Chta-Shun Yth 
We shall now impose two restrictions on our study : 
(i) we shall assume that the channel is symmetric, and (ii) we shall 
exclude sloshing modes (with motion in the x-y plane only) from con- 
sideration. Asymmetric channels can be similarly treated without 
any substantial additional difficulties, and sloshing modes need a se- 
parate treatment. We shall describe the boundary of the symmetric 
channel by 
and consider only the branch 
x Ath fleas (83) 
Then the direction numbers (nj) s 2; 0) of the normal to the boun- 
dary are 
Dye So in tes re es oth ae Olan. (84) 
Restriction (ii) enables us touse the following expansions : 
Peek (85) 
and 
ams = NL # ROR S ereddore opts (86) 
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