Chta-Shun Yth 
f',2 must vanish at y=d, being the height of the upper surface measur- 
ed from the lowest point of the channel | 
Indeed, the theory given here is a natural generalisation of 
the classical shallow-water theory for a single fluid of constant den- 
sity. If there is only one single fluid, and if it has a free surface, the 
last equation in (125) gives, with n=1, b=b,, and A=A), 
Ge Gos 404 or ec = gh 
h being the average depth. This is a classical result, 
ACKNOWLEDGMENT 
This work has been sponsored by the Office of Naval Re- 
search, under Grant NR-062-448 to the University of Michigan. 
REFERENCES 
1 KELLAND, P..,, 1839,""On Waves!’ Trans. RS. Edinz ital 
14, 
2 LAMB, H., 1932, ''Hydrodynamics", Cambridge Univ. 
Press and The MacMillan Co. , Sixth Edition. 
3 MacDONALD, H.M., 1894, ''Waves in canals", Proc, Lond. 
Math. Soe.5, Vol. 25, p. 101, 
4 STOKES, G.G., 1839, "Report on recent researches in 
Hydrodynamics, Brit. Assoc, Rep., 1846. 
5 YIH, C.-S., 1965, ''Dynamics of nonhomogeneous fluids", 
The MacMillan Co., New York. 
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