[1] British Patent Specification, No. 5306 of 1878, and No. 602 of
1880.
[2] Ibid. No. 3988 of 1878.
ELECTRIC WAVES. S 1. Clerk Maxwell proved that on his theory
electromagnetic disturbances are propagated as a wave motion through the
dielectric, while Lord Kelvin in 1853 (_Phil. Mag._ [4] 5, p. 393)
proved from electromagnetic theory that the discharge of a condenser is
oscillatory, a result which Feddersen (_Pogg. Ann._ 103, p. 69, &c.)
verified by a beautiful series of experiments. The oscillating discharge
of a condenser had been inferred by Henry as long ago as 1842 from his
experiments on the magnetization produced in needles by the discharge of
a condenser. From these two results it follows that electric waves must
be passing through the dielectric surrounding a condenser in the act of
discharging, but it was not until 1887 that the existence of such waves
was demonstrated by direct experiment. This great step was made by Hertz
(_Wied. Ann._ 34, pp. 155, 551, 609; _Ausbreitung der elektrischen
Kraft_, Leipzig, 1892), whose experiments on this subject form one of
the greatest contributions ever made to experimental physics. The
difficulty which had stood in the way of the observations of these waves
was the absence of any method of detecting electrical and magnetic
forces, reversed some millions of times per second, and only lasting for
an exceedingly short time. This was removed by Hertz, who showed that
such forces would produce small sparks between pieces of metal very
nearly in contact, and that these sparks were sufficiently regular to be
used to detect electric waves and to investigate their properties. Other
and more delicate methods have subsequently been discovered, but the
results obtained by Hertz with his detector were of such signal
importance, that we shall begin our account of experiments on these
waves by a description of some of Hertz's more fundamental experiments.
[Illustration: FIG. 1.]
[Illustration: FIG. 2.]
To produce the waves Hertz used two forms of vibrator. The first is
represented in fig. 1. A and B are two zinc plates about 40 cm. square;
to these brass rods, C, D, each about 30 cm. long, are soldered,
terminating in brass balls E and F. To get good results it is necessary
that these balls should be very brightly polished, and as they get
roughened by the sparks which pass between them it is necessary to
repolish them at short intervals; they should be shaded from light and
from sparks, or other source of ultra-violet light. In order to excite
the waves, C and D are connected to the two poles of an induction coil;
sparks cross the air-gap which becomes a conductor, and the charges on
the plates oscillate backwards and forwards like the charges on the
coatings of a Leyden jar when it is short-circuited. The object of
polishing the balls and screening off light is to get a sudden and sharp
discharge; if the balls are rough there will be sharp points from which
the charge will gradually leak, and the discharge will not be abrupt
enough to start electrical vibrations, as these have an exceedingly
short period. From the open form of this vibrator we should expect the
radiation to be very large and the rate of decay of the amplitude very
rapid. Bjerknes (_Wied. Ann._ 44, p. 74) found that the amplitude fell
to 1/e of the original value, after a time 4T where T was the period of
the electrical vibrations. Thus after a few vibrations the amplitude
becomes inappreciable. To detect the waves produced by this vibrator
Hertz used a piece of copper wire bent into a circle, the ends being
furnished with two balls, or a ball and a point connected by a screw, so
that the distance between them admitted of very fine adjustment. The
radius of the circle for use with the vibrator just described was 35
cm., and was so chosen that the free period of the detector might be the
same as that of the vibrator, and the effects in it increased by
resonance. It is evident, however, that with a primary system as greatly
damped as the vibrator used by Hertz, we could not expect very marked
resonance effects, and as a matter of fact the accurate timing of
vibrator and detector in this case is not very important. With
electrical vibrators which can maintain a large number of vibrations,
resonance effects are very striking, as is beautifully shown by the
following experiment due to Lodge (_Nature_, 41, p. 368), whose
researches have greatly advanced our knowledge of electric waves. A and
C (fig. 2) are two Leyden jars, whose inner and outer coatings are
connected by wires, B and D, bent so as to include a considerable area.
