Section 4, Vol. Vii., P. 186, 1854.

“Philosophical Magazine,” section 4, vol. viii., p. 74, 1854.

“Proceedings of the Royal Institution,” January 15, 1875.

“Researches in Chemistry and Physics,” p. 484.

“Connaissance des Temps,” 1825, p. 370.

See Chapter VII., Part II.

The effect of the air of London is sometimes strikingly evident.

“Philosophical Transactions,” 1874, Part I., p. 208, and Chapter VII. of this volume.

Since this was written I have sent the sound through fifteen layers of calico, and echoed it back through the same layers, in strength sufficient to agitate the flame. Thirty layers were here crossed by the sound. The sound was subsequently found able to penetrate two hundred layers of cotton net; a single layer of wetted calico being competent to stop it.

The cut reached me too late for introduction at the proper place.

INDEX

Acoustic clouds, echoes from, 325 —— reversibility, 461-469 —— transparency, great change of, 323

Air, process of the propagation of sound through the, 33 —— propagation of sound through air of varying density, 41 —— elasticity and density of air, 54 —— influence of temperature on the velocity of sound, 55 —— thermal changes produced by the sonorous wave, 60 —— ratio of specific heats at constant pressure and at constant volume deduced from velocities of sound, 62 —— mechanical equivalent of heat deduced from this ratio, 64 —— inference that atmospheric air possesses no sensible power to radiate heat, 66 —— velocity of sound in, 69 —— musical sounds produced by puffs of air, 89 —— other modes of throwing the air into a state of periodic motion, 91 —— reflection from heated air, 338

Albans, St., echo in the Abbey Church of, 50

Amplitude of the vibration of a sound-wave, 42

Arago, his report on the velocity of sound, 328

Atmosphere, reflection from atmospheric air, 335

Atmosphere, its effect on sound, 365

Auditory nerve, office of the, 32 —— manner in which sonorous motion is communicated to the, 33

Bars, heated, musical sounds produced by, 87 —— examination of vibrating bars by polarized light, 209

Beats, theory of, 385 —— action of, on flame, 387 —— optical illustration of, 390 —— various illustrations of, 397 —— dissonance due to beats, 399, 428

Bell, experiments on a, placed in vacuo, 36-37

Bells, analysis of vibrations of, 190, 198 —— fluctuations of, 351-354

Bourse, at Paris, echoes of the gallery of the, 49

Burners, fish-tail and bat’s-wing, experiments with, 277

Carbonic acid, velocity of sound in, 65 —— reflection from, 335 —— oxide, velocity of sound in, 69

Chladni, his tonometer, 168 —— his experiments on the modes of vibration possible to rods free at both ends, 174 —— his analysis of the vibrations of a tuning-fork, 176

Chladni, his device for rendering the vibrations visible, 178 —— illustrations of his experiments, 180

Chords, musical, 432

Clang, definition of, 153

Claque-bois, formation of the, 175, 197

Clarinet, tones of the, 237

Clouds, sounds reflected from the, 49

Corti’s fibres, in the mechanism of the ear, 426

Cottrell, Mr., his experiment of an echo from flame, 339

Derham, Dr., on fog-signals, 306

Diatonic scale, 263

Difference-tones, 404

Diffraction of sound, 76 note, 78

Disks, analysis of vibrations of, 187, 198

Dissonance, cause of, 428 —— graphic representation of, 430

Doppler, his theory of the colored stars, 113

Ear, limits of the range of hearing of the, 106, 118 —— causes of artificial deafness, 108, 119 —— mechanism of the ear, 424 —— consonant intervals in relation to, 426

Echoes, 48 —— instances of, 48-50 —— aërial, production of, 328-329 —— from flame, 339-340 —— reputed cloud echoes, 328

Eolian harp, formation of the, 159-160

Erith, effects of the explosion of 1864 on the village and church of, 53

Eustachian tube, the, 198 —— mode of equalizing the air on each side of the tympanic membrane, 109, 119

