Proceedings of the Royal Society. 425- 



of this paper means to include the consideration of those causes 

 which regulate the propagation of the tides, so as to exclude en- 

 tirely the examination of the meclianism by which they are prima- 

 rily produced. The generation of the tidal elevation in the Pacific 

 or Atlantic Ocean is a question entirely of celestial mechanics. 

 But the tides, after having been generated by solar and lunar at- 

 traction in a manner that is found to be perfectly in accordance 

 with the varying intensities of these forces, do not subside at the 

 instant when these forces cease to act, but continue to exist during 

 a long period of time, reaching our shores three days after their 

 birth ; aud have obeyed, during this long interval, laws perfectly 

 independent of the original influence by which they were produced, 

 and presented phenomena in direct opposition to it. They have 

 obeyed the laws of terrestrial hydrodynamics. The law of the 

 propagation of the tidal wave through the ocean and around our 

 shores, belongs therefore to terrestrial, not to celestial mechanics. 



Although our knowledge of the celestial mechanism of the tides 

 has recently attained a high degree of accuracy, our knowledge of 

 the terrestrial mechanism has been hitherto almost entirely conjec- 

 tural. In the former department, the system of Bernouilli, based 

 on the discoveries of Sir Isaac Newton, presents us with a theory 

 of the tides in close accordance with the phenomena. Laplace, in 

 his elaborate discussion of the tides of Brest, executed by M. Bon- 

 nard, has verified this accordance to a high degree of precision ; and 

 the recent researches on the tides, by Mr Lubbock and Mr Whevvell, 

 may be considered as having rendered the celestial mechanics 

 of the tide as perfect as any other department of Astronomy, the 

 errors of prediction being now reduced within the limits of the er- 

 rors of observation ; so that Mr Lubbock has stated that he does 

 not look forward to any material improvement in this department 

 of our knowledge. 



But our acquaintance with the terrestrial mechanism of the 

 tides is in a very different condition. In reference to the pheno- 

 mena of this department, Laplace has said, in the third chapter of the 

 fourth book of the Mecanique Celeste, and he repeats the opinion 

 in the first chapter of the thirteenth book, at a much later date, 

 where he says : " Que les circonstances accessoires produisent des 

 varietes considerables dans les hauteurs et dans les heures des 

 marees des ports meme tres rapproches ;" and then he adds, " II 

 est impossible de soumettre an calcul ces varietes, parceque les cir- 

 constances dont elles dependent, ne sont connues." Mr Lubbock, 

 in like manner, speaking of the fluctuation of the establishment, 

 says, " This perplexing fluctuation presents an insuperable obstacle 

 to extreme accuracy in tide predictions, until it can be explained ; 

 at present we are only left to conjecture respecting the cause." 

 And Mr Whewell says, in 1837, " I cannot conclude this paper 

 without again pointing out that a great number of curious facts 

 in fluid motion are established in these Tide Researches, of which 

 it may be hoped the theory of hydrodynamics will one day be able 

 to render a reason." 



