CONTENTS.

viscosity A fluid's resistance to flow; its "thickness.". Warm water. Mixture of water and alcohol. Bell’s experiment. Bird-calls. Sondhauss’s laws regulating pitch. Notes examined by flames. Aeolian tones original: "Aeolian tones"; sounds produced by wind blowing across an object, such as a wire, named after the Greek god of wind, Aeolus.. Strouhal’s observations. Aeolian harp vibrates perpendicularly original: "transversely" to the direction of the wind. Dimensional formula.]

CHAPTER XXII.

§§ 373—381. . . . . . . . . . . . . . 415

[Vibrations of solid bodies. General equations. Plane waves of stretching original: "dilatational" and twisting original: "distortional". Stationary waves. Initial disturbance limited to a finite region. Theory of Poisson and Stokes. Waves from a single center. Secondary waves scattered original: "dispersed" from a small obstacle. Linear source. Linear obstacle. Complete solution for a repeating original: "periodic" force acting at a single point within an infinite solid. Comparison with Stokes and Hertz. Reflection of plane waves hitting a surface at a right angle original: "perpendicular incidence".] Principle of physical similarity original: "dynamical similarity"; the principle that allows the behavior of large systems to be predicted by studying smaller models.. Theory of ships and models. Application of the principle of similarity to flexible original: "elastic" plates.

CHAPTER XXIII.

§§ 382—397. . . . . . . . . . . . . . 432

[Facts and theories of hearing original: "audition". Range of pitch over which the ear is capable of perceiving sound. Estimation of pitch. Preyer’s observations. Volume original: "amplitude" necessary for audibility. Estimate of Toepler and Boltzmann. The author’s observations using whistles and tuning forks. Hearing with two ears original: "binaural audition". Locating sounds. Ohm’s law of hearing original: "audition"; the theory that the ear perceives complex sounds by breaking them down into simple tones.. Necessary exceptions. Two simple vibrations of nearly the same pitch. Bosanquet’s observations. Mayer’s observation that a deep original: "grave" sound may drown out a high-pitched original: "acute" sound, but not the other way around original: "vice versa". Effect of fatigue. How best to hear overtones. Helmholtz’s theory of hearing original: "audition". Degree of damping The rate at which a vibration or sound fades away. of the vibrators inside the ear. Helmholtz’s estimate. Mayer’s results. How many vibrations original: "impulses" are required to define original: "delimit" pitch? Kohlrausch’s results. Beats of overtones. Harmonious original: "consonant" intervals mainly defined by these. Combination tones Tones heard when two loud notes are played together, which are not present in the original notes themselves.. According to Helmholtz, these are due to a failure of superposition The principle that different sound waves should pass through each other without changing one another.. In some cases, combination tones exist outside the ear. Difference tones on the harmonium. Helmholtz’s theory. Summation tones. The difficulty in hearing them perhaps explained original: "explicable" by Mayer’s observation. Are powerful sound sources original: "generators" necessary for difference tones to be heard? Can beats turn into a difference tone? Periodic changes of a suitable pitch are not always recognized as tones. The difference tone involves a vibration of a specific volume original: "amplitude" and timing original: "phase". Audible difference tones from inaudible sources. Harmonious original: "consonant" intervals of pure tones. Helmholtz’s views. Defining original: "delimitation" the musical interval of a "Fifth" by second-order difference tones. The scale of magnitude of various difference tones. When the Octave is added, the first difference tone is enough to define the Fifth. Does the ear notice differences in timing original: "phase-differences"? Helmholtz’s observations on tuning forks. Evidence from out-of-tune harmonies original: "mistuned consonances". Lord Kelvin finds the beats of imperfect harmonics are noticeable even—