Falsetto voice, causes of the, 239

Faraday, Mr., his experiment on sonorous ripples, 195

Fiddle, formation of the, 123 —— sound-board of the, 123 —— the iron fiddle, 169, 197 —— the straw-fiddle, 175, 197

Flames, sounding, 261, 302 —— rhythmic character of friction, 260, 301 —— influence of the tube surrounding the flame, 263, 302 —— singing-flames, 264, 302 —— effect of unisonant notes on singing-flames, 275 —— action of sound on naked flames, 275, 302-304 —— influence of pitch, 283 —— extraordinary delicacy of flames as acoustic reagents, 285 —— the vowel-flame, 286 —— discovery of a new sensitive flame by Philip Barry, 288 —— echo from, 339 —— action of beats on flame, 387

Flute, tones of the, 237

Fog, its want of power to obstruct sound, 348 —— observations in London, 348 —— fog-signals in, 355 —— artificial, experiments on, 357

Fog-signals, researches on the acoustic transparency of the atmosphere in relation to the question of, 305 —— station at South Foreland, 309 —— instruments and observations, 309 —— variations of range, 315-316 —— contradictory results, 317 —— solution of contradictions, 317-323 —— extraordinary case of acoustic opacity, 318 —— in fogs, 355 —— minimum range of, 371 —— its position, 370 —— disadvantages of the gun, 368

Foreland, South, fog-signal station at, 309 —— fog at, 354

Gaines’s Farm, account of the battle of, 324

Gases, velocity of sound in, 69

Gun, range of, for fog-signals, 312-313 —— inferiority to the siren, 369 —— its disadvantages as a signal, 368

Hail, doubt as to its power to obstruct sound, 342

Harmonic tones of strings, 152-154

Harmony, 410 —— notions of the Pythagoreans, 411 —— Euler’s theory, 419 —— conditions of harmony, 411 —— influence of overtones on harmony, 429 —— graphic representations of consonance and dissonance, 431

Harmonica, the glass, 176

Hawksbee, his experiment on sounding bodies placed in vacuo, 36

Hearing, mechanism of, 424

Heat, thermal changes in the air produced by the sonorous wave, 60 —— ratio of specific heats at constant pressure and at constant volume deduced from velocities of sound, 64

—— mechanical equivalent of heatdeduced from this ratio, 66 —— inference that atmospheric air possesses no sensible power to radiate heat, 68 —— musical sounds produced by heated bars, 87

Helmholtz, his theory of resultant tones, 405, 406 —— —— consonance, 414, 420

Herschel, Sir John, his article on “Sound” quoted, 50 —— his account of Arago’s observation on velocity of sound, 328

Hooke, Dr. Robert, his anticipation of the stethoscope, 75 —— his production of musical sounds by the teeth of a rotating wheel, 85

Horn, as an instrument for fog-signalling, 310-311

Hydrogen, action of, upon the voice, 40 —— deadening of sound by, 38 —— velocity of sound in, 55, 69

Inflection of sound, 53 —— case of the Erith explosion, 53

Interference of sonorous waves, 381-382, 407 —— extinction of sound by sound, 383, 408 —— theory of beats, 385, 408

Intervals, optical illustration of, 440

Joule’s equivalent, 67

Jungfrau, echoes of the, 49

Kaleidophone, Wheatstone’s, formation of, 170, 196

Kundt, M., his experiments, 344

Laplace, his correction of Newton’s formula for the velocity of sound, 58-59

Le Conte, Professor, his observation upon sensitive naked flames, 274-275 —— on the influence of musical sounds on the flame of a jet of coal-gas, 454-460

Lenses, refraction of sound by, 51

Light, analogy between sound and, 45-50 —— analogy of, 320

Liquids, velocity of sound in, 69 —— transmission of musical sounds through, 113 —— constitution of liquid veins, 291 —— action of sound on liquid veins, 294, 303-304 —— Plateau’s theory of the resolution of a liquid vein into drops, 295 —— delicacy of liquid veins, 300

