Brard 
flat rectangle P; P, P,, P;, andis therefore equal to the circula- 
tion dT of,the velocity v in the closed contour of this rectangle. 
Consequently 
(2 ga) 
Conversely, if the velocity V is discontinuous through a 
surface > Saas and if the jump is nee to Das oe then the_ above 
formula afeaes a vortex sheet. (, )) .s,1_«)), with tp = =Np VP: ) - 
= V(P. )| € 
The expression (2.1) is the local intensity of the ''vortex 
ribbon'' located benyesm & and L, . Itis a constant along the rib- 
bon if no nea sae @ ’ coming toed the regions outside x joins the 
distribution _1_ — over nae We will see in the next Section that the 
opposite case is frequent. 
POINCARE'S FORMULA 
We consider in the fluid a closed surface S witha tangent 
plane at every point. Let D; D, be the interior and the exterior 
of S. The unit vector n hs eae to S is in the inward direction. 
The interior side Sj of S is considered as included in D;, and 
the exterior side S, as included in D, 
The time t is fixed. 
The velocity V is supposed continuous and twice continuously 
differentiable within D;. Let A bea vector function of its origin 
M and defined by 
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