is one quarter of the wave-length of its stationary wave. This is
easily seen if we remember that the fixed end must be a _node_, and
the end moved up and down must be an _anti-node_, or ventral segment,
and the distance between a node and an anti-node is one quarter of a
wave-length. Accordingly the vibrating column of air in the jar also
has a fundamental mode of vibration, such that the length of the column
is one quarter of a wave-length. Hence the vibrating prongs of the
256-period tuning-fork, when held over the 1·1 foot long column of air,
are able to set the air in great vibratory movement, for the impulses
from the prongs come at exactly the right time. Accordingly, the loud
sound you hear when the fork is held over the jar proceeds, not so
much from the fork as from the column of air in the jar. The prongs of
the fork give little blows to the column of air, and these being at
intervals equal to the natural time-period of vibration of the air in
the jar, the latter is soon set in violent vibration.

We can, in the next place, pass on now to discuss some matters
connected with the theory of music. When regular air-vibrations or
wave-trains fall upon the ear they produce the sensation of a musical
tone, provided that their frequency lies between about 40 per second
and about 4000. The lowest note in an organ usually is one having 32
vibrations per second, and the highest note in the orchestra is that of
a piccolo flute, giving 4752 vibrations per second. We can appreciate
as sound vibrations lying between 16 and 32,000, but the greater
portion of these high frequencies have no musical character, and would
be described as whistles or squeaks.

When one note has twice the frequency of another it is called the
_octave_ of the first. Thus our range of musical tones is comprised
within about seven octaves, or within the limits of the notes whose
frequencies are 40, 80, 160, 320, 640, 1280, 2560, and 5120.

These musical notes are distinguished, as every one knows, by certain
letters or signs on a _clef_. Thus the note called the middle C of a
piano has a frequency of 248, and is denoted by the sign

The octave is divided into certain musical _intervals_ by notes, the
frequencies of which have a certain ratio to that of the fundamental
note. This ratio is determined by what is called the _scale_, or
_gamut_. Thus, in the major diatonic natural scale, if we denote
the fundamental note by C, called _do_ or _ut_ in singing, and its
frequency by _n_, then the other notes in the natural scale are denoted
by the letters, and have frequencies as below.

     _do_   _re_   _mi_   _fa_   _sol_   _la_   _si_   _do′_
      C      D      E      F       G      A      B      C^1
      n     ⁹⁄₈n    ⁵⁄₄n   ⁴⁄₃n     ³⁄₂n    ⁵⁄₃n   ¹⁵⁄₈n    2n

Hence if the note C has 248 vibrations per second, then the note D will
have 9 × 248 ÷ 8 = 279 vibrations per second. On looking at the above
scale of the eight notes forming an octave, it will be seen that there
are three kinds of ratios of frequencies of the various notes.

  (1) The ratio of C to D, or F to G, or A to B, which is
      that of 8 to 9.

  (2) The ratio of D to E, and G to A, which is that of
      9 to 10.

  (3) The ratio of E to F, or B to C^1, which is that of
      15 to 16.

The first two of these intervals or ratios are both called _a tone_,
and the third is called _a semitone_. The two tones, however, are not
exactly the same, but their ratio to one another is that of ⁸⁄₉ to
⁹⁄₁₀ or of 80 to 81. This interval is called a _comma_, and can be
distinguished by a good musical ear.

Several of these intervals or ratios of frequencies have received
names. Thus the interval C to E, = 4:5, is called a _major third_, and
the interval E to G, = 5:6, is called a _minor third_; the interval
C to G, = 2:3, is called a _fifth_, and that of C to C^1, = 1:2,
is called an _octave_. For the purposes of music it has been found
necessary to introduce other notes between the seven notes of the
octave. If a note is introduced which has a frequency greater than any
one of the seven in the ratio of 25 to 24, that is called a _sharpened_
note; thus the note of which the frequency is ³⁄₂_n_ × ²⁵⁄₂₄ would be
called _G sharp_, and written G♯. In the same way, if the frequency
of any note is lowered in the ratio of 24 to 25, it is said to be
_flattened_. Then the note whose frequency is ³⁄₂_n_ × ²⁴⁄₂₅ would be
called _G flat_, and written G♭.

It is obvious that if we were to introduce flats and sharps to all the
eight notes we should have twenty-four notes in the octave, and the
various intervals would become too numerous and confusing for memory
or performance. Hence in keyed instruments the difficulty has been
overcome by employing a _scale of equal temperament_, made as follows:
The interval of an octave is divided into twelve parts by introducing
eleven notes, the ratio of the frequency of each note to its neighbours
on either side being the same, and equal to the ratio 1 to 1·05946.

The scale thus formed is called the _chromatic scale_, and by this
means a number of the flats and sharps become identical; thus, for
instance, C♯ and D♭ become the same note. The octave has therefore
twelve notes, which are the seven white keys, and the five black ones
of the octave of the keyboard of a piano or organ.

Every one not entirely destitute of a musical ear is aware that
certain of these musical intervals, such as the fifth, the octave,
or the major third, produce an agreeable impression on the ear when
the notes forming them are sounded together. On the other hand, some
intervals, such as the seventh, are not pleasant. The former we call
_concords_, and the latter _discords_. The question then arises—What is
the reason for this difference in the effect of the air-vibrations on
the ear? This leads us to consider the nature of simple and complex air
vibrations or waves.

Let us consider, in the first place, the effect of sending out into
the air two sets of air waves of slightly different wave lengths.
These waves both travel at the same rate, hence we shall not affect
the combined effects of the waves upon the air if we consider both
sets of waves to stand still. For the sake of simplicity, we will
consider that the wave-length of one train is 20 inches, and that
of the other is 21. Moreover, let the two wave-trains be so placed
relatively to one another that they both start from one point in the
same phase of movement; that is, let their zero points, or their humps
or hollows, coincide. Then if we draw two wavy lines (see Fig. 56)
to represent these two trains, it will be evident that, since the
wave-length of one is 1 inch longer than that of the other—that is, a
distance equal to twenty wave-lengths—one wave-train will have gained
a whole wave-length upon the other, and in a distance equal to ten
wave-lengths, one wave train will have gained half a wave-length upon
the other. If we therefore imagine the two wave-trains superimposed,
we shall find, on looking along the line of propagation, an alternate
doubling or destruction of wave-effect at regular intervals. In other
words, the effect of superimposing two trains of waves of slightly
different wave-lengths is to produce a resultant wave-train in which
the wave-amplitude increases up to a certain point, and then dies away
again nearly to nothing, as shown in the lowest of the three wave-lines
in Fig. 56.

[Illustration: FIG. 56.—The formation of beats by two wave-trains.]

We must, then, determine how far apart these points of maximum
wave-amplitude or points of no wave effect lie. If the wave-length of
one train is, as stated, 20 inches, then a length of ten wave-lengths
is 200 inches, and this must be, therefore, the distance from a
place of maximum combined wave-effect to a place of zero wave-effect.
Accordingly, the distance between two places where the two wave trains
help one another must be 400 inches, and this must also be the distance
between two adjacent places of wave-destruction. If, therefore, we look
along the wavy line representing the resultant wave, every 400 inches
we shall find a maximum wave-amplitude, and every 400 inches a place
where the waves have destroyed each other. We may call this distance
_a wave-train length_, and it is obviously equal to the product of
the constituent wave-lengths divided by the difference of the two
constituent wave-lengths.

It follows from this that if we suppose the two wave-trains to move
forward with equal speed, the number of maximum points or zero points
which will pass any place in the unit of time will be equal to the
_difference_ between the frequencies of the constituents. Let us now
reduce this to an experiment. Here are two organ-pipes exactly tuned
to unison, and when both are sounded together we have two identical
wave-trains sent out into the air. We can, however, slightly lengthen
one of the pipes, and so put them out of tune. When this is done you
can no longer hear the smooth sound, but a sort of waxing and waning
in the sound, and this alternate increase and diminution in loudness
is called _a beat_. We can easily take count of the number of beats
per second, and by the reasoning given above we see that the number
of beats per second must be equal to the difference between the
frequencies of the two sets of waves. Thus if one organ-pipe is giving
100 vibrations per second to the air, and the other 102, we hear two
beats per second.

Now, up to a certain point we can count these beats, but when they
come quicker than about 10 per second, we cease to be able to hear them
separately. When they come at the rate of about 30 per second they
communicate to the combined sound a peculiar rasping and unpleasant
effect which we call a discord. If they come much more quickly than 70
per second we cease to be conscious of their presence by any discordant
effect in the sound.

The theory was first put forward by the famous physicist, Von
Helmholtz, that the reason certain musical intervals are not agreeable
to the trained ear is because the difference between the frequencies of
the constituent fundamental tones _or the harmonics present in them_
give rise to beats, approximately of 30 to 40 per second.

In order to simplify our explanations we will deal with two cases only,
viz. that of the _octave_ interval and that of the _seventh_. The first
is a perfect concord, and the second, at least on stringed instruments,
is a discord. It has already been explained that when a string vibrates
it does so not only as a whole, but also in sections, giving out a
fundamental note with superposed harmonics. Suppose we consider the
octave of notes lying between the frequencies 264 and 528, which
correspond to the notes C and C^1 forming the middle octave on a piano.
The frequencies and differences of the eight tones in this octave are
as follows:—

FREQUENCIES OF THE NOTES OF THE MIDDLE OCTAVE OF A PIANO.

              Notes.   Frequency.   Difference.

                C        264
                                        33
                D        297
                                        33
                E        330
                                        22
                F        352
                                        44
                G        396
                                        44
                A        440
                                        55
                B        495
                                        33
                C^1      528

It will thus be seen that the differences between the frequencies of
adjacent notes are such as to make beats between them which have a
number per second so near to the limits of 30 to 40 that adjacent notes
sounded together are discords.

Suppose, however, we sound the _seventh_, viz. _C_ and _B_, together.
The frequencies are 264 and 495, and the difference is 231. Since,
then, the difference between the frequencies lies far beyond the
limit of 30 to 40 per second, how comes it that in this case we have
a discord? To answer this question we must consider the harmonics
present with the fundamentals. Write down each frequency multiplied
respectively by the numbers 1, 2, 3, 4, etc.—

                                C.       B.
            Fundamental        264      495
            First harmonic     528      990
            Second   ”         792     1475
            Third    ”        1056     1980
            Fourth   ”        1320     2475
            Fifth    ”        1584     2970

On looking at these numbers we see that although the difference
between the frequencies of the two fundamentals is too great to
produce the disagreeable number of beats, yet the difference between
the frequencies of the fundamental of note B (495) and the first
harmonic of note C (528) is exactly 33, which is, therefore, the
required number. Accordingly, the discordant character of the seventh
interval played on a piano is not due to the beats between the primary
tones, but to beats arising between the first harmonic of one and the
fundamental of the other. It will be a useful exercise to the reader
to select any other interval, and write down the primary frequencies
and the overtone frequencies, or harmonics, and then determine whether
between any pairs disagreeable beats can occur.

The presence of harmonics or overtones is, therefore, a source of
discord in some cases, but nevertheless these overtones communicate a
certain character to the sound.

Helmholtz’s chief conclusions as regards the cause of concord and
discord in musical tones were as follows:—

(1) Musical sounds which are pure, that is, have no harmonics mixed up
with them, are soft and agreeable, but without brilliancy. Of this kind
are the tones emitted by tuning-forks gently struck or open organ-pipes
not blown violently.

(2) The presence of harmonics up to the sixth communicates force and
brilliancy and character to the tone. Of this kind are the notes of the
piano and organ-pipes more strongly blown.

(3) If only the uneven harmonics, viz. the first, third, fifth, etc.,
are present, the sound acquires a certain nasal character.

(4) If the higher harmonics are strong, then the sound acquires great
penetrating force, as in the case of brass instruments, trumpet,
trombone, clarionet, etc.

(5) The causes of discord are beats having a frequency of 30 to 40 or
so, taking place between the two primary tones or the harmonics of
either note.

The pleasure derived from the sound of a musical instrument is
dependent, to a large extent, on the existence of the desirable
harmonics in each tone, or on the exclusion of undesirable ones.

In the next place, let us consider a little the means at our disposal
for creating and enforcing the class of air-waves which give rise to
the sensations of musical tones. Broadly speaking, there are three
chief forms of musical air-wave-making appliance, viz. those which
depend on the vibrations of columns of air, on strings, and on plates
respectively.

One of the oldest and simplest forms of musical instrument is
that represented by the _pan-pipes_, still used as an orchestral
accompaniment in the case of the ever-popular peripatetic theatrical
display called _Punch and Judy_.

