Johann Heinrich Jacob Müller.

Principles of physics and meteorology online

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We must, therefore, make the string half the length in order to
make it yield the octave, other conditions remaining the same.
But as the octave makes twice as many vibrations as the funda-
mental note, a string half the length will make double the number
of vibrations.

To obtain the fifth, we must shorten the string to f of its length ;
but the fifth makes f times as many vibrations as the fundamental
note in an equal time.

The number of vibrations of strings is, therefore, inversely as
their length.


To obtain an octave with an equal length of string, we must
Fig. 220. attach 4 times as heavy a weight, and

as heavy a one for the fifth.

Laws of the Vibrations of Blades and
Rods. If a blade or rod be fastened at
one end (see Fig. 220), and be touched
by the bow of a violin, or simply brought
out of equilibrium by the hand, it will
make a series of vibrations between I
and l f , which, if sufficiently rapid, will
produce a note. If different lengths be
given to the same blade, the number of
the vibrations made in a given time will
be inversely as the square roots of the
vibrating lengths.

Of Reed-pipes. A tongue is generally
a vibrating plate set in motion by a current of air.

Let p (Fig. 221) be a plate of metal 0.078 to 0.118 inch in
Fig. 221. thickness, having a rectangular opening a b c d, 1.181
inch in length, and from 0.275 to 0.314 inch in breadth,
over which a very thin elastic brass plate is fastened,
as represented in the diagram. This plate can vibrate
on touching the edges a b, b c, and c d. In this man-
ner we have a very simple tongue-work, which can be
set in motion by putting the plate p lengthwise to the
lips, and blowing so as to direct the air against the free end of the
plate /. The latter is made to vibrate by the current of air; the
aperture is alternately opened and closed while the current first
pours in, and then is checked in its course ; in this manner sound-
waves arise, whose length depends upon the number of vibrations
which the dimensions and elasticity of the plate I admit of its
making in a given time. With the exception of greater intensity,
the note is the same as if the plate were made to vibrate by me-
chanical means. If we fasten several such bars to one plate,
choosing such as will yield the succeeding notes of a gamut, we
may make an instrument on which we may play various tunes.

The tongue- work of an organ depends upon similar principles,
although in this case the tongue is differently attached. Here we
distinguish two contiguous tubes, t and t f (Fig. 224), a stop b
dividing them, and the actual tongue-piece passing through the




Fig. 223.

stop. The tongue-work itself is represented on a larger scale in
Fig. 223, and consists essentially of
three parts, the channel r, the tongue
/, and the tuning-wire z.

The channel is a prismatic, or half
cylindrical tube, closed below, and
open at the top, having an aperture
at the side by which both tubes are
joined together.

The tongue is the vibrating plate ;
in its natural position, the lateral
opening of the channel is either en-
tirely or almost closed by it ; that is
to say, it touches upon the edges of
the opening with its three free edges
during its oscillations ; the fourth side
being secured to the tube either by a
screw or by soldering.

The tuning-wire is a strong metal wire, doubly curved below,
and pressed against the tongue along its whole breadth. It may
be pushed up and down in the stop with some friction, and thus
the vibrating portion of the tongue may be lengthened
or shortened, for the part over the tuning- wire cannot

The wind of the bellows enters through the pedal of
the tube t f 9 and pressing against the tongue to procure
an outlet, forces itself through the channel, and escapes
from the tube t. The tongue, thus brought out of its
equilibrium, returns immediately by means of its elas-
ticity, making vibrations in this manner, which last as
long as the current of air continues. Fig. 222 repre-
sents a reed-pipe in which the part of the tube opposite
to the tongue is of glass, the better to show its working.

In organs the reed-pipes are often constructed some-
what differently, by the edges of the tongue striking
upon the edges of the channel, as exhibited in Fig. 224.

If a reed-pipe vibrate of itself in free air if, conse-
quently, no pipe, or only a relatively short one, be
placed over it, its rapidity of vibration, and therefore its note,

Fig. 224.


depend upon its elasticity and dimensions ; if, however, a long
tube be put on, it will essentially modify the note ; the motion of
the tongue depends, therefore, more upon the motion of the air-
waves passing backwards and forwards in the long pipe than
upon its own elasticity; it, therefore, vibrates less of itself than
from external agents.

