The problem of diurnal latitude variations is very closely connected with such fundamental questions as the causes of the closing sum, making more precise the coefficients of the forced nutation terms, study of the diurnal free nutation, etc.

Commission 4 of the International Astronomical Union has deferred the question of revisions to the constants and theory of nutation in anticipation that there might be recommendations from Symposium No. 78 in Kiev. The present rigid-Earth theory of nutation does not adequately represent current precise astronomical observations for the major nutation terms. Discrepancies between the presently adopted theory and observations can accumulate to 0″1 in right ascension and significantly affect the determination of UT1 and materially influence the derivation of the new fundamental catalog of star positions and proper motions, FK5 There appears to be no obvious choice for a non-rigid-Earth model at present. The analysis of solid-Earth tides shows nutation coefficients in substantial agreement with astronomical observations and these values have been used in the reduction of radio interferometric and laser ranging observations. In the absence of a non-rigid-Earth model which can satisfy all requirements it is suggested that the coefficients found from the investigation of solid-Earth tides be adopted as a working standard until such a model can be adopted as a basis for nutation.

The lunar laser range data from the McDonald Observatory in Texas have been used so far to determine major improvements in the lunar ephemeris and librations, to provide a new test of gravitational theory, and to determine single-day UT0 values on about 200 days during the period 1970-1974. The mean uncertainty in the UT0 values is 0.5 msec, and the smallest uncertainty is 0.2 msec (Stolz et al. 1976). The changes in the angular position of the moon with time are believed to be well enough known so that their uncertainty does not substantially degrade the accuracy of the UT0 values.

Long Baseline Interferometry (L.B.I.) refers to a dramatic technical breakthrough in astronomy accomplished almost exactly ten years ago in the spring of 1967 by a group of workers at the National Research Council of Canada and some major Canadian Universities. The Canadian effort was duplicated within a month by an independent American effort and it was realized soon afterward that the new technique of L.B.I. held enormous potential for geodynamical as well as astronomical studies.

The theoretical researches on this subject were first developed in a consistent theory, in 1765, by Euler, who studied the theory of the motion of a rotating rigid body. Bradley shortly before, in 1737, had discovered the first forced nutation, with a period of 18.6 years, which was explained by d'Alembert.

I wish to discuss an effect that is caused by the secular decrease in the Earth's rotation. I shall show that this deceleration induces mass flows across level surfaces and that these flows redistribute temperature and density in the Earth and produce an excess equatorial bulge. This mechanism does not require large lower mantle viscosity, unlike mechanisms discussed by Munk and MacDonald (1960) and McKenzie (1966). Therefore it does not suffer from the difficulties pointed out by Goldreich and Toomre (1969).

In contrast to the deduction of the equations of precession and nutation adopted as a standard by the IAU, the authors develop a rigorous theory of the rotation of the Earth taking into account the inequality of the equatorial moments of inertia of the Earth and retaining small terms usually neglected to simplify an approximate solution.

The equation is expressed in terms of the so-called Beletsky-Chernousko's variables used in astrodynamics.

Density within the Earth is expressed by means of generalized Fourier series as a function of the coordinates of a point: its distance from the geocenter, colatitude, and longitude. The following data are used to obtain the coefficients of the series: the parameters of the Earth ellipsoid (assumed to be biaxial), the dynamical flattening of the Earth, the Stokes constants, and the density jumps at four surfaces according to seismological data.

The model of the Earth proposed by the authors is composed of five layers, the density in each layer being expressed as a function of the distance from the center of the Earth by a polynomial of fourth degree. To verify the model, periods of the fundamental modes of spherical and torsion oscillations are derived and compared with observations of the free oscillations of the Earth. The maximum difference is within the errors of the observed periods.

The first approximation of the figure of a fluid planet is obtained by assuming hydrostatic equilibrium with respect to its gravitational self-attraction and the centrifugal force. When the speed of rotation is not too fast, the equipotential surfaces may be considered to an excellent approximation as ellipsoids of revolution. It is easy to show that these hydrostatic equipotential surfaces are surfaces of equal density (p).

The theory of Molodensky (1961) on dynamical effects of a stratified fluid outer core upon nutations and diurnal Earth tides is reconstructed on a new and probably much simpler ground. A theory equivalent to Molodensky's is well represented on the basis of two linear equations for angular-momentum balance of the whole Earth and the fluid outer core, which differ from the well-known equations of Poincaré (1910) only in the existence of products of inertia due to deformations of the whole Earth and fluid outer core. The products of inertia are characterized by four parameters which are easily computed for every Earth model by the usual Earth tide equations. A reciprocity relation exists between two of the parameters. The Adams-Wiliamson condition is not a necessary premise of the theory. Amplitudes of nutations and tidal gravity factors are computed for three Earth models. A dissipative core-mantle coupling is introduced into the theory qualitatively. The resulting equations are expressed in the same form as those of Sasao, Okamoto and Sakai (1977). Formulae for secular changes in the Earth-Moon system due to the core-mantle friction are derived as evidences of internal consistency of the theory.

