The meridians would increase by approximately 721-1190 km. To these tensile deformations in the outer part of the Earth's shell would be added the tensile deformation due to the fusion of substance in a layer about 600 km thick. According to Lyubimova's calculations, the resultant elongation of the radii should have been 50 km.
Thus, over the entire period of about four billion years the Earth's crust must have been subjected to continuous tensile stresses and faulting both in the polar and the equatorial regions. The stresses and faults must have been especially great in the first half of this period, but considerably less pronounced during the last stages of the geological history of the Earth. Consequently, the Earth's surface should not be carrying any large, A similar value for the polar flattening of the Earth (1:297.6) was obtained by calculations based on the conditions of its hydrostatic equilibrium. Consequently, the present state of the Earth is in fact extremely close to that of hydrostatic equilibrium. Therefore, throughout its existence, the Earth's hydrostatic equilibrium, disturbed by variations of its rotational velocity, was restored by repeated transformations of its figure in accord ance with the above law for the transformation of the form of an ellipsoid by variations of its polar flattening.
Physically, changes in the Earth's figure are explained as follows: a variation of the Earth's rotational velocity inevitably changes the centrifugal forces acting on every unit of mass; the equilibrium between the centrifugal forces and the centripetal forces produced by the attraction of mass elements toward the Earth's center is thus broken. The changes in centrifugal force are considerably more pronounced in the equatorial than in the polar regions, and this difference enhances the mass imbalance. A decrease in the Earth's rotational velocity and the corresponding decrease in the centrifugal forces causes a considerably larger increase in the centripetal acceleration of the mass elements in the equatorial region than it does in the polar regions. This disparity generates compressive stresses in the shell which are con siderably stronger in the equatorial region than in the polar regions.
When the difference between these stresses reaches the compressive strength of the shell and exceeds it, the shell's endosphere undergoes plastic deformations, with matter flowing from the equatorial to the polar regions. The equatorial region of the shell's exosphere (crust) undergoes irreversible compressive deformations, while tensile deformations occur in the polar regions. These deformations in the endosphere and exosphere
of the shell restore the equilibrium of the Earth's figure. If the centri fugal forces varied identically per unit mass at all latitudes, the transfor mation of the Earth's figure with reduced rotational velocity would merely involve a slight uniform compaction of its substance and a corresponding decrease of its volume; in the case of increased velocity, the density would decrease slightly while the volume would be slightly increased, but there would be scarcely any variation in the polar flattening. It is clear that the variation of the centrifugal forces at the critical parallels due to changes in the Earth's rotational velocity is always equal to the mean variation of centrifugal forces over the entire surface of the Earth.
Needless to say that actually the Earth's crust is not fixed at the critical parallels, and a decrease in the velocity of the Earth's rotation may always cause a slight meridional shift of the crust together with the subcrustal masses toward the poles.
However, even these slight shifts of the crust along the meridians (conforming to the slight variations in the length of the meridional arcs and their curvatures) would be strongly limited by the necessity for a considerable preliminary (or simultaneous) latitudinal contraction of the crust and its radial subsidence in the equatorial region. The preli minary buildup of compressive stresses necessary for the latitudinal contraction of the crust in this region significantly impedes any (even slight) shift of the crust along the meridians and its transformation toward the new equilibrium profile. An increase in the Earth's rotational velocity cannot cause crustal shifts along the meridians (with the exception of small local shifts along shear surfaces) because of the necessary contraction of the meridians in their entirety (the contraction being larger in the polar regions). An increase in the polar flattening will cause a considerable contraction of the Earth's crust in the polar regions along the parallels; this contraction necessitates a buildup of considerable com pressive stresses, and therefore the rearrangement of the crust toward the new equilibrium profile will occur at some time later than (or at least simultaneously with) the commencement of the deformations involved in the latitudinal and meridional extension of the crust in the equatorial region.