If we take a metal or wooden pipe closed at the bottom, and blow gently
across the open end, we obtain a musical note. The air in the pipe is
set in vibration, and the tone we obtain depends on the length of the
column of air, which is the same as the length of the pipe. The manner
in which this air-vibration is started is as follows: On blowing across
the open end of the pipe closed at the bottom a partial vacuum is
made in it. That this is so, can be seen in any scent spray-producer,
in which two glass tubes are fixed at right angles to each other.
One tube dips into the scent, and through the other a puff of air is
sent across the open mouth of the first. The liquid is sucked up the
vertical tube by reason of the partial vacuum made above it. If we
employ a pipe closed at the bottom and blow across the open end, the
first effect of the exhaustion is that the jet of air is partly sucked
down into the closed tube, and thus compresses the air in it. This air
then rebounds, and again a partial vacuum is made in the tube. So the
result is an alternate compression and expansion of the air in the
closed tube. The column of air is alternately stretched and squeezed,
and a state of stationary vibration is set up in the air in the tube;
just as in the case of a rope fixed at one end and jerked up and down
at the other end. The natural time-period of vibration of the column of
air in the tube controls the behaviour of the jet of air blown across
its mouth, the energy of the jet of air being drawn upon to keep the
column of air in the tube in a state of oscillation. Thus a flutter is
excited in the air in the tube, which is maintained as long as there
is a blast of air across its mouth, and this communicates to the air
outside a wave-motion. We have, therefore, a musical note produced, the
wave-length of which is four times the length of the closed tube across
the mouth of which we are blowing. Accordingly, a very simple musical
instrument such as the pan-pipes consists of a row of tubes closed at
the bottom, the tubes being of different lengths. A current of air from
the mouth is blown across the tubes taken in a certain order, and we
can obtain a simple melody by that process of selection.

[Illustration: FIG. 57.—A closed organ-pipe.]

An organ-pipe is only a more perfect means for doing the same thing.
Organ-pipes may be either open or closed pipes. Also they have
either a reed or a flute at one end for the purpose of establishing
air-vibrations when a current of air is blown into the pipe. The form
of organ-pipe most easy to understand is the closed flute pipe. This
consists of a wooden tube closed at the upper end, and at the lower end
having a foot-tube and mouthpiece as shown in section in Fig. 57. When
a gentle current of air is blown in at the foot-tube, it impinges on
the sharp edge or chamfer of the mouthpiece, and it acts just as when
blown across the open end of a simple closed pipe. That is to say, it
sets up a state of alternate compression and expansion of the air in
the pipe. At the closed end, period-changes in density in the air are
established, but no great movement takes place. At the open end or
mouth there are no great changes of density, but the air is alternately
moving in and out at the mouthpiece. The steady blast of air against
the chamfer, therefore, sets up a state of steady oscillation of the
air in the pipe, the air being squeezed up and extended alternately
so that there is first a state of compression, and then a state of
partial rarefaction in the air at the closed end of the pipe. In this
case, also, the wave-motion communicated to the surrounding air has a
wave-length equal to four times the length of the pipe.

If we open the upper end of the pipe, it at once emits a note which has
a wave-length equal to double the length of the pipe. Hence the note
emitted by an open-ended organ-pipe is an octave higher than that given
out by a closed organ-pipe of the same length.

The action of an open organ-pipe is not quite so easy to comprehend
as that of a closed pipe. The difficulty is to see how stationary air
waves can be set up in a pipe which is open at both ends. The easiest
way to comprehend the matter is as follows: When the blast of air
against the lip of the pipe begins to partially exhaust the air in it,
the rarefaction so begun does not commence everywhere in the pipe at
once. It starts from the mouthpiece end, and is propagated along the
pipe at a rate equal to the velocity of sound. The air at the open
ends of the pipe moves in to supply this reduced pressure, and, in so
doing, overshoots the mark, and the result is a region of compression
is formed in the central portions of the pipe (see Fig. 58). The
next instant this compressed air expands again, and moves out at the
two open ends of the pipe. We have thus established in the pipe an
oscillatory state which, at the central region of the pipe, consists
in an alternate compression and expansion or rarefaction of the air,
whilst at the open end and mouthpiece end there is an alternate rushing
in and rushing out of the air. Hence in the centre of the pipe we have
little or no movement of the air, but rapid alternations of pressure,
or, which is the same thing, density; and at the two ends little or no
change in density, but rapid movement of the air in and out of the pipe.

[Illustration: FIG. 58.—An open organ-pipe.]

An analogy between the vibration of the air in a closed and open
organ-pipe might be found in considering the vibration of an elastic
rod—first, when clamped at one end, and secondly, when clamped at the
two ends. The deflection of the rod at any point may be considered
to represent change of air-pressure, and the fixed point or points
the open end of the pipe at which there can be no change of density,
because there it is in close communication with the open air outside
the pipe. It is at once evident that the length of the open organ-pipe,
when sounding its fundamental tone, is one-half of the length of the
air wave it produces. Accordingly, from the formula, _wave-velocity_ =
_frequency_ × _wave-length_, we see that, since the velocity of sound
at ordinary temperature is about 1120 feet per second, an approximate
rule for obtaining the frequency of the vibrations given out by an open
organ-pipe is as follows:—

      _Frequency_ = 1120 _divided by twice the length of pipe_.

We say _approximate_, because, as a matter of fact, for a reason rather
too complicated to explain here, the wave-length of the air-vibrations
is equal to rather more than double the length of the pipe. In fact,
what we may call the effective length of the pipe is equal to its real
end-to-end length increased by a fraction of its diameter, which is
very nearly four-fifths.

[Illustration: FIG. 59.]

We can confirm by experiments the statements made as to the condition
of the air in a sounding organ-pipe. Here is a pipe with three little
holes bored in it at the top, middle, and bottom (see Fig. 59). Each of
these is covered with a thin indiarubber membrane, and this, again, by
a little box which has a gas-pipe leading to it and a gas-jet connected
with it. If we lead gas into the box and light the jet, we have a
little flame, as you see. If, then, the indiarubber membrane is pressed
in and out, it will cause the gas-flame to flicker. Such an arrangement
is called a _manometric flame_, because it serves to detect or measure
changes of pressure in the pipe. The flicker of the flame when the
organ-pipe is sounded is, however, so rapid that we cannot follow it
unless we look at the image in a cubical revolving mirror of the kind
already used. When so regarded, if the flame is steady, we see a broad
band of light.

If we sound the organ-pipe gently and look at the bands of light
corresponding to the three flames, we see that the flames at the top
and bottom of the pipe are nearly steady, but that the one at the
middle of the pipe is flickering rapidly, the band of light being
changed to a saw-tooth-like form (see Fig. 60).

This shows us that rapid changes of pressure are taking place at the
centre of the pipe.

Again, if we prepare a little tambourine (by stretching parchment-paper
over a wooden ring), and lower it by a string into the sounding
organ-pipe, we shall find that grains of sand scattered over this
tambourine jump about rapidly when the membrane is held near the top or
the bottom of the pipe, but are quiescent when it is at the middle.

[Illustration: FIG. 60.]

This shows us that there is violent movement of the air at the ends,
but not in the centre, thus confirming the deductions of theory.

It should be noted that if the pipe is over-blown or sounded too
strongly, harmonics will make their appearance, and the simple state of
affairs will no longer exist.

The celebrated mathematician, Daniel Bernoulli, discovered that an
organ-pipe can be made to yield a succession of musical notes by
properly varying the pressure of the current of air blown into it.
If the pipe is an open one, then, if we call the frequency of the
primary note 1, obtained when the pipe is gently blown, if we blow
more strongly, the pipe yields notes which are the harmonics of the
fundamental one, that is to say, have frequencies represented by 2, 3,
4, 5, etc., as the blast of air increases in force.

Thus, if the pipe is one about 2 feet in length, it will yield a note
near to the middle C on a piano. If more strongly blown, it gives
a note, C^1, an octave higher, having double the frequency. If more
strongly blown still, it yields a note which is the fifth, G^1, above
the last, and has three times the frequency of the primary tone; and so
on.

If the pipe is closed at the top, then over-blowing the pipe makes it
yield the odd harmonics, or the tones which are related in frequency to
the primary tone in the ratio of 1, 3, 5, etc. Hence, if a stopped pipe
gives a note, C, its first overtone is the fifth above the octave, or
G^1.

It is usual, in adjusting the air-pressure of an organ-bellows, to
allow such a pressure as that some of the overtones, or harmonics,
shall exist. The presence of these harmonics in a note gives brilliancy
to it, whereas an absolutely pure or simple musical tone, though not
disagreeable to the ear, is not fully satisfying. Any one with a good
ear can detect these harmonics or overtones in a single note sounded
on a piano or organ due to the subdivision of the vibrating string or
air-column into sections separated by nodes.

It will be seen that the acoustic action of the organ-pipe depends
essentially upon some operation tending at the commencement to make an
expansion of the air in the pipe at one end, and subsequently to cause
an increase of air-pressure in it.

This can be effected not only by blowing into the pipe, but in another
way, by introducing a hot body into a pipe open at both ends. We can
show here as an illustration of this an interesting experiment due to
Lord Rayleigh. A long cast-iron water-pipe about 4 inches in diameter
and 8 feet long is suspended from the ceiling. About 1 foot up the
tube from the lower end a piece of iron-wire gauze is fixed (see Fig.
61). By means of a gas-burner introduced into the tube, we heat the
gauze red hot, and on withdrawing the lamp the tube suddenly emits a
deep organ-like note for a few moments. The heated metal creates an
up-draught in the tube at the lower end, and, as in the case of the
open organ-pipe, causes also an in-suction of air at the upper end.
The column of air is thus set vibrating with a point of alternate
condensation and rarefaction in the centre, and in-draughts and
out-rushes of air at the ends. Indeed, this rush of air into and out of
the pipe at the lower end during the time it is sounding its note is so
violent that if the hands are placed just below the bottom end of the
tube they will feel chilled, as if placed near an electric fan, by the
blast of air. Closing the bottom end of the pipe with a sheet of metal
at once stops the air-movement, and with it the musical note.

[Illustration: FIG. 61.]

[Illustration: FIG. 62.—Singing flame.]

In another form the experiment has long been known under the name of a
_singing flame_. A small jet of burning hydrogen gas is introduced into
a glass tube about 3 feet in length. The jet must consist of a long
narrow brass tube, and the proper position for the jet must be found by
trial (see Fig. 62). When this is done, however, the tube emits a clear
musical note, due to the tube acting as an open organ-pipe. If the
flame is examined in a revolving mirror when the tube is singing, it
will be found to be in vibration in sympathy with the movement of air
in the tube. The tube often refuses to start singing, but may be made
to do it by giving it a little tap. The actions taking place in the
tube are something as follows: When the flame is introduced, it heats
and rarefies the air around it. This causes an in-rush of air both
at the top and bottom of the tube. A state of steady oscillation is
then established, in which the air at the centre undergoes periodical
expansions and compressions, and the pressure of the air round the
flame changes in the same manner. The flame is therefore alternately
expanded and contracted. When it expands, it heats the air more. When
it is compressed, it heats it less. This variation of the flame causes
air to be sucked in or expelled from both open ends of the tube, and
establishes the state of steady vibration in accordance with the length
of the tube. The flame and the air-column act and react on each other,
and establish a state of stationary aerial oscillation in accordance
with the natural time-period of the column of air. The tube can be made
to give out not only its fundamental note, but a series of harmonics,
or overtones, with frequencies 2, 3, 4, 5, etc., times the fundamental
note, by varying the position of the flame, which must always be just
under the place where a node, or place of alternate condensation and
rarefaction, occurs.

We may, in the next place, with advantage briefly examine the
principles of construction of one musical instrument, and allude to
some recent improvements. One of the most interesting of all the
musical appliances devised by human ingenuity is the violin, comprising
as it does in its construction an art, a science, and a tradition. In
principle the violin is nothing but a wooden box, along the top of
which are stretched four strings, which are strained over a piece of
wood called a bridge. These strings have their effective length altered
in playing by placing the finger of the performer at some place on
them, and they are set in vibration by drawing over them a well-rosined
bow made of horsehair. The vibrating string communicates its vibrations
to the surface of the box or body by means of the bridge, and this
again to the air in the interior. The body thus serves two purposes.
It acts as a resonating-chamber, and also it affords a large surface
of contact with the surrounding air, whereby a greater mass of air is
set simultaneously in wave-motion. The four strings are normally tuned
in _fifths_, so that the fundamental note of each is an interval of a
fifth above the next.

