504 O. Grim 
condition on the surface of the body is satisfied to a sufficient degree as long as the ship 
body is sufficiently slender, i.e., as long as L/B and L/T are great and the angle between 
the tangent on the waterlines and the plane of symmetry is small. 
Relative to the methods of singularities an improvement is obtained because the rela- 
tion between the singularities, the frequency and the contour parameters is satisfied to a 
higher degree. 
To better recognize the improvement, Eq. (22) is transformed into the identical formula 
+0 
Wx. z= 4h) Ux) 4,00 { 0, [(x-).y.2] dé 
n=0 
- © 
+| {ce AE) - U(x) A(x) 9, [(x- 8.2] dé} . (24) 
The first term represents the nearly two-dimensional flow around the section x because 
the integrals are independent of x. Only in consequence of the functions A (x) a velocity 
component in x-direction arises. By this velocity component, however, the boundary condi- 
tion is not considerably disturbed and it is nearly satisfied if the distribution functions are 
correspondingly chosen. Only the first term is taken into account for the common strip 
method. If the hydrodynamic pressure and the force in a vertical direction generated on a 
section are computed only from this term the same force as in part I is obtained. Applying 
the representation R used in part I one obtains 
5 
< i) U, BR dx (05) 
L 
for the total force to generate the motion with velocity U, or for the total moment 
° ( xU, BR dx 
w fo) y (26) 
L 
Here it is assumed for the computation of the moment that the weight of the body is 
distributed over the length in the same manner as the displacement. Of course, a different 
distribution of the weight can be taken into account. 
The common strip method will be improved if the second term in Eq. (24) is also ap- 
plied. This improvement is already included in Ref. 11. An additional improvement is dis- 
cussed in the following considerations. 
The second member in Eq. (24) may be explained physically as a flow generated at x by 
a distribution [A (€) — A ,(/| situated outside x. Since this distribution lies in y = 0, z = 0 
and since the sia body is slender (i.e., the distribution does not change too rapidly with €, 
this additional flow at x will depend only a little on y inside the ship body, i.e., for 
