Font size

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

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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46