The theory of nutation and the variation of latitude: the Roche model core

The theory given in a previous paper is modified by the use of a core with the density a quadratic function of the radius, the variation of density being wholly due to pressure. Three pairs of cubic terms are introduced into the displacements. The period of the Eulerian nutation would be 395 days, and the amplitude of the i9-yearly nutation would be multiplied by a factor . Allowance for the effect of the ocean would increase the former period to about 430 days, and in both respects there is now tolerable agreement with observaations. Correcting factors are given for the other principal nutations. Those for the fortnightly nutation do not differ much from those for the central particle model. There are substantial changes for the semiannual nutations, owing to changes in free periods that occur in their neighbourhoods. The i -yearly nutation in longitude remains anomalous.