Transmission of vibrations of sound between solid, fluid, and
aeriform bodies. If several solid bodies be united together in a
whole, the vibrations issuing from one part of this system, distri-
bute themselves with the greatest ease, as advancing waves over
the whole mass ; having reached the confines, the waves pass only
partially into the contiguous medium, the aeriform or fluid body ;
they are partially reflected, however, and regular vibrations are
formed in the separate parts of the solid system by the interference
of the reflected with the fresh incident waves. Such a system
forms a whole, which, if a point be made to vibrate, will be like
a single solid body divided into separate vibrating parts, divided
by nodes of oscillation. Each separate part loses, to a certain
degree, its individuality, while its connection with the contiguous
parts hinders it from vibrating as it would do if it were isolated.

While sound-waves are easily distributed over a system of solid
bodies, they pass less easily from a solid to a liquid, and with still
less facility to a gasiform body ; thus it happens that many strongly
vibrating solid bodies only yield a very weak tone, owing to their
inability properly to impart their vibrations to the air. This is the
case with the tuning-fork, for instance, which gives forth only a
faint sound on being struck with force, and held free in the air.

In order to heighten the tone of such a body, the transmission
of its vibrations through the atmosphere must be increased by
resonance, that is, by endeavoring to transfer the regular vibra-
tions of the sounding body to another. One means with which we
are already acquainted, is to bring the low-toned but strongl
vibrating body before a tube of proper length, and to cause th<
enclosed air to sound.

A second method of strengthening the tone, is by bringing the
sounding body in contact with another of proportionately l
surface, and capable of being readily made to vibrate. There ai
then regular sound-waves formed upon it, as we have already men-
tioned, which are more readily transmitted to the air, owing to the
large area of the sounding (resonant) body. If, for instance, w<


put the strongly struck tuning-fork, which yielded in the open air
but a faint sound, upon a box of thin elastic wood, the note will be
given with much more intensity. On this principle depends the
sounding-board used in different musical instruments. In flutes,
organ-pipes, &c., no such application is necessary, as the regular
vibrations of a mass of air yield the note, and easily distribute
themselves through the surrounding atmosphere.

As vibrations of solid bodies create sound-waves in the air, so,
likewise, sound-waves may, when diffusing themselves through the
atmosphere, cause a solid body to vibrate by coming in contact
with it. Thus, for instance, we see the string of an instrument
vibrate if it come in contact with the sound-waves of the note it
yields, or with those of one of its harmonic notes ; and in this
manner the panes of glass in a window shake with violence from
the influence of certain notes of the voice, or from the report of a
cannon. This phenomenon, which is strikingly manifested in
susceptible bodies, also occurs in larger masses and in less elastic
bodies ; all the pillars and walls of a large church shake more or
less strongly during the ringing of the bells.





The Organs of Speech. It is well known that the wind-pipe is
a tube ending at one extremity in the throat, and at the other in
the lungs. Its especial use is to give a free passage to air both
in inspiration and expiration; it is almost cylindrical, being com-
posed of cartilaginous rings, which are united together by flexible
membranous rings. At its lower extremity, it separates into two
tubes, the bronchi, one of which goes to the right, the other to the
left. Each of these branches is further ramified in all directions
in the tissue of the lung. At its upper end the wind-pipe termi-
nates in the larynx, which is essentially the organ of speech.

The larynx consists of four cartilages, which ossify in extreme
old age ; they are the cricoid, the thyroid, and the two arytenoid
cartilages. These cartilages are connected with one another, and
likewise with the upper rings of the wind-pipe, and may be moved
in the most varied ways by means of different muscles. The
inner wall of the larynx forms a prolongation of the wind-pipe,
contracting until it becomes nothing more than a mere chink,
directed backward, known as the glottis.

