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VIII. The rotation of an elastic spheroid

1896; Royal Society; Volume: 187; Linguagem: Inglês

10.1098/rsta.1896.0008

2053-9258

S. S. Hough,

Astro and Planetary Science

It is well known that, if a rigid body whose principal moments of inertia are A, A, C be set rotating about its axis of symmetry, and then be subjected to a slight disturbance, it will execute oscillations about its mean position, in consequence 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 A : C — A. 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 important 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 to be well founded; and it is with a view to examining these assumptions that I have attempted to exhibit the solution of the problem in an analytical form.