The performer varies the note given by each string by shortening its
vibrating length by pressing the finger upon it. The skilled violinist
has also great control over the tone, and can determine the harmonics,
or overtones, which shall accompany the fundamental by altering the
point on the string at which the bow is applied, and lightly touching
it at some other point.

The great art in the construction of the violin rests in the
manufacture of the wooden body. Its form, materials, and minute details
of construction have been the subject of countless experiments in past
ages, and until quite recently no essential improvement was made in
the instrument as completed by the masters of violin construction
three centuries ago. In classical form the violin consists of a wooden
box of characteristic shape, composed of a back, belly, and six ribs.
These are shaped out of thin wood, the belly being made of pine, and
maple used for the rest. A neck or handle is affixed to one end, and a
tail-piece, to which the gut-strings are fastened, to the other.

The strings are strained over a thin piece of wood which rests on two
feet on the belly. One of these feet rests over a block of wood in
the interior of the box called the sound-post, and this forms a rigid
centre; the other foot stands on the resonant part of the belly. The
belly is strengthened in addition by a bar of wood, which is glued to
it just under the place where the active foot of the bridge rests. The
ribs or sides of the box are bent inwards at the centre to enable the
playing-bow to get at the strings more easily. The selection of the
wood and its varnishing is the most important part of the construction.
The wood must be elastic, and its elasticity has to be preserved by the
use of an appropriate hard varnish, or else it will not take up the
vibrations imparted by the strings. The old makers used wood which was
only just sufficiently seasoned, and applied their varnish at once.

An essential adjunct is a good bow, which is of more importance than
generally supposed. Something may be got out of a poor violin by a good
player, but no one can play with a bad bow.

The process of eliciting a musical tone from the violin is as follows:
The player, holding the instrument in the left hand, and with its tail
end pressed against the left shoulder, places a finger of the left hand
lightly on some point on a string, and sweeps the bow gently across
the string so as to set it in vibration, yielding its fundamental note,
accompanied by the lower harmonics. The purity and strength of the
note depend essentially upon the skill with which this touch of the
bow is made, creating and sustaining the same kind of vibration on the
string throughout its sweep. The string then presses intermittently
on the bridge, and this again turns, so to speak, round one foot as
round a pivot, and presses intermittently on the elastic wooden belly.
The belly takes up these vibrations, and the air in the interior is
thrown into sympathetic vibration by resonance. The sound escapes by
the _ƒ_-holes in the belly. The extraordinary thing about the violin
is that the shape of the box permits it to take up vibrations lying
between all the range of musical tones. The air-cavity does not merely
resonate to one note, but to hundreds of different rates of vibration.

The peculiar charm of the violin is the quality of the sound which
a skilled player can elicit from it. That wonderful pleading,
sympathetic, voice-like tone, which conveys so much emotional meaning
to the trained musical ear, is due to the proper admixture of the
harmonics, or overtones, with the fundamental notes. The string
vibrates not merely as a whole, but in sections. Hence the place at
which the bow touches must always be an anti-node, or ventral point,
and the smallest change in this position greatly affects the quality of
the tone.

Quite recently an entirely new departure has been made in violin
construction by Mr. Augustus Stroh, a well-known inventor. He has
abolished the wooden body and bridge, and substituted for them an
aluminium trumpet-shaped tube as the resonant chamber, ending in a
circular corrugated aluminium disc, on the centre of which rests an
aluminium lever pivoted at one point. The strings are strained over
this lever, and held on a light tube, which does duty as a point of
attachment of all parts of the instrument. The strings are the same,
and the manipulation of the instrument identical with that of the
ordinary violin. The vibrations of the strings are communicated by
the pivoted lever over which they pass to the corrugated aluminium
disc, and by this to the air lying in the trumpet-tube. This tube
points straight away from the player, and directs the air waves to
the audience in front. The tone of the new violin is declared by
connoisseurs to be remarkably full, mellow, and resonant. The notes
have a richness and power which satisfies the ear, and is generally
only to be found in the handiwork of the classical constructors of
the ordinary form of violin. One great advantage in the Stroh violin
is that every one can be made perfectly of the same excellence. The
aluminium discs are stamped out by a steel die, and are therefore
all identical. The element of chance or personal skill in making has
been eliminated by a scientific and mechanical construction. Thus
the musician becomes possessed of an instrument in which scientific
construction predominates over individual art or tradition in
manufacture, yet at the same time the musical effects which skill in
playing can produce are not at all diminished.

Whilst our attention has so far been fixed on the external operations
in the air which constitute a train of music-making waves, it seems
only appropriate to make, in conclusion, a brief reference to the
apparatus which we possess in our ears for appreciating these subtle
changes in air-pressure with certainty and pleasure. The ear itself is
a marvellous appliance for detecting the existence of waves and ripples
in the air, and it embodies in itself many of the principles which
have been explained to-day.

[Illustration: FIG. 63.—Diagram of the human ear.]

The organ of hearing is a sort of house with three chambers in it,
or, rather, two rooms and an entrance hall, with the front door
always open. This entrance passage of the ear is a short tube which
communicates at one end with the open air, being there provided with a
sound-deflecting screen in the shape of an external ornamental shell,
commonly called the ear. In many animals this external appendage
is capable of being turned into different positions, to assist in
determining the direction in which the sound wave is coming. The
entrance tube of the ear is closed at the bottom by a delicate membrane
called the tympanum, or drum. Against this drum-head the air waves
impinge, and it is pressed in and out by the changes of air-pressure.
This drum separates the outer end from a chamber called the middle ear,
and the middle ear communicates, by a sort of back staircase, or tube
called the Eustachian tube, with the cavity at the back of the mouth
(see Fig. 63).

Behind the middle ear, and buried in the bony structure of the skull,
is a third, more secret chamber, called the inner ear. This is
separated from the middle ear by two little windows, which are also
covered with delicate membranes. In the middle ear there is a chain
of three small bones linked with one another, which are connected at
one end with the tympanum, or drum, and at the other end with the
so-called oval window of the inner ear. Helmholtz has shown that this
little chain of bones forms a system of levers, by means of which the
movements of the tympanum are diminished in extent, but increased in
force in the ratio of 2 to 3.

The internal ear is the real seat of audition, and it comprises the
parts called the labyrinth, the semicircular canals, and the cochlea.
These are cavities lined with delicate membranes and filled with fluid.
In the cochlea there is an organ called Corti’s organ, which is a
veritable harp of ten thousand strings. This consists of innumerable
nerve-fibres, which are an extension of the auditory nerve. The details
of the organic structure are far too complicated for description
here. Suffice it to say that air waves, beating against the tympanum,
propagate vibrations along the chain of bones into the fluids in the
inner ear, and finally expend themselves on these nerve-fibres, which
are the real organs of sound-sensation.

Helmholtz put forward the ingenious hypothesis that each fibre in the
organ of Corti was tuned, so to speak, to a different note, and that a
composite sound falling upon the ear was analyzed or disentangled by
this organ into its constituents. Although this theory, as Helmholtz
originally stated it, has not altogether been upheld by subsequent
observation, it is certain that the ear possesses this wonderful power
of analysis. It can be shown by mathematical reasoning of an advanced
kind that any musical sound, no matter what its quality, can be
resolved into the sum of a number of selected pure sounds such as those
given by a tuning-fork.

Consider now for one moment the physical state of the air in a
concert-room in which a large orchestra is performing. The air is
traversed by a chaos of waves of various wave-lengths. The deep notes
of the violincello, organ, and trumpets are producing waves 10 to 20
feet in wave-length, which may be best described as billows in the air.
The violin-strings and middle notes of the piano, harp, or flute are
yielding air waves from 6 or 8 feet to a few inches long, whilst the
higher notes of violins and flutes are air ripples some 3 or 4 inches
in length.

If we could see the particles of the air in the concert-room, and
fasten our attention upon any one of them, we should see it executing
a most complicated motion under the combined action of these
air-wave-producing instruments. We should be fascinated by the amazing
dance of molecules to and fro and from side to side, as the medley of
waves of compression or rarefaction embraced them and drove them hither
and thither in their resistless grasp.

The tympana of our ears are therefore undergoing motions of a like
complicated kind, and this complex movement is transmitted through the
chain of bones in the middle ear to the inner ear, or true organ of
sensation. But there, by some wondrous mechanism not at all yet fully
understood, an analysis takes place of these entangled motions.

The well-trained ear separates between the effect due to each kind of
musical instrument, and even detects a want of tuning in any one of
them. It resolves each sound into its harmonics, appreciates their
relative intensity, is satisfied or dissatisfied with the admixture.
In the inner chamber of the ear physical movements are in some wholly
inscrutable manner translated into sensations of sound, and the
confused aggregation of waves and ripples in the air, beating against
the tympanic membrane there, takes effect in producing impulses which
travel up the auditory nerve and expend their energy finally in the
creation of sensations of melody and tune, which arouse emotions,
revive memories, and stir sometimes the deepest feelings of our minds.

                              CHAPTER V.

               ELECTRIC OSCILLATIONS AND ELECTRIC WAVES.

In the previous chapters your attention has been directed to the
subject of waves on water and waves in air, and we shall now proceed
to discuss some of the more difficult matters connected with the
production of waves in the æther. We shall find that this portion of
our subject makes more demands upon our powers of comprehension, since
much that we have to consider is not directly the object of sense
perception, and the inferences which we have to make from observed
facts are less simple and easy to follow. Nevertheless, I trust that
if you have been able to grasp clearly the nature of a surface-wave on
water and of a compressional wave in air, you will not readily allow
yourselves to be discouraged from encountering a new class of ideas,
but will be able to advance still further, and gain a more or less
clear conception of the nature of an electric wave in the æther.

In the first place, we must consider the medium in which these waves
are created. We can see with our eyes a water-surface, and we are
able to understand without much difficulty that the surface can be
thrown into humps and hollows, or become wrinkled, and also that these
elevations and depressions can change their position, thus creating a
surface wave which moves forward. The movement of the water wave is,
therefore, only the result of a local elevation of the surface which
travels along or takes place progressively at different places on the
surface. Then, again, in the case of an air wave, although we cannot
see the air, we are able, with some little assistance from experiments,
to present to ourselves a clear mental picture of a progressive
movement through the air of a region of compression, that is to say, a
certain slice, layer, or zone of the air is more compressed than the
neighbouring portions, and this region of compression changes its place
progressively. It has been carefully explained that the production of
a wave of any kind implies, therefore, two things—first, a medium or
material in which the wave exists; and, secondly, some kind of periodic
change or movement which is experienced by the various portions of this
medium at different places successively.

If, therefore, we are given any medium, say water or air, and asked
to explain the production of a wave in it, we have first to consider
what kind of changes can take place in it, or on it, which can appear
progressively at different parts. In the case of the water-surface,
some parts may be heaped up higher than the rest, and the heaping up
may occur at successive places in such fashion that when it disappears
at one place it reappears at a contiguous or neighbouring place. In the
case of air, some portion may be compressed more than the rest, and
the place of compression may move forward, so that as the compression
is released in one place it makes its appearance in an adjacent one.
In the first case, we have a wave of elevation on water; in the second
case, a wave of compression in the air.

In the next place, let me carry you with me one step more. Here is a
glass bulb from which the greater part of the air has been removed. We
say, therefore, that there is a _vacuum_ in the bulb. It is impossible
for us to remove absolutely every trace of air from the bulb, and so
produce what would be called a _perfect vacuum_; but we can imagine
it to be accomplished, and we can picture to ourselves the glass bulb
absolutely deprived of every trace of air or other material substance.
The question then arises—Is the bulb really empty, or is there still
_something_ in its interior?

The same inquiry may be put in another way. The air we breathe forms
an atmosphere which surrounds our earth as a garment, but it decreases
rapidly in density as we ascend. At a height of about 50 miles above
the earth there is reason to believe the air is exceedingly rarefied
and, except for the presence of meteoric dust, the space between the
sun and the earth, and between the stars and the earth, is in all
probability a highly perfect vacuum, in the sense that it is empty of
generally diffused matter. The question then arises—Is interstellar
space absolutely and completely empty? We know perfectly well that
rays of light come to us from the sun and stars through this empty
space, and a fact of capital importance is, that these rays of light,
swift-footed though they are, take time to travel. It was long ago
suspected that this was the case, and the celebrated Galileo made the
first experimental attempt to determine the velocity of light. No real
knowledge on the subject was gained, however, until after he had made
his discovery that the planet Jupiter is accompanied by four moons (a
fifth moon has been discovered since), and that these rotate round
the planet in definite periods of time, constituting, therefore, the
“hands” of a perfect celestial clock. The sunlight, falling on the
great globe which forms the body of the planet Jupiter, casts behind
it a conical shadow; and the little moons, in their rotation, are
plunged into this shadow cone at intervals, and then for a time become
invisible, or eclipsed.

