Vortex Theory for Bodtes Moving tn Water 
of the elementary forces [palme) ny d i ono . This may be writ- 
ten in the form : 
iG & Q? r“(M_) m7 ep T(M) AV,(M) ) aX am) 2.2)e3 
where 
Va(M) = + yim) + 7 (| = = FM) ; (7. 3) 
This relative velocity is calculated inside the bound vortex sheet by 
using the vortex distribution ; it can be considered as the incident 
velocity on the element of bound vortex filament T( € a>.) which 
is at rest with respect to the body. 
The equilibrium of the set E of fluid points located inside 
D; requires 
ly > 1 72 Ma 
a = ax y, = V a Q 
Aes E BW MEANS: day" Sele 
This gives 
1 2 Zz 
a ee) ! 
p4(M,) 5 =e (M,) + constant on ag (7.4 
The system of forces exerted on the set E' of fluid points 
belonging to the bound vortex sheet is thus 
—_> 
ie [(oar,) Hyg - P(M,) Fy) 2X09 | ; |- pT(M) AV, (M) aX] 
a 5) 4 
Finally we have : 
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