within the range of experiment, and have now to submit the following
solution of the enigma: The first step was to ascertain whether the
sensitive flame, referred to in my recent paper in the “Philosophical
Transactions,” could be safely employed in experiments on the mutual
reversibility of a source of sound and an object on which the sound
impinges. Now, the sensitive flame usually employed by me measures from
eighteen to twenty-four inches in height, while the reed employed as a
source of sound is less than a square quarter of an inch in area. If,
therefore, the whole flame, or the pipe which fed it, were sensitive to
sonorous vibrations, strict experiments on reversibility with the reed
and flame might be difficult, if not impossible. Hence my desire to
learn whether the seat of sensitiveness was so localized in the flame
as to render the contemplated interchange of flame and reed permissible.
The flame being placed behind a cardboard screen, the shank of a funnel
passed through a hole in the cardboard was directed upon the middle
of the flame. The sound-waves issuing from the vibrating reed, placed
within the funnel, produced no sensible effect upon the flame. Shifting
the funnel so as to direct its shank upon the root of the flame, the
action was violent.
To augment the precision of the experiment, the funnel was connected
with a glass tube three feet long and half an inch in diameter, the
object being to weaken, by distance, the effect of the waves diffracted
round the edge of the funnel, and to permit those only which passed
through the glass tube to act upon the flame.
Presenting the end of the tube to the orifice of the burner (_b_, Fig.
1), or the orifice to the end of the tube, the flame was violently
agitated by the sounding-reed, R. On shifting the tube, or the burner,
so as to concentrate the sound on a portion of the flame about half an
inch above the orifice, the action was _nil_. Concentrating the sound
upon the burner itself, about half an inch below its orifice, there was
no action.
[Illustration: FIG. 1.]
These experiments demonstrate the localization of “the seat of
sensitiveness,” and they prove the flame to be an appropriate
instrument for the contemplated experiments on reversibility.
The experiments then proceeded thus: The sensitive flame being placed
close behind a screen of cardboard 18 inches high by 12 inches wide, a
vibrating reed, standing at the same height as the root of the flame,
was placed at a distance of 6 feet on the other side of the screen. The
sound of the reed, in this position, produced a strong agitation of the
flame.
The whole upper half of the flame was here visible from the reed; hence
the necessity of the foregoing experiments to prove the action of the
sound on the upper portion of the flame to be _nil_, and that the
waves had really to bend round the edge of the screen, so as to reach
the seat of sensitiveness in the neighborhood of the burner.
The positions of the flame and reed were reversed, the latter being now
close behind the screen, and the former at a distance of 6 feet from
it. The sonorous vibrations were without sensible action upon the flame.
The experiment was repeated and varied in many ways. Screens of various
sizes were employed; and, instead of reversing the positions of the
flame and reed, the screen itself was moved, so as to bring in some
experiments the flame, and in other experiments the reed, close behind
it. Care was also taken that no reflected sound from the walls or
ceiling of the laboratory, or from the body of the experimenter, should
have anything to do with the effect. In all cases it was shown that the
sound was effective when the reed was at a distance from the screen,
and the flame close behind it; while the action was insensible when
these positions were reversed.
[Illustration: FIG. 2.]
Thus, let _s e_, Fig. 2, be a vertical section of the screen. When the
reed was at A and the flame at B there was no action; when the reed was
at B and the flame at A the action was decided. It may be added that
the vibrations communicated to the screen itself, and from it to the
air beyond it, were without effect; for when the reed, which at B was
effectual, was shifted to C, where its action on the screen was greatly
augmented, it ceased to have any action on the flame at A.
We are now, I think, prepared to consider the failure of reversibility
in the larger experiments of 1822. Happily an incidental observation
of great significance comes here to our aid. It was observed and
recorded at the time that, while the reports of the guns at Villejuif
were without echoes, a roll of echoes lasting from 20 to 25 seconds
accompanied every shot at Montlhéry, being heard by the observers
there. Arago, the writer of the report, referred these echoes to
reflection from the clouds, an explanation which I think we are now
entitled to regard as problematical. The report says that “tous
les coups tirés à Montlhéry y étaient _accompagnés_ d’un roulement
semblable à celui du tonnerre.” I have italicized a very significant
word—a word which fairly applies to our experiments on gun-sounds
at the South Foreland, where there was no sensible interval between
explosion and echo, but which could hardly apply to echoes coming
from the clouds. For supposing the clouds to be only a mile distant,
the sound and its echo would have been separated by an interval of
nearly ten seconds. But there is no mention of any interval; and, had
such existed, surely the word “followed,” instead of “accompanied,”
would have been the one employed. The echoes, moreover, appear to
have been _continuous_, while the clouds observed seem to have been
_separate_. “Ces phénomènes,” says Arago, “n’ont jamais eu lieu qu’au
moment de l’apparition de quelques nuages.” But from separate clouds a
continuous roll of echoes could hardly come. When to this is added the
experimental fact that clouds far denser than any ever formed in the
atmosphere are demonstrably incapable of sensibly reflecting sound,
while cloudless air, which Arago pronounced echoless, has been proved
capable of powerfully reflecting it, I think we have strong reason to
question the hypothesis of the illustrious French philosopher.[90]
And, considering the hundreds of shots fired at the South Foreland,
with the attention especially directed to the aërial echoes, when no
single case occurred in which echoes of measurable duration did not
accompany the report of the gun, I think Arago’s statement, that at
Villejuif no echoes were heard when the sky was clear, must simply
mean that they vanished with great rapidity. Unless the attention
was specially directed to the point, a slight prolongation of the
cannon-sound might well escape observation; and it would be all the
more likely to do so if the echoes were so loud and prompt as to form
apparently part and parcel of the direct sound.
