Brard 



But, when M is in the vicinity of p, as P is on an edge of 2, the discontinuity 

 is the half of the previous one. Consequently, Eq, (25) gives 



7oo(m') - "/^^(m") = r^^(P) , (m',m" infinitely close to P) , (26) 



which was easy to foresee. 



We have yet to determine ToqCP). 



In order to do that, we need to know a condition which must be satisfied on 

 Sg J. Let us assume, as a first approximation, that 2 may be regarded as nearly 

 parallel to the (x,y) -plane even in the vicinity of (Jg j. In this case, the condition 



d^ [^-ooCm) + Ko(f^)] = - d^ ^oo(M) > x(M) = x(P)-0 , (27) 



may be expressed rather easily. It is a singular Fredholm's equation of the 

 first kind which yields the unknown function r^gCP). 



Similar reasonings may be repeated for r^ and r^^, and finally, the prob- 

 lem consisting in the determination of the wake is, in principle, solved, at least, 

 under the condition that the Sg j-line is known. The latter problem, of course, 

 depends upon the mechanism which governs the transport into the wake of the 

 vorticity which originates in the boundary layer. For the present moment, if a 

 complete, explicit solution had to be given, it would be necessary to consider 

 the (5g J -line as supplied by the experiment. 



In the considerations above, we don't take into account the tendency of the 

 free vortices to wind around themselves and to form two vortices only at some 

 distance from the body. This question would be of importance. But, on this 

 paper, we mainly need to have an idea on the structure of the various potentials 

 which sum gives the motions of the fluid outside the body. 



We note finally that 



4. Case of an Unsteady Quasi -Rectilinear Motion 

 Parallel to the ( z , x ) - Plane 



Let t ' = Ut/L be the reduced time (l = length of the body). 



We assume that the components of the absolute velocity of the origin of the 

 axis attached to the body and the absolute angular velocity (of components p,q, r 

 on these axis) satisfy the following conditions: 



832 