As soon, however, as these eclipses of Jupiter’s moons began to be
regularly observed, it was found that the intervals of time between two
eclipses of any one moon were not equal, but exhibited a progressive
variation in magnitude, and were longer by about 16 minutes and 26
seconds at one time of the year than at the other. The astronomer
Roemer, in the year 1675, correctly concluded that this difference must
be due to the fact that rays of light take time to traverse the earth’s
orbit, and not to any want of regularity in the operation of this
celestial timepiece. Hence, although the eclipses do happen at equal
intervals of time, our information about them is delayed by the time
taken for the ray of light to travel over the variable distance between
Jupiter and our earth. These observations, critically considered,
led, therefore, to the conclusion that the speed of light rays is
about 186,500 miles a second. By means which it would take too long to
describe here, experimental measurements of the velocity of light have
been made many times since by various investigators by methods which
do not involve astronomical observations, and the result has been to
confirm the above value, and to give us a very exact knowledge of the
speed with which rays of light travel through space. It is as shown in
the table below:—

                        THE VELOCITY OF LIGHT.

                                                         Miles per
                                                          second.
    From observations on Jupiter’s satellites (Roemer)    186,500
      ”  experimental measurements by Foucault  (1862)    185,177
      ”        ”        ”        ”    Cornu     (1874)    185,487
      ”        ”        ”        ”      ”       (1878)    186,413
      ”        ”        ”        ”    Michelson (1879)    186,364
      ”        ”        ”        ”      ”       (1882)    186,328
      ”        ”        ”        ”    Newcomb   (1882)    186,333

When anything takes time to travel from one place to another, it can
only be one of two things. It must either be an actual object which is
transferred bodily from place to place, like a letter sent by post or
a bullet fired from a gun, or else it must be a wave-motion created in
a medium of some kind which fills all space. The illustrious Newton
suggested an hypothesis or supposition as to the nature of light, viz.
that it consists of small _corpuscles_ shot out violently from every
luminous body. It is a wonderful testimony to Newton’s exalted powers
of thought, that the most recent investigations show that hot and
luminous bodies, such as the sun and a lamp, are in fact projecting
small bodies called corpuscles into space, but there is abundant
proof that these are not the cause of light. Subsequently to the date
of Newton’s speculations on the nature of light, the alternative
hypothesis was developed, viz. that it consists in a wave-motion in a
universally diffused medium called the æther. A great gulf, however,
separates mere conjecture and speculation from that accumulation of
rigid proof which scientific investigation demands, and hence, although
this conception of an æther had arisen as an hypothesis in the minds of
Huyghens, Descartes, and many other philosophers, it was not accepted
by Newton, and the general assent of scientific investigators to the
hypothesis of a universal æther was long deferred. The philosopher
to whom we owe the crucial demonstration of the validity of, and
indeed necessity for, this assumption was Dr. Thomas Young, the first
Professor of Natural Philosophy in the Royal Institution of London.
Young was a man whose exalted intellectual powers were not properly
appreciated by the world until after his decease. His researches in
physical optics alone are, however, epoch-making in character. He it
was who first gave a proof that under some circumstances it is possible
for two rays of light to destroy each other, and thus produce darkness.
Briefly described, the experiment is as follows: If a beam of light of
one colour, say red, proceeding from a single source of light, falls
upon a screen in which are two small holes very near together, we
shall obtain from these holes two streams of light originating, as it
were, from closely contiguous sources. If we then hold a white screen
not far from these holes, and receive on it the light proceeding from
them, we shall find that the screen is marked with alternate bands
of red light and black bands. If we cover up one of the small holes,
the black bands vanish and the screen is uniformly illuminated. Young
pointed out that this effect was due to _interference_, and that the
difference of the distances from any black band to the two holes was an
exact odd multiple of a certain small distance called the wave-length
of the light. If light is a substance, no possible explanation can be
given which will enable us to account for the combination of two rays
of light producing darkness at their meeting-point. If, on the other
hand, rays of light consist of waves of some kind in a medium, then,
as we have seen in the case of water ripples and air waves, it is
quite possible for two wave-trains to annihilate each other’s effect
at a certain point, if a hollow of one wave-train reaches that place
coincidently with a hump belonging to the other.

Accordingly, the experiment of producing _interference_ between
two sets of light rays so that they destroy each other is a strong
argument in favour of the view that light must consist in some kind of
wave-motion existing in a medium susceptible of supporting it, filling
all space, and existing in all transparent bodies. This medium we call
the _luminiferous æther_.

The term “æther,” or “ether,” has been in use for many centuries to
express the idea of something more rare, tenuous, or refined than
ordinary matter.

The classical writers employed it to describe the space above the
higher regions of the atmosphere, which was, as they; supposed,
occupied by a medium less palpable or material than even air itself.
Thus Milton, speaking of the downfall of the enemy of mankind
(“Paradise Lost,” Book I. line 44), says—

        “... Him the Almighty Power
    Hurled headlong, flaming, from the _æthereal_ sky
    With hideous ruin and combustion down.”

But although poets and philosophers had made free use of the notion
of an æther, or even assumed the existence of several æthers, the
conception did not become a serious scientific hypothesis until it was
experimentally shown by Young that the phenomena of optics imperatively
demand the assumption of such a medium in space which is not ordinary
matter, but possesses qualities of a special kind, enabling it to have
created in it waves which are propagated with the enormous velocity
of nearly one thousand million feet a second. The proofs which have
accumulated as to the validity of this hypothesis to explain optical
effects show that this medium or æther must exist, not only in free
space, but also in the interior of every solid, liquid, or gaseous
body, although its properties in the interior of transparent bodies are
certainly very different from those which it possesses taken by itself.
This æther fills every so-called vacuum, and we cannot pump it out from
any vessel as we can the air. It occupies, likewise, all celestial
space, and suns and stars float, so to speak, in an illimitable ocean
of æther. We cannot remove it from any enclosed place, because it
passes quite easily through all material solid bodies, and it is for
the same reason intangible, and it is not possessed of weight. Hence
we cannot touch it, see it, smell it, taste it, or in any way directly
appreciate it by our senses, except in so far as that waves in it of a
certain kind affect our eyes as light.

The fact that there is such a space-filling æther is, therefore, only
to be deduced by reasoning from experiments and observations, but it is
not directly the object of our sense-perceptions in the same way that
water or air can be. Nevertheless, there is abundant proof that it is
not merely a convenient scientific fiction, but is as much an actuality
as ordinary gross, tangible, and ponderable substances. It is, so to
speak, matter of a higher order, and occupies a rank in the hierarchy
of created things which places it above the materials we can see and
touch.

The question we have next to discuss is—What are the fundamental
properties of this æther? and what are the terms in which we must
describe its qualities? In order to answer these questions, we must
direct attention to some electrical effects, since it has been shown
that most of the electrical phenomena, like those of optics, point
to the necessity for the assumption of a similar universal medium,
different from ordinary matter. Abundant proof has been gathered in,
that the electro-magnetic medium and the luminiferous æther are one and
the same.

We are met at the very outset of our electrical studies by the term
_electric current_. Most of us know that the operation of electric
telegraphs and telephones, electric lamps and electric railways, depend
upon this employment of an agency called an electric current.

The question then arises—What _is_ an electric current? and the
answer to this question is not easy to give in a few words. We can,
however, begin by explaining what an electric current can do, and how
its presence can be recognized. Before me on the table is a spiral of
copper wire, and in this wire, by special means, I can create what we
call an electric current. I shall ask you to notice that when this is
done two effects are immediately produced. In the first place, the wire
becomes _hot_, and, secondly, it becomes _magnetic_. The fact that it
is hot is evident, because it is now nearly red hot, and is visibly
incandescent in the dark. If we dip the wire in iron filings, you will
see that these cling to the wire and are taken up by it, just as when
an ordinary steel magnet is substituted for the wire. The copper wire,
when traversed by the current, also attracts a compass needle, and we
thus demonstrate in another way its magnetic quality.

Whenever, therefore, we find these two states of heat and magnetism
present together in and round a wire, we may take it as an indication
that it forms part of a circuit through which an electric current is
flowing. An electric current is a physical state or condition which can
only exist in or all along a closed path which is called an electric
circuit. This electric circuit may consist of a metallic wire, or, as
we generally call it, a conductor, or, as we shall see, it may also in
part consist of what is usually called a non-conductor.

It is necessary, in the next place, to point out that an electric
current has a directive quality. It belongs to that category of things
like forces and movements, which have direction as well as magnitude.
It is not completely defined by the answer to the question—How much? We
must also ask—In what direction? The direction of an electric current
is settled by holding a small compass needle near to the conductor or
wire in which the current exists. The little magnet will set itself
with its north pole in one direction or in the opposite, _across_ the
wire. That is to say, the axis of the compass needle places itself at
right angles to that of the wire. The direction of the electric current
is decided in accordance with the following conventional rule: Imagine
yourself placed with your arms extended straight out like a cross,
and that the wire conveying the current is placed before your face in
a vertical position. Imagine, also, that the position in which the
compass needle naturally sets when held between you and the wire is
such that its North pole is on your right-hand side. Then the current
would be said to move _upwards_ in the wire. A current which is always
in one and the same direction in a wire is called a _continuous_,
_direct_, or _one-way_ current.

A current which periodically changes its direction so that it is first
in one direction and then in the other is called an _alternating_ or
_two-way_ current.

I can now show you two experiments, the employment of which will
enable us always to decide whether a current in a wire is a one-way
or a two-way current. In the first experiment you see a copper wire
stretched between the poles of a powerful horseshoe magnet. When a
one-way current is sent through the wire, it is pulled either up
or down, like a fiddle or harp string being plucked by the finger.
If, however, we send a two-way current through the wire, it moves
alternately up and down, and vibrates just like a harp-string when
plucked and left to itself.

The next experiment gives us, however, a more convenient method of
ascertaining the presence in a wire of an alternating or two-way
electric current. If two wire circuits are laid parallel to each
other, and we send through one of these an electric current, then,
in accordance with Faraday’s most notable discovery, we find that
the beginning or the ending of the one-way current in the first
wire gives rise at the moment to a transitory current in the second
wire. If, however, we pass through the first wire, which we call the
primary circuit, a two-way current, then, since this is, so to speak,
continually beginning and ending, we have a similar alternating or
two-way electric current produced in the secondary circuit.

This fact may be most neatly and forcibly illustrated by the employment
of the following pieces of apparatus: An insulated wire is wound many
times round a great bundle of iron wire, thus forming what is called
an electro-magnet. Through this wire is passed a strong alternating
electric current which reverses its direction 160 times a second.

Over the top of the electro-magnet we hold another coil of insulated
wire, the ends of which are connected to a small electric glow lamp
(see Fig. 64). When held near to the pole of the electro-magnet, we
find the little lamp in the secondary coil lights up brilliantly,
because there is created in that circuit a secondary or induced
alternating electric current by the action of the other current in the
primary or electro-magnet circuit. Thus we see that one alternating
electric current can, so to speak, give birth to another in a second
circuit held parallel to the first. In like manner this secondary
current can give rise to a third or tertiary current, and the third to
a fourth, and so on indefinitely.

[Illustration: FIG. 64.]

We can always make use of this test to ascertain and prove the
existence of an alternating current in any electric circuit. If we
provide a coil of insulated wire, having its ends connected to a small
incandescent lamp, and hold this lamp coil or secondary circuit near to
and parallel with any other circuit in which we suspect the existence
of an alternating electric current, and if the lamp in the secondary
circuit lights up, then we can say with certainty that there is an
alternating or two-way electric current in the first circuit.

Having, then, indicated briefly the effects which are produced by an
electric current when it exists in a conducting circuit, and the way in
which we can determine its presence and direction, we must pass on to
discuss some other facts connected with its production.

It is a maxim in philosophy that every effect must have a cause; hence
we must assign a name to the cause of the effect we call electric
current. This cause we call _electromotive force_.

