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amplitude angle aperture applicable approximately arbitrary axis Boyle's law calculated centre coefficients condensation condition constant corresponding Crown 8vo cylinder denote density depends determined differential equation dimensions direction dissipation distance disturbance divergent effect equal expressed finite fluid force function given Green's theorem harmonic incompressible fluid inertia infinite integral intensity investigation kinetic energy Laplace's length limit loop medium natural density node normal velocity numerous obstacle obtained open end P. G. Tait parallel phase Phil pipe piston pitch plane waves plate pole positive potential pressure problem progressive wave quantity radius rarefaction ratio refraction represented resonator result rigid satisfied shewing simple source solution source of sound space sphere spherical spherical harmonics suppose surface symmetrical temperature term theorem theory tion tube vanish velocity of propagation velocity of sound velocity potential velocity-potential vibration wave-length zero