PROCEEDINGS 



OF 



THE ROYAL SOCIETY. 



1834-1835. No. 22. 



November 19, 1835. 



JOHN WILLIAM LUBBOCK, Esq., Vice-President and Treasurer, 

 in the Chair. 



The Rev. WMliam Bentwick Latham Hawkins, M.A., was elected 

 a Fellow of the Society. 



" On the Empirical Laws of the Tides in the Port of Liverpool." 

 By the Rev. William Whewell, M.A., F.R.S. 



The author employs the results of the discussion of sixteen years of 

 tide observations made at Liverpool, published by Mr. Lubbock in the 

 Philosophical Transactions for the present year, in testing and im- 

 proving the formulae, expressing the mathematical laws of the inequa- 

 lities of the phenomena of the tides, which had already been deduced 

 by the author from the London tide observations. He finds that the 

 Liverpool observations have not only confirmed, in the most satisfac- 

 tory manner, these formula?, but have furnished the means of greatly 

 improving them. The corrections for lunar parallax and declination, 

 which, as far as they depended on the former investigation, might be, 

 considered as in some measure doubtful, and only locally applicable, 

 have now been fully verified as to their general form ; the nature of 

 the local differences in the constants of the formulae has also, in part, 

 come into view $ and the investigation has, moreover, shown that, 

 notwithstanding the great irregularities to which the tides are subject, 

 the results of the means of large masses of good observations agree 

 with the formulae with a precision not far below that of other astrono- 

 mical phenomena. The formulae obtained point directly to a very 

 simple theory of the circumstances of tides, namely, that the tide at 

 any place occurs in the same way as if the ocean assumed the form 

 of equilibrium, corresponding to a certain antecedent time, and differ- 

 ent place. The ocean, in its position of equilibrium, would have the 

 form of a spheroid, of which the pole would revolve round the earth, 

 following the moon at a certain distance of terrestrial longitude. This 

 distance is termed by the author the retroposition of the theoretical 

 tide in longitude, its mean value being what he has termed in other 

 communications, the corrected establishment of the place. If from an 

 original equilibrium tide, a derivative tide were sent off, along any chan- 



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