A Vortex Theory for the Maneuvering Ship 



= ijj) [y\(m,0) + ;vx;(m,t')] , (32) 



^ *^ 'o + 



and, in the case "b/': 



7i(m,t') = (-g) [7t(m,0+) + hyl(m,t')] 



t ' 

 + f ~. {^) , [y*i(^'0) + by*(m, t'-r')] dr ' ' 



/ ^(^)., ^n(».f-')dx', (33) 



+ 



"0 



when (w/U)^, is continuous far t' >0. 



If (w/U)^, has discontinuities of the first kind for t ' > 0, one has the general 

 formulae: 



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



* 



and 



t ' 



7i(m,t') = (-^) ^ 7*1(^,0+) + j (^) , ^ S7*(m, t'-T')dr' . (33') 



In the case of the quasi- steady motion, we would have a circulation 

 and a density of doublets 

 That leads in the case "a^," to the deficiencies 



843 