The edges of the glottis are principally formed by the chordce
vocales, which merge anteriorly in the thyroid cartilage, while, at
the opposite extremity, one chorda vocalis is incorporated in the
other, and the second to the other arytenoid cartilage, so that
according as the cartilages are brought nearer to, or further from
each other by the corresponding muscles, the chordae vocales
become more or less stretched, while the glottis diminishes or
enlarges. The chordae vocales themselves consist of a very elastic

Above the edges of the glottis there are two sac-like cavities,
one to the right, the other to the left side, stretching from eight to
nine lines laterally, and having a depth of five or six lines ; these
are the ventriculi morgagni. The upper edges of these ventricles



rm, as it were, a second glottis, lying five or six lines above the
other. The upper glottis may be covered by the epiglottis, which
is an almost triangular membrane, or rather a cartilage; it is
attached to the glottis anteriorly, and, when covering it, hinders
all food and drink from getting into the wind-pipe, since they
must pass over it to enter the oesophagus.

The formation of the larynx will be more clearly illustrated by
the accompanying figures. Fig. 225 presents an anterior view of
it; Fig. 226 gives a lateral view; Fig. 228 gives a posterior, and
Fig. 227 a superior view, leaving out the muscles that move the

Fig. 225.

Fig. 226.

Fig. 227.

Fig. 228.


cartilages, and thus stretch the chordae vocales. In all these
figures the cricoid cartilage is designated by a, the thyroid carti-
lage by bj the arytenoid cartilages by c, and the epiglottis by d.
The latter is represented turned upwards to show it more dis-
tinctly. In Fig. 227 we see the glottis formed by the two lower
chordae vocales stretched between the thyroid and the arytenoid
cartilages. In this figure we also see the upper chordae vocales,
together with the ventriculi morgagni, lying between them and the
lower chordae vocales.

The formation of notes in the larynx is quite similar to that of
reed-pipes. A tongue-work depends upon this principle, that a
body yielding on a blow, either no notes, or such only as are very
faint and soundless, may, by continual impulses of the air, create a
note corresponding to its length and elasticity. In the larynx the
vibrations of the chordae vocales, by which the glottis is closed and
opened in rapid alternations, occasion the notes, as we may easily
see by the following contrivance made to imitate the larynx.

Cut a piece measuring about 1J inches from a thin plate of
caoutchouc, and let it be of sufficient breadth to be folded round
a glass-tube about six or seven lines in diameter; lay this so round
the glass cylinder that one-half may surround the latter, and the
other half project beyond it; if we bring the two freshly cut
edges of the caoutchouc together, they will adhere firmly, and
we thus obtain a caoutchouc cylinder fastened to, and projecting
beyond the glass cylinder, to which it must be secured in the
manner represented in Fig. 229. If, now, we fasten the caoutchouc
Fig. 229. cylinder, at its upper extremity, to two sepa-

rate points, pulling it apart, a chink will be
formed (as seen in the figure) with caoutchouc
edges, and if we blow into the pipe superiorly,
we obtain a tone which is high in proportion
to the force exerted by the lips. We may thus
clearly see the vibrations of the two caout-
chouc projections forming the chink.

The height and depth of the tones of the
larynx likewise depend upon the tension of
the chordae vocales.
The Organ of Hearing consists of three main parts : the outer
ear formed by the pinna, and the external meatus, the cavity of
the tympanum separated from the above meatus, by the membrane


of the tympanum, and the labyrinth. The labyrinth consists of
osseous cavities filled with a fluid, and through which the auditory
nerve is distributed ; in order to enable these nerves to act, the
sound- vibrations of the fluid, which is wholly surrounded by bones,
must be transmitted into the labyrinth ; this is effected by two
openings of the labyrinth leading into the cavity of the tympanum ;
they are termed the fenestra ovalis and the fenestra rotunda ; the
latter is covered with a tender membrane, while the former has a
small bone inserted into it, by means of a membranous investment.
This bone, which is termed the stapes, we shall describe more

Fig. 230 represents the labyrinth on an enlarged scale, and

Fig. 230.

partly opened. It consists of three parts, the cochlea, the vesti-
bule, and the semi-circular canals. The auditory nerve is dis-
tributed partly in the vestibule, where it rests on the ampullse, the
tubes lining the semi-circular canals, and filled with a peculiar
fluid; and more especially in fine ramifications to the cochlea.
The convolutions of the cochlea are separated into two parts by
a fine osseous partition-wall running parallel to one of these con-
volutions. This wall is very porous and cellular, and ramifica-
tions of the auditory nerve terminate in these cells, as may be
seen in the exposed part of the cochlea in our figure.

