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 $ cos 



y = c sinh <j> sin 



The curves <j> = const, are the ellipses 



(2). 



c 2 cosh 2 (/> c 2 sinh 2 < 

 and the curves ty const, are the hyperbolas 



if =1 _ 



c 2 cos 2 i|r c' 2 sin 2 ty 

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



(3), 



(*), 



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

 we see by (2)-<a-the preceding Art. that the velocity there 

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

 portions of the axis of x which lie outside the points ( c, 0) may 

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



