in the air; and, as the motions of one fluid may often be illustrated
by those of another, the invisible motions of the air have been
properly enough compared to the visible waves of water produced by
throwing a stone therein. These waves spread themselves in all
directions in concentric circles, whose common centre is the spot
where the stone fell, and when they strike against a bank or other
obstacle, they return in the contrary direction to the place from
whence they proceeded. Sound in like manner expands in every
direction, and the extent of its progress is in proportion to the
impulse on the vibrating chord or bell.
Such is the yielding nature of fluids, that when other waves are
generated near the first waves, and others again near these, they
will perform their vibrations among each other without interruption;
those that are coming back will pass by those that are going
forwards, or even through them, without interruption: for instance,
if we throw a stone into a pond, and immediately after that, another,
and then a third, we shall perceive that their respective circles
will proceed without interruption, and strike the banks in regular
succession.
The atmosphere in the same manner possesses the faculty of conveying
sounds in the most rapid succession or combination, as distinctly as
they were produced. It possesses the power not only of receiving and
propagating simple and compound vibrations in direct lines from the
voice, or an instrument, but of retaining and repeating sounds with
equal fidelity after repeated reflection and reverberation, as is
evident from the sound of a French horn among hills.
Newton was the first who attempted to demonstrate that the waves or
pulses of the air are propagated in all directions round a sounding
body, and that during their progress and regress they are twice
accelerated and twice retarded, according to the law of a pendulum
vibrating in a cycloid. These propositions are the foundation of
almost all our reasoning concerning sound. When sonorous bodies are
struck, they, by their vibration, excite waves in the air, similar to
those caused by a stone thrown into water; some parts of these waves
entering the ear, produce in us that sensation which we call sound.
How these pulsations act upon the auditory nerve, to produce sound,
we know not, as we see no necessary connexion between the pulses and
the sensation, nor the least resemblance between them; but we can
trace their progress to a certain extent, which I shall now endeavour
to do.
The external part of the ear is called the auricle, or outward ear,
which is a cartilaginous funnel, connected to the bones of the
temple, by means of cellular substance, and likewise by its own
proper ligaments and muscles. This cartilage is of a very compound
figure, being a kind of oval, marked with spirals standing up, and
hollows interposed, to which other hollows and ridges correspond on
the opposite side. The outer eminence is called helix. Within the
body of the cartilage arises a forked eminence called antihelix,
which terminates in a small and short tongue called antitragus. The
remaining part of the ear, called the concha or shell, is anteriorly
hollow, but posteriorly convex, growing gradually deeper; with a
crooked line or ridge running along its middle, which is immediately
joined to the meatus auditorius, or entrance into the ear; before
which stands a round moveable appendix, which serves as a defense,
called tragus.
Against this funnel of the ear the sonorous waves strike, and its
different parts are most admirably contrived to reflect them all into
the meatus auditorius: if it would not occupy too much time, it might
be shown, that all these curves and spirals are contrived in the best
manner possible, and with a most perfect knowledge of the geometry of
sounds, to reflect the sonorous pulses accurately, and in the
greatest possible quantity, into the ear.
This external part of the ear is differently formed in different
animals; and admirably suited to their various situations and habits.
In man it is close to the head, but so formed as to collect the
various pulses with great accuracy; in other animals it is more
simple, where less accuracy is required, but it is, in general, much
larger, having the appearance of an oblong funnel; and this gives
them a greater delicacy of hearing, which was necessary for them.
In animals which are defenceless and timid, and which are constantly
obliged to seek their safety in flight, the opening of this funnel is
placed behind, that they may better hear the noises behind them. This
is particularly instanced in the hare. Beasts of prey have this
opening before, that they may more easily discover their prey; as the
lion and tiger. Those that feed on birds have the opening directed
upwards, as the fox; and it is inclined downwards in animals, such as
the weasel, which seek their prey on the earth.
To this external part of the ear, which I have described, is
connected the meatus auditorius, or passage to the internal ear,
which is somewhat of a compressed cylindrical figure, lessening as it
bends inwards: a considerable part of it is bony, and it is bent
towards the middle. Across this passage, at its inner extremity, is
stretched a thin membrane, called membrana tympani. Upon the surface
of this membrane, the sonorous waves, which have been directed
inwards by the external ear, strike, and cause it to vibrate like the
membrane of a drum. This membrane is stretched over a cavity in the
bone, called the os petrosum, which cavity is called the tympanum, or
drum of the ear, which is of a rounded figure, divided in its middle
by a promontory, and continued backwards to the cells of the mastoid
bone. Besides this continuation of the tympanum into the mastoid
cells, it has a free communication with the mouth, by means of a tube
I shall soon describe.
