Brard 



V , V' 1 ait2 2W J Lq Lu , Lw 





Yc+Yi + Y! = |pAU2|^|mi3^ - (M+Mi)lf " (P + M^) ^ 



^ (3) 



+ (^24 + ^^g) -[}7 + ^^26-^ ^ -[yy 



z^ + z. + z: . ipAu^l^jcM+zx,)^- mIs^- (m + m;) ^+ (^;5 + ^^g) ^} 



In these formulae the squares and product of ^g'^g ^^® neglected. Lastly, 

 the components of the resultant moment are: 



£, . £i . £: = § pALu^ f {-M,3 - ^-15 - ^^g) ^ 



+ (1^24 + ^^g) ~2 " ^'^1 "^I^^O -^ + C^13 + /^^la) — 



3ll, + 3Ki + }lIl = ipALU^ 1^1^13 + 2^13^+ (M3-Mi)^ 



^ (4) 



Lu , / ^ ^ Lw ,, , ^ L^ q 



^+(^^35+^g) —2 - (^2+/^>^2) -^ 



+ (^15 - M^g) 77^+ (^^35 +^g) —2 - (^2+/^^2) 



^c + ^i + 5^1 = I PALU^ 1^ |-(M2 - /X,) ^ + (-24 + -15 - /-^g) T ' "26 If 



+ (-26 -^g) 7^ + (^l3+/^>'l3) T7T"^^3+/^^3) TT h 



12.4. Case When the Wake Generated in a Motion Parallel 

 to the (x,y) -Plane is not Parallel to the (z,x) -Plane 



We assume that, because of singularities, appendages, and so on, on the 

 upperside of the hull, one of the two arcs which constitute the arc (2' along 

 which the free vortices are shed is in the (z,x)-plane, is on the upperside of 

 the hull. The other arc of (5' is on the portside when 



^ + ^ > 



u u 



880 



