58 Mr. Lubbock on Bernoulli's Theory of the Tides. 



of high water coincides with the law assigned to it by Ber- 

 noulli so nearly, that in this respect Bernoulli's theory and 

 observation may be considered as leading to identical results. 

 The hypothesis of the moving fluid spheroid, however vio- 

 lent it may appear, which ensues as a necessary consequence 

 from the fundamental differential equations which regulate the 

 motions of fluids, when certain quantities are neglected, may 

 therefore securely be a'dmitted as a first approximation. The 

 inequalities due to changes in the moon's parallax and decli- 

 nation are much more minute, and it is more difficult to de- 

 tect the law which they follow empirically. The discussions 

 which Mr. Dessiou has effected of the London and the Liver- 

 pool observations have been made with reference to the moon's 

 transit preceding the time of high water, which seems to me 

 the most convenient course for the object we had immediately 

 in view, namely, to obtain tables to serve for the purpose of pre- 

 dicting the phenomena. But it is probable that the tide-wave, 

 in as much as it results from the action of the sun and moon, 

 maybe considered as developed in the main ocean, and as trans- 

 mitted through the seas which encompass England, modified 

 solely by the wind, and by the resistance of various kinds 

 which it encounters in its passage. Hence, as Bernoulli re- 

 marks, the phasnomena on our coasts are referable to the places 

 of the luminaries some time previously; and owing to the in- 

 equalities in the moon's motion, the moon's parallax and de- 

 clination corrections depend in some measure upon the transit 

 employed. For since the time of the moon's synodic revolu- 

 tion is 29*53 days, the mean interval of time between two suc- 

 cessive transits is 24 h 49 m : if, therefore, I had taken the transit 

 of the day previous, instead of that immediately previous to 

 the high water, all my intervals with par. 57' in the tables pub- 

 lished in the Philosophical Transactions would have been 

 increased by 24 h 49 m , and the argument of the table (moon's 

 transit) would have been diminished by 49 m . The angular 

 velocity of the moon being nearly as the square of the parallax, 

 the mean interval between her transits with par. 54 f is 24 h 43 m 

 only ; all my intervals for par. 54' would therefore have been 

 increased by 24 h 43 m only. If I had taken the transit last 

 but two, all my intervals corresponding to par. 57' would 

 have been increased by 37 h 13 m , the argument of the tables 

 would have been diminished by l h 13 m , and I should have 

 found the fundamental hour for the port of Liverpool 2 m only, 

 instead of l h 15 m . Moreover, all my intervals correspond- 

 ing to 54' parallax would have been increased by 37 h 4 m 



only. 



37h 13 m _ 3 



