Figure 43 — Flow net for a line dipole: w = fi/z . 

 by substituting in terms of polar coordinates with origin at (a;., y ) so that 



T = {{x-x^f +(y-yo)^l '' '^-^0 = '•cos (9, y -^0 = rs 



in 6 



it is found that 



cos {d - <*) sin {d -a) 

 = fi } , t'' = - fi r 



cos {d -a) sin {6 -ct) 



[37s,t] 

 [37u,v] 



The singularity now occurs at 2 = 3^, or at {x^, y^), and the plane of symmetry passes through 

 a;., y. and is inclined at an angle a to the a>axis; these facts verify the statement made as to 

 the location and orientation of the dipole. 



The geometrical properties of the transformation are discussed in Section 24. 



(For notation and method; see Section 34; Reference 1, Article 63; Reference 2, 

 Section 8.23.) 



77 



