Stationary Waves in Water. 105 



Over yjr=0. 



Start with those determinations which at w=—<x> 

 give (B — e w )l, (l-~e 2w )i real and positive. 



- x> <<f)<Q gives a free surface over which y goes from 



-E B » to »— jK 3 - 1 )' 



2/A ^yLt 



and 6 from 7r to — tt/2. 

 0<<£<logB : a rigid boundary parallel to //-axis ; 



(9= -tt/2. 

 logB<(£< +oo : a rigid boundary over which #=77r/6. 

 Over ^ = 7r. 



— x> <(f><0 : a free surface over which 



y 



3 /^ V* w 



0< j> < +QO : a rigid boundary parallel to the ?/-axis 

 6 = tt/2. 

 Fiff. 6. 



Fig. 6 shows that near the solution approximates to that 

 for a weir, near 0' to that for a sluice. 