Lissajous, M., his method of giving optical expression to the vibrations of a tuning-fork, 93 —— illustration of beats of two tuning-forks, 390

Mayer, his formula of the equivalent of heat, 66

Melde, M., his experiments with vibrating strings, 141, 427 —— and with sonorous ripples, 194

Metals, velocity of sound transmitted through, 72 —— determination of velocity in, 73

Molecular structure, influence of, on the velocity of sound, 73, 212

Monochord or sonometer, the, 121

Motion, conveyed to the brain by the nerves, 31 —— sonorous motion. See SOUND.

Mouth, resonance of the, 241-242

Music, physical difference between noise and, 82, 117 —— a musical tone produced by periodic, noise by unperiodic, impulses, 83, 117 —— production of musical sounds by taps, 84, 117 —— —— by puffs of air, 89, 117 —— pitch and intensity of musical sounds, 90, 92, 117 —— description of the siren, 97 —— definition of an octave, 105 —— description of the double siren, 110 —— transmission of musical sounds through liquids and solids, 113 —— musical chords, 432-433 —— the diatonic scale, 432-433 —— See also HARMONY.

Musical-box, formation of the, 169, 197

Nerves of the human body, motion conveyed by the, to the brain, 31 —— rapidity of impressions conveyed by, 31 note

Newton, Sir Isaac, his calculation of the velocity of sound, 58

Nodes, 131-132 —— the nodes not points of absolute rest, 135 —— nodes of a tuning-fork, 175, 177 —— rendered visible, 177, 180 —— a node the origin of vibration, 251

Noise, physical difference between music and, 82, 117

Octave, definition of an, 105

Organ-pipes, 219, 256

Organ-pipes, vibrations of stopped pipes, 221, 256 —— —— Pandean pipes, 224 —— —— open pipes, 224, 256, 260 —— state of the air in sounding-pipes, 227, 257 —— reeds and reed-pipes, 234

Otolites of the ear, 425

Overtones, definition of, 153 —— relation of the point plucked to the, 155 —— corresponding to the vibrations of a rod fixed at both ends, 165 —— of a tuning-fork, 177 —— rendered visible, 177, 179 —— of rods vibrating longitudinally, 207 —— of the siren, 415 —— influence of overtones on harmony, 429

Pandean pipes, the, 224

Piano-wires, clang of, 158 —— curves described by vibrating, 160

Pipes. See ORGAN-PIPES

Pitch of musical sounds, 90 —— illustration of the dependence of pitch on rapidity of vibration, 100 —— relation of velocity to pitch, 211-212 —— velocity deduced from pitch, 233

Plateau, his theory of the resolution of a liquid vein into drops, 295

Pythagoreans, notions of the, regarding musical consonance, 410

Rain, reputed power of obstructing sound, 341-342 —— artificial, passage of sound through, 345

Reeds and reed-pipes, 234

Reeds, the clarinet and flute, 237

Reflection of sound, 45 —— from gases, 332 —— aërial, proved experimentally, 258

Refraction of sound, 51

Resonance, 213 —— of the air, 213-214, 256 —— of coal-gas, 216 —— of the mouth, 242

Resonators, 213

Resultant tones, discovery of, 399 —— conditions of their production, 400 —— experimental illustrations, 401 —— theories of Young and Helmholtz, 404, 406

Reversibility, acoustic, 461-469

Robinson, Dr., his summary of existing knowledge of fog-signals, 307 —— Professor, his production of musical sounds by puffs of air, 89

Rod, vibrations of a, fixed at both ends; its subdivisions and corresponding overtones, 165, 197 —— vibrations of a rod fixed at one end, 166, 197 —— —— of rods free at both ends, 173, 197

