512 
MR. HENNESSY’S RESEARCHES IN TERRESTRIAL PHYSICS. 
posed to be spheroidal, oblate, and nearly spherical. Both shell and nucleus are 
supposed to be formed of strata increasing’ in density, according to unknown laws, 
as the radii of these strata decrease. 
If the earth were solid from its surface to its centre, all the phenomena of its rota- 
tion could be determined by the integration of three differential equations relative to 
its motion about its centre of gravity, and of three more relative to the motions of 
its principal axes referred to three rectangular axes fixed in space. The constants 
contained in these equations would depend on the attractions of exterior bodies, on 
the impressed forces, and on the arrangement of the particles composing the earth. 
It is evident that similar equations would suffice for the case of an empty shell con- 
stituted in the manner above mentioned, after the substitution of the constants 
depending on the magnitude and internal constitution of the shell for those depend- 
ing on the magnitude and internal constitution of the entirely solid spheroid. By 
adopting this method, no new analytical transformations are required in discovering 
the phenomena of the shell’s independent rotation, for we can thus avail ourselves of 
the researches already made by geometers relative to the rotation of the entirely 
solid spheroid. I have therefore thought it sufficient for our present purposes to 
merely present the following conclusions to which I have arrived, by using the 
method above indicated. 
1st. If the original impressed forces were the same in direction and intensity for 
the shell as for the entirely solid spheroid, the angular velocity of the former about 
its instantaneous axis would be greater than the angular velocity of the latter about 
its instantaneous axis. 
2nd. The influence of exterior disturbing forces would be insensible relative to the 
rotation of the shell about its centre, provided that its strata possess nearly similar 
laws of arrangement with those of the solid spheroid. 
3rd. The motions in space of the axes of the shell due to the action of exterior 
disturbing bodies, would be affected to a greater degree than similar motions of the 
axes of the solid spheroid. 
If no other forces acted on the fluid nucleus besides the attractions of its own 
particles, the attraction of the shell, and centrifugal force, its surface would be an 
ellipsoid of revolution, and it would rotate steadily about the axis of its greatest mo- 
ment of inertia. If the action of exterior disturbing bodies be added to these forces, 
tidal oscillations in the surface of the nucleus would tend to be produced ; but it is 
evident, that unless the disturbing forces were very great, the position in space of 
the axis of rotation of the mass would be much less affected than if it existed in the 
solid state. Let, in addition to the forces already enumerated as acting on the fluid 
nucleus, certain molecular forces be conceived to act on its particles, by which the 
whole mass might in general acquire a tendency to expand or contract, and also to 
change its form. This class of forces may be conceived to be resolved into two pressures 
acting at the inner surface of the shell, one of them being supposed to be constant 
for every point, and the other variable. If, moreover, the constitution of the shell 
