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CHAPTER 47.
ELECTRIC OSCILLATIONS.

686. Henry's Theory of Oscillatory Discharge of Leyden Jar.

Seventy-five years ago the identity of static and voltaic electricity
was not regarded as proven. It had just been discovered that a
voltaic current sent through a coil wrapped about a steel bar
converted the bar into a magnet. It occurred to investigators
that this fact afforded a means of making the desired proof. A

steel needle was placed in a coil, one
end of which was connected to the
outer coating of a Leyden jar (Fig.
367), the other end terminating in a
knob near the knob which communi-
cated with the inner lining. When a
spark was caused to pass between the
knobs, this charge passed through the
coil and if it were of the same nature
as voltaic electricity it should mag-
netize the needle. When this was done
it was found, according to expectation,
that the needle became magnetized.
Flg * 367 * However, when these investigations

were continued it was noted that although the charge was sent
through the coil always in the same direction, the polarity of the
resulting magnets varied in an anomalous manner so that it was
not possible to predict which end of the needle would be the north
pole. In seeking to explain this, Henry in 1842 advanced the
theory that the discharge of a Leyden jar, although appearing to
our senses as a single spark, was in reality an oscillation of a
current back and forth, and the polarity of the needle depended
therefore upon the direction of the last oscillation.

687. Thomson's Mathematical Proof of Oscillation. Some ten
years after Henry announced his theory, Sir William Thomson
(Lord Kelvin) advanced a mathematical proof of its correctness.
His deduction may be shown as follows:




HIGH POTENTIAL. 557

Suppose that a Ley den jar of capacity K is discharged through
a conductor of resistance R and of inductance L, and suppose
that at any given instant it contains a charge q. The energy of
the electro-static field of the jar at this instant is (Par. 97)



This energy is being dissipated in two ways; (a) in establishing
an electro-magnetic field about the conductor and (b) in heating
this conductor.

If the instantaneous value of the current be /, the energy of
the electro-magnetic field is (Par. 359) ^ / N, or since N = LI
(Par. 434)



Since / = - , the rate at which the charge is diminishing,
this may be written



The rate at which energy is being lost by the jar is equal to the
rate at which energy is being gained by the field plus the rate at
which it is being expended in heating the circuit.

The rate at which energy is being lost by the jar is

q_ dq
K ' dt

The rate at which it is being gained by the field is



T
'



dq



dt dP
The rate at which it is being dissipated in heat is



whence



whence



q dq _ T dq

K' dt ~ dt



2-i + ZX-



558 ELEMENTS OF ELECTRICITY.

A differential equation of this form may be solved by substi-
tuting mt for q (Murray, Differential Equations, Par. 50),
Making this substitution we have

R 1

whence j / E

e m <(m 2 + m+-^)=0

which is satisfied when

m 2 -f-r-fl
or when



The values of w are real when the quantity under the radical
is positive, that is, when R 2 > 4 L/ K. Designating these values
of m by mi and ra 2 (since they are both negative), the cor-
responding value of q is

q = ae- m ^ + be"* 1

a and b being constants.
If t be made equal to zero, we have

q = a + b

q in this case being the value of

the charge in the jar just before the discharge began. As t in-
creases, corresponding to subsequent time, the value of q gets
steadily smaller (since the exponents of e are negative), that is,
the charge dwindles away without fluctuations or change of sign.
The discharge is therefore unidirectional.

If, however, R 2 is less than 4L/ K, the values of m in (I) above
are imaginary. In this case we may proceed as follows:

The expression for m is written



and placing a = y r
= y j-j* -jj and i = V 1, the corresponding roots may



be written

mi = a + pi



= a



HIGH POTENTIAL 559

whence as above



Q =

which can be put in the form (Murray, Par. 52)
q = at (A cos pt + B sin 00

If the expression within the parentheses be multiplied and
divided by VA 2 + B 2 , we have

A B \

, -cos fit H , sin pt}

.VA 2 + B 2 VA 2 + B 2 I

which may be written

AI (sin cos pt + cos < sin 00

which is equal to

AI sin (pt + </>)

and substituting above

In this expression, t being the only variable, we see that q varies
harmonically, in other words, the discharge is oscillatory, although,
since a is negative, the oscillations gradually die out.

