Joosen 



By changing the integration contour (3.11) is transformed into: 





-In7(.,-f)^H^.+ 0^.-ie'^^^^^^^^''^'''^"'' 



CO 



. (3.12) 



Following the same procedure as discussed before it appears that the first 

 three integrals of (3.1) with ^r = produce no first order contribution to the 

 value of cpj except for the case that bow and stern region are of order e. The 

 last two terms of (3.1) become with ^g = 



7(^1-^)' + eH-n.-i)' + e'(^i+0' 



After expansion with respect to e and with the condition of sharpness at the end- 

 points for cpj is obtained: 



^i(^i'^i'^i) = -4 r F(^i,0 In 7(7,1- f)2 + (^j+0' d^ 



•'c(fi) 



= +4J sgn(^,-a In 2|^i-^| d^ f F^(^, d^ . (3.13) 



-1 c(f) 



The function q)o + q^j can be considered as the potential associated with the 

 translator y motion of a body in an unbounded medium. 



The function F(f , O can be determined by the boundary condition (2.12). 



A discussion of the results of this section with a view to experimental re- 

 sults obtained elsewhere, will be postponed till section 6. 



THE CASE OF HIGH FROUDE NUMBER AND 

 MODERATE FREQUENCY 



The velocity potential cpi for this case is already known (see e.g., [5], [8]). 



176 



