A study of the changes in the rate of rotation of the earth

It is shown that the observed fluctuations in the moon's mean longitude are compatible with the hypothesis that the rate of rotation of the earth is affected by cumulative random changes. A solution of the secular accelerations based on this assumption yields (+2.2"±3.8")T² and (1.01" ± 0.28")T² for the T² terms in the mean longitudes of the moon and the sun, respectively. The resulting value for the secular increase in the length of the day is +0.00135s±.00038s per century. The principal uncertainty in these evaluations is due to the random process which causes the amplitude of the fluctuations to increase proportionally to the power 3/2 of the time and produces a spurious quadratic term with mean coefficient inversely proportional to the square root of the interval of time covered by the observations.