Since pt is the variable angle and t is time, is angular velocity
and the periodic time of an oscillation is 27T/0. Substituting the
value of p from above

27T 47TLK




If R be very small, which is usually the case, R 2 K 2 may be
neglected and this last expression reduces to

T = 27T VLK

whence, the periodic time

increases with an increase in L, the inductance, or in K, the
capacity.

688. Feddersen's Experiment with Revolving Mirror. In 1859
Feddersen by a simple experiment proved the correctness of
Henry's theory and of Thomson's deductions. The principle he
employed will be understood from the following. In Fig. 368, G
is the spark gap of a Leyden jar, M is a mirror mounted upon an
axis about which it is capable of rapid rotation, and P is a photo-



560



ELEMENTS OF ELECTRICITY.



graphic plate. If while the mirror is rotating a spark be passed
across the gap G, the beam of light from this spark will fall upon
the mirror and will be reflected. Owing to the movement of M,
this reflected beam will sweep like a brush across P and when the
plate is developed and printed the path will be revealed as a band
of light. Examination will show along the edges of this band a
series of bright beads, those on one side being opposite the gaps






Fig. 368.

between those on the other and showing that the brightest point
of the spark alternated between the knobs, in other words, the
spark passed back and forth. Knowing the rate of rotation of
the mirror, the time of oscillation of the spark may be determined
with accuracy, even though this time is less than a millionth of a
second.

689. Explanation of Oscillation. An explanation of this oscil-
latory discharge is afforded by what we have already learned of
inductance. Suppose a charge to be given to the jar and to be
gradually increased until the discharge takes place. As the charge
passes from the inner to the outer coating of the jar, it is a true
current and the inductance of the circuit causes it to continue to
flow beyond the point when the jar is completely discharged, in
other words, the outer coating receives an excess charge. This
then flows back in the opposite direction and, for the reason given
above, the inner coating now acquires an excess charge, and so on.
These oscillations do not continue indefinitely because at each one
a portion of the energy is spent in heating the circuit and, as we



HIGH POTENTIAL 561

shall see shortly, another portion is radiated off into space. The
total number therefore may not exceed ten or twelve.

Reflection will show that before the discharge takes place the
energy of the field is electro-static, that is, the field is composed of
tubes of force (Par. 62), but that during the discharge this energy
is electro-magnetic, the conductor being surrounded by circular
lines of force. At the end of the discharge the magnetic lines dis-
appear and the tubes of force reappear, but reversed in direction.
As the return oscillation begins, these tubes again give way to
magnetic lines of force, which in turn are in reverse direction from
the first set, and so on.

690. Maxwell's Electro- Magnetic Theory. In 1865 Maxwell
published a mathematical analysis of the effects produced in the
surrounding medium by an oscillatory discharge. As bases for
his discussion he took the facts (a) that a current flowing in a con-
ductor produces about the conductor a magnetic field, (b) that if
a magnetic field about a conductor be varied, an E. M. F. is in-
duced in the conductor, (c) that the electric force exerted in the
space about a charge varies inversely with the dielectric capacity
and (d) that the magnetic field about a current varies with the
permeability of the dielectric. To these he added the displace-
ment assumption which is that when, for example, a charge flows
into a condenser, an equal quantity of electricity moves in the
dielectric between the plates, but that this movement takes place
within the molecules of the dielectric and not from one molecule
to another. The effect is as if in each molecule a positive charge
had moved to one end, a negative charge to the other, and the
positive charged ends all pointed in the same direction, that is,
away from the positive plate of the condenser. The so-called
displacement currents, just as any other current, produce about
them a magnetic field.

As a result of his discussion he showed that these oscillations
give rise to electric waves in the surrounding space, the wave
front comprising electric displacements and magnetic forces at
right angles to each other and both at right angles to the direction
of propagation of the wave. He also showed that these waves
moved with a velocity of thirty billion centimeters per second.
Since light moves with the same velocity and is transmitted by
the same agent, the ether, he concluded that light and electricity
are identical and differ only in that the light waves are much the



562 ELEMENTS OF ELECTRICITY.

shorter. As corroborating this last conclusion, he showed that
since electric waves can not be transmitted through conductors,
these bodies should not transmit light waves. As a fact, the
metals are all opaque to light. The same reasoning would show
that a transparent solid is a non-conductor and such substances
are the best insulators. It does not follow however that all opaque
bodies are conductors, for many, such as porcelain, marble, etc.,
owe their opacity to irregular crystallization or mechanically
included impurities. The purest form of crystallized marble,
Iceland spar, is transparent.

