The Theory of Sound, Vol. II

channels. Simple apertures. Elliptic aperture. Comparison with a circular aperture of equal area. In many cases, a calculation based on area alone is sufficient. Upper and lower original: "Superior and inferior" limits for the acoustic conductivity of necks. Correction to the length of a passage due to an open end. Conductivity of passages bounded by nearly cylindrical surfaces of revolution. Comparison of calculated and observed pitch. Multiple resonance. Calculation of vibration periods for a double resonator. Communication of energy to the external atmosphere. Rate of energy loss original: "dissipation". Numerical example. Forced vibrations caused by an external source. Helmholtz’s theory of open pipes. Correction to length. Rate of energy loss. Influence of a flange. Experimental methods for determining the pitch of resonators. Discussion of motion originating within an open pipe. Motion caused by external sources. Effect of widening original: "enlargement" at a closed end. Absorption of sound by resonators. Quincke’s tubes. Operation of a resonator close to a source of sound. Strengthening original: "reinforcement" of sound by resonators. Ideal resonator. Operation of a resonator close to a double source. Savart’s experiment. Two or more resonators. Question of the formation of air jets during sound-induced original: "sonorous" motion. [Free vibrations initiated. Influence of wind upon the pitch of organ pipes. The power of wind to maintain sound. Overtones. Mutual influence of neighboring organ pipes. Whistling. Maintenance of vibrations by heat. Trevelyan’s rocker original: "Trevelyan’s rocker"; a historical device demonstrating how heat can cause a metal block to vibrate and produce sound.. Communication of heat and aerial vibrations. Singing flames. Sondhauss’s observations. Sounds discovered by Rijke and Bosscha. Helmholtz’s theory of reed instruments.]

CHAPTER XVII.

Sections original: "§§" 323—335 . . . . . . . . 236

Applications of Laplace’s functions original: "Laplace’s functions"; these are now more commonly known as spherical harmonics. to acoustic problems. General solution involving the term of the $n$^th^ order. Expression for radial velocity. Diverging waves. Origin at a spherical surface. The formation of sound original: "sonorous" waves generally requires a certain area of moving surface; otherwise, the mechanical conditions are satisfied by a local movement original: "transference" of air without significant compression original: "condensation" or expansion original: "rarefaction". Stokes’s discussion of the effect of side-to-side original: "lateral" motion. Leslie’s experiment. Calculation of numerical results. The term of the zero order is usually missing original: "deficient" when the sound originates from the vibration of a solid body. Reaction of the surrounding air on a rigid vibrating sphere. Increase of effective momentum original: "inertia". When the sphere is small in comparison with the wavelength, there is very little communication of energy. Vibration of an ellipsoid. Multiple sources. In cases of symmetry, Laplace’s functions are reduced to Legendre’s functions original: "Legendre’s functions"; now called Legendre polynomials.. [Table of zonal harmonics.] Calculation of the energy emitted from a vibrating spherical surface. Cases where the disturbance is limited to a small part of the spherical surface. Numerical results. Effect of a small sphere situated close to a source of sound. Analytical transformations. Case of continuity through a pole. Mathematical expressions for the velocity potential. Expression in terms of Bessel functions of fractional order. Particular cases. Vibrations of gas confined within a rigid spherical container original: "envelope". Radial vibrations. Vibrations across the diameter original: "Diametral vibrations". Vibrations expressed by a Laplace’s function of the second order. Table.