66] 



SPECIAL CASES. 



83 



of a liquid flowing from one side to the other of a thin plane 

 partition, through an aperture of breadth 2c ; the velocity at the 

 edges is however infinite. 



If the ellipses be taken as the stream-lines we get the case of 

 a liquid circulating round an elliptic cylinder, or, as an extreme 

 case, round a rigid lamina whose section is the line joining the foci 

 ( e, 0). 



At an infinite distance from the origin (/&amp;gt; is infinite, of the 

 order log r, where r is the radius vector ; and the velocity is 

 infinitely small of the order 1/r. 



2. Let z = w + e w ................. &amp;lt; ......... (5), 



X = (f) + 6* COS l/r, y = ty -f 6* sill i/r ............ (6). 



Or 



The stream-line i/r = coincides with the axis of x. Again the 

 portion of the line y= r rr between x = GO and x = 1, considered 



as a line bent back on itself, forms the stream-line i|r = TT ; viz. as 

 $ decreases from -f- oo through to oo , x increases from oc to 

 1 and then decreases to oo again. Similarly for the stream 

 line i|r = TJ-. 



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