278 



NOTE ON THE MOTION OF WAVES IN CANALS. 



The particular integral of which belonging to the wave that 

 proceeds in the direction of x positive is 



*-/(-'/?) .;; . 



and hence the velocity of propagation of the wave is 



Mr Russel gives A/ ~- as the velocity, but at the same time 



remarks, that in consequence of the attraction of the sides of the 

 canal fixing a portion of the fluid in its lower angle, we ought 

 in employing any formula to calculate for an effective depth in 

 place of the real one, p. 442. Instead of adopting this method, 

 let us compare the formula (D) given by the common Theory of 

 Fluid Motion, with Mr Russel's experiments. And as in our 

 theory we have considered those waves only in which the eleva- 

 tion above the surface of equilibrium is very small compared 

 with the depth c, it will be necessary to select those waves in 

 which this condition is nearly satisfied. I have therefore taken 

 from the Table, p. 443, all the waves in which 



and have supposed g = 32J feet : the results are given below. 



