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J. T.



The Nerves and Sensation—Production and Propagation of
Sonorous Motion—Experiments on Sounding Bodies placed
in Vacuo—Deadening of Sound by Hydrogen—Action of
Hydrogen on the Voice—Propagation of Sound through Air
of Varying Density—Reflection of Sound—Echoes—Refraction
of Sound—Diffraction of Sound; Case of Erith Village and
Church—Influence of Temperature on Velocity—Influence
of Density on Elasticity—Newton’s Calculation of
Velocity—Thermal Changes Produced by the Sonorous
Wave—Laplace’s Correction of Newton’s Formula—Ratio of
Specific Heats at Constant Pressure and at Constant
Volume deduced from Velocities of Sound—Mechanical
Equivalent of Heat deduced from this Ratio—Inference that
Atmospheric Air Possesses no Sensible Power to Radiate
Heat—Velocity of Sound in Different Gases—Velocity in
Liquids and Solids—Influence of Molecular Structure on
the Velocity of Sound. 31



Physical Distinction between Noise and Music—A
Musical Tone Produced by Periodic, Noise Produced
by Unperiodic, Impulses—Production of Musical
Sounds by Taps—Production of Musical Sounds by
Puffs—Definition of Pitch in Music—Vibrations of a
Tuning-Fork; their Graphic Representation on Smoked
Glass—Optical Expression of the Vibrations of a
Tuning-Fork—Description of the Siren—Limits of the
Ear; Highest and Deepest Tones—Rapidity of Vibration
Determined by the Siren—Determination of the Lengths
of Sonorous Waves—Wave-Lengths of the Voice in Man and
Woman—Transmission of Musical Sounds through Liquids and
Solids. 82



Vibration of Strings—How employed in Music—Influence of
Sound-Boards—Laws of Vibrating String—Combination of
Direct and Reflected Pulses—Stationary and Progressive
Waves—Nodes and Ventral Segments—Application of Results
to the Vibrations of Musical Strings—Experiments of
Melde—Springs set in Vibration by Tuning-Forks—Laws
of Vibration thus demonstrated—Harmonic Tones of
Strings—Definitions of Timbre or Quality, or Overtones
and Clang—Abolition of Special Harmonies—Conditions
which affect the Intensity of the Harmonic Tones—Optical
Examination of the Vibrations of a Piano-Wire 120



Vibrations of a Rod fixed at Both Ends: its Subdivisions
and Corresponding Overtones—Vibrations of a Rod fixed
at One End—The Kaleidophone—The Iron Fiddle and Musical
Box—Vibrations of a Rod free at Both Ends—The Claque-bois
and Glass Harmonica—Vibrations of a Tuning-Fork:
its Subdivisions and Overtones—Vibrations of Square
Plates—Chladni’s Discoveries—Wheatstone’s Analysis of
the Vibrations of Plates—Chladni’s Figures—Vibrations of
Disks and Bells—Experiments of Faraday and Strehlke. 165



Longitudinal Vibrations of a Wire—Relative Velocities of
Sound in Brass and Iron—Longitudinal Vibrations of Rods
fixed at One End—Of Rods free at Both Ends—Divisions and
Overtones of Rods vibrating longitudinally—Examination
of Vibrating Bars by Polarized Light—Determination of
Velocity of Sound in Solids—Resonance—Vibrations of
Stopped Pipes: their Divisions and Overtones—Relation
of the Tones of Stopped Pipes to those of Open
Pipes—Condition of Column of Air within a Sounding
Organ-Pipe—Reeds and Reed-Pipes—The Voice—Overtones of
the Vocal Chords—The Vowel Sounds—Kundt’s Experiments—New
Methods of determining the Velocity of Sound. 200



Singing Flames—Influence of the Tube surrounding
the Flame—Influence of Size of Flame—Harmonic Notes
of Flames—Effect of Unisonant Notes on Singing
Flames—Action of Sound on Naked Flames—Experiments with
Fish-Tail and Bat’s-Wing Burners—Experiments on Tall
Flames—Extraordinary Delicacy of Flames as Acoustic
Reagents—The Vowel-Flame—Action of Conversational
Tones upon Flames—Action of Musical Sounds on
Smoke-Jets—Constitution of Water-Jets—Plateau’s Theory
of the Resolution of a Liquid Vein into Drops—Action of
Musical Sounds on Water-Jets—A Liquid Vein may compete in
Point of Delicacy with the Ear 260





Introduction—Instruments and Observations—Contradictory
Results from the 19th of May to the 1st of July
inclusive—Solution of Contradictions—Aërial Reflection
and its Causes—Aërial Echoes—Acoustic Clouds—Experimental
Demonstration of Stoppage of Sound by Aërial Reflection



