Brard 



A:))i - i pALU^ ia' 



^U/^, 



+ b' 



iW. = i /-^ALU^ 



+ bj 



''(0) + [ (g) 0'(t'-T')dr' 



it),, <^'^0^ ^ J (it) >'(t'-T')dr' 



t ^Q T 



t ' 



^ (3) 



10.2. Effects of Potentials <i> 



These effects give a system of forces (X- , Y- , . . . ) which expression will be 

 added to the expression of the forces of inertia of the body in par. 12. 



11. Forces Due to the Appendages (case of par. 9) 



We assume here that the contribution of the appendages in the forces ?^ and 

 y. will be included in the expressions of the latter (see par. 12). We consider 

 now the effects of the various lifts generated by appendages as diving planes and 

 fins, rudder and aileron, sail. 



11.1. Diving Planes and Fins 



The set of forces on diving planes and fins was studied in par. 6, but with 



the restriction that 



fo3 - , fo, - , fo5 = 0. 



The absolute velocity of the axis Og of a diving plane B is 



Ve(Ob) = i^[U+u+Lq^B] + iy [v+Lr ^"g-Lp Cg] + i^Lw-Lq-fg]. 



The absolute velocity of the center of the lifting surface is 



Vj. = i^[U+ u + Lq Tg- Lr T^gj + i^ [v + Lr ,fg- Lp Cg] + i ^ [w + Lp T7g- Lq ^g] . 



In order to obtain simpler formulae, we will assume that the effect of the com- 

 ponent of Vg parallel to the span is negligible (in fact, some corrections would 

 be necessary; the lift decreases, particularly on the part of the plane which is 

 in the hydrodynamical shadow of the hull). According to this hypothesis, the 



872 