There is an air-break in the circuit connecting the inside and outside
of one of the jars, A, and electrical oscillations are started in A by
joining the inside and outside with the terminals of a coil or
electrical machine. The circuit in the jar C is provided with a sliding
piece, F, by means of which the self-induction of the discharging
circuit, and, therefore, the time of an electrical oscillation of the
jar, can be adjusted. The inside and outside of this jar are put almost,
but not quite, into electrical contact by means of a piece of tin-foil,
E, bent over the lip of the jar. The jars are placed face to face so
that the circuits B and D are parallel to each other, and approximately
at right angles to the line joining their centres. When the electrical
machine is in action sparks pass across the air-break in the circuit in
A, and by moving the slider F it is possible to find one position for it
in which sparks pass from the inside to the outside of C across the
tin-foil, while when the slider is moved a short distance on either side
of this position the sparks cease.
Hertz found that when he held his detector in the neighbourhood of the
vibrator minute sparks passed between the balls. These sparks were not
stopped when a large plate of non-conducting substance, such as the wall
of a room, was interposed between the vibrator and detector, but a large
plate of very thin metal stopped them completely.
To illustrate the analogy between electric waves and waves of light
Hertz found another form of apparatus more convenient. The vibrator
consisted of two equal brass cylinders, 12 cm. long and 3 cm. in
diameter, placed with their axes coincident, and in the focal line of a
large zinc parabolic mirror about 2 m. high, with a focal length of 12.5
cm. The ends of the cylinders nearest each other, between which the
sparks passed, were carefully polished. The detector, which was placed
in the focal line of an equal parabolic mirror, consisted of two lengths
of wire, each having a straight piece about 50 cm. long and a curved
piece about 15 cm. long bent round at right angles so as to pass through
the back of the mirror. The ends which came through the mirror were
connected with a spark micrometer, the sparks being observed from behind
the mirror. The mirrors are shown, in fig. 3.
[Illustration: FIG. 3.]
S 2. _Reflection and Refraction._--To show the reflection of the waves
Hertz placed the mirrors side by side, so that their openings looked in
the same direction, and their axes converged at a point about 3 m. from
the mirrors. No sparks were then observed in the detector when the
vibrator was in action. When, however, a large zinc plate about 2 m.
square was placed at right angles to the line bisecting the angle
between the axes of the mirrors sparks became visible, but disappeared
again when the metal plate was twisted through an angle of about 15 deg.
to either side. This experiment showed that electric waves are
reflected, and that, approximately at any rate, the angle of incidence
is equal to the angle of reflection. To show refraction Hertz used a
large prism made of hard pitch, about 1.5 m. high, with a slant side of
1.2 m. and an angle of 30 deg. When the waves from the vibrator passed
through this the sparks in the detector were not excited when the axes
of the two mirrors were parallel, but appeared when the axis of the
mirror containing the detector made a certain angle with the axis of
that containing the vibrator. When the system was adjusted for minimum
deviation the sparks were most vigorous when the angle between the axes
of the mirrors was 22 deg. This corresponds to an index of refraction of
1.69.
S 3. _Analogy to a Plate of Tourmaline._--If a screen be made by winding
wire round a large rectangular framework, so that the turns of the wire
are parallel to one pair of sides of the frame, and if this screen be
interposed between the parabolic mirrors when placed so as to face each
other, there will be no sparks in the detector when the turns of the
wire are parallel to the focal lines of the mirror; but if the frame is
turned through a right angle so that the wires are perpendicular to the
focal lines of the mirror the sparks will recommence. If the framework
is substituted for the metal plate in the experiment on the reflection
of electric waves, sparks will appear in the detector when the wires are
parallel to the focal lines of the mirrors, and will disappear when the
wires are at right angles to these lines. Thus the framework reflects
but does not transmit the waves when the electric force in them is
parallel to the wires, while it transmits but does not reflect waves in
which the electric force is at right angles to the wires. The wire
framework behaves towards the electric waves exactly as a plate of
tourmaline does to waves of light. Du Bois and Rubens (_Wied. Ann._ 49,
p. 593), by using a framework wound with very fine wire placed very
close together, have succeeded in polarizing waves of radiant heat,
whose wave length, although longer than that of ordinary light, is very
small compared with that of electric waves.