Maxwell's mathematical discussion can not be repeated here,
but by following a similar line of reasoning we show in the three
following paragraphs how he arrived at one of his conclusions.

691. Electric Elasticity. The elasticity of a body is measured
by the ratio of the stress exerted upon the body to the strain
(elongation, compression, etc.) produced. Consider a sphere
carrying a charge Q and surrounded by a concentric non-con-
ducting shell of dielectric capacity K. Displacement will take
place in the dielectric, a charge Q being induced on the inner
surface of the shell and a charge +Q being repelled to the outer
surface. If the radius of the shell be r, the force per square centi-

meter exerted upon the inner surface is ^ ^ (Par. 90). This is

the stress to which the shell is exposed. The strain per square
centimeter consists in driving the positive charge to the outer sur-

face of the shell and is therefore ~- 2 . The electric elasticity, the



ratio of the stress to the strain, is 47r/ K.

692. Electric Density. In Par. 435 there was deduced an ex-
pression for the inductance of a coil wrapped upon a circular core.
If in this expression both / and L be absolute electro-magnetic
units (instead of amperes and henrys), the expression becomes

T
L=



in which n is the total number
of turns, r is the radius of the coil and I is its length.

In Par. 687 it was shown that the energy of an electro-magnetic
field is \PL. Substituting the above value of L and dividing

2



HIGH POTENTIAL. 563

by 7rr 2 l, the volume of the core, we obtain for the energy per cubic
centimeter ^

2MT

If for n/l, the number of turns per centimeter, we write N a
this becomes l



In mechanics it is shown that the energy of a mass m moving
with a velocity v is ^mv 2 . From analogy, therefore, kir^ is
termed the electric mass per unit of volume. But mass per unit
volume is density, therefore, 4^^ is the electric density of the
field.

693. Velocity of Propagation of Electric Wave. If e be the
elasticity of a medium and 6 be its density, the velocity with
which waves are propagated through it is v = Ve/3. Substitut-
ing the values of the electric elasticity and density given in the
preceding paragraphs, we have for the velocity of propagation
of electric waves 1

= VK

This is the expression which we have already obtained in Par.
548. This velocity, by many independent methods, has been
shown to be thirty billion (3xl0 10 ) centimeters per second, or
as already stated, the same as the velocity of light.

694. Hertz's Confirmation of Maxwell's Theory. During
Maxwell's life time his theory made but moderate headway and
he died before it had ever been experimentally proven. In 1887,
twenty-two years after his theory had been announced, it re-
ceived striking and abundant confirmation by a series of brilliant
experiments performed by Hertz. The arrangement used in the
first of these experiments is shown in Fig. 369 and consists of
two parts which Hertz designated respectively as the oscillator
and the resonator. The oscillator consisted of two sixteen-inch
square zinc plates, A and B, placed two feet apart. A copper
rod from each of these and upon their common axis terminated
in polished knobs separated by a gap G of about one-quarter
of an inch. These rods were connected as shown to the terminals
of the secondary of an induction coil. When^the coil was operated,
series of sparks passed between the knobs. The resonator con-
sisted of a copper wire bent into a circle with a narrow spark gap



564



ELEMENTS OF ELECTRICITY.



between two knobs. It was found that to obtain the best results
the dimensions of the resonator had to be adjusted, or it had to
be "tuned" to suit the particular oscillator used. With the one
described, the diameter of the resonator was about twenty-
eight inches.





Fig. 369.

With the coil in operation and sparks passing between the
knobs of the oscillator, the resonator was held in various near-by
positions. When placed, as shown in the figure, along the line
GM passing through and perpendicular to the spark gap G, it
was found that sparks were produced in the gap of the resonator
whenever the axis of this gap was parallel to the spark gap of
the oscillator. Thus sparks were produced when the resonator
was held as at C but not when held as at D or at E.