I should be very loth to transgress here the limits of fair criticism,
or to throw doubt, without good reason, on the recorded observations
of illustrious men. Still, taking into account what has been just
stated, and remembering that the minds of Arago and his colleagues
were occupied by a totally different problem (that the echoes were an
incident rather than an object of observation), I think we may justly
consider the sound which he called “instantaneous” as one whose aërial
echoes did not differentiate themselves from the direct sound by any
noticeable fall of intensity, and which rapidly died into silence.
Turning now to the observations at Montlhéry, we are struck by the
extraordinary duration of the echoes heard at that station. At the
South Foreland the charge habitually fired was equal to the largest of
those employed by the French philosophers; but on no occasion did the
gun-sounds produce echoes approaching to 20 or 25 seconds’ duration.
The time rarely reached half this amount. Even the siren-echoes,
which were more remarkable and more long-continued than those of the
gun, never reached the duration of the Montlhéry echoes. The nearest
approach to it was on October 17, 1873, when the siren-echoes required
15 seconds to subside into silence.
On this same day, moreover (and this is a point of marked
significance), the transmitted sound reached its maximum range, the
gun-sounds being heard at the Quenocs buoy, 16-1/2 nautical miles from
the South Foreland. I have stated in another place that the duration
of the air-echoes indicates “the atmospheric depths” from which they
came. An optical analogy may help us here. Let light fall upon chalk,
the light is wholly scattered by the superficial particles; let the
chalk be powdered and mixed with water, light reaches the observer from
a far greater depth of the turbid liquid. The solid chalk typifies the
action of exceedingly dense acoustic clouds; the chalk and water that
of clouds of more moderate density. In the one case we have echoes of
short, in the other echoes of long, duration. These considerations
prepare us for the inference that Montlhéry, on the occasion referred
to, must have been surrounded by a highly-diacoustic atmosphere; while
the shortness of the echoes at Villejuif shows that the atmosphere
surrounding that station must have been, in a high degree, acoustically
opaque.
Have we any clew to the cause of the opacity? I think we have.
Villejuif is close to Paris, and over it, with the observed light
wind, was slowly wafted the air from the city. Thousands of chimneys
to windward of Villejuif were discharging their heated currents; so
that an exceeding non-homogeneous atmosphere must have surrounded that
station.[91] At no great height in the atmosphere the equilibrium of
temperature would be established. This non-homogeneous air surrounding
Villejuif is experimentally typified by our screen, with the source
of sound close behind it, the upper edge of the screen representing
the place where equilibrium of temperature was established in the
atmosphere above the station. In virtue of its proximity to the screen,
the echoes from our sounding-reed would, in the case here supposed,
so blend with the direct sound as to be practically indistinguishable
from it, as the echoes at Villejuif followed the direct sound so hotly,
and vanished so rapidly, that they escaped observation. And as our
sensitive flame, at a distance, failed to be affected by the sounding
body placed close behind the cardboard screen, so, I take it, did the
observers at Montlhéry fail to hear the sounds of the Villejuif gun.
Something further may be done toward the experimental elucidation of
this subject. The facility with which sounds pass through textile
fabrics has been already illustrated,[92] a layer of cambric or calico,
or even of thick flannel or baize, being found competent to intercept
but a small fraction of the sound from a vibrating reed. Such a layer
of calico may be taken to represent a layer of air, differentiated
from its neighbors by temperature or moisture; while a succession of
such sheets of calico may be taken to represent successive layers of
non-homogeneous air.
[Illustration: FIG. 3.]
Two tin tubes (M N and O P, Fig. 3) with open ends were placed so
as to form an acute angle with each other. At the end of one was
the vibrating reed _r_; opposite the end of the other, and in the
prolongation of P O, the sensitive flame _f_, a second sensitive flame
(_f′_) being placed in the continuation of the axis of M N. On sounding
the reed, the direct sound through M N agitated the flame _f′_.
