Beck and Tuck 
agreement between experiments and deep water theories to give us 
confidence in the present shallow water theory. 
In the case of heave and pitch, the theory presented in this 
paper (but with neglect of diffraction exciting forces) has been com- 
pared to Kim's (1968) shallow water strip theory by Beck and Tuck 
(1971). As expected, the present slender body theory seems to give 
more acceptable results in the very low frequency range, while the 
strip theory should be more accurate for high frequencies, In the in- 
termediate frequency range, both theories give similar predictions 
of heave and pitch motions, 
This work was supported by the Australian Research Grants 
Committee. 
APPENDIX I 
DERIVATION OF ee FOR VERTICAL MODES 
The definition off ‘T;;’is G,j = 0,1, .....- 7) 
J 
2 
Bi os 8 Meare | n,¢.dS (A. I 
ij Tai 
where 
___g ikxcos® coshk(z +h) _iky sin B 
es Oy hae ‘Cosh kh (An ta2) 
ik 2 
2 Bate CO8P (1 + ay sinB + 0(€) ) (A. 1.3) 
g 
and the result of Tuck (1970) is that for j = 1,3,5 
Me (a) 
loca [ee ples (k|x- |) dé (A. 1. 4) 
where 
26x) =) Aa (A. 1.5) 
H 