Within this cavity of the tympanum are placed four small bones, which
facilitate the hearing: the first is the malleus or hammer, so called
from its shape: the upper part of its round head rests upon the
concavity of the tympanum, from whence the handle is extended down,
along the membrane of the tympanum; this bone has several muscles,
which move it in different directions, and cause it to stretch or
brace the membrana tympani, when we wish to hear with accuracy.
Connected with the malleus is another small bone, called the incus,
or anvil, which is connected with another, called the stapes, or
stirrup, from its shape. These two bones are connected by a small
oval shaped bone, called os orbiculare, placed between them: the
whole forming a little chain of bones.
The stapes, or stirrup, has its end of an oval shape, which fits a
small hole called fenestra ovalis, in that part of the ear called the
labyrinth, or innermost chamber of the ear.
The labyrinth consists of three parts; first, the vestibule, which is
a round cavity in a hard part of the os petrosum; secondly, the
semicircular canals, so called from their shape, which however is not
exactly semicircular; thirdly, the cochlea, which is a beautifully
convoluted canal, like the shell of a snail. This part has a round
cavity called fenestra rotunda, which is covered with a thin elastic
membrane, and looks into the tympanum.
The vestibule, semicircular canals, and cochlea, the whole of which
is called the labyrinth, form one cavity, which is filled with a very
limpid fluid resembling water, and the whole lined with a fine
delicate membrane, upon which the auditory nerve is expanded, like
the retina upon the vitreous humor of the eye. This beautiful
apparatus was only lately discovered by an Italian physician, Scarpa.
The auditory nerve is a portion of the seventh pair, which is called
the portio mollis or soft portion.
There is one part of the ear still to be described, namely, the
Eustachian tube, so called from Eustachius, the anatomist, who first
described it. This tube opens by a wide elliptical aperture into the
tympanum behind the membrane; the other end, which gradually grows
wider, opens into the cavity of the mouth. By this canal the inspired
air enters the tympanum to be changed and renewed, it likewise serves
some important purpose in hearing, with the nature of which we are
yet unacquainted. It is certain that we can hear through this
passage, for if a watch be put into the mouth, and the ears stopped,
its ticking may be distinctly heard; and in several instances of
deafness, this tube has been found completely blocked up.
The waves, which have been described as propagated in the air, in all
directions from the sounding body, enter the external cartilaginous
part of the ear, which, as has before been observed, is admirably
fitted for collecting and condensing them. As soon as these pulses
excite tremors in the membrane of the tympanum, its muscles stretch
and brace it, whence it becomes more powerfully affected by these
impulses. It is on this account that we hear sounds more distinctly
when we attend to them, the membrane being then stretched.
A tremulous motion, being excited in this membrane, is communicated
to the malleus annexed to it, which communicates it to the incus, by
which it is propagated through the os orbiculare to the stapes, which
imparts this tremulous motion through the foramen ovale to the fluid
contained in the labyrinth. This tremor is impressed by the waves
excited in this fluid, on every part of the auditory nerve in the
labyrinth. The use of the foramen rotundum, or round hole, before
described, is probably the same as that of the hole in the side of a
drum; it allows the fluid in the labyrinth to be compressed,
otherwise it could not vibrate.
If the organization is sound, and tremors are communicated to the
auditory nerve, they are in some way or other conveyed to the mind,
but in what manner we cannot tell. Nature has hid the machinery by
which she connects material and immaterial things entirely from our
view, and if we try to investigate them, we are soon bewildered in
the regions of hypothesis.
Tremors may however be communicated to the auditory nerve in a
different manner from what I have described. If a watch be put
between the teeth, and the ear stopped, tremors will be communicated
to the teeth, by them to the bones of the upper jaw, and by these to
the auditory nerve. In this way a person born deaf, and having no
power of hearing through the medium of the air, may become sensible
of the pleasures of music.
That sound may be propagated by vibrations, independent of pulses of
the air, is evident from the experiment with the string and poker.
There is, strictly speaking, no such thing existing as sound; it
being only a sensation of the mind, caused by tremors of the air, or
vibrations of the sounding body.
In order to understand more clearly how pulses, or waves are caused
by the vibration of bodies, and the manner in which vibrating bodies
are affected, I shall just enumerate some of the properties of
pendulums, which however I shall not stop to demonstrate here, as
that would consume much time.
When two pendulums vibrate which are exactly of the same length,
their vibrations are performed in equal times; if they set out
together to describe equal arcs, they will agree together in their
motions, and the vibrations will be performed in equal times.
But if one of these pendulums be four times as long as the other, the
vibrations of the longer will be twice as slow as those of the
shorter; the number of vibrations being as the square roots of their
lengths.
A pendulum is fixed to one point, but a musical string is extended
between two points, and in its vibrations may be compared to a double
pendulum vibrating in a very small arc, hence we see how strings of
different lengths may agree in their motions after the manner of
pendulums; but we must observe that it is not necessary to quadruple
the length of a musical string, in order to make the time of
vibration twice as long; it will be sufficient merely to double it.
