Falttnsen 
The lowest-order equations become 
2 2 
2 
(2. + +, - x") vy, = 0 (75) 
ay az 
ee ee ee nad Sn (76) 
az 1 
yes yy. = -Cn ke = on Z= ht, y) Vie 
aN 1 3 : 
In addition ¥, must match with the far-field solution. 
A one-term far-field solution is assumed to be the potential 
associated with a line distribution of sources of density 
spread along the line y=z=0, - L/2.< x < L/2. That solution 
has been obtained in a previous section, and a one-term inner ex- 
pansion of the far-field solution can be found from (65). For any 
fixed x greater that - L/2, a one-term inner expansion is 
Hot nd Fated dia, (&) (78) 
Vr sah 2 2w oe He =| 
Va) 
re) 
In a similar way as for the zero-speed problem, one see that 
the only possibility for a solution satisfying (75), (76), (77), and 
matching (78) is by requiring that 
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