As thus carried out, this experiment does not conclusively
show the existence of waves and might be considered a simple
example of induction as explained in Par. 420. The demonstra-
tion of the existence of waves was made as follows: The oscillator
was placed so that its axis was parallel to and at some distance
from the opposite wall of the room in which the experiments
were carried out. This wall was covered with large sheets of
zinc M. Since according to Maxwell's theory the metals are
opaque to these waves, this zinc sheet should act towards them
as a mirror. Now it is well known that when waves strike a
surface normally and are reflected back along the same path,
the phenomenon of interference occurs. Beginning at the re-
flecting surface, at fixed points one-half of a wave length apart



HIGH POTENTIAL. 565

the advancing and returning waves are in opposition and com-
plete interference results, while at points midway between these
nodes the waves are in phase and the resulting amplitude is twice
that of the advancing wave. With the resonator close to the
zinc sheet M, no sparks are obtained, but moving from M towards
G, a point is found where the intensity of the sparks in the reson-
ator is a maximum. Continuing to move towards G, the sparks
in the resonator again die out, then again rise to a maximum.
These electro-magnetic radiations are therefore waves, the dis-
tance between two successive points of maximum sparking or
between two nodes of no sparking being one-half of the wave
length. With the apparatus described above, the wave length
was found to be about thirty-two feet.

By the method just outlined, the wave length can be deter-
mined. By photographing the spark seen in the revolving mirror,
the periodic time of the oscillations can be measured. The re-
ciprocal of this is the frequency, or number per second. The
product of the wave length by the frequency gives the velocity
with which the wave travels. The results entirely confirm the
previous determinations of this velocity as 3xl0 10 centimeters
per second.

695. Further Experiments by Hertz. With slight modifica-
tions in his simple apparatus, Hertz succeeded in reproducing
many of the characteristic experiments usually shown with light.
Thus, by placing the spark gap of his oscillator at the focus of a
reflector made by bending a sheet of zinc into a parabolic form,
he was able to direct the waves so that they could be detected
by a resonator placed at the focus of a corresponding reflector
at a distance of over thirty yards. By using a huge prism of pitch,
four feet on an edge, he was able to refract the beam from the
parabolic reflector. Finally, he showed that these waves are
polarized. By placing in the path of the beam from the reflector
a screen made of a number of parallel wires strung on a wooden
frame, he showed that the waves pass freely when the wires
were perpendicular to the axis of the spark gap of the oscillator
but were entirely cut off when these wires were turned so as to
be parallel to this axis.

696. Length of Electro -Magnetic Waves. The length of the
longest light waves is a little over .00007 of a centimeter, while



566 ELEMENTS OF ELECTRICITY.

we have seen above that that of the electro-magnetic waves
produced by Hertz in his first experiment was thirty- two feet.
Since the velocity of these waves is constant and is equal to the
product of the wave length by the frequency, and since the
frequency is the reciprocal of the periodic time, the wave length
varies directly with the periodic time. In Par. 687 this was shown
to be T = 2irVLK, therefore, by decreasing either the inductance
or the capacity of the oscillator, the wave length may be shortened
provided the condition for oscillatory discharge, R 2 < 4L/ K (Par.
687) be maintained. Since all conductors have both inductance
and capacity, Hertz found that he could do away with the zinc
plates of his oscillator and substitute for them simple straight
wires. Other investigators, by reducing the dimensions of the
oscillator, have produced electro-magnetic waves whose length
has been about two-tenths of a centimeter.

697. Tuning of the Resonator. By experiments based upon
several different principles it has been shown that electric oscil-
lations may also be transmitted along wires.

Consider a length of insulated wire and suppose an electric
impulse to be applied to it. The wave produced will travel the
length of the wire and having reached the far end will be reflected
and return. If on its way back it encounters another wave
traveling in the opposite direction, the two waves will combine.
If they be in phase, the amplitude of the resultant wave is doubled
and would be further increased by each successive wave. If they
be in opposition, they mutually destroy one another and complete
interference results. Between these extremes, recurring risings
and fallings result and produce an effect analogous to the "beats"
in sound waves. If the waves be of constant length, the time
required for them to travel to the end of the wire and return
varies with the length of the wire. It is therefore possible by
lengthening or shortening the wire to adjust it so that the wave
will return in exact time to receive the maximum increment
from the succeeding impulse. When this adjustment, the tuning
referred to in Par. 694, has been made, the waves in the wire
are of maximum intensity and resonance is said to have been
secured.

