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



real. To find the breadth I of the lamina in terms of the unit of 

 length, we have 



= 4 + 7r ........... ................... (65). 



To find the excess of pressure on the anterior face of the lamina, 

 we have, 



for the moving fluid - = C ^ q 2 , 



V 

 and for the dead water = C . 



P 



Now at the edge of the lamina, we have p=p , 2 = 1, so that 

 C = C + J, and the required excess is given by 



If we multiply this by dx, and integrate between the limits + 1, 



dx 1 , . 



since TT = - &amp;gt; we obtain 



or, snce 



which = TT. 



To make this result intelligible we must get rid of the arbi 

 trary assumptions made for simplicity of calculation. If q Q be the 

 general velocity of the stream, &amp;lt; the value of &amp;lt; at the edge of the 

 lamina, we have, instead of (64), 



so that (65) is replaced by 



........................ (67), 



