Hydrodynamics

amplitude angular velocity arbitrary axes axis boundary canal centre circle circuit coefficients components condition const constant coordinates corresponding cosh curves cyclic denote depth direction distance disturbing dT dT ellipsoid equal equation of continuity expression extraneous forces finite fluid formula free surface function given Green's Theorem harmonic Hence impulse infinitely small infinity integral investigation irrotational motion J. J. Thomson kinetic energy liquid Lord Kelvin Lord Rayleigh Math obtain origin oscillations parallel particle Phil plane positive pressure problem quadratic function radius region result rotation satisfied shews simply-connected sinh solid solid harmonic solid of revolution solution sphere spherical Spherical Harmonics steady motion stream-lines suppose theorem theory Thomson tides vanish velocity-potential vertical vortex vortices wave-length whence whilst zero αμ аф