Savart’s experiments on the influence of sounds on jets of water, 457

Schultze’s bristles in the mechanism of hearing, 425

Sea-water, velocity of sound in, 70

Sensitive flames, 274

Smoke-jets, action of musical sounds on, 290

Snow, its reputed power to obstruct sound, 344

Solids, velocity of sound transmitted through, 69, 72 —— musical sounds transmitted through, 115-116, 122 —— determination of velocity in, 211

Sonometer, or monochord, the, 121

Sorge, his discovery of resultant tones, 399

Sound, production and propagation of, 32, 77 —— experiments on sounding bodies placed in vacuo, 36, 77 —— deadened by hydrogen, 38 —— action of hydrogen upon the voice, 40 —— propagation of sound through air of varying density, 40 —— amplitude of the vibration of a sound-wave, 42, 77 —— the action of sound compared with that of light and radiant heat, 45 —— reflection of, 45, 77 —— echoes, 48-50, 78 —— sounds reflected from the clouds, 49-50 —— refraction of sound, 51, 77 —— diffraction of sound, 53, 78 —— influence of density and elasticity on velocity, 54, 78 —— influence of temperature on velocity of sound, 55, 78 —— determination of velocity, 57, 78 —— Newton’s calculation, 58, 80 —— Laplace’s correction of Newton’s formula, 59, 80 —— thermal changes produced by the sonorous wave, 60, 80 —— velocity of sound in different gases, 69, 81 —— —— in liquids and solids, 70-73, 81 —— influence of molecular structure on the velocity of sound, 73, 81 —— velocity of sound transmitted through wood, 74, 81 —— diffraction of, 76 note, 78 —— physical distinction between noise and music, 82 —— musical sounds periodic, noise unperiodic, impulses, 83 —— —— produced by taps, 84 —— —— by puffs of air, 89 —— pitch and intensity o£ musical sounds, 90 —— vibrations of a tuning-fork, 91 —— M. Lissajous’s method of giving optical expression to the vibrations of a tuning-fork, 93 —— definition of the wave-length, 96 —— description of the siren, 97 —— determination of the rapidity of vibration, 101 —— and of the length of the corresponding sonorous wave, 102 —— various definitions of vibration and of sound-wave, 103 —— limits of range of hearing of the ear: highest and deepest tones, 106 —— double siren, 110 —— transmission of musical sounds through liquids and solids, 113-117 —— vibrations of strings, 120 —— the sonometer, or monochord, 121 —— influence of sound-boards, 123 —— laws of vibrating strings, 125 —— direct and reflected pulses, 129 —— stationary and progressive waves, 130 —— nodes and ventral segments, 130, 133 —— application of the results to the vibration of musical strings, 138 —— M. Melde’s experiments, 141, 427 —— longitudinal and transverse impulses, 144 —— laws of vibration thus demonstrated, 148, 162 —— harmonic tones of strings, 152, 163-164 —— definitions of timbre, or quality, of overtones and clang, 153, 164 —— relation of the point of string plucked to overtones, 155-156 —— vibrations of a rod fixed at both ends; its subdivisions and corresponding overtones, 165 —— —— of a rod fixed at one end, 166 —— Chladni’s tonometer, 168 —— Wheatstone’s kaleidophone, 170, 196 —— vibrations of rods free at both ends, 173, 197 —— nodes and overtones of a tuning-fork, 175-178, 197 —— —— rendered visible, 177-179, 197-198 —— vibrations of square plates, 184, 198 —— —— of disks and bells, 187-190, 198-199 —— sonorous ripples in water, 193 —— Faraday’s and Melde’s experiments on sonorous ripples, 194-195 —— longitudinal vibrations of a wire, 200 —— relative velocities of sound in brass and iron, 203, 206 —— examination of vibrating bars by polarized light, 209 —— determination of velocity in solids, 211 —— relation of velocity to pitch, 212 —— resonance, 213, 253, 256 —— —— of the air, 213, 256 —— —— of coal-gas, 216, 256 —— description of vowel-sounds, 240 —— Kundt’s experiments on sound-figures within tubes, 244-251, 259 —— new methods of determining velocity of sound, 247-251, 259 —— causes that obstruct the propagation of, 306 —— action of fog upon sound, 307 —— contradictory results of fog-signalling, 317 —— solution of contradictions of fog-signalling, 317-318 —— extraordinary case of acoustic opacity, 318 —— great change of acoustic transparency, 323 —— noise of battle unheard, 324 —— echoes from invisible acoustic clouds, 325, 375 —— report of Arago on the velocity of, 328 —— aërial echoes of, 330 —— demonstration of reflection from gases, 332 —— reflection from vapors, 336 —— —— heated air, 337 —— echo from flame, 340 —— investigations of the transmission of sound through the atmosphere, 341 —— action of hail and rain, 341 —— action of snow, 344 —— passage through tissues, 345 —— —— artificial showers, 346 —— action of fog, 347 —— fluctuations of bells, 351-354 —— action of wind, 361 —— atmospheric selection, 365 —— law of vibratory motions in water and air, 377, 407 —— superposition of vibrations, 381 —— interference and coincidence of sonorous waves, 382-383, 407 —— extinction of sound by sound, 384, 407 —— theory of beats, 385, 408 —— action of beats on flame, 387 —— optical illustration of beats, 390, 408 —— various illustrations of beats, 397 —— resultant tones, 399, 409 —— —— conditions of their production, 400 —— —— experimental illustrations, 401 —— —— theories of Young and Helmholtz, 405-406 —— difference-tones and summation-tones, 405 —— combination of musical sounds, 410 —— sympathetic vibrations, 421 —— mode in which sonorous motion is communicated to the auditory nerve, 426