According to the respective restoring forces of self-gravitation, Coriolis force, and inertial coupling at the boundaries, the free oscillations of a contained fluid can be classified into gravitational, inertial, and toroidal oscillations. For the outer core of the Earth, however, due to the interplay of rotation, elasticity, and self-gravitation, the gravitational undertones and inertial oscillations are not distinguishable. Both have eigenfunctions consisting of spheroidal and toroidal parts of about equal amplitude, and exist in alternating allowed and forbidden zones depending on the gravitational stability of the outer core. The forbidden zones for a stable core correspond to the allowed zones for an unstable core, while for a neutrally stratified core there appear to be no forbidden zones. The eigenfunction of a toroidal mode consists essentially of a primary toroidal field and a secondary spheroidal component of the order of ellipticity, coupled at the outer core-mantle or outer core-inner core boundary. Therefore, in general, toroidal core modes appear in doublets Sn+1m Tnm and Sn−1m Tn−1m with degenerate frequency equal to 2m/n(n+1) times the angular frequency of rotation of the Earth. The ellipticities of the outer core boundaries are responsible for the removal of the degeneracy. It is shown that the primary toroidal and secondary spheroidal fields constitute the “generalized Poincare motion” which, for the fundamental mode S21T11, reduces to the “simple motion” defined by Poincare in 1910. Numerical solutions have been obtained for all three types of free core modes. While those for gravitational undertones and inertial oscillations are obtained by arbitrarily truncating the hydrodynamic equations, it is shown that the eigensolutions for toroidal modes are correct to first order in ellipticity due to the particular geometry of the outer core of the Earth.

Realistic models of the Earth are known to possess a solid anelastic inner core, mantle and crust, and a fluid core and oceans. How might we go about calculating the theoretical free period of the Chandler wobble of such an Earth model? Let xi be a set of Cartesian axes with an origin at the center of mass, and let ωi be the instantaneous angular velocity of rotation of these axes with respect to inertial space. The net angular momentum is then Cijωj + hi, where Cij is the inertia tensor, and hi is the relative angular momentum. Let us affix the axes xi in the mantle and crust by stipulating that the relative angular momentum is that of the core and oceans alone, i.e., hi (mantle and crust) = 0; hi = hi (core and oceans). For an infinitesimal free oscillation of angular frequency σ, we can write ωi = Ω(δi3 + mi eiσt), Cij = A(δilδjl + δi2δj2) + Cδi3δj3 + cij eiσt, and hi = hi eiσt, where Ω is the mean rate of rotation and A and C are the mean equatorial and polar moments of inertia.

The observed eigenperiod of the Chandler Wobble is about 435.2 sidereal days while the theoretical eigenperiod of a rigid body having the same composition and geometry as the Earth is about 305 days. The attempt to reconcile these two numbers has led scientists to study theoretically the free wobble and nutation of various classes of rotating bodies.

Cavity, topographic and geologic effects have similar influences on the observed tidal variations of tilt and strain. They cause the locally observed tilts and strains to differ from the “true” or regional values.

Recently theories of the Earth's rotation based on models with an elastic mantle and fluid core have achieved considerable success. It was assumed in these models that the dissipative (electro-magnetic and viscous) couplings between the fluid core and the mantle have negligible effects. The discrepancies between the theories and the observations were much reduced. It seems, however, that these theories are not sufficiently successful in explaining the observed phenomena concerning the Chandler wobble. For example, we had a very small polar radius in the decade around 1930, and the phase of the polar wobble was much advanced in this decade compared with the mean period of revolution. The apparent period of the polar wobble maintained an almost constant value of 1.16 yr during 1930-1942 (Sugawa 1969; Guinot 1972; Stoyko 1972). The present author (Sekiguchi 1975) found from the latitude observations between 1830 and 1860 that the amplitude was also diminished and the period had an almost constant value of 1.16 yr. The common behaviour of the polar wobble in both periods is difficult to explain as an accidental happening.

The paper deals with the behavior of the Earth's pole when exclusively random excitations are at work (e.g. internal displacements of matter, treated as a process of stochastic character). The title of the paper is similar to that of a paper of N. Sekiguchi whose probabilistic final deductions are very ingenious. However they have been applied to a wrong solution of the basic differential equation system. The correct solution is more complicated and does not afford such an advantageous practical possibility of applying the probabilistic treatment with success.

Differences of latitudes and of mean latitudes of stations located along a common meridian were studied in order to find influences of local geophysical phenomena on their variations. Some correlation of variations of the mean latitude of Belgrade with the occurrence of earthquakes in the vicinity can be noticed as well as instabilities of the mean latitude of stations located near sea coasts. Some attempts at measurements of variations of the meridian component of the vertical and a discussion of spectral analysis of latitudes and of mean latitudes of considered stations are presented.