[ 469 |] 
XII. The Oscillations of a Rotating Ellipsoidal Shell containing Fluid. 
By 8. 8. Hoven, B.A., St. John’s College, Cambridge. 
Communicated by Sir Ropert S. Baur, F.R.S. 
Received January 18,—Read February 7,—Revised March 28, 1895. 
Introduction. 
Ty a paper published in ‘ Acta Mathematica,’ vol. 16, M. Fonie announces the fact 
that the latitude of places on the earth’s surface is undergoing periodic changes in a 
period considerably in excess of that which theory has hitherto been supposed to 
require. This result has been confirmed in a remarkable manner by Dr. S. C. 
CHANDLER in America (vide ‘ Astronomical Journal,’ vols. 11, 12), who, as the result of 
an exhaustive examination of almost all the available records of latitude observations 
for the last half-century, has assigned 427 days as the true period in which the 
changes are taking place. 
The old theory, based on the assumption that the earth was rigid throughout, led 
to a period of 305 days, and M. Foute proposes to account for the extension of this 
period by attributing a certain amount of freedom to the internal portions of the 
earth. The earth he supposes to be composed of “a solid shell moving more or less 
freely on a nucleus consisting of fluid at least at its surface.” The argument advanced 
by M. Fouts in favour of this constitution of the earth, namely, the independence of 
the motions of the shell and the nucleus, appeared to me to be unsatisfactory, and I 
therefore proposed to myself to test the validity of it by examining a particular case 
which lent itself to mathematical analysis, namely, that in which the internal surface 
of the shell is ellipsoidal and the nucleus consists entirely of homogeneous fluid. 
The principal axes of the shell and of the cavity occupied by fluid are assumed to 
be coincident, and the oscillations are considered about a state of steady motion in 
which the axis of rotation coincides with one of these axes. It is clear that a steady 
motion will be possible in this case, and that such a motion will be secularly stable 
in the event of the axis of rotation being the axis of greatest moment for both the 
shell and the cavity. 
The problem was originally treated by the analysis used by PorncaRE in his 
memoir on the stability of the fluid ellipsoid with a free surface (‘ Acta Mathematica,’ 
25.1095: 
