1 08 MOTION OF A LIQUID IN TWO DIMENSIONS. [CHAP. IV 



For -v/r = 0, and > (/ 1, is real ; this corresponds to the portion 

 CA of the stream-line. To find the breadth I of the lamina on 

 the scale of our formulae, we have, putting </> = - <', 



For the free portion A I of the stream-line, we have <f> < 1, and 

 therefore, putting </> = ! s, 



Hence, taking the origin at the centre of the lamina, 



x = \ir + 2 (1 + )*, y = {s (1 + *)}* - log {* + (1 + )*}, 



or, putting s = tan 2 ^, 



a? = ITT + 2 sec 0, y = tan sec 6 log tan (J?r +%&) ...... (7). 



Line of Symmetry. 



The excess of pressure at any point on the anterior face of the 

 lamina is, by Art. 24 (7), 



the constant being chosen so as to make this vanish at the surface 

 of discontinuity. To find the resulting force on the lamina we 