S 4. _Angle of Polarization._--When light polarized at right angles to
the plane of incidence falls on a refracting substance at an angle
tan^(-1)[mu], where [mu] is the refractive index of the substance, all
the light is refracted and none reflected; whereas when light is
polarized in the plane of incidence, some of the light is always
reflected whatever the angle of incidence. Trouton (_Nature_, 39, p.
391) showed that similar effects take place with electric waves. From a
paraffin wall 3 ft. thick, reflection always took place when the
electric force in the incident wave was at right angles to the plane of
incidence, whereas at a certain angle of incidence there was no
reflection when the vibrator was turned, so that the electric force was
in the plane of incidence. This shows that on the electromagnetic theory
of light the electric force is at right angles to the plane of
polarization.
[Illustration: FIG. 4.]
S 5. _Stationary Electrical Vibrations._--Hertz (_Wied. Ann._ 34, p.
609) made his experiments on these in a large room about 15 m. long. The
vibrator, which was of the type first described, was placed at one end
of the room, its plates being parallel to the wall, at the other end a
piece of sheet zinc about 4 m. by 2 m. was placed vertically against the
wall. The detector--the circular ring previously described--was held so
that its plane was parallel to the metal plates of the vibrator, its
centre on the line at right angles to the metal plate bisecting at right
angles the spark gap of the vibrator, and with the spark gap of the
detector parallel to that of the vibrator. The following effects were
observed when the detector was moved about. When it was close up to the
zinc plate there were no sparks, but they began to pass feebly as soon
as it was moved forward a little way from the plate, and increased
rapidly in brightness until it was about 1.8 m. from the plate, when
they attained their maximum. When its distance was still further
increased they diminished in brightness, and vanished again at a
distance of about 4 m. from the plate. When the distance was still
further increased they reappeared, attained another maximum, and so on.
They thus exhibited a remarkable periodicity similar to that which
occurs when stationary vibrations are produced by the interference of
direct waves with those reflected from a surface placed at right angles
to the direction of propagation. Similar periodic alterations in the
spark were observed by Hertz when the waves, instead of passing freely
through the air and being reflected by a metal plate at the end of the
room, were led along wires, as in the arrangement shown in fig. 4. L and
K are metal plates placed parallel to the plates of the vibrator, long
parallel wires being attached to act as guides to the waves which were
reflected from the isolated end. (Hertz used only one plate and one
wire, but the double set of plates and wires introduced by Sarasin and
De la Rive make the results more definite.) In this case the detector is
best placed so that its plane is at right angles to the wires, while the
air space is parallel to the plane containing the wires. The sparks
instead of vanishing when the detector is at the far end of the wire are
a maximum in this position, but wax and wane periodically as the
detector is moved along the wires. The most obvious interpretation of
these experiments was the one given by Hertz--that there was
interference between the direct waves given out by the vibrator and
those reflected either from the plate or from the ends of the wire, this
interference giving rise to stationary waves. The places where the
electric force was a maximum were the places where the sparks were
brightest, and the places where the electric force was zero were the
places where the sparks vanished. On this explanation the distance
between two consecutive places where the sparks vanished would be half
the wave length of the waves given out by the vibrator.
