Brard 

 where A is the projected area of the body on the (x,y) -plane. 

 The first bracket in the expression of A'J|(t') is 



'^ 



The second bracket is 



(u) , If "^ ^y*i(^'0) nCm) dS(m) + J (J) ^ dr' || ^^ Sy^fm, t'-T')dr' . 

 •^ S ^ s 



The new expressions hold even when (w/U)^/ is not continuous for t' > 0. 

 Hence, putting 



Ht') = 1-F*(t') - ^^ Jl ^ Sy^Cm.t') n(m) i,dS(m'), ^^5) 



we have 



Azi(t') = z^i (J)^, - z;(t') = -z[^'\t') + A'z;(t') , (26) 



with 

 and 



A'Z;(t') . -ipAU^a,|(J)^^0CO) +/ (J)^^-^0(t'-r')dr'|. (28) 



In the last formula 



*^°^ = 1 "" ALUT If bT S^tCm^O) n(m) i^ dS(m) < 1 , 

 ^ s 



0(+oo) = . 



(25') 



In the quasi-steady motion, the component on the x-axis of the resultant 

 force is null, but not in the real motion. One has 



854 