Electromotive force may be created in many ways, and time will
not permit us to refer to these in detail, but it must be taken
that electrical machines, batteries, and dynamos are all of them
appliances for creating electromotive force, or, as it is sometimes
called, electric pressure, just as various kinds of force-pumps
are contrivances for creating pressure in fluids. We find that
electromotive force acts differently on various substances when they
are subjected to its operation. In some substances electromotive
force produces a continuous electric current, and in these cases the
material is called a _conductor_. In other cases electromotive force
creates what is called _electric strain_, or electric displacement,
and these substances are generally called _non-conductors_. The
difference between conductors and non-conductors can be illustrated by
a mechanical analogy. Consider, for instance, a force-pump consisting
of a cylinder with a tightly fitted piston; suppose the bottom of the
pump-tube to be closed by a pipe having in it a tap. If we open the
tap and apply pressure to the piston, we can force out of the pipe a
current of air which continues to flow as long as the piston is being
pressed down. In this case the pressure on the piston corresponds to
an electromotive force, and the current of air flowing out corresponds
with the electric current in the electrical circuit.

Supposing, however, that we shut the tap and then attempt to force down
the piston, we find at once an elastic resistance to motion. The piston
can be pressed down a little way, compressing the air and thus creating
a strain; but if the pressure is removed the piston flies up again, on
account of the compressional elasticity of the air. In this operation
we have a mechanical illustration of the action of electromotive force
on a material such as glass or air, which is called a non-conductor, or
sometimes a dielectric. In these bodies electromotive force produces
an electric strain, just as the mechanical force produces in the air
enclosed in the cylinder a mechanical strain. When the tap at the
bottom of the cylinder is closed, we can, by applying pressure, force
down the piston a little way, but that movement cannot be continued,
because we are building up an opposing pressure due to the elasticity
of the air.

It is possible to show you an electrical experiment which has a close
analogy with the above simple mechanical experiment. Here is a glass
tube which has platinum wires sealed into the two ends, and the tube
is partly exhausted of its air. Such a tube is called a _vacuum tube_,
and when an electrical current is passed through this rarefied air,
it causes it to become luminous, and, as you see when the room is
darkened, the tube is filled with a reddish light. A tube, therefore,
of this kind is very convenient in some experiments, because we can, in
effect, see the electric current passing through it. If I connect one
end of this tube with the earth, and the other with the terminal of an
electrical machine, and if then the handle of the electrical machine
is turned, the tube will continue to glow as long as the electrical
machine is rotated. The electrical machine must be regarded as a pump
which is forcing something called electricity through the vacuum tube,
and as long as the pressure is continued the current flows.

This corresponds with the case in which the tap at the bottom of the
force pump was open and a continuous current of air could be forced out
of it by pressing down the piston. Supposing, however, that I insert
between the vacuum tube and the electrical machine a plate of glass,
which is covered over with tinfoil on the two sides such an arrangement
constitutes what is called a condenser, or Leyden pane. We now repeat
the experiment, and begin to turn the handle of the electrical machine.
You will notice that the vacuum tube glows as before, and is filled
with a reddish light for a short time, but as we continue to turn the
handle this dies away, and after a few moments there is no further
evidence of an electric current passing through the vacuum tube.

You will understand, therefore, that an electric current cannot be
caused to flow for an indefinite time in one direction through a
glass plate, although, by the application of electromotive force, it
does evidently, as you see, pass through it for a short time. This is
analogous to the operation of the force-pump when the tap at the bottom
is closed. We then find that we can move the piston down a little way,
compressing or straining the enclosed air, but that its motion is
soon stopped by an opposing resistance. We therefore say that in the
glass plate we have created an _electric strain_ by the action of the
electromotive force, just as we describe the effect of the mechanical
pressure on the air by saying that we have created a compression in it.

But there is an additional resemblance between the electrically
strained glass and the mechanically compressed air. When any elastic
object has been strained, and is suddenly released, it regains its
position of equilibrium by a series of oscillations or vibrations.
Thus, for instance, if we take a strip of steel and fix one end of it
in a vice, and pull the other end on one side and then release it, the
steel regains its position of equilibrium only after having executed a
series of diminishing swings to and fro.

In the same way, if we place some mercury or water in a glass tube bent
in the shape of the letter ⋃, and displace the liquid by blowing
into the tube, then, on releasing the pressure suddenly, the liquid
will regain its position of equilibrium by a series of oscillations
which die gradually away. You will not have any difficulty in seeing
that this is really due to the inertia of the material, whether it be
steel or mercury or water which is displaced. In an exactly similar
manner, we find that when we have produced an electric strain in a
sheet of glass by the application of electromotive force, and if we
then remove the electromotive force and connect the two tinfoil or
metal surfaces by means of a piece of wire, the electric strain in the
glass disappears with a series of _electric oscillations_; that is to
say, the electric strain in the glass does not disappear or die away
gradually, but it is alternately reversed, at each reversal the strain
becoming less and less in magnitude. The result of this oscillatory
strain in the glass is to produce in the connecting wire an alternating
electric current.

[Illustration: FIG. 65.]

A very familiar and simple piece of electric apparatus is that known as
a Leyden jar (see Fig. 65). A Leyden jar consists of a glass vessel,
the outside and inside surfaces of which are respectively covered with
tinfoil. If we apply to these two surfaces an electromotive force,
we produce what is called an electric charge in the jar, which in
reality consists in a state of electric strain in the walls of the
vessel. When the jar is charged, if we connect together, by means of
a thick wire, the outside and the inside tinfoil surfaces, we have a
bright spark produced at the moment of making contact, and we have
a rapidly alternating electric current produced in the connecting
wire. If this connecting wire has a low resistance—in other words,
is a very good conductor—then this electric spark consists, not in a
discharge of electricity uniformly in one direction, but of a series of
rapidly succeeding sparks which are really discharges of electricity
or electric currents passing through the air alternately in opposite
directions. This can be demonstrated by taking a photograph of the
electric spark on a rapidly revolving photographic plate or strip. You
are probably all familiar with the sensitive photographic film which
is employed in hand cameras, such as the kodak. If a strip of this
sensitive film is bound round the edge of a wheel, and if the wheel is
set in very rapid rotation, and if we throw on the film, by means of a
lens, an image of an oscillatory electric spark, it will be clear to
you that, if the spark is continuous, it will produce upon the moving
photographic film an image which will be of the nature of a broad band.
If, however, the electric spark is intermittent, then this photographic
image will be cut up into a series of bars or patches, each one of
which will correspond to a separate image of one constituent of the
oscillatory spark.

Photographs of oscillatory electric sparks have in this way been taken
by many observers, and have afforded a demonstration that the electric
discharge of a Leyden jar, when taken through a wire of low resistance,
is not a continuous movement of electricity in one direction, but a
rapidly alternating electric current through the wire, forming the
oscillatory spark, and corresponding with an equally rapid alternating
electric strain in the glass, both strain and current dying gradually
away.

Although this operation takes a long time to describe, yet,
nevertheless, an oscillatory spark consisting of 20 or 30 electric
oscillations may all be over in the ¹⁄₁₀₀₀₀ or even ¹⁄₁₀₀₀₀₀ second.
In the photograph now thrown upon the screen (see Fig. 66) you see
the image of an oscillatory electric spark, each oscillation of which
lasted ¹⁄₇₀₀₀ second. We can, however, give a still further proof that
the discharge of a Leyden jar or electric condenser is, under some
circumstances, oscillatory, in the following manner:—

[Illustration: FIG. 66.—A photograph of an oscillatory electric spark
(Hemsalech).]

You have already seen that an alternating or two-way electric current
existing in one circuit can produce another alternating or two-way
electric current in a neighbouring circuit. Before me, on the table, is
an arrangement by which a battery of six Leyden jars, L, is continually
being charged and discharged through a thick wire which is wound a
dozen times round a square wooden frame, P (see Fig. 67). In proximity
to this wooden frame there is another wooden frame, S, also having
on it a dozen or two turns of insulated wire; the circuit of this
last conductor is completed by a small incandescent lamp, G. You will
notice that when the Leyden jars are charged and discharged rapidly
through the primary conductor, the little glow-lamp of the secondary
circuit lights up brilliantly, and, in virtue of what has already
been explained, you will see that this experiment is a proof that the
discharge of the Leyden jars through the primary circuit must consist
in an alternating or two-way current; in other words, it must be
oscillatory.

[Illustration: FIG. 67.]

A still further proof may be given that the discharge of a Leyden jar
or condenser, when taking place through a low-resistance circuit, is
oscillatory in the following manner:—

We employ the vacuum tube that we brought to your notice a few moments
ago. When an electric current is sent always in the same direction
through such a tube, it is well known that the two ends of the tube are
not alike in appearance. The tube, as you have seen, is filled with a
luminous glow; but this glow is interrupted, forming what is called
a dark space near one terminal of the tube, this terminal being that
which is termed the negative pole. Accordingly, this unsymmetrical
appearance in the light in the tube is a proof that the electric
current is passing through it always in one direction. We can, however,
vary the experiment, and instead of illuminating the tube by means of a
direct-discharge or induction coil, which is always in one direction,
we are able to illuminate it by means of a rapid series of discharges
from a Leyden jar. You will then see that the glow-light in the tube is
symmetrical—the tube, in other words, is alike at both ends; and this
shows us that the discharge from the tube under these circumstances
must be alternating—that is, first in one direction and then in the
other.

Whilst this apparatus is in use, we can show you with it two other
very pretty experiments dependent upon the fact that the discharge
of a Leyden jar through a low-resistance circuit is alternating or
oscillatory. A moment ago we employed this oscillatory discharge in one
circuit to induce a secondary oscillatory discharge in another metallic
circuit, and this secondary oscillatory or alternating current was
made manifest by its power to illuminate a little incandescent lamp.
If, however, we place a large glass bulb, P, which has been partly
exhausted of its air, in the interior of the primary discharge coil,
you will see that this primary oscillatory discharge of the Leyden jar
is able to create in the glass bulb a brilliant luminous ring of light
(see Fig. 68). This is called an _electrodeless discharge_, and it is
due to the fact that the rapidly oscillatory current existing in the
wire wrapped round the bulb creates a similar oscillatory discharge in
the rarefied air in the interior of the bulb, this being a conductor,
and thus renders it luminous along a certain line.

The production of these electrodeless discharges in rarefied gases has
been particularly studied by Professor J. J. Thomson.

Another experiment illustrating what is called the inductive
transformation of electrical oscillations is in the arrangement
commonly called a Tesla coil. Such a coil is now before you. It
consists of a long coil of insulated wire which is placed in the
interior of a tall glass vessel, and on the outside of this glass
vessel is wound another insulated and much longer wire. If the
alternating or oscillatory discharge of a Leyden jar is allowed to take
place through the thicker wire in the interior of the glass cylinder,
it generates in the outer or secondary wire a very powerful alternating
or oscillatory electromotive force, and we see that this is the case
by connecting the ends of this secondary circuit to two insulated
brass balls, between which a torrent of sparks now passes. We may vary
the experiment by connecting the ends of the secondary circuit of the
Tesla coil to two insulated concentric rings of thin, bare, brass
wire, and then, when the room is darkened, we see the space between
these rings filled with a brilliant purple light, which is due to the
discharge taking place through the air under the action of the rapidly
oscillatory electromotive force generated in the secondary circuit.

[Illustration: FIG. 68.—An electrodeless discharge in an exhausted
bulb.]

I trust that these experiments will have produced a conviction in your
minds that the release of the electric strain in the glass _dielectric_
of a Leyden jar results in the production of electric oscillations
or rapidly alternating electric currents in the metallic circuit
connecting the two surfaces, just as the sudden release of a compressed
spring results in a series of mechanical oscillations.

We may here remark that any arrangement of two metallic plates with
a sheet of insulator or non-conductor between them is called a
_condenser_. Thus, a condenser can be built up by coating a sheeting
of glass on its two sides with tinfoil, or in place of glass we may
use mica, paraffin paper, or any other good non-conductor. We may
even use air at ordinary pressures; and thus, if two metal plates are
placed near to one another in air, the plates being both insulated—that
is, supported on non-conductors,—this arrangement constitutes what is
called an air condenser. An air condenser, therefore, is virtually only
a kind of Leyden jar in which the glass is replaced by air, and the
tinfoil by two stout metal plates.

[Illustration: FIG. 69.—Hertz oscillator.]

