196 



Mr Love, On the Theory of Discontinuous [May 4, 



The particular cases investigated by Kirchhoff and Lord Ray- 

 leigh include all that have any practical interest at all comparable 

 with the analytical difficulties. 



12. Problem (iv). Plane obstacle situated in canal of finite 

 width. 



A stream flowing between two fixed parallel planes impinges 

 upon a lamina fixed across the stream at a given angle a. 



The ^-region is bounded by the two fixed planes, the lamina, 

 and the continuations beyond its edges of the stream-lines that 



divide upon the lamina. We shall suppose the point at oo from 

 which the stream comes to correspond to u=<x>; the points to 

 which its two parts go, to u = b, c; the point where the stream- 

 line divides, to u = a ; and the edges of the lamina to u = ± 1. 

 Then we must have 



c> 1 > a > — 1 > b. 



The w and u regions will be precisely the same as in the 

 last problem, and the relation between them will be 



dw_ u — a , 2 „ 



du (u—b)(u — c) 



The fl boundary is easily seen to be 

 l 6>=0 



n 



e^ -a 



'A* 



