X. Researches in physical geology.—second series

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On Precession and Nutaion, assuming the Interior of the Earth to be fluid and heterogeneous. Having in my last memoir completed the investigation of the amount of Precession and Nutation on the hypothesis of the earth’s consisting of a homogeneous fluid mass contained in a homogeneous solid shell, I shall now extend the investigation to the case in which both the interior fluid and exterior shell are considered heterogeneous. 1. When accelerating forces X, Y, Z act on any point x, y, z of a heterogeneous fluid mass, of which no part of the surface is free, and of which the density at the point x, y, z is ϧ, we have for the conditions of equilibrium (I.) X( d Y/ dz - d Z/ dy ) + Y ( d Z/ dx - d X/ dz ) + Z ( d X/ dy - d Y/ dx ) = 0. (II.) ϧ = constant throughout each surface of equal pressure. Now the forces which act on the internal fluid of the earth are (1.) The mutual attraction of the different particles of the fluid mass: (2.) The attraction of the solid shell on the fluid mass: (3.) The disturbing force of the sun: (4.) The disturbing force of the moon: The centrifugal force, the planes of rotation being parallel to the tangent plane at B' (fig. 2. First Series, Art. 8.): This may be separated into two parts, viz. (5.) The resolved part on any point acting in a direction perpendicular to the axis of rotation; and (6.) The resolved part parallel to the axis of rotation.

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