224 Mr Sharpe, Liquid Motion from a Single Source 



Inside the circle, that is for r < a put 



iia cos 6 fa m r m A 

 u* = c + ^r- +#(-^rcosm0) (1), 



[xa sin 6 



-S^sinmff) (2). 



Fig. 1. 



This makes u x 4- iu y a function of x — iy, and therefore repre- 

 sents irrotational motion in two dimensions, m is integral and S 

 represents the sum of a number of terms like that written down, 

 but with different values of m. 



Outside the circle, that is for r> a put 



aa cos 6 ~ fa m a m _\ ._. 



iia sin „ (a m a 



+ S ( -^z- sin md 



i3 rp \ niHL 



which make u x + iu y a function of x — iy. 



(4) 



