The Variation of Latitude

Abstract

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.