Computing Hearing and Pitching Motions 509 
since the integral in this row is a function of x only. 
The following simplified condition on the surface of the ship body S will be used: 
ae +o w| =a. 
Ss 
oy Oz (43) 
The right-hand side of this boundary condition is zero since the body is assumed to be re- 
strained and since the whole potential will be introduced. The required computations have 
already been carried out or can easily be carried out. The boundary condition furnishes the 
relation 
e”? dy + G(x) e”* dy + vH(x) e’* dy = 0 (44) 
or the definition equation for the unknown function G(x), viz., 
1 + GCx) + vHCx) = ©. é; (45) 
This is an integral equation for the unknown function G(x). 
After having determined this function G the next problem is to determine the exciting 
force. 
Into the formula for the potential H(x) will now be introduced 
: ev? 1 - ous 
® ~ ei’* G(x) ‘ 5 i 5). Ax) | Pn [(x- E).y,z| c} : (46) 
n=0 21 
Although this formula does not yield an exact value for the potential, it gives a very 
close approximation for coordinates of points at the surface of the ship. 
The hydrodynamic force per unit length in vertical direction has, for this expression, 
already been determined in part I under (c). This force amounts to 
ee (47) 
The result Eq. (46) may be conceived a two-fold deformation of the longitudinal wave 
caused by the ship body. The first member, viz., 
age: er ztix) 
7 
(48) 
may be considered the potential of a longitudinal wave with variable effective wave ampli- 
tude of which the reduction factor relative to the oncoming wave amounts to —G(x). This 
646551 O—62 34 
