Brard 
The system of forces dF. is that of the forces exerted by 
the vortex distribution on itself and is therefore equivalent to zero. 
Also the systems of forces SY, aS (i of the general theory are 
equivalent to zero. Consequently the system of the hydrodynamic 
forces exerted on the body reduces to that of the forces d Fp oe Bis 
gives the general resultant ‘ 
oo off B00 6 vy ak (M) 
2B 
and the resulting moment with respect to a given point 0: 
MH ff OM afFo) Vp (00)] d2U(M) . 
A —_ 
Since ds(M) =0, onehas: 
L 
(o, 
= bow a8 Pp 
cf “of ae (c,) taf ds(M) = 0 (8. 3) 
Stern L(o,) 
Furthermore : 
—> 
Ta off [Feo iz on | -V. fom. vo] dd (M) 
ya 
> ba ty 3 
= =p 
E o,) 6 
stern 
Ye 
bow 
of hg Med. (Vv. . OM) ds (M) . 
s ie 
tern 
bow 
=f > ag (V7, . OM) ds’(M) . (8. 4) 
(o ) 
stern 
This term is not null, at least in general, 
L252 
