III. Researches in physical geology.—Third series

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On the Thickness and Constitution of the Earth's Crust . 1. The result at which I arrived in my preceding memoir, respecting the precessional motion of the pole, on the hypothesis of the earth’s interior fluidity, is the following: P' - P 1 = (1 - ϵ/ϵ 1 ) (1 - η/1 + h / q 5 - 1) P 1 , . . . . . . . . . . (1.) where P 1 denotes the precession of a solid homogeneous spheroid of which the ellipticity = ϵ 1 , that of the earth’s exterior surface, and P' the precession of the earth, supposing it to consist of an interior heterogeneous fluid, contained in a heterogeneous spheroidal shell, of which the interior and exterior ellipticities are respectively ϵ and ϵ 1 , the transition being immediate from the entire solidity of the shell to the perfect fluidity of the interior mass. 2. In the application of this result to the actual case of the earth, we must observe, in the first place, that, supposing the interior mass to be fluid, its fluidity cannot be quite perfect , as explained in the introductory observations to my first memoir. Consequently the assumption, made in our investigations, of the absence of all tangential action between the shell and fluid will not be accurately true. Moreover, it would seem extremely probable that the transition from the solidity of the shell to the fluidity of the interior mass, instead of being immediate, must be gradual. If, however, the thickness of the shell be not considerable with reference to the earth’s radius, the fluidity of the portion not remote from the centre will be nearly perfect, and the whole of the interior mass, with the exception of that part near the actual solid portion, may, as a near approximation, be considered as perfectly fluid with reference to any mechanical action upon it. Again, supposing the change from the solidity of the exterior to the fluidity of the interior mass to be continuous, let us conceive a surface passing through all the lowest points of that portion of the mass which may be regarded as perfectly solid, and another surface through all the highest points of that portion which may be regarded as perfectly fluid. The first of these surfaces will be one of equal solidity and the second one of equal fluidity; the fluidity of the mass contained between them being imperfect. Now if we were to consider the whole of this imperfectly fluid mass as entirely solid, we should manifestly take the thickness of the shell too large to represent the actual phenomena depending on that thickness; and if, on the contrary, we should consider the whole of the imperfectly fluid portion as perfectly fluid, we should take the thickness of the shell too small. Hence there must be some surface of equal fluidity (or, if we please so to term it, of equal solidity ) intermediate to the above surfaces, such that if the whole mass superior to it were entirely solid, and that inferior to it entirely fluid, the phenomena of precession and nutation would be the same as in the actual case of a gradual transition from the solidity of the superior to the fluidity of the inferior portions of the mass. When, therefore, we speak of the interior surface of the solid shell with reference to our previous investigations as applicable to the case of the earth, it is this intermediate, or effective surface , which is always to be understood; and the thickness of the earth’s crust, as defined by this surface, I shall term its effective thickness .

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