1 It will be borne in mind that the Washington Appendix was published nearly a year after my Report to the Trinity House.

2 That is to say, homogeneous air with an opposing wind is frequently more favorable to sound than non-homogeneous air with a favoring wind. We had the same experience at the South Foreland.—J. T.

3 Had this observation been published, it could only have given me pleasure to refer to it in my recent writings. It is a striking confirmation of my observations on the Mer de Glace in 1859.

4 Had I been aware of its existence I might have used the language of General Duane to express my views on the point here adverted to. See Chap. VII., pp. 340-341.

5 This does not seem more surprising than the passage of light, or radiant heat, through rock salt.

6 Also “Proceedings of the Royal Society,” vol. xxiii., p. 159, and “Proceedings of the Royal Institution,” vol. vii., p. 344.

7 See page 372 of this volume.

8 The rapidity with which an impression is transmitted through the nerves, as first determined by Helmholtz, and confirmed by Du Bois-Reymond, is 93 feet a second.

9 And long previously by Robert Boyle.

10 A very effective instrument, presented to the Royal Institution by Mr. Warren De La Rue.

11 By directing the beam of an electric lamp on glass bulbs filled with a mixture of equal volumes of chlorine and hydrogen, I have caused the bulbs to explode in vacuo and in air. The difference, though not so striking as I at first expected, was perfectly distinct.

12 It may be that the gas fails to throw the vocal chords into sufficiently strong vibration. The laryngoscope might decide this question.

13 Poisson, “MÉcanique,” vol. ii., p. 707.

14 To converge the pulse upon the flame, the tube was caused to end in a cone.

15 It is recorded that a bell placed on an eminence in Heligoland failed, on account of its distance, to be heard in the town. A parabolic reflector placed behind the bell, so as to reflect the sound-waves in the direction of the long, sloping street, caused the strokes of the bell to be distinctly heard at all times. This observation needs verification.

16 “EncyclopÆdia Metropolitana,” art. “Sound.”

17 Placing himself close to the upper part of the wall of the London Colosseum, a circular building one hundred and thirty feet in diameter, Mr. Wheatstone found a word pronounced to be repeated a great many times. A single exclamation appeared like a peal of laughter, while the tearing of a piece of paper was like the patter of hail.

18 “Poggendorff’s Annalen,” vol. lxxxv., p. 378; “Philosophical Magazine,” vol. v., p. 73.

19 Thin India-rubber balloons also form excellent sound lenses.

20 For the sake of simplicity, the wave is shown broken at o' and its two halves straight. The surface of the wave, however, is really a curve, with its concavity turned in the direction of its propagation.

21 See “Heat as a Mode of Motion,” chap. iii.

22 In fact, the prompt abstraction of the motion of heat from the condensation, and its prompt communication to the rarefaction by the contiguous luminiferous ether, would prevent the former from ever rising so high, or the latter from ever falling so low, in temperature as it would do if the power of radiation was absent.

23 “Heat a Mode of Motion,” chap. x.

24 According to Burmeister, through the injection and ejection of air into and from the cavity of the chest.

25 On July 27, 1681, “Mr. Hooke showed an experiment of making musical and other sounds by the help of teeth of brass wheels; which teeth were made of equal bigness for musical sounds, but of unequal for vocal sounds.”—Birch’s “History of the Royal Society,” p. 96, published in 1757.

The following extract is taken from the “Life of Hooke,” which precedes his “Posthumous Works,” published in 1705, by Richard Waller, Secretary of the Royal Society: “In July the same year he (Dr. Hooke) showed a way of making musical and other sounds by the striking of the teeth of several brass wheels, proportionally cut as to their numbers, and turned very fast round, in which it was observable that the equal or proportional strokes of the teeth, that is, 2 to 1, 4 to 3, etc., made the musical notes, but the unequal strokes of the teeth more answered the sound of the voice in speaking.”