Introducing the square of calico _a b_ at the proper angle, a slight
decrease of the action on _f′_ was noticed, and the feeble echo from
_a b_ produced a barely perceptible agitation of the flame f. Adding
another square, _c d_, the sound transmitted by _a b_ impinged on _c
d_; it was partially echoed, returned through _a b_, passed along P O,
and still further agitated the flame _f_. Adding a third square, _e
f_, the reflected sound was still further augmented, every accession
to the echo being accompanied by a corresponding withdrawal of the
vibrations from _f′_, and a consequent stilling of that flame.
With thinner calico or cambric it would require a greater number of
layers to intercept the entire sound; hence with such cambric we
should have echoes returned from a greater distance, and therefore
of greater duration. Eight layers of the calico employed in these
experiments, stretched on a wire frame and placed close together as a
kind of pad, may be taken to represent a dense acoustic cloud. Such a
pad, placed at the proper angle beyond N, cuts off the sound, which
in its absence reaches _f′_, to such an extent that the flame _f′_,
when not too sensitive, is thereby stilled, while _f_ is far more
powerfully agitated than by the reflection from a single layer. With
the source of sound close at hand, the echoes from such a pad would be
of insensible duration. Thus close at hand do I suppose the acoustic
clouds surrounding Villejuif to have been, a similar shortness of echo
being the consequence.
A further step is here taken in the illustration of the analogy between
light and sound. Our pad acts chiefly by internal reflection. The sound
from the reed is a composite one, made up of partial sounds differing
in pitch. If these sounds be ejected from the pad in their pristine
proportions, the pad is acoustically _white_; if they return with their
proportions altered, the pad is acoustically _colored_.
[Illustration: FIG. 4.]
In these experiments my assistant, Mr. Cottrell, has rendered me
material assistance.[93]
NOTE, _June 3d_.—I annex here a sketch of an apparatus[94] devised by
my assistant, Mr. Cottrell, and constructed by Tisley and Spiller, for
the demonstration of the law of reflection of sound. It consists of two
tubes (A F, B R) with a source of sound at the end R of one of them,
and a sensitive flame at the end F of the other. The axes of the tube
converge upon the mirror, M, and they are capable of being placed so as
to inclose any required angle. The angles of incidence and reflection
are read off on the graduated semicircle. The mirror M is also movable
round a vertical axis.
FOOTNOTES:
[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”
“Now to the scream of a maddened beach dragged down by the wave.”
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 C^{1}, with 33 vibrations; new grand pianos may
reach A^{11}, with 27-1/2 vibrations. In large organs a lower octave is
introduced, reaching to C^{11}, 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 C^{1}, and the second C^{11}; and calling the first highest
octave c, the second c^{1}, the third c^{11}, the fourth c^{12}, 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.
[79] This figure corresponds to the interval 15:16. For it and some
other figures, I am indebted to that excellent mechanician, M. König,
of Paris.
[80] For some beautiful figures of this description I am indebted to
Prof. Lyman, of Yale College.
[81] Mr. Sang, of Edinburgh, was, I believe, the first to treat this
subject analytically.
[82] This able paper was the starting-point of the experiments on
sensitive flames, recorded in Chapters VI. and VII.; the researches of
Thomas Young and Savart being the starting-point of the experiments on
smoke-jets and water-jets.—J. T.
[83] “Philosophical Magazine,” section 4, vol. xiii., p. 413, 1857.
[84] “Philosophical Magazine,” section 4, vol. xiv., p. 1, _et seq._,
July, 1857.
[85] “Comptes Rendus” for August, 1853. Also “Philosophical Magazine,”
section 4, vol. vii., p. 186, 1854.
[86] “Philosophical Magazine,” section 4, vol. viii., p. 74, 1854.
[87] “Proceedings of the Royal Institution,” January 15, 1875.
[88] “Researches in Chemistry and Physics,” p. 484.
[89] “Connaissance des Temps,” 1825, p. 370.
[90] See Chapter VII., Part II.
[91] The effect of the air of London is sometimes strikingly evident.
[92] “Philosophical Transactions,” 1874, Part I., p. 208, and Chapter
VII. of this volume.
[93] 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.
[94] The cut reached me too late for introduction at the proper place.
INDEX
A
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
B
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
C
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
D
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
E
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
F
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
G
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
H
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
I
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
J
Joule’s equivalent, 67
Jungfrau, echoes of the, 49
K
Kaleidophone, Wheatstone’s, formation of, 170, 196
Kundt, M., his experiments, 344
L
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
M
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
N
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
O
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
P
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
R
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
S
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
T
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
V
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
W
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
Y
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