Dagan 
Using these relationships we obtain the following set of equations for 
w, and w, , similar to (7)-(14) 
Im Gr? salty Athg ('y' ='0) (38) 
re (¢ — — oo) (39) 
Een My tse tt) (| <1, w= -ht 0) (40) 
Im (iF* aie we) Be 3 Blu) +) (¥= 0) (41) 
w,— 0 ( + — ©) (42) 
Im w, = + (u, +2, ) ({o|<i, = -h +0) (43) 
where 7 = dt |dx|,_g is the slope of the body contour and under the 
linearization process L'=L’ +o0(L’), h!=h{ + o(h{) such that h, 
e and F retain their meaning of (1). Equations similar to (38)-(43) 
may be written for higher order terms. 
Due to the similarity between (38)-(40) and (7)-(10) the solu- 
tion for w, may be written at once as 
where wis defined by (17) (for details see Dagan, 1972b). 
w> , obeying (41)-(43) may be again found like in Chap. II 
by a discrete source distribution. It will display the same singular 
behavior for small F as w, (z). 
Let us consider now a small Froude number limit of w, 
(44), i.e. an expansion of the type 
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