CONFORMAL TRANSFORMATION TO PROBLEMS IN HYDRODYNAMICS. 469 



correspond to a free stream-line), the product of powers of a number of curve-factors 

 of the type of ^ 13 , with different parameters. 



Suppose the configuration of liquid flow, (halved by the line of symmetry), to be of 



Fig. 12. 



the character indicated in fig. !.'>, the fixed obstacle being polygonal witli corners 

 A, B, C, and corresponding external angles p-n-, q-n-, r-jr. Let values , /;, c be assigned 

 to w at A, B, C, these being in descending order of magnitude, and let the value 

 of iv at the end D of the polygon be zero. Consider the transformation 



this gives all the corners as specified, and has a constant modulus for ii> negative. 

 Hence the curve DE is a free stream-line. 



Fig. 13. 



The parameters are adjustable so as to make the dimensions of the polygon such 

 as may be desired. 



