(j) Hectangular cross, by Westwater. ^ ^ 

 (k) Arc and line joined together, by Sauer. 



(1) A small circular cylinder of radius a in motion but momentarily coaxial with a 

 surrounding stationary square cylindrical shell of width 2c, by J.L. Taylor:^^ 



T^^ — pna^ (1 + 1.719—). [91h] 



(m) A convex curve joined to a straight segment, by Riabouchinsky;^ ^° 

 (n) Contours described parametrically by 



X = a cos w + (6 cos 2m)/2, y - h sin u - (h sin 2m)/2, 



by Wrinch,^^^ or by other analytical formulas, by Morris, ^^' ^^^ Basset,^^° Neronoff,^-^^ 

 Milne-Thompson. ^^^ 



A general method of modifying the Schwarz-Christoffel transformation so as to intro- 

 duce rounded edges or other curvatures, by adding "curve factors," was described with 

 examples by Leathern; see also page 123. 



92. T'*'0 EQUAL LIME DIPOLES WITH AXES LONGITUDINAL; FLOW PAST 

 ONE OR TWO SIMILAR CYLINDERS 



M = f/g + fi •+ , [92a] 



\z - h z + b 



U, fi and b real constants and 6 > 0, 



cos 6. cos 



1 ^"* ^2\ X-b X- b 



4> = Vx + fi I + J = Ux + n ( + ) , [92b] 



'sin d^ sin e^\ , -^ ^^ 



(A = Uy -n \ + ) = Uy-fiy ( + — ] , [92c] 



where r^ = [(x - b)^ + y^Y^^, r^ = [{x + b)^ + y^l'-^^ and the significance of the angles 

 0j and 6^ is shown in Figure 151. Hence 



^cos 2 6»j cos 2 e^ /sin 2 6^ '. 



u = - U + fi f + j , 1) = /i [ + -] , [92d,e] 



225 