26 Galileo, finding the number of notches on his metal to be great when the pitch of the note was high, inferred that the pitch depended on the rapidity of the impulses.

27 When a rough tide rolls in upon a pebble beach, as at Blackgang Chine or Freshwater Gate in the Isle of Wight the rounded stones are carried up the slope by the impetus of the water and when the wave retreats the pebbles are dragged down. Innumerable collisions thus ensue of irregular intensity and recurrence. The union of these shocks impresses us as a kind of scream. Hence the line in Tennyson’s “Maud”

The height of the note depends in some measure upon the size of the pebble, varying from a kind of roar—heard when the stones are large—to a scream; from a scream to a noise resembling that of frying bacon; and from this, when the pebbles are so small as to approach the state of gravel, to a mere hiss. The roar of the breaking wave itself is mainly due to the explosion of bladders of air.

28 The error of Savart consists, according to Helmholtz, in having adopted an arrangement in which overtones (described in Chapter III.) were mistaken for the fundamental one.

29 “The deepest tone of orchestra instruments is the E of the double-bass, with 41-1/4 vibrations. The new pianos and organs go generally as far as C¹, with 33 vibrations; new grand pianos may reach A¹¹, with 27-1/2 vibrations. In large organs a lower octave is introduced, reaching to C¹¹, with 16-1/2 vibrations. But the musical character of all these tones under E is imperfect, because they are near the limit where the power of the ear to unite the vibrations to a tone ceases. In height the pianoforte reaches to a^iv, with 3,520 vibrations, or sometimes to c^v, with 4,224 vibrations. The highest note of the orchestra is probably the d^v of the piccolo flute, with 4,752 vibrations.”—Helmholtz, “Tonempfindungen,” p. 30. In this notation we start from C, with 66 vibrations, calling the first lower octave C¹, and the second C¹¹; and calling the first highest octave c, the second c¹, the third c¹¹, the fourth c¹², etc. In England the deepest tone, Mr. Macfarren informs me, is not E, but A, a fourth above it.

30 It is hardly necessary to remark that the quickest vibrations and shortest waves correspond to the extreme violet, while the slowest vibrations and longest waves correspond to the extreme red, of the spectrum.

31 Experiments on this subject were first made by M. Buys Ballot on the Dutch railway, and subsequently by Mr. Scott Russell in this country. Doppler’s idea is now applied to determine, from changes of wave-length, motions in the sun and fixed stars.

32 An ordinary musical box may be substituted for the piano in this experiment.

33 To show the influence of a large vibrating surface in communicating sonorous motion to the air, Mr. Kilburn incloses a musical box within cases of thick felt. Through the cases a wooden rod, which rests upon the box, issues. When the box plays a tune, it is unheard as long as the rod only emerges; but when a thin disk of wood is fixed on the rod, the music becomes immediately audible.

34 Chladni remarks (“Akustik,” p. 55) that it is usual to ascribe to Sauveur the discovery, in 1701, of the nodes of vibration corresponding to the higher tones of strings; but that Noble and Pigott had made the discovery in Oxford in 1676, and that Sauveur declined the honor of the discovery when he found that others had made the observation before him.

35 The first experiment really made in the lecture was with a bar of steel 62 inches long, 1-1/2 inch wide, and 1/2 an inch thick, bent into the shape of a tuning-fork, with its prongs 2 inches apart, and supported on a heavy stand. The cord attached to it was 9 feet long and a quarter of an inch thick. The prongs were thrown into vibration by striking them briskly with two pieces of lead covered with pads and held one in each hand. The prongs vibrated transversely to the cord. The vibrations produced by a single stroke were sufficient to carry the cord through several of its subdivisions and back to a single ventral segment. That is to say, by striking the prongs and causing the cord to vibrate as a whole, it could, by relaxing the tension, be caused to divide into two, three, or four vibrating segments; and then, by increasing the tension, to pass back through four, three, and two divisions, to one, without renewing the agitation of the prongs. The cord was of such a character that, instead of oscillating to and fro in the same plane, each of its points described a circle. The ventral segments, therefore, instead of being flat surfaces were surfaces of revolution, and were equally well seen from all parts of the room. The tuning-forks employed in the subsequent illustrations were prepared for me by that excellent acoustic mechanician, KÖnig, of Paris, being such as are usually employed in the projection of Lissajou’s experiments.