We know that from whatever height a pendulum falls on one side, to
the same height will it rise on the other. In the same manner will an
elastic string continue to vibrate from one side to the other for
some time, till its motion be destroyed by the resistance of the air,
and friction about its fixed points, and each of its small
vibrations, like those of a pendulum, will, for the same reason, be
performed in times exactly equal to each other.
Thus we gain from the analogy between a pendulum and a musical
string, a more adequate conception of a subject which was never
understood till this analogy was discovered. It explains to us why
every musical string preserves the same pitch from the beginning to
the end of its vibration; or as long as it can be distinguished by
the ear; and why the pitch remains still unvaried whether the sound
is loud or soft, and all this because the vibrations of the same
pendulum whether they are longer or shorter, when compared among
themselves, are found to be all performed in equal times till the
pendulum be at rest, the difference of the space, which is moved
over, compensating for the slowness of the motion till its decay.
To illustrate this subject still further, suppose we have a piece of
catgut stretched between two pins; I lay hold of it in the middle and
pull it sideways; I let it go, and you will observe that it first
straightens itself or returns to its original position. This depends
on the elasticity of its particles, which tend to reunite when they
have been separated by an external force, just in the same way that
the particles of a piece of caoutchouc or Indian rubber attract each
other when pulled asunder; and this force not only enables the string
to restore itself to its former situation, but will carry it nearly
to an equal distance on the other side, just in the same manner as a
ball falling down an inclined plane will rise nearly to the same
height up another, or a pendulum will rise nearly to the height from
which it fell.
In this way will a string move backwards and forwards, till friction
and the resistance of the air have destroyed the velocity which it
acquired by the force of elasticity.
It is obvious that when a string is thus let fly from the finger,
whatever be its own motion, such will also be the motion of the
particles of the air which fly before it: the air will be driven
forwards, and by that means condensed. When this condensed air
expands itself, it will expand not only towards the string, but as
its elasticity acts in all directions, it will also expand itself
forwards and condense the air that is beyond it, this last condensed
air, by its expansion, will produce the same effect on the air that
lies still further forwards, and thus the motion produced in the air,
by the vibration of the elastic string, is constantly carried
forwards and conveyed to the ear.
It will be proper however to observe, that these pulses are sometimes
produced without any such vibration of the sounding body, as we find
it in musical strings and bells. In these cases we have to discover
by what cause these condensations or pulses may be produced without
any apparent vibrations in what is considered as the sounding body.
We have two or three instances of this kind; one in wind instruments,
such as the flute or organ pipe; another in the discharge of a gun.
In an organ, or flute, the air, which is driven through the pipe,
strikes against the edge of the lips of the instrument in its
passage, and by being accumulated there, is condensed, and this
condensation produces waves or pulses in the air.
When a gun is discharged, a great quantity of air is produced, by the
firing of the gunpowder, which being violently propelled from the
piece, condenses the air that encompasses the space where the
expansion happens; for whatever is driven out from the space where
the expansion is made will be forcibly driven into the space all
around it. This condensation forms the first pulse, and as this, by
its elasticity, expands again, pulses of the same sort will be
produced and propagated forwards.
There is likewise another curious instance of the production of
sound, when a tube is held over a stream of inflamed hydrogen gas
issuing out of a capillary tube in a bottle.
Sounding bodies propagate their motions on all sides, directly
forwards, by successive condensations and rarefactions, so that sound
is driven in all directions, backwards and forwards, upwards and
downwards, and on every side; the pulses go on succeeding each other
like circles in disturbed water.
Sounds differ from each other both with respect to their tone and
intensity: in respect to their tone, they are distinguished into
grave and acute: in respect to their intensity, they are
distinguished into loud and low, or strong and weak. The tone of a
sound depends on the velocity with which the vibrations are
performed, for the greater the number of vibrations in a given time,
the more acute will be the tone, and on the contrary, the smaller the
number, the more grave it will be. The tone of a sound is not altered
by the distance of the ear from the sounding body; but the intensity
or strength of any sound depends on the force with which the waves of
the air strike the ear; and this force is different at different
distances; so that a sound which is very loud when we are near the
body that produces it, will be weaker if we are further from it,
though its tone will suffer no alteration; and the distance may be so
great that we cannot hear it at all. It has been demonstrated, that
the intensity of sound at different distances from the sounding body
is inversely as the square of the distance.
Sound moves with the same velocity at all distances from the sounding
body, otherwise it would not produce the same tone at all distances.
Sounds of different tones likewise move with the same velocity. This
is evident from a peal of bells being heard in the same order in
which they are rung, whether we are near, or at a distance.
