Brard 

 r*(yp,t') = 7i(m'.t') - 7*(m",t') , 



(m', m " infinitely close to P), which lead to 



7*(m',0+) - 7*(m",0+) = . 



We set 



7*(m,t') = 7*(m,0+) + Syl(m,t') (26) 



with 



S7t(m,0+) = , — S7*(m,0+) = 0(1) . (27) 



The variation of S7*(m, t ') between (0, t ') is partly due to the fact that 

 7i(m, t ') depends upon the distribution of the arcs p'm^,P, P'm^,P on the hull, 

 distribution which is variable with t '. For t ' = 0+ , these arcs are concentrated 

 in the vicinity of Sg j . 



Now, consider the case "bj," when (w/U)^, is, for t' > 0, an arbitrarily 

 given function. 



For (20), we have to substitute: 



f F,(t'-r') H(t'-r')dT' = (^)^^ , (28) 







the general solution of which is: 



F,(t') = (f) F*(t'). ( -^(f) F*(t'-r')dr' (29) 



when (w/U)^, is continuous for t' > 0. One has 



r^(r,',t') = r^,(v') Fi(t') . (30) 



Because of (8) the density y^(m, t ') of the distribution of doublets on the 

 hull is: 



t ' 



7i(m,t') = f Fi(t') Hoi(m,t' -r')dT' . (31) 



That gives, in the case "aj," the expression already written above: 



842 



