NOTE ON THE MOTION OF WAVES IN CANALS. 



IN a former communication* I have endeavoured to apply the 

 ordinary Theory of Fluid Motion to determine the law of the 

 propagation of waves in a rectangular canal, supposing f the 

 depression of the actual surface of the fluid below that of equi- 

 librium very small compared with its depth ; the depth 7 as well 

 as the breadth ft of the canal being small compared with the 

 length of a wave. For greater generality, ft and 7 are supposed 

 to vary very slowly as the horizontal co-ordinate x increases, 

 compared with the rate of the variation of *, due to the same 

 cause. These suppositions are not always satisfied in the pro- 

 pagation of the tidal wave, but in many other cases of propa- 

 gation of what Mr Russel denominates the " Great Primary 

 Wave," they are so, and his results will be found to agree very 

 closely with our theoretical deductions. In fact, in my paper 

 on the Motion of Waves, it has been shown that the height of 

 a wave varies as 



ft***. 



With regard to the effect of the breadth ft, this is expressly 

 stated by Mr Russel (vide Seventh Keport of the British Asso- 

 ciation, p. 425), and the results given in the tables, p. 494, of 

 the same work, seem to agree with our formula as well as could 

 be expected, considering the object of the experiments there 

 detailed. 



In order to examine more particularly the way in which the 

 Primary Wave is propagated, let us resume the formulas, 



18 



