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.
[Illustration:
FIG. 1.—Diagrams to afford a correct impression of the measure of the
inequalities upon the earth’s surface compared to the earth’s radius.
The shell represented in _b_ is 1/100 of the earth’s radius, and in _a_
this zone is magnified for comparison with surface inequalities.]
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.
[Illustration:
FIG. 2.—Map on Mercator’s projection to show the reciprocal relation
of the land and sea areas (after Gregory and Arldt).]
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.
[Illustration:
FIG. 3.—The form toward which the figure of the earth is tending, a
tetrahedron with symmetrically truncated angles.]
=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.
[Illustration:
FIG. 4.—A truncated tetrahedron, showing how the depression upon one
side of the center is balanced by the opposite projection.]
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).
[Illustration:
FIG. 5.—Approximations to earlier and present figures of the earth.]
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).
[Illustration:
FIG. 6.—Diagrams for comparison of shore lines upon tetrahedrons which
have an angle, the first at the south and the second at the north.]
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.”
[Illustration:
FIG. 7.—The continents with submerged portions added (after Gilbert).]
=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.
[Illustration:
FIG. 8.—Diagram to indicate the altitude of different parts 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).