Illustrations of the Huttonian Theory of the Earth

by John Playfair

Note xxv. § 130.

Figure of the Earth.

429. That the earth is a spheroidal body, compressed at the poles, or elevated at the equator, is a fact established by many accurate experiments; and though these experiments do not exactly coincide, as to the degree of oblateness which they give to that spheroid, they agree sufficiently to put it beyond all dispute, that the earth, though solid, has nearly the same figure which it would assume if fluid, in consequence of its rotation on its axis.

Now, it is not at all obvious, to what physical cause this phenomenon is to be ascribed. The earth, as it exists at present, has none of the conditions that render the assumption of the figure of equilibrium in any way necessary to it. Constituted as it is, its parts cohere with forces incomparably too great to obey the laws of statical pressure, or to assume any one figure rather than another, on account of the centrifugal tendency which results from its revolution on its axis. There is no necessity that its superficies should be every where level, or perpendicular to the direction of gravity, nor that every two columns, standing on the same base, any where within it, and reaching from thence to any two points of the surface, should be of such weights as precisely to balance one another. Neither of these, indeed, is at all conformable to fact. They are, however, the very suppositions on which the determination of the spheroid of equilibrium is founded; and as they certainly do in no degree belong to the earth, it seems strange that the result deduced from them should be in any way applicable to it. This coincidence remains, therefore, to be explained; and it must greatly enhance the merit of any geological system, if it can connect this great and enigmatical phenomenon with the other facts in the natural history of the earth.

430. To establish such a connection, has, accordingly, been a favourite object with geologists, whether they have embraced the Neptunian or Volcanic theory: both have thought that they were entitled to suppose the primeval fluidity of the globe, the one by water, and the other by fire; and in whatsoever way that fluidity was produced, the result of it could be no other than the spheroidal figure of the whole mass, agreeably to the laws of hydrostatics. If in this fluid state the earth was homogeneous, the spheroid would be accurately elliptical, and the compression at the poles would be 1/230 of the radius of the equator; if the fluid was denser toward the centre, the flattening would be less: and in either case, the body, as it acquired solidity, may be supposed to have retained its spheroidal figure with little variation. But though the fluidity of the earth will account for the phenomenon of its oblate figure, it may reasonably be questioned, whether this fluidity can be admitted, in consistency with other appearances. According to what is established above, none of the appearances in the mineral kingdom indicate more than a partial fluidity in any former condition of the earth. The present strata, made up as they are of the ruins of former strata, though softened by heat, have not been rendered fluid by it, and have even possessed their softness in parts, and in succession, not altogether, nor at the same time.

The unstratified, and more crystallized substances, were cast in the bosom of others, which were solid at the time when they were fluid. In all this, therefore, there is no indication of a fluidity prevailing through the whole mass, or even over the whole surface of the earth, and therefore nothing that can explain the spheroidal figure which it has acquired. The supposition, then, of the entire body of the earth, or even of its external crust, having been fluid, though it might account for the compression at the poles, does not connect that fact with the other facts in the natural history of the globe, and fails, therefore, in the point most essential to a theory. It is liable, also, to other objections, whether it be conceived to have proceeded from fire or from water; whether it has happened on the principles of Buffon or of Werner.

431. First, let us suppose that the fluidity of the earth, or of the external crust of it, at least to a certain depth, proceeded from a solution of the whole in the waters of the ocean; and, waving all the objections that have been stated to this hypothesis, on account of the absolute insolubility of many mineral substances in water, let us suppose them all soluble in a certain degree, and let us compute the quantity of the menstruum, which, on the suppositions most favourable to the system, must have been required to this great geologico-chemical operation.

The siliceous earth, though not soluble in water per se, yet, after being dissolved in that fluid by means of an alkali, was found by Dr Black, in his analysis of the Geyser water, to remain suspended in a quantity of water, between 500 and 1000 times its own weight. This is one of the facts most favourable to the Neptunian theory; and that every advantage may be given to that theory, we shall take the least of the numbers just mentioned, and suppose that siliceous earth may be dissolved or suspended in 500 times its weight of water.

