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and night. Holden's tables, founded on four years of these observations, were remarkably accurate.

At length men of science began to perceive that such calculations were part of their business; and that they were called upon, as the guardians of the established theory of the universe, to compare it in the greatest possible detail with the facts. Mr. Lubbock was the first mathematician who undertook the extensive labours which such a conviction suggested. Finding that regular tide-observations had been made at the London Docks from 1795, he took nineteen years of these (purposely selecting the length of a cycle of the motions of the lunar orbit,) and caused them (in 1831) to be analysed by Mr. Dessiou, an expert calculator. He thus obtained" tables for the effect of the moon's declination, parallax, and hour of transit, on the tides; and was enabled to produce tide-tables founded upon the data thus obtained. Some mistakes in these as first published (mistakes unimportant as to the theoretical value of the work,) served to show the jealousy of the practical tide-table calculators, by the acrimony with which the oversights were dwelt upon; but in a very few years, the tables thus produced by an open and scientific process, were more exact than those which resulted from any of the secrets; and thus practice was brought into its proper subordination to theory.

42 Phil. Trans. 1831. British Almanac, 1832.

43

The theory with which Mr. Lubbock was led to compare his results, was the equilibrium-theory of Daniel Bernoulli; and it was found that this theory, with certain modifications of its elements, represented the facts to a remarkable degree of precision. Mr. Lubbock pointed out this feature especially in the semi-menstrual inequality of the times of high water. It was afterwards (in 1833) shown by Mr. Whewell to obtain still more accurately at Liverpool, both for the tides and heights; for by this time, nineteen years of Hutchinson's Liverpool observations had also been discussed by Mr. Lubbock. The other inequalities of the times and heights (depending upon the declination and parallax of the moon and sun,) were variously compared with the equilibrium theory by Mr. Lubbock and Mr. Whewell; and the general result was, that the facts agreed with the condition of equilibrium at a certain anterior time, but that this anterior time was different for different phenomena. In like manner it appeared to follow from these researches, that in order to explain the facts, the mass of the moon must be supposed different in the calculation at different places; a result in effect the same was obtained by M. Daussy", an active French hydrographer; for he found that observations at various stations could not be reconciled with the formulæ of Laplace's Mécanique Céleste (in which the ratio of

43 Phil. Trans. 1834. 44 Connaissance des Tems, 1838.

the heights of spring-tides and neap-tides was computed on an assumed mass of the moon) without an alteration of level which was, in fact, equivalent to an alteration of the moon's mass. Thus all things appeared to tend to show that the equilibrium-theory would give the formulæ for the inequalities of the tides, but that the magnitudes which enter into these formulæ must be sought from observation.

Whether this result is consistent with theory, is a question not so much of physical astronomy as of hydrodynamics, and has not yet been solved. A theory of the tides which should include in its conditions the phenomena of derivative tides, and of their combinations, will probably require all the resources of the mathematical mechanician.

As a contribution of empirical materials to the treatment of this hydrodynamical problem, it may be allowable to mention here Mr. Whewell's attempts to trace the progress of the tide into all the seas of the globe, by tracing what he calls Cotidal Lînes ;—lines marking the contemporaneous position of the various points of the great wave which carries high water from shore to shore". This is necessarily a task of labour and difficulty, since it requires us to know the time of high water on the same day in every part of the world; but in proportion as it is completed, it supplies steps between our

45 Essays towards an Approximation to a Map of Cotidal Lines. Phil. Trans. 1833, 1836.

general view of the movements of the ocean and the phenomena of particular ports.

Looking at this subject by the light which the example of the history of astronomy affords, we may venture to repeat, that it will never have justice done it till it is treated as other parts of astronomy are treated; that is, till tables of all the phenomena which can be observed, are calculated by means of the best knowledge which we at present possess, and till these tables are constantly improved by a comparison of the predicted with the observed fact. A set of tide-observations and tide-ephemerides of this kind, would soon give to this subject that precision which marks the other parts of astronomy; and would leave an assemblage of unexplained residual phenomena, in which a careful research might find the materials of other truths as yet unsuspected.

CHAPTER V.

DISCOVERIES ADDED TO THE NEWTONIAN THEORY.

Sect. 1.-Tables of Astronomical Refraction.

WE have travelled over an immense field of astronomical and mathematical labour in the last few pages, and have yet, at the end of every step, still found ourselves under the jurisdiction of the Newtonian laws. We are reminded of the universal monarchies, where a man could not escape from the empire without quitting the world. We have now to notice some other discoveries, in which this reference to the law of universal gravitation is less immediate and obvious; I mean the astronomical discoveries respecting light. The general truths to which the establishment of the true laws of atmospheric refraction led astronomers, were the law of deflection, which applies to all refractions, and the real structure and size of the atmosphere, so far as it is yet known. The great discoveries of Römer and Bradley, namely, the velocity of light, aberration, and nutation, gave to the former conceptions of the propagation of light a new distinctness, and confirmed the doctrines of Copernicus, Kepler, and

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