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amplitude factors angle arbitrary cross-section asymptotic value axis boundary capacitance characterize circular cylinder complex component condition contour cos(kd cp(x cylinder of arbitrary dispersion relation displacement factor domain dxdx Enter evaluation expression fl)d fluid formula Fourier free surface Green's function Harold Levine homogeneous i(K+k)a i/ci iKna iKna iKx-Ky incoming wave infinite integral equation ka-cos latter lattice load magnitude NAVAL RESEARCH normal velocity obtain OFFICE OF NAVAL oo 11 ol oscillations particular POINT LATTICES potential theory PREPARED UNDER CONTRACT problem ratio reflection and transmission reflection coefficient regular representation result s(na security classification sin(kd sinfl singular slit solution SPONSORING MILITARY string strip surface point surface waves symmetry tangent TECHNICAL REPORT tion transform transmission coefficients two-dimensional u-plane UNCLASSIFIED Ursell vanishes variational principles velocity potential vertical wave function wave motion whence