IV. Note on the Motion of Waves in Canals. By G. Green, Esq. B.A. 



of Caius College. 



[Read February 18, 1839.] 



In a former communication I have endeavoured to apply the or- 

 dinary Theory of Fluid Motion to determine the law of the propagation 

 of waves in a rectangular canal, supposing £ the depression of the 

 actual surface of the fluid helow that of equilibrium very small com- 

 pared with its depth; the depth 7 as well as the breadth /3 of the 

 canal being small compared with the length of a wave. For greater 

 generality, /3 and 7 are supposed to vary very slowly as the hori- 

 zontal 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 propagation of the tidal wave, but in many other cases 

 of propagation 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 



/8-^7-i. 



With regard to the effect of the breadth /3, this is expressly stated 

 by Mr Russel (Vide Seventh Report of the British Association, 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. 



