THE FIGURE OF THE EARTH

The lithosphere and its envelopes.—The stony part of the earth is known as the lithosphere, of which only a thin surface shell is known to us from direct observation. The relatively unknown central portion, or “core”, is sometimes referred to as the centrosphere. Inclosing the lithosphere is a water envelope, the hydrosphere, which comprises the oceans and inland bodies of water, and has a mass ¹/₄₅₄₀ that of the lithosphere. If uniformly distributed, the hydrosphere would cover the lithosphere to the depth of about two miles, instead of being collected in basins as it now is. Though apparently not continuous, if we take into account the zone of underground water upon the continents, the hydrosphere may properly be considered as a continuous film about the lithosphere. It is a fact of much significance that all the ocean basins are connected, so that the levels are adjusted to furnish a common record of deposits over the entire surface that is sea-covered.

Enveloping the hydrosphere is the gaseous envelope, the atmosphere, with a mass ¹/_1200000 that of the lithosphere. The atmosphere is a mixture of the gases oxygen and nitrogen in parts by volume of one of the former to four of the latter, with a relatively small percentage of carbon dioxide. Locally, and at special seasons, the atmosphere may be charged with relatively large percentages of water vapor; and we shall see that both the carbon dioxide and the vapor contents are of the utmost importance in geological processes and in the influence upon climate. Unlike the water which composes the hydrosphere, the gases of the atmosphere are compressible. Forced down by the weight of superincumbent gas, the layers of the atmosphere at the level of the sea sustain a pressure of about fifteen pounds to the square inch; but this pressure steadily decreases in ascending to higher levels. From direct instrumental observation, the air has now been investigated to a height of more than twelve miles from the earth’s surface.

The evolution of ideas concerning the earth’s figure.—The ideas which in all ages have been promulgated concerning the figure of the earth have been many and varied. Though among them are not wanting the purely speculative and fantastic, it will be interesting to pass in review such theories as have grown directly out of observation.

The ancient Hebrews and the Babylonians were dwellers of the desert, and in the mountains which bounded their horizon they saw the confines of the earth. Pushing at last westward beyond the mountains, they found the Mediterranean, and thus arrived at the view that the earth was a disk with a rim of mountains which was floated upon water. The rare but violent rainfalls to which they were accustomed—the desert cloudburst—further led them to the belief that the mountain rim was continued upward in a dome or firmament of transparent crystal upon which the heavenly bodies were hung and from which out of “windows of heaven” the water “which is above the earth” was poured out upon the earth’s surface. Fantastic as this theory may seem to-day, it was founded upon observation, and it well illustrates the dangers of reasoning from observation within too limited a field.

As soon as men began to sail the sea, it was noticed that the water surface is convex, for the masts of ships were found to remain visible long after their hulls had disappeared below the horizon. It is difficult to say how soon the idea of the earth’s rotundity was acquired, but it is certainly of great antiquity. The Dominican monk Vincentius of Beauvais, in a work completed in 1244, declared that the surfaces of the earth and the sea were both spherical. The poet Dante made it clear that these surfaces were one, and in his famous address upon “The Water and the Land”, which was delivered in Verona on the 20th of January, 1320, he added a statement that the continents rise higher than the ocean. His explanation of this was that the continents are pulled up by the attraction of the fixed stars after the manner of attraction of magnets, thus giving an early hint of the force of gravitation.

The earth’s rotundity may be said to have been first proven when Magellan’s ships in 1521 had accomplished the circumnavigation of the globe. Circumnavigation, soon after again carried out by Sir Francis Drake, proved that the earth is a closed body bounded by curving surfaces in part enveloped by the oceans and everywhere by the atmosphere. The great discovery of Copernicus in 1530 that the earth, like Venus, Mars, and the other planets, revolves about the sun as a part of a system, left little room for doubt that the figure of the earth was essentially that of a sphere.

The oblateness of the earth.—Every schoolboy is to-day familiar with the fact that the earth departs from a perfect spherical figure by being flattened at the ends of its axis of rotation. The polar diameter is usually given as ¹/₂₉₉ shorter than the equatorial one. This oblateness of the spheroid was proven by geodesists when they came to compare the lengths of measured degrees of arc upon meridians in high and in low latitudes.

The oblateness of the geoid is well understood from accepted hypotheses to be the result of the once more rapid rotation of the planet when its materials were more plastic, and hence more responsive to deformation. An elastic hoop rotating rapidly about an axis in its plane appears to the eye as a solid, and becomes flattened at the ends of its axis in proportion as the velocity of rotation is increased. Like the earth, the other planets in the solar system are similarly oblate and by amounts dependent on the relative velocities of rotation.