The sound- vibrations are conveyed, by means of the little bones
in the cavity of the tympanum, to the labyrinth. These bones are
the malleus, which with its handle grows into the side of the
membrane of the tympanum ; the incus joining the malleus and


connected with the stapes through the os orbiculare ; the stapes
closing the fenestra ovalis. The relative position of all these
parts may be seen in Fig. 231, representing the labyrinth on a
very much enlarged scale ; a is the external meatus that conveys

Fig. 231.

the sound-waves from the concha to the membrane of the tym-
panum. This latter divides the cavity of the tympanum from the
external meatus. The tympanic cavity is connected by the Eus-
tachian tube b with the cavity of the mouth, by which means the
air in the former cavity can always be in equilibrium with the
external air ; d is the malleus, attached on one side to the mem-
brane of the tympanum, while on the other side it is inserted into
the incus e\ f is the stapes, which, as we see, closes the fenestra
ovalis ; o is the fenestra rotunda ; n is the auditory nerve distri-
buted through the labyrinth.

The separate parts of the organ of hearing do not lie so free as
might appear from Fig. 231 ; the osseous casing which encloses the
whole being omitted for the sake of giving distinctness to the
figure. The external meatus itself passes through the temporal
bone, the cavity of the tympanum is surrounded by osseous walls,



Fig. 232.

and the labyrinth is formed in a part of the temporal bone, called,
on account of its hardness, the petrous portion, from which it can
only be separated with difficulty. In order to afford a correct idea
of the separate parts of the organ of hearing, and the manner in
which they grow in the osseous mass, we have given at Fig. 232
an actual anatomical section of the parts, represented according to
their natural size ; a is
the section of the coch-
lea, b one of the semi-
circular canals, n the
nerve, i the membrane
of the tympanum ; the
malleus, incus, and
stapes, are also clearly

The pinna serves to
receive the air-waves,
and conduct them
through the meatus to
the membranes of the
tympanum ; the latter
is thus put into vibra-
tions which are trans-
mitted through the ossi-
cles, and through the
air in the cavity of the
tympanum to the la-
byrinth. The mem-
brane of the tympanum
may be made more or

less tense, and drawn inwards by means of the muscle ; while,
by the muscle s, the stapes may be moved, and the intensity of
the sound, therefore, considerably modified.

The most essential part of the organ of hearing is the auditory
nerve; hence, the membrane of the tympanum may be injured, and
the series of the ossicles broken without the hearing wholly ceasing;
in many of the lower animals, as in the crab, the organ of hearing
consists merely of a vesicle filled with fluid, in which the vessel of
hearing is distributed.





THE most casual observation teaches us that a luminous point
sends its light in all directions ; a burning taper, for instance,
placed in the centre of a spherical surface, would be visible from
all points of that surface ; the same is the case with regard to a
phosphorescent body, an electrical spark, &c. What is evident
to our common experience on a small scale, takes place alike in
the vast expanse of heaven. The sun sheds its light in all direc-
tions of space ; its light reaches simultaneously the earth and the
other planets, the comets, and all the other bodies of the firma-
ment, be their position what it may in the boundless space of

All luminous bodies consist essentially of ponderable matter;
a vacuum may transmit, but it cannot engender light. All com-
mon bodies admit of being divided into smaller and still smaller
particles, and the ultimate physically perceptible atoms are
termed luminous points. As everybody is an assemblage of mole-
cules or atoms, so is a luminous body an assemblage of luminous

Bodies which are not self-luminous are divided into opaque, as
wood, stones, metals ; transparent, as air, water, glass ; and trans-
lucent, as thin paper and ground glass.

Opaque bodies do not suffer light to pass through their mass ;
but opacity always depends upon the thickness of the body, for all
bodies will admit of the passage of some degree of light if we
make them sufficiently thin. For instance, we may perceive a
bluish-green light through a thin gold leaf glued on a glass plate,
if we hold it to a taper, or up to the light.


