An outstanding problem is to reconcile the Moon's rotation with the persistence of its non-hydrostatic dynamical ellipticities. The first requires imperfection of elasticity under strains of order 10−7; the second apparently little under larger ones.

Lomnitz gave experimental evidence that creep is linear at elastic shears from 10−5 to 10−4, indicating that a linear rule could be right at still smaller values. Positive evidence for the Earth comes from the damping of the 14-monthly nutation, which has a relaxation time of the order of 30 yr. Most work on imperfect elasticity has assumed that under constant shear stress the strain increases with time either like t (elasticoviscosity) or like logt. If the result from the 14-monthly nutation, with elasticoviscosity, is applied to the Moon, the dynamical ellipticities would have subsided considerably in the last 200 yr. With the logarithmic rule an S pulse at 80° would have its beginning spread out over about 70 s and be unreadable. These contradictions are avoided if the increase under constant stress is about like t0.2. The resulting law involves two constants. Without change of these, applications are made to other phenomena. The rotations of the Moon and of other satellites whose rotations are known are explained; so is the persistence of the Moon's dynamical ellipticities; also the failure to detect three free oscillations that might theoretically exist. Elasticoviscosity would imply rapid disappearance of the non-hydrostatic second and third harmonics in the Earth's gravitational field; this is avoided with the new law. Study of damping of free vibrations of the Earth (including surface waves) has usually assumed the logarithmic law, but it appears that the new law fits the data at least as well, and that it may also explain those that have been interpreted in favour of layers of low velocity. It appears that the damping at depths up to 400 km or so is much more severe than the average for the Earth's shell, and more evidence for shorter periods is much needed.

Any law with an index less than 1 would forbid thermal instability (convection) and continental drift.

Coordinates of the pole from the past ILS for the period 1900.0–1962.0 were reduced to the Conventional International Origin and published by us in 1969. Among them, data for 1941.0–1962.0 were revised owing to the revisions in their original values which were made and published recently by Nicolini and Cecchini.

To obtain the coordinates of the Earth's pole almost all series of systematic latitude observations that continued for more than two years have been utilized. They are listed in Table I which comprises 92 series of observation at 72 observatories.

Computation was made by the following stages. As initial data we used normal values of latitude φ1, φ2, ……. φn, i.e. the means of instantaneous latitudes over successive intervals of time. These values were smoothed using Whittaker's numerical method which is capable of giving the most probable curve of latitude variation. The smoothed values φ′ satisfy the following condition where hi is a measure of precision, λ2 an arbitrary number by means of which the degree of smoothing is set, and Δ3 designates the third difference of φ′. Whittaker's method was applied in different modifications according to whether or not the normal values of φ′i had an equal weight and were given at equidistant moments of time.

For the origin of the system of coordinates we adopted the mean pole of the epoch of observation. Because of this the data given in Table II represent only the periodic part of the polar motion in the region of frequency from 0.77 to 2 cycles per year. In this connection the sequence of φ′ was subjected to filtration in order to eliminate variation of the mean latitude.

Coordinates of the pole were computed in two approximations. First, it was assumed that all the series are of the same accuracy and so they were taken with an equal weight.

The polar coordinates obtained on this assumption are denoted by x1, y1 and shown in the second and third columns of Table II. The divergences of the smoothed values φ′i from the latitudes computed with x1, y1 were denoted by zκi where the index κ designates the number of a series. Then for the second approximation each series of observation was taken with the weight inversely proportional to the mean value of for this series. The polar coordinates obtained in the second approximation are denoted by x2, y2 and given in the last two columns of Table II.

The full paper with the tables will be published by the Ukrainian Academy of Sciences as a separate book.

A general revision of the calculations of the ILS is necessary, for several reasons. The first fundamental step has been performed with the Melchior-Dejaiffe catalogue. From it, improved values of the screw pitches and their adjustments, new investigations upon closing errors in all the ILS stations with introduction of the tidal deflection of the vertical, new deduction of the Kimura z-term and definitive calculations of x, y, z are obtainable.

One- and two-component models for the Chandler motion are investigated with the use of historical data. Evidence for a two-component motion is more convincing from both the data-analysis and the geophysical point of view.

Spectral analyses of 70 yr of ILS-IPMS data on the variation of latitude are discussed from the point of view of the confidence limits that can be placed on statistical estimates. The available data cannot be used to support the existence of two resonant frequencies in the Chandler wobble, nor are the latter required to remove an anomaly in the value of Q for wobble as long as the oceans cannot be dismissed as an energy sink.

The 14-monthly variation of the Earth's axis is a free oscillation, and like others it is damped, and must be maintained by some irregular disturbance. In addition there are complications from the annual variation and observational error. The method adopted is first to analyse the data from 1899 to 1967 over 7-yr intervals, to eliminate the free period as well as possible and leave a mean value of the annual terms. The mean displacements fluctuated considerably. With a unit 0·001″ l(=x) ranged from – 15 to + 53, m(= – y) from the start to 1947 from – 41 to + 3, in both cases quite irregularly, but m reached – 164 in 1955–61 and has reached – 225 in 1962–8. The apparent standard errors are mostly about 6. This behaviour is inconsistent with any hypothesis of a uniform rate of drift in either the pole or the observatories. A smooth formula for interpolating the means was adopted; this and the mean annual terms were subtracted, and the remainder was analysed for harmonic terms of 14-month period. Drift of phase gave a correction to this trial period. A model on Yule's lines was used to estimate the parameters in a disturbed system. The remaining observational error over 14-month intervals turned out to be very small. The final period was 433·15 ± 2·23 mean solar days. The damping factor e–k in 14 months gave k = 0·05 ± 0·034, suggesting a time of relaxation between 14 and 73 yr, with a most probable value of 23 yr.

