Vortex Theory for Bodies Moving tn Water 
This shows that: 
If L, starts from BB', then both L, and L, end at BB'; 
If L, ends at BB', then both Ly and L, start from BB'. 
Consequently, every vortex filament 2 can be considered as the 
union of two free vortex filaments ¥ f, and & 5 ; Sat and & ty 
being two complementary arcs of the same vortex filament L, : 
similarly Z£5° and Le belong to the same vortex filament sho ; 
SA and x, are clbsed— 
When 7 goestozero, (5.17) becomes 
H(B°) = ou (B°) + #)(B*). (5.23) 
MeGording £0) .(5522), 4f sagen ap) =- 114; then 8, is in 
the direction from a towards SL, - 65 in the direction from L, 
towards L,' and Os in the direction from L f towards SP } ay Tit 
Dip asin ¢ Pegs 1, the directions of 6, , 8, and 6, are opposite to the 
preceding ones. Thus, from B to B', the variations of Ne I. and l 
are 
grep Hp: tly yz a Ecay -*(6)]- ¥ au [topper 
Tap on aes ae es) -1(L,) } hae are #1 
A 4 + Lp f sign if 
aD oe Ty (stp) a TA) v= K enw (ate) fF - Ab ae iB Me 
As it was to be expected, (5.21) and (5.23) are therefore equi- 
valent. 
Fig. 5.3 sketches the configuration of a vortex ribbon when 
there exists only one free vortex sheet. 
This case is that of a wing with a finite aspect ratio. P is 
the trailing edge of the wing. 
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