Action of Hail and Rain—Action of Snow—Action of Fog;
Observations in London—Experiments on Artificial
Fogs—Observations on Fogs at the South Foreland—Action of
Wind—Atmospheric Selection—Influence of Sound-Shadow 341



Law of Vibratory Motions in Water and
Air—Superposition of Vibrations—Interference of
Sonorous Waves—Destruction of Sound by Sound—Combined
Action of Two Sounds nearly in Unison with each
other—Theory of Beats—Optical Illustration of the
Principle of Interference—Augmentation of Intensity
by Partial Extinction of Vibrations—Resultant
Tones—Conditions of their Production—Experimental
Illustrations—Difference-Tones and
Summation-Tones—Theories of Young and Helmholtz 377



Combination of Musical Sounds—The smaller the Two
Numbers which express the Ratio of their Rates of
Vibration, the more perfect is the Harmony of Two
Sounds—Notions of the Pythagoreans regarding Musical
Consonance—Euler’s Theory of Consonance—Theory of
Helmholtz—Dissonance due to Beats—Interference of Primary
Tones and of Overtones—Mechanism of Hearing—Schultze’s
Bristles—The Otoliths—Corti’s Fibres—Graphic
Representation of Consonance and Dissonance—Musical
Chords—The Diatonic Scale—Optical Illustration of
Musical Intervals—Lissajous’s Figures—Sympathetic
Vibrations—Various Modes of illustrating the Composition
of Vibrations 410

Summary of Chapter IX 450







[Illustration: FOG-SIREN]


In preparing this new edition of “Sound,” I have carefully gone over
the last one; amended, as far as possible, its defects of style
and matter, and paid at the same time respectful attention to the
criticisms and suggestions which the former editions called forth.

The cases are few in which I have been content to reproduce what I
have _read_ of the works of acousticians. I have sought to make myself
experimentally familiar with the ground occupied; trying, in all cases,
to present the illustrations in the form and connection most suitable
for educational purposes.

Though bearing, it may be, an undue share of the imperfection which
cleaves to all human effort, the work has already found its way into
the literature of various nations of diverse intellectual standing.
Last year, for example, a new German edition was published “under the
special supervision” of Helmholtz and Wiedemann. That men so eminent,
and so overladen with official duties, should add to these the labor of
examining and correcting every proof-sheet of a work like this, shows
that they consider it to be what it was meant to be—a serious attempt
to improve the public knowledge of science. It is especially gratifying
to me to be thus assured that not in England alone has the book met a
public want, but also in that learned land to which I owe my scientific

Before me, on the other hand, lie two volumes of foolscap size,
curiously stitched, and printed in characters the meaning of which I
am incompetent to penetrate. Here and there, however, I notice the
familiar figures of the former editions of “Sound.” For these volumes
I am indebted to Mr. John Fryer, of Shanghai, who, along with them,
favored me, a few weeks ago, with a letter from which the following is
an extract: “One day,” writes Mr. Fryer, “soon after the first copy
of your work on Sound reached Shanghai, I was reading it in my study,
when an intelligent official, named Hsii-chung-hu, noticed some of the
engravings and asked me to explain them to him. He became so deeply
interested in the subject of Acoustics that nothing would satisfy him
but to make a translation. Since, however, engineering and other works
were then considered to be of more practical importance by the higher
authorities, we agreed to translate your work during our leisure time
every evening, and publish it separately ourselves. Our translation,
however, when completed, and shown to the higher officials, so much
interested them, and pleased them, that they at once ordered it to be
published at the expense of the Government, and sold at cost price. The
price is four hundred and eighty copper cash per copy, or about one
shilling and eightpence. This will give you an idea of the cheapness of
native printing.”

Mr. Fryer adds that his Chinese friend had no difficulty in grasping
every idea in the book.

The new matter of greatest importance which has been introduced into
this edition is an account of an investigation which, during the past
two years, I have had the honor of conducting in connection with the
Elder Brethren of the Trinity House. Under the title “Researches on the
Acoustic Transparency of the Atmosphere, in Relation to the Question of
Fog-signalling,” the subject is treated in Chapter VII. of this volume.
It was only by Governmental appliances that such an investigation
could have been made; and it gives me pleasure to believe that not
only have the practical objects of the inquiry been secured, but that
a crowd of scientific errors, which for more than a century and a half
have surrounded this subject, have been removed, their place being
now taken by the sure and certain truth of Nature. In drawing up the
account of this laborious inquiry, I aimed at linking the observations
so together that they alone should offer a substantial demonstration of
the principles involved. Further labors enabled me to bring the whole
inquiry within the firm grasp of _experiment_; and thus to give it a
certainty which, without this final guarantee, it could scarcely have

