Dynamic Effects of a Liquid Core

Abstract

The effect of the inertia of the Earth's core on the bodily tides and related phenomena is examined. Previous discussions, which have neglected this inertia, are found to be sufficiently accurate for the semidiurnal, fortnightly, and semiannual tides, but to need modification for those depending on terms of the forms zx, zy in the gravitational potential. A theory of these is developed for an Earth model of Wiechert type, with a fluid core, and applied to the free variation of latitude and the lunar nutation. It was known that with a rigid shell a fluid core would produce a shortening of the free period, in contradiction with observation; but it is fouhd that with a shell of reasonable rigidity (1.9 × 10 12 dynes/cm. 2 ) the motion induced in the core is much less than with a perfectly rigid shell, and that agreement between theory and observation can be obtained with a rigidity differing little from what was found satisfactory when the inertia of the core was neglected.