yields 



C^ = I (f+iF3^+ie)^Gdxdy + j 9G/9nda 



a . 



Furthermore, by using the relation 



r [2i(f+ie)3G/3x-F9^G/9x^]dxdy = - (" [2i(f+ie)G-F9G/9x] t d£ 



we may obtain the following alternative expression for C.: 



C^ = (f+ie)^ r Gdxdy - 2i(f+ie)F j Gt d£ 

 a. c 



+ F^ I 9G/9xt dl + I 9G/9nda (4.12) 



r 9G/9xt di + j 



By adding the term C.(})^ on the left and right sides of Equation (4.7), with C. 

 given by Equation (4.11) on the left side and Equation (4.12) on the right side, we 

 may obtain 



->■-)■ ->- 



[l-w(5)](})(C) = i>(D - L^(C;4)) (4.13) 



where w(5) is the ' waterplane integral" defined as 



w(t) = (f+ie)^ J G(t,$)dxdy (4.14) 



18 



