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VIII. The Rotation of an Elastic Spheroid. 
By S. S. Hough, M.A., Fellow of St. John's College , and Isaac Newton Student in 
the University of Cambridge. 
Communicated by Professor G. H. Darwin, F.R.S. 
Received December 12, 1895,—Read January 16, 1896. 
Introduction. 
It is well known that, if a rigid body whose principal moments of inertia are *1, (H 
be set rotating about its axis of symmetry, and then be subjected to a slight dis¬ 
turbance, it will execute oscillations about its mean position, in consecpience of which 
the axis of rotation will undergo periodic displacements relatively to the body in a 
period which bears to the period of rotation the ratio & : (P — *1. The object of the 
present investigation is to determine to what extent this period will be modified if the 
body, instead of being perfectly rigid, is capable of elastic deformations. 
The problem has important bearings in connection with the theory of the Earth’s 
rotation. The remarkable researches of Dr. S. C. Chandler, published in a series of 
papers in the ‘ Astronomical Journal,’* have placed it almost beyond a doubt that the 
axis of rotation of the Earth is subject to a series of displacements, the most impor¬ 
tant of which consists of a periodic motion in all respects similar in character to the 
oscillation mentioned above, but having a period considerably in excess of that which 
theory would require if the Earth could be regarded as perfectly rigid. It is natural 
to suppose that this motion has its origin in the same cause, but that the theory by 
which the period has previously been assigned is in some respects defective. The 
most plausible attempt which has yet been made to correct this theory is that given 
by Newcomb,! who shows, by an elegant geometrical method, that the elasticity of 
the solid portions of the Earth and the mobility of the ocean will each have the effect 
of prolonging the period. He then proceeds to obtain a numerical estimate of this 
extension, basing his calculations on certain results given by Thomson and Tait| 
with reference to the deformation of an elastic sphere. In order to make these 
results applicable, several assumptions have to be made which do not appear to me 
* Vol. 11, et seq. For a summary of Chandler’s results, vide ‘ Science,’ May 3, 1895. 
t ‘ Monthly Notices of the Royal Astronomical Society,’ March, 1892. 
+ ‘Natural Philosophy,’ Part II., § 837. 
8.5.96 