Taking this for the extreme degree of insolubility of mineral substances, (though there are many of which the insolubility is absolute, or, to speak in the language of calculation, infinitely great,) we may suppose the insolubility of all the rest, or the quantities of water in which they are dissolved, to be ranged in a descending scale from 500 to 0, the extreme degree of deliquescence. Then, taking the arithmetical mean between these extremes, it will give us 250, as the proportion of water in which mineral substances may at an average be dissolved. But this average is much less than the truth; for the quantity of siliceous earth is great in comparison of any of the rest, and the mineral substances that are extremely soluble in water are but in a small quantity; therefore, when we suppose mineral bodies, at a medium, to be soluble in 250 times their own weight of water, we make a supposition extremely favourable to the Neptunian system.

432. This is the proportion between the weight of the solvent, and of the substances held in solution: to have the proportion of their bulks, we may suppose the specific gravity of mineral bodies in general to be to that of water as 5 to 2, and then we have the ratio of bulks, that of 250 × 5 to 2 × 1, or of 625 to 1. It follows, then, that minerals in general cannot be supposed soluble in less than 625 times their bulk of water.

433. Again, it must be allowed to the Neptunists, that the fluidity of the whole earth is not necessary to account for its assuming the spheroidal figure. It is sufficient if the whole of that crust or shell of matter was fluid, which is contained between the actual surface of the terrestrial spheroid, and the surface of the sphere inscribed within it; that is, of the sphere which has for its diameter the polar axis of the earth. The whole of the minerals which compose this shell, must at least have been dissolved in water, and have formed the chaotic mass of Mr Kirwan. The volume of the water required for this was not less than 625 times the bulk of the spheroidal shell that has just been mentioned.

But, assuming the difference between the polar axis and the equatorial diameter to be 1/300 of the latter, which is the supposition most agreeable to the phenomena, it is easy to show that the magnitude of the above spheroidal shell, or the difference between the solid content of the earth, and the sphere inscribed in it, is greater than 1/151 and less than 1/150 of the whole earth; so that the earth is less than 151 times the spheroidal shell.

The volume of the water, therefore, necessary to hold in solution the materials of this shell, is to the volume of the whole earth as 625 to 151, or in a greater ratio than that of four to one: and such, therefore, at the very least, is the quantity of water which Mr Kirwan supposes, after it ceased to act in its chemical capacity, to have retired into caverns in the interior of the earth. Thus the Neptunists, in their account of the spheroidal figure of the earth, are reduced to a cruel dilemma, and are forced to choose between a physical and a mathematical impossibility.

If we would inquire whether the opinion of the igneous origin of minerals, as commonly received by the Vulcanists, is capable of affording a better solution of this difficulty, the theory of M. de Buffon is the first that presents itself.

434. That philosopher considers the existence of the spheroidal figure as a proof that the whole of the earth must have been originally fluid; and as the fluidity of the whole can only be ascribed to fusion, he has supposed that the earth was originally a mass of melted matter struck off from the sun by the collision of a comet; and that this mass, when made to revolve on its axis, put on a spheroidal figure, which it has retained, though now cooled down to congelation.

This system need not be considered in detail; the foundation of it is laid in such defiance of the principles of geometry and mechanics, that the architect, notwithstanding all the fertility of his invention, and all the resources of his genius, was never able to give any solidity to the structure.

But it will be said, that we may take a part of the system, without venturing on the whole, and may suppose that the earth, or at least the external crust of it, has been fluid by fire, though we do not inquire into the cause of this fire, or into the manner in which it was produced.

It is indeed true, that, when this is done, we have not the same sort of absurdity to encounter that we met with in the Neptunian system, and that the Volcanic theory does not, like it, come into direct collision with an axiom of geometry. There are, nevertheless, great objections to it; for though all the phenomena of the mineral kingdom attest a fluidity of igneous origin, yet it is a fluidity that was never more than partial; and though it has been over all the earth, has been over it in succession only. Besides, we are not entitled to assume the existence, and again the disappearance of such a great quantity of heat, without assigning some cause for the change.

