New Determination of the Polar Motion from 1890 to 1969

Abstract

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, ……. φ_n, 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 h_i 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 z_κi 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.