508 O. Grim 
The force and the moment for the whole ship body are obtained by corresponding inte- 
grations of Eq. (38) over x. 
The Force Generated by Waves on the Ship Body 
To compute the force it is assumed first that the ship body is restrained. The generat- 
ing surface wave is supposed to run in longitudinal direction from fore to aft. The method 
can, however, also be applied for all running directions. 
As compared to the Froude-Kryloff method an essential progress would be obtained if, 
instead of the quasi hydrostatic force computed from the nondeformed wave, the force E . 
computed for case (c), viz., the ship in a “longitudinal wave” is introduced. 
A different method is proposed in Ref. 11. Also this method could be improved. 
The formula for the potential of the nondeformed surface wave of orbital velocity 1 is 
as follows, omitting the time factor e’®* 
® = EY, (39) 
The following formula will be used for the total potential of the wave and deformation 
caused by the body: 
Bem fA OW oy ee 
This potential still exactly satisfies both the continuity equation and the condition on 
the free water surface. G(x) represents a presently unknown complex function in a similar 
manner as U(x). 
Using the same simplifications as before, which are deemed permissible relative to 
points on the surface of the ship, Eq. (40) is simplified to 
: evz 1 = bas 
© ~ eivx { eta G(x) A (Cs) i om (x- ).y,2] dé 
n=0 - 0 
Ls | EV es COrZa©® 
= G(s) AUR @s) | one 1))0.0) ts| (41) 
The last member in this equation can be written as follows: 
Coe sHiGx) (42) 
