If the mean variation in the Earth's rotational velocity had remained the same as it is now over the four-billion year period, contrary to the tidal theory, the lunar tides over this period would have accounted for the decrease in the Earth's rotational velocity by approximately 0.76 Under these conditions the angular velocity of the Earth's rotation immedi ately following the formation of the Moon should have been 1.85 but it has already been noted that this condition is incompatible with the tidal theory. According to this theory the difference between the velocities of the Earth's rotation and the Moon's revolution must have increased progressively to a maximum beyond which it should have decreased, rapidly at first, and then at a steadily diminishing rate.
At the present time the variation in the velocities of the Earth's rotation and the Moon's revolution is closer to the latter stage, so that the mean variation in the Earth's rotational velocity over the four billion years must have been many times larger than it has been over the last 2000 years. Consequently (in accordance with the tidal-friction theory) the angular velocity of the Earth's rotation in the period immediately following the formation of the Moon must have been considerably higher than 1.85 There is no doubt that the long-period decrease in the Earth's rotational velocity caused by the thermal expansion of the Earth must be added to the above-mentioned long-period variation in the Earth's rotational velocity caused by tidal friction. It was calculated by Lyubimova (1958) that three billion years ago the average annual increment of the Earth's radii due to internal heating amounted to 0.01 —0.005 cm. The current radial increase is approximately 0.001 cm/year, and this must cause a corresponding increase of the diurnal period and a decrease in the Earth's polar flattening, accompanied by deformations of the crust.
In addition to the long-period variations, the Earth's rotational velocity also undergoes variations having shorter cycles which are superimposed on the longer ones. These short-period variations include those caused by global phenomena, such as glaciation or considerable warming of the climate, to which the Earth was repeatedly subjected in the past, as confirmed by geological observations. The accumulation of ice and snow in the polar regions during glaciation periods decreases the moment of inertia of the Earth, thereby increasing its rotational velocity in accordance with the law of conservation of angular momentum.
On the contrary the ablation of ice and snow in the polar regions during the warmer periods increases the Earth's moment of inertia, thereby decreasing its rotational velocity according to the same law. Obviously,
such variations in the Earth's rotation do not reach magnitudes large enough to generate critical stresses in the Earth's shell. Most probably the related crustal deformations are elastic, or at any rate small-scale deformations. On the other hand, they must shift the surface gradients, thereby shifting the shore lines of seas and lakes as well as the river beds.
The long-period variations in the Earth's rotation are combined with variations produced by differentiation of the terrestrial matter, including differentiation of the substance of the outer shell in the depth interval of 100-700 km (where, according to Lyubimova, the matter has fused and solidified), possible phase transformations of matter, and other factors.
Deceleration of the Earth's rotation by a factor of 2.6-3 and possibly more would cause a correspondingly large decrease in its polar flattening (from approximately 1/40 to its present value of 1/298). This transforma tion of the figure of the Earth would generate closely related large-scale compressive deformations of the Earth's crust in the equatorial region, and tensile deformations in the polar regions. These crustal deformations would add to the tensile deformations generated by the thermal expansion of the Earth's radius, which were very large, especially in the more remote past. According to Lyubimova, the thermal expansion of matter inside the Earth would increase its radii by 90 —165 km over a period of three billion years. Such a large radial extension would generated considerable tensile stresses in the outer portion of the Earth's shell which would have certainly developed faults. Over this period, the length of the equator should have increased by approximately 560 —1030 km, while the length of the parallels should have increased by 485-875km at a latitude of 35°, by 373-799 km at 50°, by 281 —517 km at 60°, by 236-435 km at 65°, and by 194-355 km at 70°. The elongation of meridians must have nearly equaled the maximum elongation of the equator (which was approximately 559-1028 km) . The total increase in the length of the parallels due both to the change in length of the terrestrial radii (caused by the decrease of polar flattenings), and to thermal expansion would be as follows. The equator would increase by approximately 240-710 km in length, and the parallels by 485-875 km at a latitude of 35°, 530-955 km at 50°, 480-715 km at 60°, 430-630 km at 65°, and 370-530 km at 70°.