The departure of the geoid from the spherical surface, owing to its oblateness, is so small that in the figures which we shall use for illustration it would be less than the thickness of a line. Since it is well recognized and not important in our present consideration, we shall for the time being speak of the figure of the earth in terms of departures from a standard spherical surface.

The arrangement of oceans and continents.—There are other departures from a spherical surface than the oblateness just referred to, and these departures, while not large, are believed to be full of significance. Lest the reader should gain a wrong impression of their magnitude, it may be well to introduce a diagram drawn to scale and representing prominent elevations and depressions of the earth (Fig. 1).

Wrong impressions concerning the figure of the lithosphere are sometimes gained because its depressions are obliterated by the oceans. The oceans are, indeed, useful to us in showing where the depressions are located, but the figure of the earth which we are considering is the naked surface of the rock. In a broad way, the earth’s shape will be given by the arrangement of the oceans and the continents. As soon as we take up the study of this arrangement, we find that quite significant facts of distribution are disclosed.

One of the most significant facts involved in the distribution of land and sea, is a concentration of the land areas within the northern and the seas within the southern hemisphere. The noteworthy exception is the occurrence of the great and high Antarctic continent centered near the earth’s south pole; and there are extensions of the northern continent as narrowing land masses to the southward of the equator. Hardly less significant than the existence of land and water hemispheres is the reciprocal or antipodal distribution of land and sea (Fig. 2). A third fact of significance is a dovetailing together of sea and land along an east-and-west direction. While the seas are generally A-shaped and narrow northward, the land masses are V-shaped and narrow southward, but this occurs mainly in the southern hemisphere. Lastly, there is some indication of a belt of sea dividing the land masses into northern and southern portions along the course of a great circle which makes a small angle with the earth’s equator. Thus the western continent is nearly divided by a mediterranean sea,—the Caribbean,—and the eastern is in part so divided by the separation of Europe from Africa.

The figure toward which the earth is tending.—Thus far in our discussion of the earth’s figure we have been guided entirely by the present distribution of land and water. There are, however, depressions upon the surface of the land, in some cases extending below the level of the sea, which are not to-day occupied by water. By far the most notable of these is the great Caspian Depression, which with its extension divides central and eastern Asia upon the east from Africa and Europe upon the west. This depression was quite recently occupied by the sea, and when added to the present ocean basins to indicate depressions of the lithosphere, it shows that the earth’s figure departs from the standard spheroid in the direction of the form represented in Fig. 3. This form approximates to a tetrahedron, a figure bounded by four equal triangular faces, here with symmetrically truncated angles. Of all regular figures with plane surfaces the tetrahedron has the smallest volume for a given surface, and it presents moreover a reciprocal relation of projection to depression. Every line passing through its center thus finds the surface nearer than the average distance upon one side and correspondingly farther upon the other (Fig. 4).

Astronomical versus geodetic observations.—Confirmation of the conclusions arrived at from the arrangement of oceans and continents has been secured in other fields. It was pointed out that the earth’s oblateness was proven by comparison of the measured degrees of latitude upon the earth’s surface in lower and higher latitudes, the degree being found longer as the pole is approached. Any variation from the spherical surface must obviously increase the size of the measured degree of latitude in proportion to the departure from the standard form, and so the tetrahedral figure with one of its angles at the south pole will require that the degrees of latitude be longer in the southern than they are in the northern hemisphere. This has been found by measurement to be the case, and the result is further confirmed by pendulum studies upon the distribution of the earth’s attraction or gravity. If less of the mass of the earth is concentrated in the southern hemisphere, its attraction as measured in vibrations of the pendulum should be correspondingly smaller.

Other confirmations of the tetrahedral figure of the earth have been derived from a comparison of astronomical data, which assume the earth to be a perfect spheroid, with geodetic measurements, which are based upon direct measurements. Thus the arc measured in an east-and-west direction across Europe revealed a different curvature near the angle of the tetrahedral figure from what was found farther to the eastward.

Changes of figure during contraction of a spherical body.—If we inquire why the earth in cooling should tend to approach the tetrahedral figure, an answer is easily found. When formed, the earth appears to have been a but slightly oblate spheroid, or practically a sphere—the shape which of all incloses the most space for a given surface. Cooled and solidified at the surface to the temperature of the surrounding air, and the core still hot and continuing to lose heat, the core must continue to contract though the outer shell is no longer able to do so. The superficial area being thus maintained constant while the volume continues to diminish, the figure must change from the initial one of greatest bulk to others of smaller volume, and ultimately, if the process should continue indefinitely, to the tetrahedron, which of all regular figures has the minimum volume for a given surface.

