Minimum Wave Resistance for Dipole Distributions 109 
and g(x) = ie (f) go(%; f). The wave resistance is found easily from 
f 2_-1 
Cit) = 4k lf). (B17) 
which follows from (29) and (B1). Since one can prove that Eq. (29) is a positive definite 
expression it follows that /,(f) > 0, which is not obvious from the integral equation (B1). 
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[3] Wehausen, J.V., “Wave Resistance of Thin Ships,” in Proceedings of the Symposium on 
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[4] Birkhoff, G., Korvin-Kroukovsky, B.V., and Kotik, J., “Theory of the Wave Resistance 
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[5] G. Weinblum, “Schiffe Geringsten Widerstandes,” Proc. Third Internat. Congr. Appl. 
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[6] Lighthill, M.J., “A New Approach to Thin Aerofoil Theory,” Aero Quart., vol. 3, p. 3, 
Nov. 1951 
[7] Dorr, J., “Zwei Integralgleichungen erster Art, die sich mit Hilfe Mathieuscher Funk- 
tionen losen lassen,” Zeits. angew., Math. Physik 3:427-439 (1952) 
[8] Erdelyi, A., et al., “Higher Transcendental Functions,” vol. 3, NewYork:McGraw-Hill, 
p. 132, 1955 
[9] Tricomi, F.G., “Integral Equations,” New York:Interscience, pp. 143-144, 1957 
[10] MacCamy, R.C., “On Singular Integral Equations with Logarithmic or Cauchy Kernels,” 
J. Math. and Mech. 7:355-375 (May 1958) 
[11] Sretenskii, L.N., “Sur un Probleme de Minimum Dans la Theorie du Navire,” C.R. (Dokl.) 
Acad. Sci. USSR(N.S.) 3:247-248 (1935) 
[12] Pavlenko, G.E., “The Resistance of Water to the Motion of a Ship,” State Publishing 
House for Water Transport, Moscow, pp. 188-192, 1953 (in Russian) 
[13] Shen, Y.C. and Kern, G.E., “Development oy of a Subsurface Ship,” Aerojet-General 
Corp. Report 1535, 1958 
646551 O—62——9 
