IntroductionThe frequency Fc and quality factor Qc of the Chandler wobble, the Earth's free nutation with a nearly 14 month period, are of geophysical interest because they provide information about the Earth's elastic and anelastic properties at a frequency well below the seismic band. Smith and Dahlen [1981] provide a thorough review of the relationships between Fc, Qc and the Earth's physical properties.Estimates of Fc and Qc are made from observations of polar motion, the movement of the rotation axis with respect to geographical coordinates. In this study we use the monthly polar motion series of the Intemational Latitude Service (ILS) [Yumi and Yokoyama, 1980], for the period January 1900 through December 1978, with supplementary data for the period 1979-85. The ILS data form the longest available series that has been reduced in a homogeneous way, and should provide the most reliable estimates. For the period 1979-85, both the Satellite Laser Ranging (SLR) data [BIH Annual Reports] and optical astrometry data [International Latitude Observatory of Mizusawa (ILOM)] are available. We smoothed and then interpolated both SLR and ILOM series with a cubic spline to obtain pole positions at the same intervals as the ILS series. The results from the combined ILS/SLR and ILS/ILOM series were essentially identical, and the remainder of this paper will refer to the results obtained with the ILSflLOM series. We use estimators that were developed by Jeffreys in two papers appearing in 1940 and 1968. The symbols Fc and Qc denote the true values of the polar motion parameters, while F and Q indicate estimates. We refer to the estimator from the 1940 paper by the Roman numeral I, and to estimates derived from it as F(I), Q(I). Similarly, F(II) and Q(II) refer to the estimators in Jeffreys' 1968 paper. Both I and II were developed from maximum likelihood arguments, assuming that a Gaussian random process is the cause of polar motion near the Chandler frequency. While this may not be correct, Monte Carlo experiments demonstrate that it is probably not a critical assumption, particularly for estimator II. The Monte Carlo experiments also permit an evaluation of estimator bias and variance in the presence of noise. The discrete polar motion equation [Wilson, 1985] is the foundation for understanding Jeffreys' maximum likelihood estimators. This equation relates time samples of pole position, M, to time samples of the excitation axis position, X. Using the complex pole coordinate description in which the real part is associated with motion along the

Summary A new reduction of the International Latitude Service Observations for the years 1899–1977 has recently been completed under the direction of Dr S. Yumi and the International Astronomical Union Commission 19. This paper examines the annual, Chandler frequency, and long period motion of the Earth's pole implied by this new homogeneous data set. The estimated annual polar motion differs slightly from earlier results. The new value for the Chandler frequency is also very close to earlier results, but the estimated Q is somewhat larger, as might be expected by a reduction in noise level. Analysis of the long period motion shows an apparent drift and, in agreement with earlier studies using other data, there is some evidence of an approximately 30‐yr oscillation in the pole position.

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Abstract. We have estimated the Chandler frequency from a variety of polar motion time series derived from optical and space geodetic data which span various time periods from 1846 through the early 1990s. Estimates of F vary, depending upon which time series is employed, but the variation is not significant when associated intervals of confidence are considered; thus there is no evidence that the true Chandler frequency has varied. Using a maximum likelihood method, our preferred estimate of F is 0.8433 cycles per tropical year (cpy), _+0.003 cpy, or equivalently a period of 433.1 mean solar days (msd), _+ 1.7 msd. Estimates are given on the condition that the Gaussian statistical model of the excitation process is valid, and new approaches which employ observations of the polar motion excitation process should eventually provide better estimates, which may differ from those determined here. IntroductionThe theory of the motion of the Earth around its center of mass is developed in such a way that the motion is separated into two distinct parts which affect the terrestrial and celestial coordinates in different ways. The first of these is a free motion, which exists independently of external forces. Originally There are two issues to resolve when examining whether variability in estimates of F should be interpreted as variability in F. In the first place, the analysis is only meaningful when the component is above the noise level in the data. This condition is met in the case of the Chandler wobble, with a signal amplitude of a few hundred milli arc seconds (mas) and noise levels ranging from 10 mas or more in older optical data to below 1 mas in recent space geodetic data. The second issue is the adoption of an estimation technique firmly tied to the physical aspects of the problem that can provide meaningful statements of confidence, taking into consideration uncertainty introduced by both noise and the finite duration of the data set. The analysis method in this paper, based on the maximum likelihood principle described by Jeffreys [1940, 1968], meets these requirements, as discussed in section 3. 20,439