440 Lieut-Col. A. E. Richardson on Stream-line 

 the V sign denoting the real positive square root. 



— -op -< w < Q. 



dw q \Z± — W ' 



The curved stream-line AB is described, on which 

 q_ 00 =e- c , 0_ x =tt/2, 



-^ cd 



and q = ~ e v , 6 = 0. 



w <: +1. 



c(iv-d) 

 dz b+Vw (b+ \/w) 2 />M 



^ w 



= and g — >0 as w — >+l. 



The rigid boundary BC is traced out. 



It is important to notice that q steadily decreases as 

 w increases : on the underside of the plate this is shown not 

 to be the case. 



t < w <r+ so . 



.— c(w— d) 



dz _ i{b + Vw) (5+Vw) 3 ^ 



dw V w — 1 



6 = ir/2, q i = 0, and q n = e~ c . 



The straight stream-line CD is described. 



Further, since b + iv l/2 has no zeros in the upper half w- 

 plane, £ has no singularities for i/r>0. 



It will be proved later on that the domain B , of the 

 previous work, does not extend into the upper half-plane. 



The function therefore gives a possible irrotational flow 

 for -v^>0, i. e. outside the plate. 



(ii.) Flow along the bounding stream-line ijr= — 0. 



Commence at A with the same determinations as in (2) » 

 The motion along AB will be continuous with that in (i.)< 