I must now proceed to describe and show you a particular kind of air
condenser which was invented by the late Professor Hertz, and, in
consequence, is called a Hertz oscillator (see Fig. 69). It consists
of two square or round metal plates which are carried on glass or
ebonite legs, and these plates have short, stout wires attached to
them, ending in brass knobs. If these plates are placed in line with
one another, they constitute an air condenser of a very peculiar
kind, the two brass plates correspond with the tinfoil surfaces of a
Leyden jar, and the air all round them corresponds with the glass of
the jar. Supposing the plates are so arranged that the brass knobs
are about ¹⁄₄ inch apart, or rather less, if then we connect these
two brass plates to the secondary terminals of an induction coil or
electrical machine capable of giving long sparks in air, we shall
find, when the electrical machine or induction coil is set in action,
that a very bright crackling spark passes between these little knobs,
and with proper experience it is easy to adjust the distance from
the knobs so that this spark is an oscillatory spark. Under these
circumstances, what is taking place is as follows: In the first place,
an electromotive force is acting between the two plates, and creating
an electric strain in the air all round them along certain lines, and
also between the two knobs. The air, and all other gases like it,
possess this peculiar property, that whilst at ordinary pressures
they are nearly perfect non-conductors, yet, nevertheless, if they
are subjected to more than a certain electric pressure, they pass
instantly into a condition in which they become very good conductors.
Accordingly, if we progressively increase the electromotive force
acting between the plates, up to a certain point the whole arrangement
acts like a Leyden jar; but there comes a moment when the air between
the knobs breaks down and passes from a non-conductive to a conductive
condition. The two plates then resemble at that moment the surfaces of
a charged Leyden jar which are connected together by a good conductor,
and, as we have already seen, under those circumstances the discharge
is oscillatory, and the electric strain in the non-conductor, or
dielectric, viz. the air around the plates, dies away by a series of
rapidly alternating electric strains in opposite directions.

Now, at this point I must recall to your recollection that, in speaking
about the production of air waves, I pointed out that one condition
essential to the production of an air wave was that there must be a
very sudden application or release of the air-pressure, such as is
caused by an explosion or escape of compressed air. We cannot produce
an air wave by moving any object such as a fan slowly to and fro
through the air. In order to produce an air wave we must strike the
air a very sudden blow, or, which comes to the same thing, we must
apply and remove a very sudden pressure to the air; and under these
circumstances we start into existence an air wave, which travels away
from the vibrating or rapidly moving body, and continues its journey
out into surrounding space.

I want to show you that, in the case of the Hertz oscillator, these
very sudden reversals of electric strain in the air or space round
about it, which take place at the moment when the oscillatory spark
passes between the knobs, creates in a similar manner what is called
an _electric wave_, which travels out into the space around. The point
you must appreciate is, that just as an air wave conveys away to
distant places a rapidly alternating compression made in the air by a
vibrating body at a particular place, so an electric wave conveys away
to distant places an alternating electric strain, which is originated
at some point in the medium by the oscillatory discharge of some
form of condenser. Before, however, we can demonstrate this fact, we
must have some means for detecting the influence of what we call an
electric wave. You will remember that, in the case of experiments with
air waves, I used a sensitive flame in order to make evident to you the
presence of waves in the air which you could not see, so here I must
use an appropriate detector for electric waves, the operation of which
will render evident to us the existence in the space round our electric
oscillator of the electric waves we cannot see.

Time will not permit me to discuss all the different forms of
electric-wave detector which have been invented. For our present
purposes we must limit ourselves to the description of one plan, which
depends on the remarkable fact that finely powdered dry metal or
metallic filings are non-conductors of the electric current until they
are subjected to an electromotive force exceeding a certain value, when
the metallic filings at once pass into a conductive condition.

If you recall the remarks made just now in connection with the special
electrical properties of air and other gases, you will notice that
there is a remarkable similarity between the electrical behaviour of
air at ordinary pressures to electromotive force, and that of a loose
mass of metallic filings. Both the air and the metallic filings are
non-conductors as long as the electromotive force acting on them does
not exceed a certain value, but if it exceeds this critical value,
they pass at once into a conductive condition. The fact that pieces
of metal in loose contact with one another behave in a similar manner
was discovered more than twenty years ago by the late Professor D. E.
Hughes, who, as you may perhaps know, was the inventor of a printing
telegraph, the microphone, and many other most important electrical
instruments. Professor Hughes was a great genius, and in many respects
in advance of his age. He it was who undoubtedly discovered that an
electric spark has the power of affecting at a distance the electric
conductivity of a metallic junction consisting of two metals in loose
contact.

The peculiar behaviour of metallic filings under electromotive
force, and under the influence of electric sparks at a distance, was
subsequently rediscovered by Professor Branly; and the effect of an
electric oscillatory spark in changing the conductivity of a light
metal contact was also rediscovered by Sir Oliver Lodge, and the
phenomena investigated by many other observers. I can show you the
experiment on a large scale in the following manner:—

[Illustration: FIG. 70.—A metal disc-coherer.]

I have here a number of aluminium discs, the size of sixpences, stamped
out of thin metal, and these are arranged in a sort of semi-cylindrical
trough between two terminal screws, so that the discs are very lightly
pressed together. Under these circumstances the pile of metal discs
is not a conductor, and it will not pass the electric current from a
battery which is joined up in series with an electric bell and the pile
of discs (see Fig. 70). Supposing, however, that I make an oscillatory
spark in proximity to this pile of metal discs, as I can do by taking
the discharge from a large Leyden jar near it; the pile of discs at
once becomes a conductor; the electric current from the battery can
then pass through it, and the bell rings. Such an arrangement has been
named by Sir Oliver Lodge a _coherer_, because, under the action of
the oscillatory spark, the discs cohere or stick together. We can
separate the discs by giving them a sharp rap, and then the operation
can be again repeated.

A much more sensitive arrangement can be made by taking a small box
of wood through the bottom of which pass two nickel wires which are
parallel to one another, but not in contact. In this box is placed
a small quantity of very finely powdered metallic nickel or nickel
filings, and if the quantity of these filings is properly adjusted,
it is possible to make an arrangement which possesses the property
that there is no conductivity between the two nickel wires under
ordinary circumstances, but that they become conductively connected to
one another the moment an oscillatory electric spark is made in the
neighbourhood. We shall speak of this contrivance as an _electric wave
indicator_, and we shall employ it in subsequent experiments to enable
us to detect the presence of an electric wave.

We must then return for a moment to the consideration of the production
of electrical oscillations in circuits of various kinds. I trust it has
been made plain to you that if two metallic surfaces, separated by a
non-conductor such as air or glass, are acted upon by an electromotive
force, the non-conductor becomes electrically strained. Another way of
stating this is to say that a positive charge of electricity exists
on one metal surface, and a negative charge on the other. The only
objection which can be raised to expressing the facts in this manner
is that it fastens attention rather upon the conductors than upon
the insulator, which is the real storehouse of the energy. If these
two metal surfaces are then connected together by a conductor of low
resistance, the charges disappear by a series of oscillations, and
the result is an electric current in the conducting circuit connecting
the plates, which rushes backwards and forwards in the circuit, but
gradually diminishes in strength until it completely dies away. You
may picture to yourselves the electrical effect as analogous to the
following experiment with two air-vessels: Supposing we have two
strong steel bottles, into one of which we compress a quantity of
air, and in the other we make a vacuum by pumping out nearly all the
air. These vessels would correspond with two conductors, one charged
with positive electricity and the other with negative. Imagine these
vessels connected by a wide pipe in which is placed a tap or valve,
which can be opened suddenly so as to permit the air to rush over from
the full vessel to the empty one. If this is done, it is a matter of
experience that the equality of pressure between the two vessels is not
at once established, but in virtue of the inertia quality of the air,
it only takes place after a series of oscillations of air in the pipe.
In rushing over from the full vessel to the empty one the air, so to
speak, overshoots the mark, and the state of the vessels as regards
air-pressure is exactly interchanged. The air then rushes back again,
and it is only after a series of to-and-fro movements of the air in the
pipe that an exact equality of pressure in the two vessels is attained.

The electrical actions which take place in connection with an electric
discharge between two conductors, one of which is charged positively
and the other negatively, are exactly analogous to the above-described
experiment with two air-vessels, one of which has air in it under
compression, and the other has had the air removed from it. You will
notice, however, that the oscillations of the air in the pipe in the
air-vessel experiment depend essentially upon the fact that air is a
substance which has _inertia_, or mass, and you will naturally ask
what is it which has inertia, or its equivalent, in the electrical
experiment? The answer to this question is as follows: Every electric
circuit has a quality which is called _inductance_, in virtue of which
an electric current cannot be started in it instantly, even under any
electromotive force, and conversely when the current is started it
cannot be immediately brought to rest. From the similarity of this
quality of the circuit to the inertia of ordinary material substances,
it has been sometimes called the _electric inertia_ of the circuit.
The word “inertia” really means inactivity, or laziness, but the term
as used in mechanics implies something more than mere inactivity. It
involves the notion of a persistence in motion when once the body is
set moving.

When a material substance is in motion it possesses energy, and has the
power of overcoming up to a certain point resistance to its motion.
This energy-holding power, or capacity for storing up energy of motion,
which is characteristic of all material substances, is a consequence
of their inertia. The fact is otherwise expressed by stating that the
_mass_ of a material substance is one element in the production of
energy of motion.

An electric current in one sense resembles a moving substance,
for it is an exhibition of energy in association with matter. The
current-energy is measured by the product of two factors: one is half
the square of the current-strength, and the other is the inductance
of the circuit. The analogy between the two cases may be more exactly
brought out by pointing out that the energy of motion of a moving body
is measured by the product of its mass and half the square of its
velocity. Hence it follows that the power of overcoming resistance, or,
in other words, of doing useful work or mischief, which is possessed
by a heavy body in motion is proportional, not simply to its speed,
but to the square of its speed. If a bullet, moving with a certain
speed, can just pass through one plank 1 inch thick, then, when moving
with twice the speed, it will pass through four such planks, and
if moving with three times the speed, through nine planks of equal
thickness. The energy of an electric current is similarly measured by
the product of the inductance of the circuit and half the square of
the current-strength. In the same or equal circuits two currents, the
strengths of which are in the ratio of 1 to 2, have energies in the
ratio of 1 to 4. The greater, therefore, the inductance of an electric
circuit, the greater is the tendency of an electric current set flowing
in it to run on after the electromotive force is withdrawn. The
inductance of a circuit is increased by coiling it into a coil of many
turns, and decreased by stretching it out in a straight line.

The important idea to grasp in connection with this part of the subject
is that, just as there are two forms of mechanical energy, viz. energy
of mechanical strain and energy of motion, so also there are two
forms of electrical energy, viz. energy of electro-static strain and
electric-current energy.

If, for instance, we bend a bow or extend a spring, this action
involves the expenditure of mechanical energy, or work, and the energy
so spent is stored up as energy of strain, or, as it is called,
distorsional energy in the distorted bow or spring. When, however,
the bow communicates its energy to the arrow or the spring to a ball,
and so sets these in motion, we have in the flying arrow or ball a
store of energy of motion. If a slip of steel spring is fixed at one
end, and then set in vibration, we have a continual transformation of
energy from the motional to the distorsional form. At one moment the
spring is moving violently, and at the next it is bent to its utmost
extent; and these states succeed each other. The store of energy in the
vibrating spring is, however, gradually frittered away, partly because
the continual bending of the steel heats it, and this heat dissipates
some of the energy; but also because the spring, if vibrating quickly
enough, imparts its energy to the surrounding air, and creates air
waves, which travel away, and rapidly rob the vibrating spring of its
stock of energy.

In a precisely similar manner all electrical oscillation effects depend
upon the fact that electric energy can exhibit itself in two forms. In
one form it is electro-static energy, or energy of electric strain. In
this form we have it when we charge a Leyden jar. The glass is then,
as explained, in a state of electrical strain, and its condition is
analogous to that of a stretched spring. The same holds good when we
have two conductors insulated from each other in air. We have then
an electrical strain in the air. It is important, however, to notice
that, since a perfect vacuum can support electric strain, it follows
that, in the cases where air or glass constitute this non-conductor, or
dielectric, of a condenser, the whole of the energy cannot be stored in
the material substance, the glass or the air. The real storehouse of
the energy is the æther, as modified by the presence of the ordinary
matter in the same place.

When we discharge the Leyden jar or condenser, the electro-static
energy in the dielectric disappears, and we obtain in its place an
electric current in the connecting conductor; and this, as described,
is an exhibition of energy in another form. If the resistance of the
connecting conductor is small, then we have electrical oscillations
established which consist in an alternate transformation of the energy
from an electro-static form to the electric-current form.

At each oscillation some energy is frittered away into heat in the
conductor, and if the conductor and condenser have a special form,
energy may be rapidly removed from the system by the electric waves
which are formed in the surrounding æther or dielectric. These waves
consist in the propagation through the medium of lines of electric
strain, just as an air wave consists in the propagation through the
air of regions of air-compression, or a water wave consists in the
propagation of an elevation on the surface.