That a contracting sphere does indeed pass through such a series of changes has been shown by the behavior of contracting soap bubbles and of rubber balloons, as well as by experiments upon the exhaustion of air contained in hollow metal spheres of only moderate strength. In all these instances, the ultimate form produced indicates an indenting of four sides of the sphere which have the positions of the faces of a tetrahedron. The late Professor Prinz of Brussels secured some extremely interesting results in which he obtained intermediate forms with six angles, but unfortunately these studies were not prepared for publication at the time of his death.

The earth’s departure from the spheroid in the direction of the modified tetrahedron is, as we have seen, no hypothesis, but observed fact revealed in (1) the concentration of the land about a central ocean in the northern hemisphere; in (2) the antipodal relation of the land to the water areas, and in (3) the threefold subdivision of the surface into north and south belts by the two greater oceans and the Caspian Depression.

The earlier figures of the earth.—The manner in which continent and ocean are dovetailed into each other in an east-and-west direction has been generally adduced as additional evidence for the tetrahedral figure as above described. Closer examination shows that instead of being in harmony with this figure, it indicates a departure from it, and, as we shall see, a significant departure which undoubtedly has its origin in the earlier history of the planet. The mediterranean seas of both the eastern and the western hemispheres likewise interfere with the perfection of the tetrahedral figure and require an explanation.

Let us then examine in outline the past history of the world with reference especially to the evolution of the continents and to the times and the manners of surface change. It is now well known that there have been three major periods of great deformation of the earth’s shell. The first of these of which we have record came at the end of the first great era of geologic history, the so-called Eozoic era; a second great transformation came at the close of the second or Paleozoic era; and a third began at the end of the next or Mesozoic era, an adjustment which is apparently continuing to-day. Each of these great surface deformations was accompanied by great volcanic eruptions of which we have the evidence in the lavas remaining for our inspection, and each was followed by the formation of great glaciers which spread over large areas of the existing continents.

Before the earliest of these great changes, the earth appears to have approximated in its figure somewhat closely to the ideal spheroid, for it was everywhere enveloped in the hydrosphere as a universal ocean. Toward the close of this period came the adjustments which brought the lithosphere to protrude through the hydrosphere in shield-like continents whose distribution, as shown by the rocks of this period, is of great significance. Within the northern hemisphere rose three land shields spaced at nearly equal intervals and at nearly equal distances from the northern pole. One of these was centered where now is Hudson Bay, another about the present Baltic Sea, and the relics of the third are found in northeastern Siberia. These earliest continents have been referred to as the Laurentian, Baltic, and Angara shields. Within the southern hemisphere shields appear to have developed in somewhat similar grouping, namely, in South America, in South Africa, and in Australia (Figs. 3 and 5).

These coigns or angles of a form into which the earlier spheroid of the earth was being transformed have persisted through the greater part of subsequent geologic time, and have been enlarged by the growth of sediments about them as well as by the later elevation and wrinkling of these deposits into marginal mountain ranges.

The continents and oceans which arose at the close of the Paleozoic era.—At the close of the second great era in the recorded history of the earth, the now somewhat enlarged continents were profoundly altered during a series of convulsive movements within the surface shell of the lithosphere. When these convulsions were over, there was a new disposition of land and sea, but one quite different from the present arrangement. Instead of being extended in north-south belts, as they are at present, the continents stretched out in broad east-west zones, one in the northern and the other in the southern hemisphere. To the broad southern continent of which so little now remains, the name “Gondwana Land” has been given, and to the sea which divided the northern from the southern continent the name “Ocean of Tethys.” The northern continent stretched across the site of the present Atlantic Ocean as the “North Atlantis”, its northern shore to the westward being somewhat farther south than the present northern coast of North America, since life forms migrated in the northern ocean from the site of Behring Sea to that of the present North Atlantic.

This arrangement of land and water during the middle period of the earth’s recorded history, when considered with reference both to its earlier and to its later evolution, may perhaps be best accounted for by the assumption that the lithosphere was then shaped like Fig. 5 (middle). In this figure two truncated tetrahedrons are joined in a common plane of contact which may be described as the twin plane. This medial depression upon the lithosphere was occupied by the intercontinental sea, the Ocean of Tethys.

Near the close of this second great era of the earth’s continental history, crustal convulsions, which were perhaps the most remarkable in the entire record, resulted in the almost complete disappearance of the southern continent and a concentration of the land within the northern hemisphere as a somewhat interrupted belt surrounding a central polar ocean (Figs. 3 and 5).