36 A string steeped in a solution of the sulphate of quinine, and illuminated by the violet rays of the electric lamp, exhibits brilliant fluorescence. When the fork to which it is attached vibrates, the string divides itself into a series of spindles, and separated from each other by more intensely luminous nodes, emitting a light of the most delicate greenish-blue.

37 The subject of musical intervals will be treated in a subsequent lecture.

38 “This quality of sound, sometimes called its register, color, or timbre.”—Thomas Young, “Essay on Music.”

39 “Lehre von den Tonempfindungen,” p. 135.

40 The action of such a string is substantially the same as that of the siren. The string renders intermittent the current of air. Its action also resembles that of a reed. See Lecture V.

41 Chladni also observed this compounding of vibrations, and executed a series of experiments, which, in their developed form, are those of the kaleidophone. The composition of vibrations will be studied at some length in a subsequent lecture.

42 I copy this figure from Sir C. Wheatstone’s memoir; the nodes, however, ought to be nearer the ends, and the free terminal portions of the dotted lines ought not to be bent upward or downward. The nodal lines in the next two figures are also drawn too far from the edge of the plates.

43 Under the shoulder of the Wetterhorn I found in 1867 a pool of clear water into which a driblet fell from a brow of overhanging limestone rock. The rebounding water-drops, when they fell back, rolled in myriads over the surface. Almost any fountain, the spray of which falls into a basin, will exhibit the same effect.

44 This experiment succeeds almost equally well with a glass tube.

45 This experiment is more easily executed with hydrogen than with coal-gas.

46 Only an extremely small fraction of the fork’s motion is, however, converted into sound. The remainder is expended in overcoming the internal friction of its own particles. In other words, nearly the whole of the motion is converted into heat.

47 The clear illustrations of organ-pipes and reeds introduced here, and at page 226, have been substantially copied from the excellent work of Helmholtz. Pipes opening with hinges, so as to show their inner parts, were shown in the lecture.

48 I owe it to this eminent artist to direct attention to his experiments communicated to the Royal Society in May, 1855, and recorded in the “Philosophical Magazine” for 1855, vol. x., page 218.

49 The velocity in glass varies with the quality; the result of each experiment has therefore reference only to the particular kind of glass employed in the experiment.

50 This experiment was first made with a hydrogen-flame by Sir C. Wheatstone.

51 A gas-jet, for example, can be ignited five inches above the tip of a visible gas-flame, where platinum-leaf shows no redness.

52 “Philosophical Magazine,” March, 1858, p. 235. In the Appendix Prof. Le Conte’s interesting paper is given in extenso. Some years subsequently Mr. (now Professor) Barrett, while preparing some experiments for my lectures, observed the action of a musical sound upon a flame, and by the selection of suitable burners he afterward succeeded in rendering the flame extremely sensitive. Le Conte, of whose discovery I informed Mr. Barrett, was my own starting-point.

53 A gas-bag properly weighted also answers for these experiments.

54 In the actions described in the case of the blow-pipe and candle-flames, it was the jet of air issuing from the blow-pipe, and not the flame itself, that was directly acted on by the external vibrations.

55 Numerous modifications of these experiments are possible. Other inflammable gases than coal-gas may be employed. Mixtures of gases have also been found to yield beautiful and striking results. An infinitesimal amount of mechanical impurity has been found to exert a powerful influence.