Returning again to the discussion of the production of electrical
oscillations, it is necessary to consider a little more in detail the
manner in which we can create an electrical oscillation in what we have
called an _open electric circuit_. Let me begin with an experiment, and
it will then be easier for you to understand the particular points to
be explained.

[Illustration: FIG. 71.]

Before me are two long brass rods, each of them about 5 feet in length,
and the ends of these rods are provided with polished brass balls (see
Fig. 71). The rods are placed in one line and supported on pieces
of ebonite, and are so fixed that the two balls are separated from
one another by a space of about ¹⁄₄ inch. The two rods constitute,
therefore, two insulated conductors. These rods are connected by
coils of wire with the terminals of an instrument called an induction
coil, which I shall not stop to describe, but which you may regard
as a kind of electrical machine for producing electromotive force.
If we set the induction coil in action, it creates between its
terminals an intermittent but very powerful electromotive force, which
gradually increases up to a certain value, at which it breaks down
the conductivity of the air-gap between the two balls. Let us think
carefully what happens as the electromotive force of the induction coil
is increasing. One of the rods is in effect being electrified with
positive, and the other with negative, electricity, and these charges
are increasing in magnitude. The two rods constitute, as it were, the
two coated surfaces of a kind of Leyden jar, or condenser, of which
the surrounding air is the non-conductor. Accordingly, by all that has
been previously explained, you will easily understand that there is an
electric strain in the air which exists along certain lines, called
lines of electro-static strain, and this state in the air is exactly
similar to the condition in which the glass of a Leyden jar finds
itself when the jar is charged. If we were to delineate the direction
of this electric strain by lines drawn through the space around the
rods, we should have to draw them somewhat in the fashion represented
by the dotted lines in Fig. 71. As the electrical state of the rods
gradually increases in intensity, a point is reached at which the air
between the balls can no longer maintain this strain, and it breaks
down and passes into a conductive condition. The state of affairs round
the rods is then similar to that of a Leyden jar being discharged. An
electric current is produced across the air-gap, moving from one rod to
the other, and the intensely heated air in between the balls is visible
to us as an electric spark. This spark, if photographed, would be found
to be an oscillatory spark. The electric current in the rods cannot
continue indefinitely: it gradually falls off in strength, but as it
flows it creates in the space around the rods an electric strain which
is in the opposite direction to that which produced it, although taking
place along the same lines.

After a very short time, therefore, the electrical conditions which
existed at the moment before the air broke down are exactly reproduced,
only the direction of the strain is reversed. In other words, the rod
which was positively electrified is now negatively, and _vice versâ_.
Then this state of strain again begins to disappear, producing in
the rod an electric current, again in the reverse direction; and so
the energy, which was originally communicated to the space round the
rods in the form of an electric strain, continually changes its form,
existing at one moment as energy of the electric current passing across
the spark gap, and the next moment as energy of electric strain. We
may ask why this state of things does not continue indefinitely, and
the answer to that question is twofold. First because the rods possess
a property called electrical resistance, and this acts towards the
electric current just as friction acts towards the motion of material
substances; in other words, it fritters away the energy into heat. So
at each reversal of the electric current in the rod a certain quantity
of the original store of energy has disappeared, due to the resistance.

There is, however, a further and more important source of dissipation
of energy, and this is due to the fact that an electrical oscillation
of this kind taking place in a finite straight circuit, or, as it
is called, an open electric circuit, creates in the space around an
electric wave. The rapid reversal of the electric strain in the air
results in the production of an electric wave, just as in the case of
an explosion made in air, the rapid compression of the air results in
the production of an air wave. It is not easy for those who come to the
subject for the first time to fully grasp the notion of what is implied
by the term “an electric wave.”

In the first lecture, you will perhaps remember, I pointed out that
the production of a wave in a medium of any kind can take place if
the medium possesses two properties. In the first place, it must
elastically resist some change or distortion, and, in the second place,
when that distortion is made it must tend to disappear if the medium
is left to itself, and in so doing the displacement of the medium must
overshoot the mark and be reproduced in the opposite direction, owing
to some inertia-like quality or power of persistence in the medium.

It would lead us into matters beyond the scope of elementary lectures
if we were to attempt to summarize all the evidence which exists
tending to show that the phenomena of electricity and magnetism
must depend upon actions taking place in some medium called the
_electro-magnetic medium_. All the great investigators at the beginning
of the last century, when electrical and magnetic phenomena were
beginning to be explored, came to this conclusion, and in the writings
of Joseph Henry, of Ampère, and of Faraday we find references again
and again to their conviction that the phenomena of electricity imply
the existence of a medium exactly in the same way as do the phenomena
of optics. It is only, however, in recent years that we have had
evidence before us, some of which will be reviewed in the next lecture,
which affords convincing proof that the luminiferous æther and the
electro-magnetic medium must be the same. The consideration of the
simplest electrical effects is sufficient to show that, if this medium
exists, it possesses at least two properties, one of which is that it
offers an elastic resistance to the production of electric strain in
it by means of electromotive force. A question which is sure to arise
in the minds of those who consider this subject carefully is, What is
the nature of an electric strain? And the only answer which we can give
at the present moment is that we must be content to leave the question
unanswered. We do not know enough yet about the mechanical structure
of the electro-magnetic medium, or æther, to be able to pronounce in
detail on the nature of the change we call an electric strain. It
may be a motion of some kind, it may be a compression or a twist, or
it may be something totally different and at present unthinkable by
us, but, whatever it is, it is some kind of change which is produced
under the action of electromotive force, and which disappears when the
electromotive force is removed.

Clerk-Maxwell, to whom we owe some of our most suggestive conceptions
of modern electricity, coined the phrase _electric displacement_ to
describe the change which we are here calling an electric strain.
One essential element in Maxwell’s theory of electricity is that an
electric strain or displacement, whilst it is being made or whilst
it is disappearing, is in effect an electric current, and it is for
that reason sometimes spoken of as a displacement current. We have
seen that every electric circuit possesses a quality analogous to
inertia, that is to say, when a current is produced in it it tends to
persist, and it cannot be created at its full value instantly by any
electromotive force.

Just as we cannot, at the present moment, pronounce in detail on the
real nature of electric strain, so we cannot say whether that quality
which we call inductance of a circuit is dependent upon a true inertia
of the electro-magnetic medium or on some entirely different quality
more fundamental.

It may be remarked, in passing, that there is a strong tendency in the
human mind to seek for and be satisfied with what we called mechanical
explanations. This probably arises from the fact that the only things
which we can picture to ourselves in our minds very clearly are
movements or changes in relative positions. If we can in imagination
reduce any physical operation to some kind of movement or displacement
taking place in some kind of material, we seem to arrive at a kind of
terminus of thought which is more or less satisfactory. We invariably
aim at being able to visualize an operation concerning which we are
thinking, and it requires some mental self-control to be able to
content ourselves with a general expression which does not lend itself
readily to visualization. There are plenty of indications, however,
that this mental method of procedure, and this endeavour to reduce all
physical operations to simple mechanics and to movements of some kind,
may in the end be found to be unjustifiable; and the time may arrive
when we may be more satisfied to explain mechanical operations in terms
of electrical phraseology rather than aim at dissecting electrical
effects into mechanical operations. Thus, for instance, instead of
speaking of electric inertia, it may be really more justifiable to
speak of the inductance of ordinary matter. The final terms in which
we endeavour to offer ourselves an explanation of physical events
are in all probability very much a matter of convenience and custom.
We may, however, for present purposes rest content by thinking of
the electro-magnetic medium as in some sense like a heavy elastic
substance which is capable of undergoing some kind of strain or
distortion, the said strain relieving itself as soon as the distorting
force is withdrawn; but, in addition, we must think of the medium
as possessing a quality analogous to inertia, so that as distortion
vanishes it overshoots the mark, and the medium only regains its
state of equilibrium at the particular point considered, by a series
of oscillations or alternate distortions, gradually decreasing in
amount. Any medium which possesses these two qualities has, in virtue
of explanations already given, the property of having waves created in
it, and what we mean by an electric wave is a state of electric strain
which is propagated through the æther with a velocity equal to that of
light, just as an air wave consists of a state of compression which is
propagated through the air with a velocity of 1100 feet a second.

[Illustration: FIG. 72.—Electric-radiation detector (Fleming).]

To sum up, we may then say that whenever rapid electrical oscillations
are created in open circuit, such as the two rods above described, the
arrangement constitutes a device for creating an impulse or effect
in the surrounding space called an _electric wave_ in the æther or
electro-magnetic medium; just as an organ-pipe or piano-string or other
musical instrument constitutes a device for creating waves in the air
by means of mechanical oscillations. The existence of these electric
waves, and their transference to distant places, can be rendered
evident by their action as already described upon finely powdered
metals. An apparatus which shows this effect very well is now arranged
before you. At one end of the table I have a pair of rods connected to
an induction coil, constituting a Hertz radiator, the action of which
has just been described. At the other end of the table are two similar
long rods, but their inner ends are connected to two small plates
of silver, which form the sides of a very narrow box, and between
these plates is placed a very small quantity of metallic powder. The
construction of this little box is as follows: A thin slip of ivory
has a little gap cut out of it (see Fig. 72), and on the two sides of
this slip of ivory are bound two silver plates bent in the shape of the
letter L, forming, therefore, a very narrow box with silver sides.
The two silver plates are connected to the two long rods. As already
explained, the metallic filings or finely powdered metal are not in
their ordinary condition an electric conductor. Accordingly, if we
connect to one of the silver plates one terminal of a battery joined in
series with an electric bell, the other end of the bell being connected
to the second silver plate, this battery cannot send a current through
the bell, because the circuit is interrupted by the non-conductive
metallic powder in the little box. Supposing, then, that we cause a
spark to pass between the balls of the radiator, and start an electric
wave. When this electric wave reaches the long rods connected to the
receiving arrangement, it sets up in these rods a sudden electromotive
force, and this electromotive force, as already explained, if of
sufficient magnitude, causes the loose mass of metallic filings to
pass from a non-conductive to a conductive condition. At that moment,
therefore, the battery is able to send an electric current through
the bell, and to cause it to ring. We can, however, stop the ringing
by giving the little box containing the metallic filings a tap,
which separates them from one another and interrupts the electric
conductivity. The function of the two rods connected with the receiver
is not quite the same as the function of the two rods connected to the
radiator. In order to create a vigorous electric wave, we must have a
radiator which possesses what is called considerable electric capacity,
and also considerable inductance, and we can only do this in general by
using long rods. On the other hand, at the receiving end the efficacy
of the rods is due to the fact that they, so to speak, add together the
electric strain taking place over a considerable distance; in other
words, the electromotive force which is set up in the receiving circuit
is dependent on the length of the rods. The longer, therefore, these
rods, the greater is the distance at which we can obtain the effect
which is shown to you with a given spark-length.

One point it is important to notice, and that is, that the rods of the
receiver _must_ be parallel to the rods of the radiator if we are to
obtain any effect at a distance. If we turn the rods of the radiator
round so that they are at right angles to those of the receiver, you
see that no sparks produced at the radiator balls cause the bell in
connection with the receiver to ring. The reason for this is because
the electric strain, which is propagated out into the space, exists
in a direction parallel to the radiator rods all along a line drawn
perpendicular to the rods through the spark-gap. The receiver rods
will not have electromotive force produced in them by this travelling
line of electric strain unless they are parallel to its direction.

It is to be hoped that the above explanations have afforded indications
of what is meant by an electric wave. On the other hand, there may be
many who find it exceedingly difficult to derive clear ideas when the
subject is presented to them clothed in such general terms as we have
been obliged to use.

It may assist matters, therefore, if, before concluding this chapter,
a word or two is said on the subject of recent investigation into the
inner mechanism of an electric current and an electric strain. It is
impossible to do this, however, without making mention, in the briefest
possible way, of modern researches into the constitution of matter. If
you can imagine yourselves furnished with a little crystal of ordinary
table salt, chemically called chloride of sodium, and the means of
cutting it up under an immensely powerful microscope, you might go on
dividing it up into smaller and smaller pieces. If this process could
be continued sufficiently far, we should ultimately obtain a very
small fragment of salt, which, if still further divided, would yield
two portions of matter not alike and not salt. This smallest possible
portion of salt is called a molecule of sodium chloride. Chemical facts
teach us that this molecule is made up of two still smaller portions of
matter, which are called respectively _atoms_ of chlorine and sodium.