Sound-boards, influence of, 123-124

Sound-figures within tubes, M. Kundt’s experiments with, 244-251

Stars, Doppler’s theory of the colored, 113

Steam-siren, description of, 309 —— conclusive opinion as to its power for a fog-signal, 370

Stethoscope, Dr. Hook’s anticipations of the, 74

Stokes, Professor, his explanation of the action of sound-boards, 124 —— his explanation of the effect of wind on sound, 363

Straw-fiddle, formation of the, 175, 197

Strings, vibration of, 120 —— laws of vibrating strings, 125 —— combination of direct and reflected pulses, 129 —— stationary and progressive waves, 130 —— nodes and ventral segments, 130-133 —— experiments of M. Melde, 141, 427 —— longitudinal and transverse impulses, 144 —— laws of vibration thus demonstrated, 148, 162 —— harmonic tones of strings, 152, 163-164 —— timbre, or quality, and overtones and clang, 153, 164 —— Dr. Young’s experiments on the curves described by vibrating piano-wires, 160 —— longitudinal vibrations of a wire, 200 —— —— with one end fixed, 204 —— —— with both ends free, 206

Summation-tones, 405

Siren, description of the, 97 —— sounds, description of the, 97 —— its determination of the rate of vibration, 101 —— the double siren, 110, 411-412 —— the echoes of the, 330

Tartini’s tones, 399. See RESULTANT TONES.

Timbre, or quality of sound, definition of, 153

Tisley, Mr., his apparatus for the compounding of rectangular vibrations, 447

Toepler, M., his experiment on the rate of vibration of the flame, 268

Tonometer, Chladni’s, 168

Trumpets, range of, for fog-signals, 313

Tuning-fork, vibrations of a, 93 —— M. Lissajous’s method of giving optical expression to the vibrations, 93 —— strings set in motion by tuning-forks, 142 —— vibrations of the tuning-forks as analyzed by Chladni, 176 —— nodes and overtones of a, 171, 197 —— interference of waves of the, 395

Vapors, reflection from, 336

Velocity of sound, influence of density and elasticity on, 54 —— influence of temperature on, 55 —— determination of, 57 —— Newton’s calculation, 58 —— velocity of sound in different gases, 69 —— and transmitted through various liquids and solids, 70-73 —— relative velocities of sound in brass and iron, 203, 206 —— relation of velocity to pitch, 212 —— velocity deduced from pitch, 233

