112 MOTION OF A LIQUID IN TWO DIMENSIONS. [CHAP. IV 



79. An interesting variation of the problem of Art. 77 has 

 been discussed by Bobyleff*. A stream is supposed to impinge 

 symmetrically on a bent lamina whose section consists of two 

 equal straight lines forming an angle. 



If 2a be the angle, measured on the down-stream side, the boundaries of 

 the plane of can be transformed, so as to have the same shape as in the 

 Art. cited, by the assumption 



f-CTs 



provided C and n be determined so as to make = 1 when =--e~ l( *&quot;~ a \ and 

 ( = - l when = e~ { ( ^ +al . This gives 



The problem is thus reduced to the former case, viz. we have 





Hence for \^ = 0, and 0&amp;gt;$&amp;gt; 1, we have, putting 0= as before, 



q 



The subsequent integrations are facilitated by putting q = t^\ whence 



4t 



/! i Frvn 1 

 .l^-in 



Thus 



We have here used the formulae 



P r * J -A 



+9*--*+*i+j* 



where 



Since q = d&amp;lt;f&amp;gt; /ds, where 8s is an element of a stream-line, the breadth of 

 either half of the lamina is given by (iii), viz. it is 



1+ ?-&quot; + ^ 



* Journal of the Russian Physico -Chemical Society, t. xiii. (1881) ; Wiedemann s 

 Bciblntter, t. vi., p. 103. 