We have good reason to believe that all solids, liquids, and gases are
composed of molecules, and these are built up of atoms, few or many.

In the case of some substances, such as _salt_, the molecule is very
simple and composed of two atoms. In other substances, such as albumen
or white of egg, the molecules are very complicated and composed of
hundreds of atoms. The word _atom_ means something which “_cannot be
cut_,” and until comparatively recent time the opinion was held that
atoms of matter were the smallest indivisible portions of matter which
could exist.

More than twenty-five years ago, Sir William Crookes showed, by
numerous beautiful experiments, that in a vacuum tube, such as you have
seen used to-day, a torrent of small particles is projected from the
negative terminal when an electric current is passed through the tube.
This stream of particles is called the cathode stream, or the cathode
radiator. Within recent times, Sir Joseph Thomson has furnished a proof
that this cathode stream consists of particles very much smaller than
chemical atoms, each particle being charged with negative electricity.
These particles are now called _corpuscles_, or _electrons_.

It has been shown that these electrons are constituents of chemical
atoms, and when we remove an electron from an atom we leave the
remainder positively electrified. An atom can, therefore, by various
means be divided into two portions of unequal size. First, a very
small part which is charged with negative electricity, and, secondly,
a remaining larger portion charged with positive electricity. These
two parts taken together are called ions, _i.e._ wanderers. The
negative ions, or electrons, or corpuscles, taken together constitute
what we call negative electricity, and up to the present no one has
been able to show that the corpuscle can be unelectrified. Hence the
view has been expressed that what we call electricity is a kind of
matter, atomic in structure, and that these negative ions or corpuscles
collectively are, in fact, the atoms of the electric fluid. These
corpuscles can move freely in the interior of some solids, moving
between the molecules of the solid just as little dogs can run about in
and amongst a crowd of people in a street. In these cases the substance
is called a conductor of electricity. In other substances the movement
of the corpuscles is more restricted, and these constitute the various
kinds of so-called non-conductors.

The corpuscle, being a small charge of negative electricity, creates
in all surrounding space a state called _electric force_. It is
impossible to expound this action more in detail without the use of
mathematical reasoning of a difficult character. Suffice it to say
that this electric force must be a particular condition of strain or
motion in the æther. If the corpuscle is in rapid motion, it creates
in addition another kind of strain or motion called _magnetic force_.
The electric force and the magnetic force are related to each other
in free space in such a manner that if we know the difference between
the values of the electric force at two very near points in space, we
are able to tell the rate at which the magnetic force is changing with
time in a direction at right angles to the line joining these near
points in space. We cannot specify in greater detail the exact nature
of these states or conditions which constitute magnetic force and
electric force, until we know much more than we do at present about the
real nature of the æther. The two fundamental qualities of the æther
are, however, its capacity to sustain these states we call the magnetic
force and the electric force.

The electrons of which we have spoken not only give rise to electric
and magnetic force when in movement, but they are themselves set
in motion by these forces. Thus electric force at any point moves
electrons placed at that spot, and an electron in motion is affected
and has its direction of motion changed when magnetic force acts on it.

Leaving further remarks on the relations of atoms, electricity, and
æther until the end of the last lecture, we may conclude the present
one by explaining the manner in which the observed facts connected with
a Hertz oscillator are interpreted in terms of this electron hypothesis
of electricity.

Take the simple case of two long insulated metal rods separated by a
spark-gap. The process of charging one rod positively and the other
negatively consists in forcing more corpuscles, or negative ions
or electrons, into one conductor and removing some from the other.
Any source of electromotive force, such as a dynamo or induction
coil, is, on this hypothesis, a sort of _electron-pump_, which pumps
electrons from one conductor and puts them into another. One conductor,
therefore, gains in electron-pressure, and the other loses.

The excess of electrons in one conductor endeavour to escape, and
a strain is produced on the electrons or atoms in the surrounding
dielectric or air, which may be looked upon as the effort of the
electrons, more or less tethered to the atoms, to escape. The air in
the spark-gap is subjected to the most intense strain, and when this
reaches a certain intensity some of the electrons are torn away from
their atoms, and the air in the gap then becomes a conductor. The
excess of electrons in one conductor rush through the channel thus
prepared, and this constitutes an electric current. The first rush
carries over too many electrons to equilibrate the electron-pressure,
and hence the first torrent of migrating electrons in one direction
is followed by a back-rush in the opposite one, this again in turn by
another in the original direction, and so the equality in the number
of electrons in each conductor is only established after a gradually
diminishing series of to-and-fro rushes of electrons across the
air-gap. This action constitutes a train of electrical oscillations.
At the same time that these operations are going on in and between
the conductors, the electrons attached to the atoms of the air or
other dielectric all around are being violently oscillated. These
oscillations may not proceed to such an extent as to detach electrons
from their atoms, but they are sufficient to create rapidly reversed
electric and magnetic forces. It appears that the very rapid movement
to and fro of an electron causes a wave in the æther, just as the rapid
movement of the hand through water causes a wave in water, or the
vibration of the prong of a tuning-fork creates a wave in the air.

The electron has some grip on the æther, such that the sudden starting
or stopping of the electron makes a disturbance which we may popularly
describe as a _splash in the æther_. Hence, if a large number of
electrons are suddenly started into motion in the same direction, the
effect on the æther is something like casting a multitude of stones on
the surface of still water, or the simultaneous action of a number of
small explosions in the air. Anything, therefore, which, so to speak,
lets the electrons go gradually, or softens the first rush, is inimical
to the production of a vigorous electric wave. On the other hand,
anything which causes the first rush of electrons from one conductor
to another across the air-gap to be very sudden is advantageous, and
results in a powerful wave. Experience shows that the nature of the
metal surfaces, whether polished or rough, has a great influence on
the wave-making power of the radiator. If the spark-balls or surfaces
are rough and not polished, it seems to tone down the violence of the
first electron rush, and the wave-making power of the oscillator is not
so great as if the balls are polished.

At this point, however, it will be best to withhold further discussion
on points of theory until we have considered the facts to be brought
before you in the next lecture, showing that the electric radiation
manufactured by means of electric oscillations is only one variety of a
vast range of æther waves, some forms of which are recognizable by us
as light and radiant heat.

                              CHAPTER VI.

                    WAVES AND RIPPLES IN THE ÆTHER.

Having in the last chapter explained the nature and mode of production
of electric oscillations, and shown that when these take place in an
open electric circuit or long straight rod they give rise to certain
actions at a distance, rendered evident by the changes taking place
in the conductivity of metallic powders, we have now to present the
outlines of a proof that these actions are really due to a wave-motion
of some description set up in the æther, which in nature is essentially
the same as that which constitutes the agency we call light.

We shall begin by studying a few of the epoch-making discoveries we
owe to the celebrated Heinrich Hertz, announced in a series of famous
researches with which he surprised and delighted the scientific world
in the years 1887 and 1888. These investigations opened a new and
remarkable field of experimental work.

The precise form of apparatus used by Hertz in these researches
is, however, unsuited for lecture demonstration, and I shall use
on this occasion some arrangements of my own, which are only
convenient modifications of appliances previously employed by other
experimentalists. The devices here shown are, however, very convenient
for public demonstrations.

This apparatus consists of two parts, a part for generating electric
waves, which we shall call the radiator, and a part for detecting them,
which is called the receiver.

The radiator consists of a zinc box, A (see Fig. 73), which is provided
with hollow trunnions, and can be fixed to a suitable stand and turned
in any direction. The box has an open end to it, and in its interior
there are two brass rods about 4 inches long, each terminating in brass
balls, S, 1 inch in diameter. These rods are thrust through corks
fixed in the end of two ebonite tubes, which pass through the hollow
trunnions of the box. The rods have their ends attached to very closely
wound spirals of gutta-percha-covered wire contained in the ebonite
tubes. These spirals are called _choking coils_. When the balls are
arranged in the interior of the box in their proper position, they are
about ¹⁄₁₆ inch apart, and the rods to which they are attached are in
line with each other.

[Illustration: FIG. 73.—Electric wave radiator (A) and receiver (B).]

The outer ends of the choking coils are connected to an induction
coil or electrical machine, say a small Wimshurst machine, suitable
for producing electric sparks about 2 or 3 inches in length. If then
sparks are taken between the balls, we have an arrangement which is,
in fact, a small Hertz oscillator or radiator. It has been fully
explained in the last chapter that the action of the induction coil
or electrical machine is first to create a difference in the electric
condition of the balls, such that one is positively electrified and
the other negatively. The balls and rods and the surrounding air, as
already explained, then form a sort of Leyden jar or condenser, and
in virtue of the electromotive force the air is electrically strained
around the balls. When this strain reaches a particular value, the
air between the balls passes at once into a conductive condition, and
we have a discharge which is oscillatory in nature produced between
the conductors. We may consider that the electrical charges on the two
rods rush backwards and forwards, setting up on the rods an oscillatory
surface electric current, and that this is accompanied by a very rapid
reversal of the strain in the surrounding non-conductor or dielectric.
This state of affairs results in sending out into space an effect
called an electric wave.

[Illustration: FIG. 74.—Electric radiation detector (Miller).]

Turning, then, to the receiver B (Fig. 73), we notice that this
consists of a similarly shaped metal box, having in it a board to which
are fixed two short nickel wires. These are crossed without touching
in the interior of a small ebonite box (see Fig. 74). The wires are
just covered inside the box with a very small quantity of fine nickel
filings. To the end of the zinc receiver-box is fixed a long lead pipe,
in the interior of which are two insulated wires, _c_, _d_.

These wires are joined to the extremities of the nickel wires in the
receiver-box and then, passing through the lead pipe, they enter
another metal box which contains a battery and electric bell. The pinch
of nickel filings in the small ebonite box is not an electric conductor
in its ordinary condition, and hence the electric circuit, including
the battery and bell, is not complete. If, however, an electric
oscillation is set up in the nickel receiver-wires, the mass of metal
particles connecting them at once becomes a conductor, because little
metallic granules stick or cohere together. The battery is thus able
to send an electric current through the circuit, which includes the
coherer, and the electric bell is caused to ring. It may be mentioned
that in the actual apparatus employed the arrangement is not quite
so simple. The coherer would be permanently injured if we were to
attempt to send through it an electric current strong enough to ring an
electric bell. Hence we associate with the coherer a contrivance called
a _relay_. A single voltaic cell, E (a dry cell) (see Fig. 75), is
joined up in series with the coherer C and this relay R. The latter is
a sort of switch or circuit-closer of such kind that when a very feeble
current passes through it it closes a second circuit through which a
much stronger current can pass. The transition of the nickel filings
from a non-conductive to a conductive condition is, therefore, only the
means by which a very small current of electricity is allowed to pass
through the circuit of an electro-magnet which forms the circuit of the
relay. This action causes a piece of iron to be attracted, and this
again in turn closes another circuit, and so enables the current from a
second battery, F, of five or six cells to actuate the electric bell G.
The arrangement of the two batteries, the relay coherer, and bell will
be understood by studying the diagram of connections in Fig. 75.

The really important condition in securing success in the performance
of the experiments made with this apparatus is that the long wires
which connect the receiver-box with the metal box containing the bell,
battery, and relay shall be entirely enclosed in a lead pipe without
joint, which is soldered at one end into the receiver-box and at the
other into the battery-box. Another practical point is that these
wires, where they enter the battery-box, must have included in their
circuit two little coils of insulated wire of a good many turns, which
are called “choking coils.” A third element of success is that the
coherer or sensitive conductor shall be sensitive enough, but not too
sensitive. This condition can only be obtained by a process of trial
and failure. Being provided with these two pieces of apparatus, we can
now proceed to exhibit a series of experiments of great interest.

[Illustration: FIG. 75.]

In the first place, let the radiator-box and receiver-box be placed a
few feet apart with their open mouths facing each other, like two guns
arranged to fire down each other’s throats. Then, if all is in order
when we make an electric spark between the two balls of the radiator,
the electric bell in connection with the receiver will begin to ring,
showing that the coherer in the receiver-box has been affected and
made conductive by the electric wave sent out from the radiator-box.
If a smart rap is then given to the receiver-box the clinging metallic
filings in the ebonite box will be separated again and, the circuit
being interrupted, the bell will stop ringing.

This being done, the radiator-box is then turned a little on one side
by rotating it round its hollow trunnions like a gun until the open
mouths of the two boxes no longer face each other. It will then be
found, on repeating the former experiment, that the bell will not ring
when a spark is made between the balls. A little experimenting will