XXIII. On the Motion of Waves in a variable Canal of small Depth 

 and Width. BY George Green, Esq. B.A. of Caius College. 



[Read May 15, 1837.] 



The equations and conditions necessary for determining the motions 

 of fluids in every case in which it is possible to subject them to Analysis, 

 have been long known, and will be found in the First Edition of the 

 Mec. Anal, of Lagrange. Yet the difficulty of integrating them is such, 

 that many of the most important questions relative to this subject seem 

 quite beyond the present powers of Analysis. There is, however, one 

 particular case which admits of a very simple solution. The case in 

 question is that of an indefinitely extended canal of small breadth 

 and depth, both of which may vary very slowly, but in other respects 

 quite arbitrarily. This has been treated of in the following paper, and 

 as the results obtained possess considerable simplicity, perhaps they may 

 not be altogether unworthy the Society's notice. 



The general equations of motion of a non-elastic fluid acted on by 

 gravity (g) in the direction of the axis a, are. 



