25 



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- 

 librium theory of Bernouilli, particularly with respect to the semimen- 

 strual inequality. This agreement was the more important, as af- 

 fording the indication of the real existence of a phpical 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 

 empirical 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 

 formulae 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 formul£e 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- 

 mathematical 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," and 

 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. 