435. Since, then, neither the hypothesis of the Neptunists or the Vulcanists, affords any good explanation of the figure of the earth, or such a one as can connect it with the other appearances in its natural history, it remains to inquire, whether the system that supposes a partial and successive fluidity, like Dr Hutton's, has any resource for explaining this great phenomenon.

Of this subject Dr Hutton has not treated; and when I was first made acquainted with his system, it appeared to me a very serious objection to it, that it did not profess to give an explanation of so important a fact as the oblate figure of the earth. On considering the matter more closely, however, I found that there were principles contained in it from which a very satisfactory solution (and, I think, the only satisfactory solution) of that difficulty might be deduced. This solution I shall endeavour to explain, in as far, at least, as is necessary for the purpose of general illustration.

It is laid down in Dr Hutton's theory, that the surface of the earth is perpetually changed by the detritus of the land; and that from the materials thus afforded, new horizontal strata are perpetually formed at the bottom of the sea. If this be true, and if the alternations of decay and renovation have been often repeated, it is certain, that the figure of the earth, whatever it may have originally been, must be brought at length to coincide with the spheroid of equilibrium.

436. Here it is necessary to remark, that the expressions, figure of the earth, and surface of the earth are each of them occasionally taken in two different senses.

The surface of the earth, in its most obvious sense, is that which bounds the whole earth, and includes all its inequalities; it is a surface extremely irregular, rising to the tops of the mountains, descending to the bottoms of the valleys, and having the continuity of its curvature often interrupted, or suddenly changed. This may be called the actual surface, and the figure bounded by it, the actual figure, of the earth.

The surface of the earth, in another sense, is one that is every where horizontal, and is the same which water assumes when at rest.

This superficies is determined by the circumstance of its being constantly perpendicular to the direction of gravity; it is the surface marked out by levelling, and may be supposed to be continued from the sea, through the interior of the land, till it meet the sea again. The figure bounded by this horizontal surface, may properly be called the statical figure of the earth.

When it is said that the figure of the earth is an oblate spheroid, it is the statical, not the actual figure which is meant; and the degrees of the meridian which astronomers measure, are also referred to the superficies of the former.

437. Suppose now a body like the earth, but with its actual figure infinitely more irregular, having a sea circumfused around it, the water will descend into the lowest situations, and will so arrange itself, that its surface shall be perpendicular every where to the plumb-line, or to the direction of gravity, in which state only it can remain at rest. The figure of the superficies which the sea must thus take will be of a continuous curvature, and will return into itself; though it may, if the actual figure is very irregular, be far either from a sphere or a spheroid. If, however, we suppose the solid parts of this mass subject to be dissolved or worn away, and carried down to the ocean, there will be a tendency to give to the whole body the same figure that it would have assumed, if it had been entirely fluid, and subject to the laws of hydrostatics. This tendency is the result of two principles.

438. Let us suppose the body just described to have no rotation, so that the particles of it are actuated only by the forces of cohesion and of attraction.

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.

441. If the preceding conclusions are just, and if the figure of equilibrium is only an asymptotic figure, to which that of the earth may approximate, but cannot perfectly attain, we are not to be surprised if considerable deviations from it are actually observed. This has accordingly happened, insomuch, that the results deduced from the most accurate measurement of degrees of the meridian, differ from one another, in the oblateness they give to the earth, by nearly one half of the quantity to be determined. When we compare the degrees measured in France, and in some other countries of Europe, with those measured in Peru, we obtain for the compression at the poles, less than 1/300 of the radius of the earth. But when we compare the degrees measured in France with one another, and with those lately measured in England, we find that they are best represented by a spheroid that has its compression 1/150 of its semi-axis.[233] There is reason to think, therefore, that the meridians are not elliptical; and other observations seem to show, that they are not even similar to one another; or that the earth is not, strictly speaking, a solid of revolution; so, also, the comparison of the degree measured at the Cape of Good Hope, with those measured on the opposite side of the equator, creates a suspicion, that the northern and southern hemispheres are not perfectly alike, and that the earth is not equally compressed at the Arctic and the Antarctic poles. These irregularities, though they do not affect the general fact of the earth's compression at the poles, show that the true statical figure is but imperfectly attained; and though this may be accounted for, without having recourse to the principles involved in our theory, it is in a manner very unsatisfactory, and, by help of suppositions, not at all consistent with the original fluidity ascribed to the whole mass, or to the exterior crust of the earth.

