of Oceanic Tides. 273 



r=a + 1-02071 cos 2 \ + 0-000776 cos 2 \cos2(<9 -/**), 



or 



r=a+ 1-01993 cos 2 A, + 0-001552 cos 2 \cos 2 (0-/^). 

 We have also 



2^___ jW A -_-.. 2212 ft 



Hence it will be found, by calculating with the data thus ob- 

 tained, that 2c l afl A =0-000000109 ft., and 



2c,fl(l + -^ + -^-)= -0-022252 ft. 



Consequently the velocities at the ocean-surface have the follow- 

 ing values : — 



ft. 

 u= +0-000000109 cos 2 \ sin 2(0-^), 

 v= —0-022252 cos X cos 2(0— pi) , 

 w= + 0-011126 sin 2\ sin 2(0 — (it). 



What is chiefly noticeable in these results is the small amount 

 of the change of elevation of the water at a given position. It is 

 even less than that which resulted from my first attempt, which 

 I thought to be conclusive against it. It now, however, appears 

 to me that this objection was not valid, and that the error of that 

 method consisted solely in not making use of the equation (a). 

 As this equation is taken into account in the present method, I 

 can perceive no reason why the results should not be admissible. 

 The small tide is consistent with the values of the velocities v 

 and w, the latter in particular tending always to diffuse the ele- 

 vation or depression of the waters over a larger area. The mode 

 of action conceived of by Newton in Props. 36 and 37 of Book 

 III. is in accordance with this theory, especially if the ocean be 

 of very great depth, the amount of tide being greater as b is 

 less. 



If the foregoing reasoning be good, the large amounts of tide 

 observed on sea-shores must be produced by the obstacles which 

 continents and islands present to the free horizontal movement 

 of the waters, as well as by the contraction of the channel of 

 the tidal stream by the configuration of the coasts, and in no 

 small degree, it may be, by the inequalities of the bottom of the 

 ocean. This view appears to receive confirmation from facts 

 stated by Whewell in Series XIII. of his " Researches on the 

 Tides" (Phil. Trans, for 1848), viz. that "the tides of islands in 

 mid-ocean are very small" (p. 2); that there are "very small 

 tides, or no tides, at the islands in the centre of the Pacific, 



Phil Mag. S. 4. Vol. 39. No. 261. April 1870. T 



