Brard 
We thus obtain : 
oy (Re) be r= ee) vb, (Mi, t), (TNE ate 
This expression takes the same values in both cases aj and 
a, provided that in the uniform motion of the body corresponding to 
case a,, Vp(0) and Q ¢ be identical at tg with those of the real 
non-uniform motion. Since %, is harmonic within Dj , it is uniquely 
determined in that domain by (7.12). We have 
Hpsiaie) =~ Bale) & 0m) + 82) 22(4,,4,) on Dy 
(7.13), 
2 
Now, let us consider the velocity potential ® inside D,. 
Euler's equation gives, after (4. 1'), 
1 ODi a 51 1 92 aks lace 
Pas = ? oP ? ->V J 
p ee at . 7 ‘i z Eto) Z Ce tS) 2 Pe ts) on ds, 
(7. 14) 
at 
By comparing with (7.1), , we obtain 
1 
OD (m',t ) = 0 on >» ~=incase a,. (7. 15) 
ot eo e 1 ay 
In cases a, and a,» we have 
D= 2 inside D, ‘ (7. 16) 
and according to (6,7) and (6.10), 
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