Some very interesting experiments made by Sarasin and De la Rive
(_Comptes rendus_, 115, p. 489) showed that this explanation could not
be the true one, since by using detectors of different sizes they found
that the distance between two consecutive places where the sparks
vanished depended mainly upon the size of the detector, and very little
upon that of the vibrator. With small detectors they found the distance
small, with large detectors, large; in fact it is directly proportional
to the diameter of the detector. We can see that this result is a
consequence of the large damping of the oscillations of the vibrator and
the very small damping of those of the detector. Bjerknes showed that
the time taken for the amplitude of the vibrations of the vibrator to
sink to 1/e of their original value was only 4T, while for the detector
it was 500T', when T and T' are respectively the times of vibration of
the vibrator and the detector. The rapid decay of the oscillations of
the vibrator will stifle the interference between the direct and the
reflected wave, as the amplitude of the direct wave will, since it is
emitted later, be much smaller than that of the reflected one, and not
able to annul its effects completely; while the well-maintained
vibrations of the detector will interfere and produce the effects
observed by Sarasin and De la Rive. To see this let us consider the
extreme case in which the oscillations of the vibrator are absolutely
dead-beat. Here an impulse, starting from the vibrator on its way to the
reflector, strikes against the detector and sets it in vibration; it
then travels up to the plate and is reflected, the electric force in the
impulse being reversed by reflection. After reflection the impulse again
strikes the detector, which is still vibrating from the effects of the
first impact; if the phase of this vibration is such that the reflected
impulse tends to produce a current round the detector in the same
direction as that which is circulating from the effects of the first
impact, the sparks will be increased, but if the reflected impulse tends
to produce a current in the opposite direction the sparks will be
diminished. Since the electric force is reversed by reflection, the
greatest increase in the sparks will take place when the impulse finds,
on its return, the detector in the opposite phase to that in which it
left it; that is, if the time which has elapsed between the departure
and return of the impulse is equal to an odd multiple of half the time
of vibration of the detector. If d is the distance of the detector from
the reflector when the sparks are brightest, and V the velocity of
propagation of electromagnetic disturbance, then 2d/V = (2n + 1)(T'/2);
where n is an integer and T' the time of vibration of the detector, the
distance between two spark maxima will be VT'/2, and the places where
the sparks are a minimum will be midway between the maxima. Sarasin and
De la Rive found that when the same detector was used the distance
between two spark maxima was the same with the waves through air
reflected from a metal plate and with those guided by wires and
reflected from the free ends of the wire, the inference being that the
velocity of waves along wires is the same as that through the air. This
result, which follows from Maxwell's theory, when the wires are not too
fine, had been questioned by Hertz on account of some of his
experiments on wires.
S 6. _Detectors._--The use of a detector with a period of vibration of
its own thus tends to make the experiments more complicated, and many
other forms of detector have been employed by subsequent experimenters.
For example, in place of the sparks in air the luminous discharge
through a rarefied gas has been used by Dragoumis, Lecher (who used
tubes without electrodes laid across the wires in an arrangement
resembling that shown in fig. 7) and Arons. A tube containing neon at a
low pressure is especially suitable for this purpose. Zehnder (_Wied.
Ann._ 47, p. 777) used an exhausted tube to which an external
electromotive force almost but not quite sufficient of itself to produce
a discharge was applied; here the additional electromotive force due to
the waves was sufficient to start the discharge. Detectors depending on
the heat produced by the rapidly alternating currents have been used by
Paalzow and Rubens, Rubens and Ritter, and I. Klemencic. Rubens measured
the heat produced by a bolometer arrangement, and Klemencic used a
thermo-electric method for the same purpose; in consequence of the great
increase in the sensitiveness of galvanometers these methods are now
very frequently resorted to. Boltzmann used an electroscope as a
detector. The spark gap consisted of a ball and a point, the ball being
connected with the electroscope and the point with a battery of 200 dry
cells. When the spark passed the cells charged up the electroscope.