It is likewise found that sounds of the same tone but of different
intensities are propagated with the same velocity. A low sound cannot
indeed be heard so far as a loud one; but sounds, whether low or
loud, will be conveyed in an equal time to any equal distance at
which they can both be heard. The report of a cannon does not move
faster, or pass over a given space sooner, than the sound of a
musical string.
The principal cause of the decay of sound is the want of perfect
elasticity in the air: whence it happens that every subsequent
particle has not the entire motion of the preceding particle
communicated to it, as is the case with equal and perfectly elastic
bodies; consequently the further the motion is propagated, the more
will the velocity with which the particles move be diminished; the
condensation of the air will be diminished also, and consequently its
effect on the ear. That the want of perfect elasticity in the air is
the principal cause of the decay of sound, appears from this, that
sounds are perceived more distinctly when the north and easterly
winds prevail, at which time the air is dry and dense, as appears
from the hygrometer and barometer; and, of course, the air in this
state must be more elastic, for the vapours diffused through the
atmosphere, unless dilated by intense heat, diminish the spring of
the air.
That sound is not propagated to all distances instantaneously, but
requires a sensible time for its passage from one place to another,
is evident from the discharge of a gun at a distance; for the report
is not heard till some time after the flash is seen. Light moves much
more swiftly than sound; it comes from the sun in eight minutes,
which is at the rate of 74,420 leagues in a second; so that the
velocity of light may be considered as instantaneous, at any distance
on the earth; and, as sound takes up a considerable time in its
passage, the interval between the flash and the report of the gun
shows the space it passes over in a given time, which is found to be
1142 feet in a second; so that if three seconds elapse between the
time when we see the flash and hear the report of the gun, it must be
distant 1142 yards.
From experiments that have been made at different times, by various
philosophers, we may collect the following results. First, That the
mean velocity of sound is a mile in about 4 3/4 seconds, or 1142 feet
in a second of time. Secondly, That all sounds, whether they be weak
or strong, have the same velocity. Thirdly, That sound moves over
equal spaces in equal times, from the beginning to the end.
The tone of a musical string, or a bell, appears continuous. This
depends upon a law of sensation, formerly mentioned, namely, that
impressions made upon any of the organs of sense do not immediately
vanish, but remain some time; and we hear sound continuous from these
vibrations, for the same reason that we hear it continuous when we
draw a stick quickly along a rail, or a quill along the teeth of a
comb; the vibrations succeed each other so quickly that we hear the
succeeding before the effect of the preceding is worn off; though it
must be evident that the impression produced by each pulse or wave of
the air is perfectly distinct and insulated.
The act of combining sounds in such a manner as to be agreeable to
the ear, is called music. This art is usually divided into melody and
harmony. An agreeable succession of sounds is called melody; but when
two or more sounds are produced together, and afford an agreeable
sensation, the effect is called harmony. When two sounds are produced
together, and afford pleasure to the sense of hearing, the effect is
called a concord; but when the sensation produced is harsh or
disagreeable, it is called a discord. These different effects seem to
depend upon the coincidence of the vibrations of the two strings, and
consequently on the coincidence of the pulses which they excite in
the air. When the strings are equally stretched, and of the same
length and thickness, their vibrations will always coincide, and they
produce a sound so similar to each other, that it is called unison,
which is the most perfect concord. When one string is only half the
length of the other, the vibrations coincide at every second
vibration of the shorter string: this produces a compound sound,
which is more agreeable to the ear than any other, except the unison;
this note, when compared with the tone produced by the longer string,
is called the octave to it, because the interval between the two
notes is so divided by musicians that from one to the other they
reckon eight different tones.
If the strings be of the length, two and three, the coincidence of
the pulses will happen less frequently, viz. at every third vibration
of the shorter string, and the concord will be less perfect. This
forms what is called a fifth. The less frequent the coincidence of
the vibrations, the less perfect will be the concord, or the less
pleasure will it afford to the mind; till the vibrations coincide so
seldom, that the sound produced by both strings at once is harsh and
disagreeable, and is called a discord.
The effects of music upon the mind, the power by which it moves the
heart, touches the passions, and excites sometimes the highest
pleasure, and sometimes the deepest melancholy, depend upon melody.
By a simple melody the ignorant are affected as well as those skilled
in music. The pleasures arising from harmony or a combination of
sounds are acquired rather than natural. Its pleasures are the result
of experience and knowledge in music; music affords a source of
innocent and inexhaustible pleasure, but its effects are different on
different persons: some are enthusiastically fond of it, while others
hear the sweetest airs with a listlessness bordering upon
indifference. This has been supposed to depend on a musical ear,
which is not given by nature to all. The cause of this difference is
by no means evident. It does not depend on the delicacy of the sense
of hearing, for there are some persons half deaf, who have the
greatest relish for music; while others who have a very acute sense
of hearing have no relish for music. In some instances I think a
musical ear has been acquired where it did not seem originally to
exist.