Ventral segments, 132

Vertical jets, action of sound on, 297, 304

Vibrations of a tuning-fork, 93 —— method of giving optical expression to the vibrations of a tuning-fork, 93 —— illustration of the dependence of pitch on rapidity of vibration, 101 —— the rate of vibration determined by the siren, 101 —— determination of the length of the sound-wave, 102, 118 —— various definitions of vibrations, 103, 118 —— vibrations of strings, 120 —— laws of vibrating strings, 125 —— direct and reflected pulses illustrated, 129 —— application of the result to the vibration of musical strings, 138 —— M. Melde’s experiments on the vibration of strings, 141, 427 —— longitudinal and transverse impulses, 144 —— Vibrations of a red-hot wire, 147 —— laws of vibration thus demonstrated, 148, 162 —— new mode of determining the law of vibration, 148, 150 —— harmonic tones of strings, 152, 163 —— vibrations of a rod fixed at both ends; its subdivisions and corresponding overtones, 165 —— vibrations of a rod fixed at one end, 166 —— Chladni’s tonometer, 168 —— Wheatstone’s kaleidophone, 170 —— vibrations of rods free at both ends, 173 —— nodes and overtones rendered visible, 177-179 —— vibrations of square plates, 184 —— —— of disks and bells, 187-190 —— longitudinal vibrations of a wire, 200, 255 —— —— with one end fixed, 204 —— —— with both ends free, 206 —— divisions and overtones of rods, vibrating longitudinally, 207 —— examination of vibrating bars by polarized light, 209 —— vibrations of stopped pipes, 221 —— —— of open pipes, 224 —— a node the origin of vibration, 251 —— law of vibratory motions in water and air, 377 —— superposition of vibrations, 381 —— theory of beats, 385 —— sympathetic vibrations, 421 —— M. Lissajous’s method of studying musical vibrations, 433 —— apparatus for the compounding of rectangular vibrations, 447

Violin, formation of the, 123 —— sound-board of the, 123 —— the iron fiddle, 169, 197

Voice, human, action of hydrogen upon the, 40 —— sonorous waves of the, 104 —— description of the organ of voice, 238 —— causes of the roughness of the voice in colds, 239 —— causes of the squeaking falsetto voice, 239 —— Müller’s imitation of the action of the vocal chords, 240 —— formation of the vowel-sounds, 240-241 —— synthesis of vowel-sounds, 242-243

Vowel-flame, the, 286

Vowel-sounds, formation of the, 240 —— synthesis of, 242-243

Water-Waves, stationary, phenomena of, 136

Water, velocity of sound in, 70 —— transmission of musical sounds through, 113 —— effects of musical sounds on jets of water, 291-292 —— delicacy of liquid veins, 294 —— theory of the resolution of a liquid vein into drops, 295, 304 —— law of vibratory motions in water, 377

Wave-length, definition of, 96 —— determination of the length of the sonorous wave, 102

Wave-length, definition of sonorous wave, 104

Wave-motion, illustration, 128-133 —— stationary waves, 133 —— law of, 377

Waves of the sea, causes of the roar of the breaking, 88 note

Weber, Messrs., their researches on wave-motion, 133

Wetterhorn, echoes of the, 49

Wheatstone, Sir Charles, his kaleidophone, 170 —— his apparatus for the compounding of rectangular vibrations, 448

Whistles, range of, for fog-signals, 313

Wind, effect on sound, 361

Wires. See STRINGS

Wood, velocity of sound transmitted through, 74 —— musical sounds transmitted through, 115 —— the claque-bois, 175 —— determination of velocity in wood, 211

Woodstock Park, echoes in, 56

Young, Dr. Thomas, his proof of the relation of the point of a string plucked to the overtones, 155 —— on the curves described by vibrating piano-wires, 160-161 —— his theory of resultant tones, 404