82 



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



66. The following examples of this are important. 



1. Assume z = ccoshw (1), 



or x = c cosh &amp;lt;/&amp;gt; cos 1 



y = c sinh (/&amp;gt; sin - 



The curves $ = const, are the ellipses 



__ -| 



and the curves &amp;gt;/r = const, are the hyperbolas 



(2). 

 (3), 



a?&quot; 



c 2 cos 2 



c 2 sin 2 



= 1 



these conies having the common foci ( c, 0). 



Since at the foci we have = 0, ty = HTT, n being some integer, 

 we see by (2) o~the preceding Art. that the velocity there 

 is infinite. If the hyperbolas be taken as the stream-lines, the 

 portions of the axis of a; which lie outside the points (+ c, 0) may 

 be taken as rigid boundaries. We obtain in this manner the case 



