426 Proceedings t^the Royal Society. 



In 1834, the author of this paper had determined the law of the 

 interference of a certain species of wave in the resistance of fluids, 

 and this species of wave appeared to present very striking analo- 

 gies to the tide-wave. In 1835, Mr Whewell expressed his decid- 

 ed conviction of their similarity, and Mr Robison and Mr Russell 

 were, in 1836, appointed a Committee of the British Association 

 to investigate the subject. The Report of these observations was 

 given to the British Association in 1837 ; but as the observations 

 themselves are not necessarily connected with the particular con- 

 clusions which may be drawn from them, these conclusions, at 

 which the author had arrived, were made the subject of a separate 

 paper to this Society. 



The paper embraced three subjects of examination. 



I. Hegarding the true nature of the tide icave, — 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 velocitij of the tide-wave is tiiat due to the deptli 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 difterent 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. Ihe application of our hnowMgc 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, wliich have hi- 

 therto been wholly unexplained or imperfectly understood. (1.) 

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

 and the time of flood diminished by proj)agation, after a consider- 

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

 places which 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 tiie sea or channels of rivers. (4.) The cause of the 

 breaking surge or tide-bar. (5.) The variation in the form of the 

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

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



III. The 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. 



