XI. Essay towards a first approximation to a map of cotidal lines

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Abstract
Ever since the time of Newton, his explanation of the general phenomena of the tides by means of the action of the moon and the sun has been assented to by all philosophers who have given their attention to the subject. But even up to the present day this general explanation has not been pursued into its results in detail, so as to show its bearing on the special phenomena of particular places,—to connect the actual tides of all the different parts of the world,—and to account for their varieties and seeming anomalies. With regard to this alone, of all the consequences of the law of universal gravitation, the task of bringing the developed theory into comparison with multiplied and extensive observations is still incomplete; we might almost say, is still to be begun. Daniel Bernoulli, in his Prize Dissertation of 1740, deduced from the Newtonian theory certain methods for the construction of tide tables, which agree with the methods still commonly used. More recently Laplace turned his attention to this subject; and by treating the tides as a problem of the oscillations rather than of the equilibrium of fluids, undoubtedly introduced the correct view of the real operation of the forces; but it does not appear that in this way he has obtained any consequences to which Newton’s mode of considering the subject did not lead with equal certainty and greater simplicity; moreover by confounding, in the course of his calculations, the quantities which he designates by λ and λ', the epochs of the solar and lunar tide (Méc. Cél. vol. ii. p. 232. 291.), he has thrown an obscurity on the most important differences of the tides of different places, as Mr. Lubbock has pointed out.

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