Vortex Theory for Bodtes Moving tn Water 
(ii) _When T is determined so that V(M; Vz ve (M;), the jump 
of V - VE through >, is equal to Vr(M, Jor and 
V_. (M) == V, (M,) 8 
is perpendicular to VR on »S and the edges of the vortex-ribbons 
on oy are orthogonal to the streamlines € of the relative motion 
over ), é 
If, furthermore, no free vortices are shed by the hull, 
these edges make closed rings ~ on yy . (Figure 4). Let do be 
the element of arc of a particular streamline . The intensity of 
the vortex ribbon between two rings L , ©” close to each other is 
dI(M) = V (M_) do(M_). (3. 13) 
(iii) If G=0 inside D,; then, dI’ is a constant when M 
describes LY , and the fluid cation inside D, andinside D, 
depends on the velocity potential 
= Hee = a(M'), (R = MM’) 
& (M 
This potential is generated by a normal dipole distributions. [I is 
determined up to an additive constant. 
If w @ £0 inside Dj, then, dI is no longer a constant 
between Y and ww’; ds being the element of arc of A » one has 
Ot dio des 26 idicw da 
dads 
The same aba Cee See in the case of the vortex distributions 
(D, 7 2 ® p) al Par I) - see Section V, Figure 5.1. 
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