Immediately after the publication of the first brief abstract of the
investigation, it was subjected to criticism. To this I did not deem it
necessary to reply, believing that the grounds of it would disappear
in presence of the full account. The only opinion to which I thought
it right to defer was to some extent a private one, communicated to
me by Prof. Stokes. He considered that I had, in some cases, ascribed
too exclusive an influence to the mixed currents of aqueous vapor and
air, to the neglect of differences of temperature. That differences
of temperature, when they come into play, are an efficient cause of
acoustic opacity, I never doubted. In fact, aërial reflection arising
from this cause is, in the present inquiry, for the first time made
the subject of experimental demonstration. What the relative potency
of differences of temperature and differences due to aqueous vapor, in
the cases under consideration, may be, I do not venture to state; but
as both are active, I have, in Chapter VII., referred to them jointly
as concerned in the production of those “acoustic clouds” to which the
stoppage of sound in the atmosphere is for the most part due.

Subsequently, however, to the publication of the full investigation
another criticism appeared, to which, in consideration of its source,
I would willingly pay all respect and attention. In this criticism,
which reached me first through the columns of an American newspaper,
differences in the amounts of aqueous vapor, and differences of
temperature, are alike denied efficiency as causes of acoustic
opacity. At a meeting of the Philosophical Society of Washington the
emphatic opinion had, it was stated, been expressed that I was wrong
in ascribing the opacity of the atmosphere to its flocculence, the
really efficient cause being _refraction_. This view appeared to me so
obviously mistaken that I assumed, for a time, the incorrectness of the
newspaper account.

Recently, however, I have been favored with the “Report of the United
States Lighthouse Board for 1874,” in which the account just referred
to is corroborated. A brief reference to the Report will here suffice.
Major Elliott, the accomplished officer and gentleman referred to at
page 261, had published a record of his visit of inspection to this
country, in which he spoke, with a perfectly enlightened appreciation
of the facts, of the differences between our system of lighthouse
illumination and that of the United States. He also embodied in his
Report some account of the investigation on fog-signals, the initiation
of which he had witnessed, and indeed aided, at the South Foreland.

On this able Report of their own officer the Lighthouse Board at
Washington make the following remark: “Although this account is
interesting in itself and to the public generally, yet, being addressed
to the Lighthouse Board of the United States, it would tend to convey
the idea that the facts which it states were new to the Board, and that
the latter had obtained no results of a similar kind; while a reference
to the appendix to this Report[1] will show that the researches of our
Lighthouse Board have been much more extensive on this subject than
those of the Trinity House, and that the latter has established no
facts of practical importance which had not been previously observed
and used by the former.”

The “appendix” here referred to is from the pen of the venerable Prof.
Joseph Henry, chairman of the Lighthouse Board at Washington. To his
credit be it recorded that at a very early period in the history of
fog-signalling Prof. Henry reported in favor of Daboll’s trumpet,
though he was opposed by one of his colleagues on the ground that
“fog-signals were of little importance, since the mariner should know
his place by the character of his soundings.” In the appendix, he
records the various efforts made in the United States with a view to
the establishment of fog-signals. He describes experiments on bells,
and on the employment of reflectors to reinforce their sound. These,
though effectual close at hand, were found to be of no use at a
distance. He corrects current errors regarding steam-whistles, which
by some inventors were thought to act like ringing bells. He cites the
opinion of the Rev. Peter Ferguson, that sound is better heard in fog
than in clear air. This opinion is founded on observations of the noise
of locomotives; in reference to which it may be said that others have
drawn from similar experiments diametrically opposite conclusions. On
the authority of Captain Keeney he cites an occurrence, “in the first
part of which the captain was led to suppose that fog had a marked
influence in deadening sound, though in a subsequent part he came to
an opposite conclusion.” Prof. Henry also describes an experiment made
during a fog at Washington, in which he employed “a small bell rung by
clockwork, the apparatus being the part of a moderator lamp, intended
to give warning to the keepers when the supply of oil ceased. The
result of the experiment was, he affirms, contrary to the supposition
of absorption of the sound by the fog.” This conclusion is not founded
on comparative experiments, but on observations made in the fog alone;
for, adds Prof. Henry, “the change in the condition of the atmosphere,
as to temperature and the motion of the air, before the experiment
could be repeated in clear weather, rendered the result not entirely

This, I may say, is the only experiment on fog which I have found
recorded in the appendix.

