506 O. Grim 
Again, as mentioned before, the common strip method results if only the first row is 
taken into account. The second row, again, represents essentially a plane flow around the 
sections. 
To carry out the computations a further simplification, besides the one already men- 
tioned, is applied for the third row. In this row only the member for n = 0 of the series over 
n members will be considered. The reason is that this member causes the greatest long- 
distance effect since the functions 9, fade away at a greater distance from the origin of the 
disturbance more rapidly the greater n is. Besides, the potential of a periodical source is 
described by 9, and only by this term circular waves, which transport energy, are described. 
Therefore, instead of the third row in Eq. (29), 
Vz 
+00 
wiEB | [U(E) A, (CE) + UE) ALE) - Cx) ASC 
- U(x) A,(x)| 9, [(x- 4).0,0] d& (30) 
is written and, the integral being a function of the coordinate x only, this row can be written 
e’?2 F(x). (31) 
The next problem is to determine U such that the condition on the surface of the body 
is satisfied to a sufficient extent. This means that the influence of the second member in 
(24) on the boundary condition is approximately eliminated. 
A simplification is introduced relative to this boundary condition; viz., the velocity in 
longitudinal direction is neglected so that 
ae ae - By = U, dy 
S 
Oy OZ (32) 
where S = the surface of the ship body. 
The potential (29) is introduced into the left-hand side of this simplified boundary con- 
dition. This can be done without difficulty since solutions are known for the corresponding 
two-dimensional cases. 
; o® dz + 2 ay] =U dy + Ue dy. + yer EC x)idye 
Ss 
“oy (33) 
The sum of these members equals U, dy from Eq. (32). The simplified boundary condi- 
tion leads, therefore, to the following equation for the unknown function U: 
U(x) + vF(x) = 0. (34) 
