they would be condensed and precipitated in rain. Thus, all the agents of destruction would be let loose on the two great circumpolar continents; rivers would be formed; the land would become deeply intersected by ravines; those ravines would gradually open into wide valleys; the masses of greatest resistance would be shaped into hills and mountains: and from a superficies originally smooth and uniform, the same inequalities would be produced which at present diversify the surface of the earth.

While the parts of the sphere without the spheroid are thus continually diminished, the loose earth and sand washed down from them, will be deposited at the bottom of the sea, and will form strata parallel to the surface of the superincumbent water. The actual and statical figure are thus brought nearer one another; and, at the same time the statical is changed, on the principle already explained, (the change in the direction of gravity,) and is made continually to approximate to a state, which when it has attained, no farther change can take place, viz. an oblate elliptic spheroid, of which the surface is perpendicular to the direction of gravity, having the equatorial diameter to the polar axis in the ratio of 230 to 229.

440. In the preceding reasonings, we have supposed the process of decay and subsequent stratification to be carried on without interruption, till the whole of the land is covered by the sea. This supposition is useful for explaining the nature of the forces which have determined the figure of the earth; but there is no reason to think that it has ever been realized in its full extent, the elevation of strata from the bottom of the sea interrupting the progress, and producing new land in one place, as the old decays in another. The very same land also, which is wasted at its surface, may perhaps be lifted up by the forces that are placed under it; or it may be let down, undergoing alterations of its level, from causes that we do not perceive, but of which the action is undoubted, ([§ 388.]) But notwithstanding these interruptions, the general tendency to produce in the earth a spheroidal figure may remain, and more may be done by every revolution, to bring about the attainment of that figure than to cause a deviation from it. This figure, therefore, though never likely to be perfectly acquired, will be the limiting or asymptotic figure, if it may be so called, to which the earth will continually approach.