The previous result (Aoki, 1969) on the explanation of the excess secular change in the obliquity of the ecliptic frictional couplings in the rigid constituents, the mantle and the core, is extended by using a model of an elastic and electrically conducting mantle and a hydromagnetic core. The secular change of the obliquity of the ecliptic referred to the mantle is found to be 1/3.2 times of the observed value, if the electrical conductivities of the fluid core and the mantle are assumed to be 3·10−6 emu and 3·10−9 emu respectively. A large secular deceleration of the Earth's rotational speed obtained in the previous result is proved to be strongly reduced because of weak excitation of the perturbing potential for a long time variation.

A report is given on work in progress on the available observational evidence for an excess secular change of the obliquity of the ecliptic. Some of the recent determinations suggested that the conventionally adopted value of the secular change requires a correction of the order of per century. Since an error of this size in the adopted motion of the ecliptic must be ruled out, the observed corrections may indicate either a rotation of the equatorial plane with respect to an inertial system about an axis passing through the equinox or the existence of systematic errors of the observations. In following Aoki's suggestion of a real motion of the equator, the averaged proper motions in the systems FK4 and N30 yield a rotation of the galaxy with an angular velocity of 43.6 km s−1 kpc−1 near the Sun and a positive gradient of the circular velocity in the galaxy near the Sun. If the distance of the Sun from the galactic center is 10 kpc, the circular velocity of the galaxy would be 436 km s−1. Should, however, the circular velocity be less than 300 km s−1, the distance of the Sun from the galactic center would have to be smaller than 7 kpc.

For the following reasons such far reaching conclusions are not well founded:

(1) Fundamental observations of the stars, the Sun and the planets carried out before about 1900 show appreciable systematic deviations from the average of the observations carried out after 1900. The excess secular change of the obliquity is suspected to be the consequence of systematic errors of older observations.

(2) The determinations of individual values of Δɛ from observations of the Sun and the planets show a steep decrease of Δɛ from about 1780 to 1900; the individual values of Δɛ derived from observations after 1900 do not deviate significantly from zero and do not show a significant secular decrease. On the other hand, a small secular decrease cannot be excluded.

(3) The first results of determinations of Oort's constant B from proper motions of stars with respect to galaxies do not indicate significant deviations from the results derived on the basis of proper motions measured in the fundamental system.

This investigation, which is not yet completed, concentrates on an analysis of fundamental observations of stars, the Sun and planets. From the systematic errors of observations which have contributed to the formation of the FK4 it can already be stated that modern observations cannot exclude the possibility of an excess secular change of the obliquity within the limits of per century and, consequently, the possibility of a real motion of the equatorial plane within these limits. It appears, therefore, that Aoki's suggestion deserves further attention, but that its effect on galactic rotation is smaller than was originally assumed.

The results, given below, of investigations are based on 14 yr of observations carried out with the Danjon astrolabe at the Paris Observatory; such observations allow the measurement of time and latitude.

Previous analysis, based on 6,5 yr showed some periodic terms and, in particular, it had been possible to determine values of the nearly diurnal nutation (results presented at the 6th Symposium on Earth Tides, 1969).

Several authors tried to derive the period, amplitude and initial phase of the free diurnal nutation using separate series of latitude and time observations. The results obtained by them are compaired and discussed in the present paper.

With a triaxial deformable Earth model an attempt is made to integrate the dynamics of polar wandering with that of the tectonic movements of the Earth's upper layers. Polar wandering is interpreted as a mechanical response of the rotating Earth to the episodic energy perturbation in the upper layers, whereas the tectonic movements are the adjustments of the upper layers to the polar instability. The present analysis suggests that the attempt of the Earth to adjust itself for polar stability is the driving mechanisms of continental drift and sea-floor spreading, and also that the Earth's wobble is rather a quasi-permanent (slow damping) phenomenon and has two components. And that the Earth would not reach its rotational equilibrium as long as the excess heat-generation in its interior continues to supply energy for its cyclic dynamical evolution.

According to the mantle convection theory, mantle materials come up to the surface of the Earth at the mid-oceanic ridge system, go off in two horizontal directions, and finally at the trench and orogenic belt system they return to the interior of the Earth. We assume no return flow in the deeper part of the mantle and calculate the change of products of inertia of the Earth due to the above mass transfer. The polar wandering thus calculated is towards the direction of about 90° east and its absolute value is about 0.9 × 10−2 s/yr.

