Vortex Theory for Bodtes Moving tn Water 
with the boundary conditions 
Va (M.) = ¥V 
2 (M,) - Vi (mM) - ¥ 
z (M,) on ES 
a+ 345 -{M) =0on). 
Vo is due to causes located outside 2; e and one may consider that 
there exists a velocity potential ®, such that 
at least in the region of Dj close to De evandinside D,, + > 
Va + V- is irrotational outside D + Dix; i thereiore; Mz. 
and Mj being given on f, and f; » respectively - with 
MeM;j = ny (0+), one can find a path starting from Mj, and arriving 
at M, sothat V be irrotational everywhere along this path. Putting 
> 
V= Vd F) (4. 9) 
we obtain, by integrating (4.1) along the path : 
‘ se pyeee 
(M,)-p,(M,) = - » @%) 
Hence (4.6) gives: 
(4. 10) 
One has 
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