Ten frequency components of short period latitude variations and corrections for the declination at an epoch and the proper motion in declination are estimated simultaneously. The short period variations are nearly diurnal and semi-diurnal and are supposed to be due to nutations and Earth tides. Analysis is by the least-squares chain method with weights for individual observations, recently developed by Manabe et al. (1977). Weights are assigned on the assumption that the observational errors follow a normal distribution, whose dispersion changes night by night. Among all possible 1024 combinations of the short period variations, the best is chosen on the basis of the minimum AIC procedure. The data used are the results of the homogeneous recalculation of the ILS observations, 1399-1978. This is considered to be the optimal astrometric data set for investigating nutations, because of its long time-span, homogeneity and size. Declinations are estimated for each of the seven observational periods with mean errors smaller than 001. The mean errors of the proper motions are of the order 0002/y. Among the short period variations, significant estimates are obtained for the terms corresponding to the lunar fortnightly, solar semi-annual and lunar nodal nutations, and the M2 tide. The mean errors are shown to be greatly reduced and the entire data set is analyzed. An effort is made to distinguish the preferred theoretical model.