In 1867 the steam-siren was mounted at Sandy Hook, and examined by
Prof. Henry. He compared its action with that of a Daboll trumpet,
employing for this purpose a stretched membrane covered with sand, and
placed at the small end of a tapering tube which concentrated the
sonorous motion upon the membrane. The siren proved most powerful. “At
a distance of 50, the trumpet produced a decided motion of the sand,
while the siren gave a similar result at a distance of 58.” Prof. Henry
also varied the pitch of the siren, and found that in association with
its trumpet 400 impulses per second yielded the maximum sound; while
the best result with the unaided siren was obtained when the impulses
were 360 a second. Experiments were also made on the influence of
pressure; from which it appeared that when the pressure varied from
100 lbs. to 20 lbs., the distance reached by the sound (as determined
by the vibrating membrane) varied only in the ratio of 61 to 51. Prof.
Henry also showed the sound of the fog-trumpet to be independent of
the material employed in its construction; and he furthermore observed
the decay of the sound when the angular distance from the axis of the
instrument was increased. Further observations were made by Prof. Henry
and his colleagues in August, 1873, and in August, and September,
1874. In the brief but interesting account of these experiments a
hypothetical element appears, which is absent from the record of the
earlier observations.

It is quite evident from the foregoing that, in regard to the question
of fog-signalling, the Lighthouse Board of Washington have not been
idle. Add to this the fact that their eminent chairman gives his
services gratuitously, conducting without fee or reward experiments and
observations of the character here revealed, and I think it will be
conceded that he not only deserves well of his own country, but also
sets his younger scientific contemporaries, both in his country and
ours, an example of high-minded devotion.

I was quite aware, in a general way, that labors like those now for the
first time made public had been conducted in the United States, and
this knowledge was not without influence upon my conduct. The first
instruments mounted at the South Foreland were of English manufacture;
and I, on various accounts, entertained a strong sympathy for their
able constructor, Mr. Holmes. From the outset, however, I resolved to
suppress such feelings, as well as all other extraneous considerations,
individual or national; and to aim at obtaining the best instruments,
irrespective of the country which produced them. In reporting,
accordingly, on the observations of May 19 and 20, 1873 (our first two
days at the South Foreland), these were my words to the Elder Brethren
of the Trinity House:

“In view of the reported performance of horns and whistles in other
places, the question arises whether those mounted at the South
Foreland, and to which the foregoing remarks refer, are of the best
possible description.... I think our first duty is to make ourselves
acquainted with the best instruments hitherto made, no matter where
made; and then, if home genius can transcend them, to give it all
encouragement. Great and unnecessary expense may be incurred, through
our not availing ourselves of the results of existing experience.

“I have always sympathized, and I shall always sympathize, with the
desire of the Elder Brethren to encourage the inventor who first
made the magneto-electric light available for lighthouse purposes. I
regard his aid and counsel as, in many respects, invaluable to the
corporation. But, however original he may be, our duty is to demand
that his genius shall be expended in making advances on that which
has been already achieved elsewhere. If the whistles and horns that
we heard on the 19th and 20th be the very best hitherto constructed,
my views have been already complied with; but if they be not—and I
am strongly inclined to think that they are not—then I would submit
that it behooves us to have the best, and to aim at making the South
Foreland, both as regards light and sound, a station not excelled by
any other in the world.”

On this score it gives me pleasure to say that I never had a difficulty
with the Elder Brethren. They agreed with me; and two powerful
steam-whistles, the one from Canada, the other from the United States,
together with a steam-siren—also an American instrument—were in due
time mounted at the South Foreland. It will be seen in Chapter VII.
that my strongest recommendation applies to an instrument for which we
are indebted to the United States.

In presence of these facts, it will hardly be assumed that I wish
to withhold from the Lighthouse Board of Washington any credit that
they may fairly claim. My desire is to be strictly just; and this
desire compels me to express the opinion that their Report fails to
establish the inordinate claim made in its first paragraph. It contains
observations, but contradictory observations; while as regards the
establishment of any principle which should reconcile the conflicting
results, it leaves our condition unimproved.

But I willingly turn aside from the discussion of “claims” to the
discussion of science. Inserted, as a kind of intrusive element,
into the Report of Prof. Henry, is a second Report by General Duane,
founded on an extensive series of observations made by him in 1870 and
1871. After stating with distinctness the points requiring decision,
the General makes the following remarks:

“Before giving the results of these experiments, some facts will be
stated which will explain the difficulties of determining the power of
a fog-signal.

“There are six steam fog-whistles on the coast of Maine: these have
been frequently heard at a distance of twenty miles, and as frequently
cannot be heard at the distance of two miles, and this with no
perceptible difference in the state of the atmosphere.

“The signal is often heard at a great distance in one direction, while
in another it will be scarcely audible at the distance of a mile. This
is not the effect of wind, as the signal is frequently heard much
further against the wind than with it.[2] For example, the whistle on
Cape Elizabeth can always be distinctly heard in Portland, a distance
of nine miles, during a heavy northeast snowstorm, the wind blowing a
gale directly from Portland toward the whistle.[3]

“The most perplexing difficulties, however, arise from the fact that
the signal often appears to be surrounded by a belt, varying in radius
from one mile to one mile and a half, from which the sound appears to
be entirely absent. Thus, in moving directly from a station the sound

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