52 



Sir William Thomson on Stationary 



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VI. On Stationary Waves in Flowing Water. — Part IV. 

 Stationary Waves on the Surface produced by Equidistant 

 Ridges on the Bottom. By Sir William Thomson, F.R.S.* 



THE most obvious way of solving this problem is by the 

 use of periodic functions, which we have been so well 

 taught by Fourier in his ' Mathematical Theory of Heat ; ' and 

 in this way it was solved in Part III. (formulas 1 to 15); the 

 solution being (15) Part III. with 



te=l, m=2ir/a (1); 



where a denotes the distance from ridge to ridge. Thus, 

 reproducing (15) Part III. with the notation modified to shorten 

 it in form and to suit it for numerical computation, we have 



*=?. 



4zA/a . cos vty 



g ei+e- 



M, . 



~{e i -e~ l ) 



(2); 



Communicated by the Author. 



