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Tlie paper embraced three sulyects of examination. 



I. Regarding the true nature of the tide wave, — By observations 

 made on the tides of the rivers Dee (in Cheshire) and Clyde, it 

 was ascertained that the tidal elevation is a large compound wave 

 consisting of a series of elements, each of which is identical with 

 the wave of the first order, or great primary wave of transla- 

 tion, of which the author had already determined the nature and the 

 laws. The velocity of the tide-wave is that due to the depth of the 

 centre of gravity of the transverse section of the channel below 

 the surface. The tide wave is a wave of translation, but the velo- 

 city of translation of the particles is entirely diflFerent from the ve- 

 locity of propagation of the wave, the former being variable, and 

 the latter constant. When the velocity of propagation is greatest, 

 the velocity of translation is often least. The translation takes 

 place almost uniformly to the greatest depth hitherto observed. 



II. 'J he application of our knowledge to the explanation of 

 the ordinary and extraordinary observed phenomena of the tide. — 

 The identity of the tide-wave with the wave of translation af- 

 fords an explanation of the following phenomena, which have hi- 

 therto been wholly unexplained or imperfectly understood. (1 ) 

 The dislocation of the tide by which the time of ebb is increased, 

 and the time of flood diminished by propagation, after a consider- 

 able space. (2.) The difference between the height of tides in 

 places wliich are adjacent, and have been expected to have nearly 

 the same tides. (3.) The variation of the establishment from time 

 to time, arising from changes in the dimensions and form of the 

 bottom of the sea or channels of rivers. (4.) The cause of the 

 breaking surge or tide-bar. (3.) The variation in the form of the 

 curve of semi-menstrual inequality in the height and in the interval 

 at different places, and the exaggeration of the other inequalities. 



III. 7 he deduction of practical maxims for the improvement of 

 tidal channels. — The last part of the paper is directed to the de- 

 termination of the principles by which tidal channels may be im- 

 proved, so as to facilitate the ascent of the tide, — to increase its 

 volume, — to diminish the duration of ebb, and increase that of flood- 

 tide, — and to impede the action of the tide in moving sand, pro- 

 ducing bars, and injuring the banks of tidal channels or rivers. 