Upon the assumption of twin tetrahedrons in the intermediate era of continental evolution, both the Ocean of Tethys of that time and its present remnants, the Caribbean and Mediterranean seas, are accounted for. The V-shaped continent extensions and the A-shaped oceans of the southern hemisphere (Fig. 2) may likewise be considered as relics of the now largely submerged tetrahedron of the southern hemisphere, since this had its apex to the northward (Fig. 6).

Thus we see that the lithosphere can scarcely be regarded as a perfect spheroid, since in the course of geologic ages it has undergone successive departures from this original form. In its present state it has been described as tetrahedral, though we must keep in mind that the sharp angles of that figure are deeply truncated. The soundings first by Nansen and more recently by Peary in the Arctic basin, far to the north of the continental border, showed that this depression is characterized by profound depths, and so have afforded confirmation of the tetrahedral figure. To match this depression at the northern extremity of the earth’s axis, a high continent reaching to elevations in excess of 10,000 feet has been penetrated by Sir Ernest Shackleton at the opposite extremity of this polar diameter. Considering its size and its elevation, the Antarctic continent with its glacier mantle is the largest protuberance upon the surface of the lithosphere.

In our study of the departures of the earth from the standard spheroidal surface, we might even go a step farther and show how the tetrahedron, which best represents the symmetry of the present figure, is somewhat deformed by a flattening perpendicular to the Pacific Ocean. To draw attention to this flattening of the earth, it has sometimes been described as “potato-shaped”, since the outline perpendicular to this face is imperfectly heart-shaped or like a flattened “peg top.”

The flooded portions of the present continents.—We are accustomed to think of the continents as ending at the shores of the oceans. If, however, we are to regard them as platforms which rise from the ocean depressions, their margins should be considerably extended, for a submerged shelf now practically surrounds all the continents to a nearly uniform depth of 100 fathoms or 600 feet. The oceans thus more than fill their basins and may be thought of as spilling over upon the continents. In Fig. 7, the submerged portions of the continents have been joined to those usually represented, thus adding about 10,000,000 square miles to their area, and giving them one third, instead of one fourth, of the lithosphere surface.

The floors of the hydrosphere and atmosphere.—The highest altitudes upon the continents and the profoundest deeps of the ocean are each removed about 30,000 feet, or nearly 6 miles, from the level of the sea. In comparison with the entire surface of the lithosphere, these extremes of elevation represent such small areas as to be almost inappreciable. Only about ¹/₈₀ of the lithosphere surface rises more than 6000 feet above sea level, and about the same proportion lies deeper than 18,000 feet below the same datum plane (Fig. 8). Almost the entire area of the lithosphere is included either in the so-called continental plateau or platform, in the oceanic platform, or in the slope which separates the two. The continental platform includes the continental shelf above referred to, and represents about one third of the entire area of the planet. This platform has a range of elevation from 6000 feet above to 600 feet below sea level and has an average altitude of about 2300 feet. The oceanic platform slopes more steeply, ranges in depth from 12,000 to 18,000 feet below sea level, and comprises about one half the lithosphere surface. The remaining portion of the surface, something less than one eighth of all, is included in the steep slopes between the two platforms, between 600 and 12,000 feet below sea. The two platforms and the slope between them must not, however, be thought of as continuous features upon the surface, but merely as representing the average elevations of portions of the lithosphere.

Reading References for Chapter II

On the evolution of ideas concerning the earth’s figure:—

Suess. The Face of the Earth (Clarendon Press, 1906), vol. 2, Chapter 1.

v. Zittel. History of Geology and Paleontology (Walter Scott, London, 1901), Chapters 1-2.

The departure of the spheroid toward the tetrahedron:—

W. Lowthian Green. Vestiges of the Molten Globe, Part 1. London, 1875. (Now a rare work, but it contains the original statement of the idea.)

J. W. Gregory. The Plan of the Earth and Its Causes, Geogr. Jour., vol. 13, 1899, pp. 225-251 (the best general statement of the arguments for a tetrahedral form).

W. Prinz. L’Échelle reduite des expÉriences gÉologiques, Bull. Soc. Belge d’Astronomie, 1899.

B. K. Emerson. The Tetrahedral Earth and Zone of the Intercontinental Seas, Bull. Geol. Soc. Am., vol. 11, 1911, pp. 61-106, pls. 9-14.

M. P. Rudski. Physik der Erde (Tauchnitz, Leipzig, 1911), Chapters 1-3 (the best discussion of the geoid from the purely mathematical standpoint, so far as the spheroid is concerned).

The earlier figures of the earth:—

Th. Arldt. Die Entwicklung der Kontinente und ihrer Lebewelt. Engelmann, Leipzig, 1907. (Contains a valuable series of map plates, showing the probable boundaries of the continents in the different geological periods).