t 193 ] 
X. Researches in Physical Geology. — Second Series. By W. Hopkins, Esq. M.A. 
F.R.S., Fellow of the Royal Astronomical Society, of the Geological Society, and 
of the Cambridge Philosophical Society. 
Received February 17, — Read March 7, 1839. 
On Precession and Nutation, assuming the Interior of the Earth to he fluid and 
heterogeneous. 
HAVING in my last memoir completed the investigation of the amount of Preces- 
sion 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 heteroge- 
neous. 
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 f, we have for the conditions of equilibrium 
(II.) § = 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 
JB' (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. 
The forces (1.) and (2.) satisfy condition (I.), as is well known ; as do likewise (3.), 
(4.) and (5.), (First Series, Arts. 8, 9, 10.). The force (6.), as has been shown (First 
Series, Art. 10.), gives Z = 2 u 1 s j3 . x, which does not really satisfy the condition ex- 
pressed by equation (I.), since it does not satisfy the well-known equations from 
which it is derived*. If, therefore, the forces (1.) (2.) (3.) (4.) and (5.) only acted on 
* It is hardly necessary to remark that equation (I.) is satisfied by Z = 2 w 2 e /3 . x, only in conse- 
quence of the introduction of the extraneous factor Y (which here = 0) in the e limi nation of p from the three 
equations from which (I.) is derived. 
MDCCCXL. 2 C 
