Brard 
with By, (t') infinitely close toa point B Pass) , determines the time 
t' .at*which “Phase lett . It may happen that the position of B on 
R depends on t'. In that case, B can be defined by its abscissa 
0B on . During the time interval (t', t'+dt') a free vortex 
filament of density d,:d, is lying on a closed contour By Br Cr 
Cr By , with Br Be =d, (B) and B,C; = VR (Bey t') dt'. Ate 
this vortex filament is lying on the closed contour Mg My; N¢ N¢ Mg : 
where 
! ! = ae ! = ! 
Be M; { bee) eared) ahs tae M,N; Va(My > t) dt 
t! 
We have therefore 
t 
z e) 
dQ. (M, ? t) = eee d To, (7), 7) dr (5. 30) 
t! 
or equivalently, 
t 
rf fe) B 
du, (M, , t) i ai dd. (ae Hy) a(1), 797 (a 3a 
t! 
If B is independent of t', then we obtain by integrating from one of 
the edges of Dis 
Bpa(M.. pot) =uhbe (= po) -(#, -#,) ; 
pa alan Ey EE ae 
t (5. 32) 
with B(t')M, = x: 1) dr 
t' 
In the latter case, the support of the vortex sheet is generated by the 
relative trajectories of the fluid points leaving rh ae Su a 2° 
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