Computing Hearing and Pitching Motions 507 
The application of the hypothetical two-dimensional case (c) is again confirmed by the 
appearance of the function e”? in the second and third row of Eq. (33). 
In the equation for U, only the coordinate x appears. This equation is an integral 
equation. 
Having determined U the task of determining the hydrodynamic forces remains. 
Having satisfied Eq. (34), one may write for the potential instead of (29) 
+0 
ce cr 
0 = 5U, 2 AOD | on x= e.¥.2] de 
n=0 -@ 
© +0 
gc) ay ie cal P(e Seyi y nz Orde wil (35) 
This expression does not satisfy the continuity condition any longer and is, therefore, 
not exact. However, the expression may be used for coordinates which correspond to the 
surface of the ship. For these coordinates this equation certainly represents a sufficient 
approximation. The computation of the hydrodynamic pressure and the integration of this 
pressure over the contour of the section in transverse direction to determine the force act- 
ing in a vertical direction has already been carried out in part I. 
From the first member in Eq. (35) one obtains as in the common strip method: 
5— UR. (36) 
@ 
From the second and third member in (35), 
B 
6— UE. (37) 
@ 
for, the second member in (35) describes a “longitudinal wave” at x of orbital velocity U 
and the third member the additional two-dimensional potential computed for (c) in part I. 
E , represents the nondimensional parameter of the force which is related to (c) of part I 
and which is generated by the “longitudinal wave.” 
The total force in a vertical direction on a section of a ship body amounts then to 
B 
On [UR =F UE | (38) 
The second member represents the correction to the common strip method. U, R, and E are 
complex functions. 
