Transcrtttcal Flow Past Slender Shtps 
The theory appears to be in fair agreement with experiment and indi- 
cates that this direction or research should be fruitful. 
V. ACKNOWLEDGMENT 
We are greatly indebted to Professors Th. Y. Wu and 
J.N. Newman who encouraged us and nudged us along the path to a 
possible solution. One of us (G.K. L.) wishes to express his sincere 
thanks to Mrs. Lea who typed and retyped this manuscript expertly 
and willingly. 
REFERENCES 
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for Slender Ships"’, Journal Ship Research, 1964. 
2: TUCK, E.O., "Shallow-Water Flows Past Slender Bodies"! 
Journal of Fluid Mechanics, Vol. 26, Part I, 1966. 
3 COLE, J.D., ''Perturbation Methods in Applied Mathematics'"' 
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4 VAN DYKE, M.D., ''Perturbation Methods in Fluid Mechanics'"' 
Academic Press, New-York, 1964. 
5 SPREITER, J.R. and ALKSNE, A.Y. ''Thin Airfoil Theory 
Based on Approximate Solution of the Transonic Flow equation" 
NACA Technical Report 1359, 1958. 
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Ti FELDMAN, J.P. '"Transcritical Shallow Water Flow Past 
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9 GRAFF, W. and BINEK, H., ''Untersuchung des Modelltank- 
einflusses an einem Flachwasserschiff'' Forschung sberichte 
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LOT he 
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