The coordinates x and y of the pole related to mean pole of the epoch in the period 1900–1962 for the ILS station were calculated utilising the method proposed by Orlov (1955). The values of the latitudes are those reduced in the homogeneous system of Carnera-Cecchini by Proverbio et al. (1969). The values of the amplitudes and periods of the polar motion were calculated. The comparison of the data seems to confirm a correlation between the amplitudes and periods of Chandler motion, that is the validity of the time-variable model suggested by Melchior (1949) and other authors.

Guinot and Feissel (1968), Okazaki and Nasaka (1970) reported the marked discrepancy between annual terms of the polar motion obtained by time and latitude observations. The disturbing effects of local non-polar terms in latitude variation on pole coordinates are discussed in the first half of this paper.

From an analogy between time and latitude observations, we can conclude that Δx and Δy in the pole coordinates obtained from time observations are proportional to a part of the common fictitious term ΔT in the rotation of the Earth. Using ΔT obtained from Okazaki's data for the same interval as Guinot's and Feissel's data, a test example is given as follows: If we apply the above corrections to the pole coordinates obtained from time observations, we can derive the coordinates x and y which are comparable to those of the ILS. Δαα, ΔS and local non-polar terms (z5 – z4) in the ILS latitude determination may be considered as the sources of ΔT.

Computations of the polar coordinates are carried out by the use of time data and of latitude data separately. The results from time data and those from latitude data are proved to have mutual differences in annual term in particular. That is, polar loci obtained from latitude results give almost circular forms, while those from time results give elliptic forms elongated rather seriously on the X-axis.

Short period terms ranging from 0.3 to 6.0 yr. are resolved from 13.5 yr data of UT1 and polar motion on periodograms, considering the mutual interference effects caused by truncation of data. Beside principal terms known well, 26 month term is reconfirmed but any Chandlerian term is not found in UT1. Minor amplitude terms are found around 0.48, 0.86, 1.36, 1.58, 3, and 4 yr in UT1, and 1.12, 1.26, and 1.43 yr in polar motion.

It may become possible to explain much of the behaviour and remarkable regularity of fluctuations in reported annual and secular polar motions if the potential that causes an immediate excitation is also a factor in that excitation's rate of change afterwards.

The Chandler frequency, for example, being a function of the deformation excitation, should then vary with the librational and nutational displacements of the pole of rotation. It is found that the frequency does in fact do so.

The annual excitation would be affected as well. The steady and seasonal primary excitations are known to cause free and forced nutations that are accompanied by periodic secondary excitations. These would arise partly at once and partly in the course of time; they would modulate the primary annual excitation and also one another, according to the period of the beats between the annual and Chandler nutations. It is found that the reported annual excitation shows phase and amplitude fluctuations of this kind. (The data also show another large excitation that occurred briefly on two occasions).

Finally, the amplitude and phase of the secular librations appear to have followed an expression that is obtained by integrating the rates of change of excitation. This expression is a function of the amplitude of the annual excitation and the period of the beats between the annual and Chandler nutations.

The paper estimates the expected rates of changes in the coordinates of various observatory networks (IPMS, BIH, VLBI, etc.) due to the secular motion of the pole and/or continental drift according to the Le Pichon Model. Based on these estimates, suggestions are made as to what to observe and over what time span to separate the effect of continental drift and secular polar motion.

The phenomenon known as the secular polar motion is, in essence, a relative displacement of the mean pole of the epoch of observation and the Conventional International Origin (CIO). The latter is attached to the zeniths of the five international latitude stations. If the zeniths were fixed relative to one another, or, in the terminology of A. Danjon, formed an invariable constellation, then the CIO could be considered as fixed with respect to such a constellation. But this is not the case: displacements of zeniths with respect to one another do occur. The question is how large they are.

Observations of astronomical latitude made at Washington are analyzed for a secular trend. Comparison with the variation of latitude based on the path of the rotational pole of the International Polar Motion Service shows linear trends in good agreement. No evidence is found for a 24 yr libration of the pole. Systematic differences between observed and derived latitudes indicate that there are nonpolar variations in Washington latitude. Evidence is presented for the correlation of seismic activity with abrupt changes in the nonpolar variation, and the consequences of a changing geopotential surface are discussed with regard to observations of the rotational pole of the Earth.

An analysis on the secular motion of the pole has been carried out utilising the latitude observations of the ILS stations reduced to the ØII(i) system (Proverbio et al., 1969).

The existence of long periodic terms in the polar motion as found out by Markowitz (1960) was confirmed.

The secular displacement of the polar motion calculated abstracting from long period terms results 0″.00294 for year along the meridian 65°.6 W.

A probable drift of continental blocks with average Northward rate of 1–2 cm/year for Eurasia and 1 cm/year for North America has been suggested. The possible drift emphasized for Japan is on the contrary of 1 cm/year southwards.

Locations of Doppler satellite observing stations have been revised to obtain a set which is more self-consistent and more consistent with the CIO pole. Residuals of satellite observations for 1970 have been analyzed using the new coordinates to determine mean and standard errors for five days of observations of latitude versus station, time of day, and elevation angle. The accuracy of the determination of latitude is about 4 meters at moderate and high elevation angles. But since more satellite passes occur at lower elevation angles, the accuracy of determination of a component of position based on five days of observation of one satellite is only about 2 meters.