Transparent bodies yield a passage to light, and allow of our
seeing with distinctness the form of objects beyond them. Gases,
fluids, and most crystalized bodies appear to be perfectly transr
parent when taken in small quantities ; for, in this case, they seem
to be wholly colorless, and not only admit of our seeing the form,
but also the color of objects : transparent bodies appear, however,
to be colored if they are thick a proof that they must absorb
some portion of light. A drop of water, for instance, appears
wholly colorless, whilst the same fluid, taken in a mass, has a
well-marked green hue.

Translucent bodies admit of the transmission of some portion
of light, without, however, allowing the form or color of objects
being recognized. As long as a ray of light remains in the same
medium, it advances in a straight line ; but, as soon as it comes in
contact with another body, it is partly thrown back, reflected from
its surface ; it partly, however, enters the body, if it be transparent,
in an altered direction, and is then refracted. We shall consider the
subject of reflection and refraction more fully in a subsequent page.

The velocity with which light travels is so great, that it tra-
verses all distances upon earth in an imperceptibly small space of
time. By means of observations on the eclipses of Jupiter's satel-
lites, astronomers have ascertained that light is transmitted with
such velocity as to traverse the space between the sun arid the
earth in eight minutes and thirteen seconds, passing, consequently,
over 195,000 English miles in one second. A cannon ball going
at the rate of 1200 feet in a second would require fourteen years
to go from the sun to the earth.

Shadows and half Shadows. A consequence of the straight
transmission of light is, that a dark body exposed to rays of light,
throws a shadow ; if only lighted by a single luminous body, it
is easy to define the shadow. The totality of all the lines
issuing from the luminous Fig. 233.

point, and striking the dark
body,forms a conical surface,
and the part of it lying beyond the dark body forms the limits of
the shadow.

If the luminous body have any considerable expansion, there

will be a half shadow distinguishable beyond the true shadow.

The shadow, which in this case is the central shadow^ is the

.space receiving no light ; the half shadow, on the contrary, is the




aggregate of all the spots receiving light from some luminous
points, but not from others. Let A (Fig. 234) be a large lumi-
nous sphere, B a small opaque one. The figure clearly shows the

Fig. 234.

Fig. 235.

extent of the true shadow and the half-shadow. The shadow
would assume the appearance shown at Fig. 235, if received upon
a screen m f n. The diameter of the true shadow
diminishes with the distance of the luminous
body, while the diameter of the half shadow
increases. The true shadow is, therefore, sur-
rounded by a narrow half shadow, close to the
shading bodies ; close to the back of the shading
body, the outline is somewhat sharply defined ;
at an increased distance, the width of the half
shadow is more considerable, and the transition from the true
shadow to the full light, on that account, more gradual, while the
shadow, instead of being sharply defined, seems imperceptibly
disappearing. Beyond the point s, the true shadow entirely
ceases, and the half shadow, increasing continually in breadth,
becomes, on that account, fainter and more undefined.

In this manner we may understand how the shadow of a body
exposed to the sun's light, is sharply defined close behind it, while
at a greater distance it becomes quite undefined. Thus, for
instance, we cannot accurately mark the point where the shadow
of the apex of a steeple is lost upon the ground. A hair held up
in the sunlight close to a sheet of paper will cast a sharp shadow,
while, if held two inches from it, a shadow is scarcely to be ob-
served. If, now, the light issuing from a luminous point be thrown
upon a screen, through which a small aperture has been made,



the light passing through this opening will form a well defined
ray ; if we let this ray fall upon a second screen, we shall have a
luminous spot upon a dark ground. In this manner, we obtain
on the wall of a perfectly dark room opposite to a minute aper-
ture in the shutter, an image of an external luminous point, send-
ing rays of light through the aperture into the chamber, and thus
inverted images of all external objects may be thrown upon a
wall (Fig. 236). If we allow the light of the sun to pass through

Fig. 236.

a small opening, we shall, at all times, have a round image of the
sun, let the shape of the opening be what it may. This, at first
sight, apparently strange fact, admits of a simple explanation. If
the sun were a single luminous point, a light spot would be formed

Online LibraryJohann Heinrich Jacob MüllerPrinciples of physics and meteorology → online text (page 19 of 55)