As an analogy, a pendulum has a natural period of vibration.
If successive impulses be applied to the pendulum and be timed
at its natural period, their effects are cumulative and, although



HIGH POTENTIAL. 567

the individual impulses may be very feeble, they may finally
produce motion through a wide arc. If, on the other hand, they
be not timed at this period, little or no oscillation will be pro-
duced.

Reflection will show that resonance may be obtained in another
way, that is, by varying the length of the wave instead of varying
the length of the circuit. It was shown in the preceding paragraph
how this may be done by varying the periodic time. There are,
therefore, two ways of obtaining resonance in a resonator: (a) by
shortening or lengthening the resonator and thus changing its
natural period to suit the period of the waves and (b) by vary-
ing the period of the waves to suit the natural period of the
resonator.

698. Principle of Wireless Telegraphy. Hertz showed by his
experiments that there could be produced at will electric waves
which travel through space with the velocity of light. He also
showed that by suitably-arranged apparatus these waves could
be detected at a distance from their point of origin. It was
quickly realized that these two observations comprised the funda-
mental principle of wireless telegraphy. Subsequent development
has taken place along two lines: (a) the improving of the sending
apparatus or oscillator so that a greater amount of energy could
be thrown out in the form of waves, and (b) the perfecting of the
receiving apparatus, increasing its sensitiveness so that the waves
could be detected at greater and greater distances. Foremost
among those engaged in these problems was Marconi who in
1895 took out his first patents on methods of wireless telegraphy.

In order to bring out clearly the object of the various parts
of the modern apparatus, we shall describe the simpler forms
and show why changes were found desirable.

699. The Aerial. The primary form of apparatus for pro-
ducing electric waves was the oscillator of Hertz. As stated
above, it was soon discovered that the zinc plates could be re-
placed by straight wires. It was next found that if these wires
be placed in a vertical position instead of horizontal, that the
lower one could be dispensed with, the earth taking its place.
In either case, the length of the waves produced remained the
same, that is, a little over four times the length of the upper wire.
To this vertical wire the names aerial or antenna are applied.



568 ELEMENTS OF ELECTRICITY.

With other conditions constant, the distance to which signals
can be sent varies as the square of the length of the aerial and
for this reason Marconi at first proposed that it should be sup-
ported by kites or balloons. This proposition was found to be
impracticable for permanent installations and antennae are now
supported by towers or masts.

The signaling distance also increases directly with the amount
of energy radiated. In Par. 97 it was shown that the energy

of a condenser is ^V 2 K, K being its capacity. In this case

the aerial and the grounded wire and the earth below the spark
gap constitute the condenser. We may therefore increase its
capacity by increasing the length of the aerial, but, as shown
above, the practical limit of length is soon reached. The next
solution therefore is to add to the capacity by using a number
of wires in the aerial. The capacity of a single wire is consider-
able. Pierce states that a straight wire f inch in diameter and
100 feet long has the same capacity as an isolated metallic disc
16 feet in diameter. If, however, more than one wire be used,
owing to the mutual action of the like charges which they carry,
the capacity is far from increasing in proportion to the number
of wires, in fact, it increases more nearly as the square root of
this number, that is, sixteen wires two feet apart have only four
times the capacity of a single wire.

700. The Transmitter. A simple form of transmitter is shown
diagrammatically in Fig. 370. A is the aerial and D is the lower
wire grounded at E. B is a battery in circuit with the primary
of an induction coil C. The terminals of the secondary are con-
nected to A and D on opposite sides of the spark gap G. When
the key K is closed, the E. M. F. induced in the secondary drives
a charge into A until a spark jumps across G, thereby producing
the desired electrical oscillations.

We saw above that the signaling distance increases directly
with the amount of energy radiated and we also saw that the



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