486 O. Grim 
evz 
Oy =, Cone 
(4) 
iahue 
WY, = > «Sin (vy).- 
The whole potential or the stream function, respectively, consists of the potential of 
the wave (4) and the potential (2) by which the deformation of the wave caused by the body 
is described. In Eq. (2) the factor U will then be omitted. For instance: 
© 
ene eens ’ eX sin (Ky) 
a sin (on) + A, in | eee dK 
2 © 
+ peed. | Kon CK + y)e® £ ceding (Rag) ae 
n=1 0 
Of course, the coefficients A have different values in this case as for the heaving 
motion. 
In case (b) the condition at the boundary of the contour is 
W= 0, (6) 
In the hypothetical case (c) the basis is a representation of a transverse section of the 
three-dimensional ship in a longitudinal wave. The potential of the nondeformed wave with ° 
the orbital velocity 1 is 
Vz 
Qi = = cos (vx). (7) 
From this it follows that the velocity of the water particles in a vertical direction 
amounts to 
e”’? cos (vx) (8) 
and the hydrodynamic pressure to 
Vz 
- ipw cos (Vx). (9) 
The value of cos (vx) may be understood as the phase shift for the following and may 
be omitted in Eqs. (8) and (9). 
The following question may be asked: Which two-dimensional potential D(y,z) describes 
such a velocity on the contour of the section of a two-dimensional body that the boundary 
