Computation of Shallow Water Shtp Mottons 
is the flux across the section H at station x in the jth mode. The 
results (3.1), (3.2) for Tj; g and T;,, i,j = 1,3,5 now follow di- 
rectly from (A.1.1), while that for j = 7 follows after using sym- 
metry, Tid = Toi : 
It remains to evaluate the quantities A;(x) in terms of hull 
geometry, an easy task for j = 1,3,5 using the elementary results 
i nad SAP ae ets (A. 1. 6) 
H 
and* 
i nad = -B(x) (A. denim) 
H 
with n, = -xn,. For j= 7 we have 
2 _ _ 9¢0 
SPARE xs ¢O a (A. 1. 8) 
% 3¢0 340 Oo 
- stpeas Sy 10 "30" | 
Carrying out the differentiations of (A. 1.2) and integrating we obtain 
a 72 Lm 
. _ikx.cos' 6 i cosB y sin B Zz 
A(x) =e | Been n, [- =? n, k + al al 
H 
which leads to (3.6), using the further elementary results 
i gee 2 | znad = S(x). (A. 1. 9) 
H 
H 
* The corresponding result in Tuck (1970) has a sign error which 
occurs twice and therefore does not affect the final answer for T,4 : 
1569 
