Figure 72 — Nearly circular cylinder between 



walls, obtained with use of dipoles in 



a stream. See Section 46. 



To obtain the first of these equations, divide (46j) through by y, then let y -» 0, noting that sin 

 {2ny/a)/y -» 2 n/a, and solve for ar = r . The second equation has a root < r^ < ffl/2 for any 

 B/V > 0. 



A cylinder may be inserted along the surface S. Then, if walls are also inserted along 

 the lines y = - a/2, the formulas, modified as stated, represent a stream that flows between the 

 walls and past this cylinder. 



Equation [46k] may be solved for r by using the series [331] for sinh~ : 



a \aU I & \aUl iO \aU I 



5/2 



'.-o[-HTf^(?y h-y^ 



[46m, n] 



To obtain a similar series for r , assume that 



='«[-M?r-^(^f ] 



write [461] in the form 



110 



