Excerpt from The Tidal and Other Problems

In the treatment of the earth's deformations, which is to be the subject of a following paper, it is essential to know whether changes in the rate of the earth's rotation must be regarded as one of the important factors or not. If the rate of rotation has appreciably varied during geological history, it is almost certain that the oblateness of the earth-spheroid has also varied, for unless the rigidity of the earth greatly exceeds that of any known substance, it must have been modified in form under changing rotation so as to approach the shape it would assume if it were a perfect fluid. It would be an error to assume, as is sometimes done, that the earth would conform to the fluidal shape perfectly, but that it would approach to this with a measurable degree of closeness seems to be beyond question. If there was a change from a high rotational speed, and con sequent high degree of oblateness, to a slower speed with less oblateness, the surface area of the earth must have been reduced, because the nearer such a body approaches a sphere, the less the area of its surface, the greater its average gravity, and hence the greater its degree of compression. This is brought out numerically, with a high order of approximation, in the accompanying paper of Professor Slichter. There will be occasion in the course of the present paper to consider in detail the application of this supposed reduction.

Whatever therefore may be the difficulties attending a treatment of past rates of rotation of the earth, it is imperative that this element of the problem of deformation be recognized and evaluated so far as lies in our power.

The problem may be approached on two rather distinct lines, one of which is astronomic but rests back so radically on postulates derived from theories of cosmogony that it may almost be called cosmogonic, and the other of which is geologic and rests on the direct or implied teachings of terrestrial evidence.

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