The hypothesis that earthquakes may be the principal excitation of the Chandler motion of the rotation pole is examined in the light of recent theoretical and observational developments. There is some doubt about the amount of excitation by a large earthquake necessary to maintain the Chandler Wobble, but it appears to be about 10 ft. Theoretical calculations for the Alaskan Earthquake (M = 8½) give available excitations in the range 1–5 ft, but there are considerable uncertainties in these calculations. Earthquakes may be able to provide all of the required excitation, or only a small portion (10% or less). The problem is confused by observational studies, which show differences between various sets of data on polar motion which seem to be larger than the expected error in each set. The earthquake hypothesis, though reasonable, is still very much open to debate.

Values of the Chandlerian period and the damping coefficient of the polar motion are calculated for every ten years from 1900.0 to 1970.0, using a method developed by Sekiguchi (1966). The damping coefficient is variable between 0.074 and 0.008 (yr)−1 through this period, and correlative with the variation of the Chandlerian period, as Sekiguchi (1961) theorized.

The direction of anomalous polar motion is compared with that of the motion expected from the source mechanism generating the earthquakes associated with the motion. The result supports the hypothesis that major earthquakes excite the Chandler wobble.

The electromagnetic coupling between the Earth's core and the mantle is studied when the geomagnetic dipole field varies periodically. The oscillation of the geomagnetic dipole moment with a period of 8000 years, its amplitude being 50% of the present moment, is capable of causing a fluctuation of 10−11 rad/s in the angular velocity of the mantle. The angular velocity increases with a decrease in the dipole moment.

Solar activity may affect the rotation of the solid Earth by coupling between the lower neutral atmosphere and the solid Earth. It attacks directly the lower atmosphere in the non-axially symmetric mode and may trigger off variation of the amplitude of the annual terms in the polar motion. The indirect effect of solar activity may be associated with some proper oscillation of the atmospheric coupling with the ocean in the axially symmetric mode of the atmospheric motion. The shift of airmass along the rotating axis of the Earth corresponds well with the changes of the Earth's rotational velocity and the Chandler amplitude in the polar motion for long time variation.

Long period bodily tides (fortnightly and monthly) cause periodic changes of the Earth's moment of inertia and consequently the angular speed of its rotation.

During the past few years the use of atomic clocks has made it possible to determine the amplitudes of these periodic variations of the Earth's rotation with high accuracy and has made this method very effective in determining Love's number K, which is dependent on the internal structure of the Earth (the most detailed studies were made in the U.S.S.R. – Pilnik and Gubanov).

But up to now it was taken (Anderson, Woolard, Melchior, and others), that the formulae of Jeffreys and Woolard, which are used in this method, are valid only for incompressible Earth models.

It is shown in this paper that the formulae are valid for the case of an actual compressible heterogeneous Earth. Thus, the method receives a real practical value. The use of lasers and radio methods in the near future will make this method even more effective.

The full text of the paper will be published in the magazine Physics of the Earth in No. 3, 1972.

The torques of the frictional forces on the bottoms of the seas are calculated in an approximate inertial system and not in the corotating system used hitherto. In this way, the loss of rotational energy of the Earth – corresponding to the mean torque – can be compared with the value obtained from astronomical observations. The calculations are based on velocities which are computed by numerical integrations of the hydrodynamical equations. Initial results are presented for the North Sea, the Bering Sea and rough models of theworld ocean.

The classical problem of determining the secular retardation of the Earth's rotation due to the effect of tides (oceanic and bodily) has an important geophysical value in determining the possible existence of processes inside the Earth, which lead to secular variations of rotation of the whole Earth or its external layers.

Using new cotidal charts of the world ocean calculated by Bogdanov for the main tidal waves M2, S2, K1 and O1 and using the method of moments of tidal forces the retarding moment was found to be 8.3 × 1023 dyn cm. This is twice the amount of previous evaluations. (This method is superior to the method of calculating the dissipation of energy or the moments of frictional forces). This amount corresponds to a retardation of 3.8 μs/century in the speed of the Earth's rotation. But the observations of the Sun give only 1.9 μs/century for the retardation. Thus, there seem to be nontidal and probably internal processes, which accelerate the Earth's rotation by about 2 μs/century. And this is without taking account of additional smaller effects of bodily tides. The search for these processes is an important problem.

The full text of the paper will be published in the magazine Physics of the Earth, No. 2, 1972.