56 Referring to these effects, Helmholtz says: “Die erstaunliche Empfindlichkeit eines mit Rauch imprÄgnirten cylindrischen Luftstrahls gegen Schall ist von Herrn Tyndall beschrieben worden; ich habe dieselbe bestÄtigt gefunden. Es ist dies offenbar eine Eigenschaft der TrennungsflÄchen die fÜr das Anblasen der Pfeifen von grÖsster Wichtigkeit ist.”—“Discontinuirliche Luftbewegung,” Monatsbericht, April, 1868.

57 When these two tuning-forks were placed in contact with a vessel from which a liquid vein issued, the visible action on the vein continued long after the forks had ceased to be heard.

58 The experiments on sounding flames have been recently considerably extended by my assistant, Mr. Cottrell. By causing flame to rub against flame, various musical sounds can be obtained—some resembling those of a trumpet, others those of a lark. By the friction of unignited gas-jets, similar though less intense effects are produced. When the two flames of a fish-tail burner are permitted to impinge upon a plate of platinum, as in Scholl’s “perfectors,” the sounds are trumpet-like, and very loud. Two ignited gas-jets may be caused to flatten out like Savart’s water-jets. Or they may be caused to roll themselves into two hollow horns, forming a most instructive example of the WirbelflÄchen of Helmholtz. The carbon-particles liberated in the flame rise through the horns in continuous red-hot or white-hot spirals, which are extinguished at a height of some inches from their place of generation.

59 “Essay on Sound,” par. 21.

60 “Report of the British Association for 1863,” page 105.

61 A very sagacious remark, as observation proves.

62 Powerful electric lights have since been established and found ineffectual.

63 This is also Sir John Herschel’s way of regarding the subject. “Essay on Sound,” par. 38.

64 In all cases nautical miles are meant.

65 Sir John Herschel gives the following account of Arago’s observation: “The rolling of thunder has been attributed to echoes among the clouds; and, if it is considered that a cloud is a collection of particles of water, however minute, in a liquid state, and therefore each individually capable of reflecting sound, there is no reason why very large sounds should not be reverberated confusedly (like bright lights) from a cloud. And that such is the case has been ascertained by direct observation on the sound of cannon. Messrs. Arago, Matthieu, and Prony, in their experiments on the velocity of sound, observed that under a perfectly clear sky the explosions of their guns were always single and sharp; whereas, when the sky was overcast, and even when a cloud came in sight over any considerable part of the horizon, they were frequently accompanied by a long-continued roll like thunder.”—“Essay on Sound,” par. 38. The distant clouds would imply a long interval between sound and echo, but nothing of the kind is reported.

66 A friend informs me that he has followed a pack of hounds on a clear calm day without hearing a single yelp from the dogs; while on calm foggy days from the same distance the musical uproar of the pack was loudly audible.

67 The horn here was temporarily suspended, but doubtless would have been well heard.

68 Experiments so important as those of De la Roche ought not to be left without verification. I have made arrangements with a view to this object.

69 The Elder Brethren have already had plans of a new signal-gun laid before them by the constructors of the War Department.

70 Described in Chapter V., p. 229.

71 The figure is but a meagre representation of the fact. The band of light was two inches wide, the depth of the sinuosities varying from three feet to zero.

72 In his admirable experiments on tuning, Scheibler found in the beats a test of differences of temperature of exceeding delicacy.

73 Sir John Herschel and Sir C. Wheatstone, I believe, made this experiment independently.

74 A subject to be dealt with in Chapter IX.

75 Nor indeed any of those tones whose rates of vibration are even multiples of the rate of the fundamental.

76 According to Kolliker, this is the number of fibres in Corti’s organ.

77 The comparison employed by Mr. Sedley Taylor appeals with graphic truth to a mountaineer. Considering, the above curve to represent a mountain-chain, he calls the discords peaks, and the concords passes.

78 This supposition is of course made for the sake of simplicity, the real period of oscillation of a pendulum 28 feet long being between two and three seconds.