Brard 
3 im tie 3 AR ae 
= ® (M tii 0+) = 1 ff 2-0; t) sa, MPI a2 (P) (7.42). 
» 
Koi at t, has the same components as at t, - 0. ee is null at t,, 
but the yore of forces necessary for Sesh the jump is infinite. 
Furthermore, at=to +70 Gs is generally finite. Of course, when 
t +oco , the deficiency 6 a calculated by taking into consi- 
deration the new velocities Vz (0) and E tends to zero ; 
also tends to zero and 
a 
ete ee ee (7. 43) 
Cc 
The effect of WS A may be considerable. For instance, it has 
been shown that the jump of the lift of a wing with an infinite aspect 
ratio is at tg t+ 0 equal to half the difference between its final value 
and its value at tg - 0 (See [2] ; [3] \). 
THE ORIGIN OF THE FORCES EXERTED BY THE FLOW ON A 
BOUND VORTEX DISTRIBUTION 
The above considerations started from the idea that a dyna- 
mical relationship necessarily exists between the hull of a moving 
body and the vortex distribution satisfying the adherence condition on 
the hull surface. 
Another viewpoint is that any vortex filament which does not 
move with the fluid is necessarily submitted to forces exerted by the 
adjacent sets of fluid points. 
The proof is classical. It is sufficient to summarize it. 
Let Foe a vortex filament, Fa its bound part, ds, an 
arc AY, . Let O denote the middle a the arc ds, >) Oz. fe axis 
in the eee of ds » ane Fr ,4@", 2 2 system ‘of semi-polar 
coordinates. Let D' denote the domain 
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