442 Lieut.-Col. A. R. Richardson on Stream-line 



c(w-d) 



dz^ = 1 ie _ i(b + icV 2 ) Qb+w 1 '*? 

 dw q (w—iyi 2 



gives 



Q — 77-/2 + tan 



+ 2c$ 



9 



2 - d) { h +S) \ 



, en) 



where < tan -1 ... <7r. 



n 



(a) (j> — > — co . 



°. /3 — >oo, 77— > X) ; 

 .*. 6 = 7r/2, i. e. all stream-lines are parallel at <£= — go . 



(b) yfr > . . 



^— >co, /3— >0, 77 — >0 ; 



.*. 6 — *7?"/2, i.e. all stream-lines outside the plate are 

 parallel at infinity. 



The term 



& 



^-d)(l> + g) 



2 1 2 





< i + i 



< 1. 



<>+k«)t 



Hence if c<ir/'2 this term is <tt/2. 



Now a diagram giving w 1 2 and (fp — l) 1 '' 2 along a stream- 

 line -\Jr>0 shows that 



tan 



1* 



*4 



tan" 1 2 7- 2 <7r/2. 



Hence, if i/r>0, no stream-line can have a greater angular 

 change than it. 