Ritter utilized the contraction of a frog's leg as a detector, Lucas and
Garrett the explosion produced by the sparks in an explosive mixture of
hydrogen and oxygen; while Bjerknes and Franke used the mechanical
attraction between oppositely charged conductors. If the two sides of
the spark gap are connected with the two pairs of quadrants of a very
delicate electrometer, the needle of which is connected with one pair of
quadrants, there will be a deflection of the electrometer when the
detector is struck by electric waves. A very efficient detector is that
invented by E. Rutherford (_Trans. Roy. Soc._ A. 1897, 189, p. 1); it
consists of a bundle of fine iron wires magnetized to saturation and
placed inside a small magnetizing coil, through which the electric waves
cause rapidly alternating currents to pass which demagnetize the soft
iron. If the instrument is used to detect waves in air, long straight
wires are attached to the ends of the demagnetizing coil to collect the
energy from the field; to investigate waves in wires it is sufficient to
make a loop or two in the wire and place the magnetized piece of iron
inside it. The amount of demagnetization which can be observed by the
change in the deflection of a magnetometer placed near the iron,
measures the intensity of the electric waves, and very accurate
determinations can be made with ease with this apparatus. It is also
very delicate, though in this respect it does not equal the detector to
be next described, the coherer; Rutherford got indications in 1895 when
the vibrator was 3/4 of a mile away from the detector, and where the
waves had to traverse a thickly populated part of Cambridge. It can also
be used to measure the coefficient of damping of the electric waves, for
since the wire is initially magnetized to saturation, if the direction
of the current when it first begins to flow in the magnetizing coil is
such as to tend to increase the magnetization of the wire, it will
produce no effect, and it will not be until the current is reversed that
the wire will lose some of its magnetization. The effect then gives the
measure of the intensity half a period after the commencement of the
waves. If the wire is put in the coil the opposite way, i.e. so that the
magnetic force due to the current begins at once to demagnetize the
wire, the demagnetization gives a measure of the initial intensity of
the waves. Comparing this result with that obtained when the wires were
reversed, we get the coefficient of damping. A very convenient detector
of electric waves is the one discovered almost simultaneously by
Fessenden (_Electrotech. Zeits._, 1903, 24, p. 586) and Schlomilch
(_ibid._ p. 959). This consists of an electrolytic cell in which one of
the electrodes is an exceedingly fine point. The electromotive force in
the circuit is small, and there is large polarization in the circuit
with only a small current. When the circuit is struck by electric waves
there is an increase in the currents due to the depolarization of the
circuit. If a galvanometer is in the circuit, the increased deflection
of the instrument will indicate the presence of the waves.
S 7. _Coherers._--The most sensitive detector of electric waves is the
"coherer," although for metrical work it is not so suitable as that just
described. It depends upon the fact discovered by Branly (_Comptes
rendus_, 111, p. 785; 112, p. 90) that the resistance between loose
metallic contacts, such as a pile of iron turnings, diminishes when they
are struck by an electric wave. One of the forms made by Lodge (_The
Work of Hertz and some of his Successors_, 1894) on this principle
consists simply of a glass tube containing iron turnings, in contact
with which are wires led into opposite ends of the tube. The arrangement
is placed in series with a galvanometer (one of the simplest kind will
do) and a battery; when the iron turnings are struck by electric waves
their resistance is diminished and the deflection of the galvanometer is
increased. Thus the deflection of the galvanometer can be used to
indicate the arrival of electric waves. The tube must be tapped between
each experiment, and the deflection of the galvanometer brought back to
about its original value. This detector is marvellously delicate, but
not metrical, the change produced in the resistance depending upon so
many things besides the intensity of the waves that the magnitude of the
galvanometer deflection is to some extent a matter of chance. Instead of
the iron turnings we may use two iron wires, one resting on the other;
the resistance of this contact will be altered by the incidence of the
waves. To get greater regularity Bose uses, instead of the iron
turnings, spiral springs, which are pushed against each other by means
of a screw until the most sensitive state is attained. The sensitiveness
