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 tidal deformation is nearly as great as though it were of steel. This conclusion has been confirmed recently by Simon Newcomb, from the study of the observed periodic changes in latitude. For an ideally rigid earth the period would be 360 days, but if as rigid as steel, it would be 441, the observed period being 430 days.

Among text-books on elasticity may be mentioned the works of Lamé, Clebsch, Winkler, Beer, Mathieu, W. J. Ibbetson, and F. Neumann, edited by O. E. Meyer.

Riemann's opinion that a science of physics only exists since the invention of differential equations finds corroboration even in this brief and fragmentary outline of the progress of mathematical physics. The undulatory theory of light, first advanced by Huygens, owes much to the power of mathematics: by mathematical analysis its assumptions were worked out to their last consequences. Thomas Young[95] (1773–1829) was the first to explain the principle of interference, both of light and sound, and the first to bring forward the idea of transverse vibrations in light waves. Young's explanations, not being verified by him by extensive numerical calculations, attracted little notice, and it was not until Augustin Fresnel (1788–1827) applied mathematical analysis to a much greater extent than Young had done, that the undulatory theory began to carry conviction. Some of Fresnel's mathematical assumptions were not satisfactory; hence Laplace, Poisson, and others belonging to the strictly mathematical school, at first disdained to consider the theory. By their opposition Fresnel was spurred to greater exertion. Arago was the first great convert made by Fresnel. When polarisation and double refraction were explained by Young and Fresnel, then Laplace was at last won over. Poisson drew from Fresnel's formulæ the seemingly paradoxical deduction that a small circular disc, illuminated by a luminous point,