=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.