of the coherer depends on the electromotive force put in the
galvanometer circuit. Very sensitive ones can be made by using springs
of very fine silver wire coated electrolytically with nickel. Though the
impact of electric waves generally produces a diminution of resistance
with these loose contacts, yet there are exceptions to the rule. Thus
Branly showed that with lead peroxide, PbO2, there is an increase in
resistance. Aschkinass proved the same to be true with copper sulphide,
CuS; and Bose showed that with potassium there is an increase of
resistance and great power of self-recovery of the original resistance
after the waves have ceased. Several theories of this action have been
proposed. Branly (_Lumiere electrique_, 40, p. 511) thought that the
small sparks which certainly pass between adjacent portions of metal
clear away layers of oxide or some other kind of non-conducting film,
and in this way improve the contact. It would seem that if this theory
is true the films must be of a much more refined kind than layers of
oxide or dirt, for the coherer effect has been observed with clean
non-oxidizable metals. Lodge explains the effect by supposing that the
heat produced by the sparks fuses adjacent portions of metal into
contact and hence diminishes the resistance; it is from this view of the
action that the name coherer is applied to the detector. Auerbeck
thought that the effect was a mechanical one due to the electrostatic
attractions between the various small pieces of metal. It is probable
that some or all of these causes are at work in some cases, but the
effects of potassium make us hesitate to accept any of them as the
complete explanation. Blanc (_Ann. chim. phys._, 1905, [8] 6, p. 5), as
the result of a long series of experiments, came to the conclusion that
coherence is due to pressure. He regarded the outer layers as different
from the mass of the metal and having a much greater specific
resistance. He supposed that when two pieces of metal are pressed
together the molecules diffuse across the surface, modifying the surface
layers and increasing their conductivity.
S 8. _Generators of Electric Waves._--Bose (_Phil. Mag._ 43, p. 55)
designed an instrument which generates electric waves with a length of
not more than a centimetre or so, and therefore allows their
properties to be demonstrated with apparatus of moderate dimensions.
The waves are excited by sparking between two platinum beads carried
by jointed electrodes; a platinum sphere is placed between the beads,
and the distance between the beads and the sphere can be adjusted by
bending the electrodes. The diameter of the sphere is 8 mm., and the
wave length of the shortest electrical waves generated is said to be
about 6 mm. The beads are connected with the terminals of a small
induction coil, which, with the battery to work it and the sparking
arrangement, are enclosed in a metal box, the radiation passing out
through a metal tube opposite to the spark gap. The ordinary vibrating
break of the coil is not used, a single spark made by making and
breaking the circuit by means of a button outside the box being
employed instead. The detector is one of the spiral spring coherers
previously described; it is shielded from external disturbance by
being enclosed in a metal box provided with a funnel-shaped opening to
admit the radiation. The wires leading from the coherers to the
galvanometer are also surrounded by metal tubes to protect them from
stray radiation. The radiating apparatus and the receiver are mounted
on stands sliding in an optical bench. If a parallel beam of radiation
is required, a cylindrical lens of ebonite or sulphur is mounted in a
tube fitting on to the radiator tube and stopped by a guide when the
spark is at the principal focal line of the lens. For experiments
requiring angular measurements a spectrometer circle is mounted on one
of the sliding stands, the receiver being carried on a radial arm and
pointing to the centre of the circle. The arrangement is represented
in fig. 5.
[Illustration: FIG. 5.]
With this apparatus the laws of reflection, refraction and
polarization can readily be verified, and also the double refraction
of crystals, and of bodies possessing a fibrous or laminated structure
such as jute or books. (The double refraction of electric waves seems
first to have been observed by Righi, and other researches on this
subject have been made by Garbasso and Mack.) Bose showed the rotation
of the plane of polarization by means of pieces of twisted jute rope;
if the pieces were arranged so that their twists were all in one
direction and placed in the path of the radiation, they rotated the
plane of polarization in a direction depending upon the direction of
twist; if they were mixed so that there were as many twisted in one
direction as the other, there was no rotation.