[233] Exposition du Systéme du Monde, par La Place, p. 61, 2d edit.

442. As the principles here laid down explain how a solid body may attain very nearly the figure which a fluid would acquire in order to preserve its parts in equilibrium; and since the oblate figure belongs to other of the planets as well as the earth, and the globular to all the great bodies of the universe, this suggests an analogy that goes deep into the economy of nature, and extends far beyond the limits within which the mineralogist is wont to confine his speculations.

443. That no very irregular figure is found among the planetary bodies, may therefore be considered as a proof of the universality of that system of waste and reconsolidation that we have been endeavouring to trace in the natural history of the earth. A farther proof of the same arises from considering, that for every given mass of matter, having a given period of rotation, there are two different spheroids that answer the conditions of establishing an equilibrium among its parts, the one near to the sphere, and the other very distant from it, and so oblate as to have a lenticular form. Thus the earth, supposing it homogeneous, might either be in equilibrium, by means of the figure which it actually has, or of one in which the polar was to the equatorial diameter as 1 to 768. The same is true of the other planets; and yet we no where find that this highly compressed spheroid is actually employed by nature. The reason, no doubt, is, that in so oblate a spheroid, the equilibrium between the gravitating and the centrifugal force is of the kind that does not re-establish itself when disturbed; so that the parts let loose, and not kept in their place by firm cohesion, would fly off altogether. In such a body, the waste at the surface would lead to an entire change of form, and therefore the constitution here supposed could not be permanent.

444. In the system of Saturn, we have a great deviation from the general order, which, nevertheless, has led to a very unexpected verification of some of the conclusions deduced above. A principle extremely like that which is the basis of all the foregoing reasonings, led one of the greatest philosophers of the present age to discover the revolution of Saturn's ring on its axis, and even to determine the velocity of that revolution, such as it has been since found by observation. La Place, laying it down as a maxim, that nothing in nature can exist, where there are causes of change, not balanced or compensated by other causes,[234] concluded, that the-parts of the ring must be held from falling down to the body of the planet by some other force than their mere cohesion to one another. Were it otherwise, every particle detached from the ring, by any means, must descend in a straight line, almost perpendicular to the surface of Saturn; and the final destruction of the ring must be inevitable. The only force that could balance this effect of gravitation, seemed to be a centrifugal force, arising from the rotation of the ring on an axis passing through its centre, and perpendicular to its plane. La Place proceeded to inquire what celerity of rotation was adequate to this effect, and found that one of ten hours and a quarter would be required, which is almost precisely the time afterwards determined by Dr Herschel from actual observation. If, with this rotation, the ring is a solid annulus generated by the rotation of a very flat ellipsis about a given point in its greater axis, coinciding with the centre of Saturn, it may be so constituted, that the attraction of Saturn, combined with the centrifugal force, may produce a force perpendicular to its surface, and may enable detached parts to remain at rest, animals, for instance, to walk on its surface, and fluids to be in equilibrio. The system of Saturn is thus fortified against the lapse of time, as effectually as that of the earth itself; and the means by which this is accomplished, seem to prove, that the weapons which time employs, are in both cases the same, viz. the slow wearing and decomposition of the solid parts. This slow wearing may have produced the figure by which its action is most effectually resisted.

[234] La Place, ubi supra, p. 242.

445. Thus Dr Hutton's theory of the earth comes at last to connect itself with the researches of physical astronomy. The conclusion to be drawn from this coincidence is to the credit of both sciences. When two travellers, who set out from points so distant as the mineralogist and the astronomer, and who follow routes so different, meet at the end of their journey, and agree in their report of the countries through which they have passed, it affords no slight presumption, that they have kept the right way, and that they relate what they have actually seen.