/I \ / 2a\ 



half, on which 6 = - n, makes with the real axis of ^ the angle -I — n - a ] - I — I n = - 



I _ 77 + « I . These two lines on the i^-plane thus enclose an angle 2a between and below 

 them; and the arc included between them on the unit circle for c^ corresponds to the entire 

 lower half of the unit circle on the i^j-plane; see Figure 188, in which the free streamlines are 

 copied from Tumlirz.''^^ 



If ^ is then assumed to be related to z by the usual Equation [110a] or dz = - ^dw, the 

 two lines and the enclosed arc correctly represent the dividing streamline, l"CAI, I"CA'I', 

 on the s-plane, of which the portions AI and A'l' are free; see Figure 188. The variable i^^ 

 may be assumed to be related to t and w in the same way as ^ was in Section 113. Then, 

 from Equation [113c] and Equation [113a], 



dz ^ - Cdw, M = - — , C^ = - i - {i - '^) 

 /2 ^ 



[115b, c,d] 



Figure 188 - Symmetrical angle-lamina in a stream with wake behind it. 

 (The free streamlines are copied from Reference 188, Volume 121.) 



On the right-hand half of the lamina, t is real and el < - 1 as before; hence, for continuity, 



, 1/2 r^ 



(r-1) = - ViS^ - 1, and 



C^ =- t + y/i^ -1, — =- t-^/t^ -1. 



If ds is an element of length along the lamina and dz the corresponding element of z, from 

 Figure 188 



289 



