of the ocean; secondly, the comparison of the observed laws at cer-
tain places with the theory; and lastly, the laws of the diurnal in
equality of the tide.
It is to Mr. Lubbock that we are indebted for the first accurate comparison of the theory of the tides as given by Bernouilli in his treatise Du flux et reflux de la mer, with the results of observation as deduced from a period of nineteen years in the port of London. In this memoir, which was published in our Transactions for 1831, there was given a most elaborate discussion by Mr. Dessiou, under Mr. Lubbock's directions, of more than 13,000 observations, and the results were of great importance, not merely as furnishing the materials and the general rules for the construction of tide tables, but also for the general accordance which they exhibited with the equi- librinm theory of Bernouilli, particularly with respect to the semimen strual inequality. This agreement was the more importamt, as affording the indication of the real existence of a physical connection between the theory and observation, and as consequently justifying such a further examination of its consequences as might lead to the discovery or suggestion of such modifications of it as would lead to its general accordance with the laws of all the facts observed.
In a subsequent discussion of the tides of Liverpool, published in our Transactions in 1835 and 1836, Mr. Lubbock showed, as had partly indeed been suggested by Mr. Whewell in his papers on the empirieal laws of the tides of London and Liverpool, that by refer- ring the tide, not to the lunar transit immediately preceding, but to an anterior lunar transit, one, two, or more days before, that the formulæ furnished by the equilibrium theory would be brought into almost perfect accordance with the observed inequalities in the heights and times of the tides which are due to the changes in the moon's parallax. This was a most important step in the connexion between theory and observation, and has been found to apply, to a considerable extent, to all the periodical inequalities of the tides, though very different epochs are required for different inequalities. Thus Mr. Whewell has shown that the diurnal inequality in the heights of high and low water, which is due to the change in the moon's declination, would require to be referred to the lunar transit four days preceding.
But though the formule furnished by theory can be thus adjusted to represent generally the results of observation for any assigned station, yet our theory is quite incompetent to assign the physico- matheinatical grounds upon which such adjustments are made: the complete solution of such a problem would probably require a know- ledge of the laws of hydrodynamics much beyond that which we now possess.
The first memoir which was published by Mr. Whewell was an Essay towards a first approximation to a map of cotidal lines," aud appeared in our Transactions for 1833.
By cotidal lines, Mr. Whewell means those lines which may be drawn through all those points of the ocean which have high-water at the same moment of absolute time.
