by use of the binomial expansion; hence, using also In (1 + a;) = a; - ^ /2 . . . . , writint 

 cosh(^-^o-za)=-(e^ '° +e ^ ^ 



the first power of I/2, 



), using Equation [83a, d,e], keeping only 



C=ln 



23 



42^ 



22 



= ln — 



42^ 



w; = Vze-'^ + — ( In 2 + In ^- ) 



277 \ c ° I 



+ U (b cos a + ia sin a ) 



22 



[83h] 



Thus at infinity w-* Vze "* and represents a stream approaching at velocity U from a direction 

 making an angle a with the positive ar-axis; see Section 35 and Figure 131. 



Figure 131 — Symbolism for flow past an elliptic cylinder. 



The variables ^, jj are the elliptic coordioates described in the last section. They are 

 related to x and y by Equations [82c, d] or [82v,w]. The ^curves are confocal ellipses with 

 foci at (± c, 0). Here ^ > 0. 



Using the hyperbolic formulas listed in Section 32, from w = cf] + ii/j, 



<f> = V {a + b) cosh {^ - f^) cos (77 - a) - 



Try 



[83i] 



xl, = V{a+ b) sinh (^- ^ ) sin (17 -a) + -— (^- ^^), 



[83j] 



197 