[Illustration: FIG. 6.]
A series of experiments showing the complete analogy between electric
and light waves is described by Righi in his book _L'Ottica delle
oscillazioni elettriche_. Righi's exciter, which is especially
convenient when large statical electric machines are used instead of
induction coils, is shown in fig. 6. E and F are balls connected with
the terminals of the machine, and AB and CD are conductors insulated
from each other, the ends B, C, between which the sparks pass, being
immersed in vaseline oil. The period of the vibrations given out by
the system is adjusted by means of metal plates M and N attached to AB
and CD. When the waves are produced by induction coils or by
electrical machines the intervals between the emission of different
sets of waves occupy by far the largest part of the time. Simon
(_Wied. Ann._, 1898, 64, p. 293; _Phys. Zeit._, 1901, 2, p. 253),
Duddell (_Electrician_, 1900, 46, p. 269) and Poulsen (_Electrotech.
Zeits._, 1906, 27, p. 1070) reduced these intervals very considerably
by using the electric arc to excite the waves, and in this way
produced electrical waves possessing great energy. In these methods
the terminals between which the arc is passing are connected through
coils with self-induction L to the plates of a condenser of capacity
C. The arc is not steady, but is continually varying. This is
especially the case when it passes through hydrogen. These variations
excite vibrations with a period 2[pi][root](LC) in the circuit
containing the capacity of the self-induction. By this method Duddell
produced waves with a frequency of 40,000. Poulsen, who cooled the
terminals of the arc, produced waves with a frequency of 1,000,000,
while Stechodro (_Ann. der Phys._ 27, p. 225) claims to have produced
waves with three hundred times this frequency, i.e. having a wave
length of about a metre. When the self-induction and capacity are
large so that the frequency comes within the limits of the frequency
of audible notes, the system gives out a musical note, and the
arrangement is often referred to as the singing arc.
[Illustration: FIG. 7.]
[Illustration: FIG. 8.]
S _9. Waves in Wires._--Many problems on electric waves along wires
can readily be investigated by a method due to Lecher (_Wied. Ann._
41, p. 850), and known as Lecher's bridge, which furnishes us with a
means of dealing with waves of a definite and determinable
wave-length. In this arrangement (fig. 7) two large plates A and B
are, as in Hertz's exciter, connected with the terminals of an
induction coil; opposite these and insulated from them are two smaller
plates D, E, to which long parallel wires DFH, EGJ are attached. These
wires are bridged across by a wire LM, and their farther ends H, J,
may be insulated, or connected together, or with the plates of a
condenser. To detect the waves in the circuit beyond the bridge,
Lecher used an exhausted tube placed across the wires, and Rubens a
bolometer, but Rutherford's detector is the most convenient and
accurate. If this detector is placed in a fixed position at the end of
the circuit, it is found that the deflections of this detector depend
greatly upon the position of the bridge LM, rising rapidly to a
maximum for some positions, and falling rapidly away when the bridge
is displaced. As the bridge is moved from the coil end towards the
detector the deflections show periodic variations, such as are
represented in fig. 8 when the ordinates represent the deflections of
the detector and the abscissae the distance of the bridge from the
ends D, E. The maximum deflections of the detector correspond to the
positions in which the two circuits DFLMGE, HLMJ (in which the
vibrations are but slightly damped) are in resonance. For since the
self-induction and resistance of the bridge LM is very small compared
with that of the circuit beyond, it follows from the theory of
circuits in parallel that only a small part of the current will in
general flow round the longer circuit; it is only when the two
circuits DFLMGE, HLMJ are in resonance that a considerable current
will flow round the latter. Hence when we get a maximum effect in the
detector we know that the waves we are dealing with are those
corresponding to the free periods of the system HLMJ, so that if we
know the free periods of this circuit we know the wave length of the
electric waves under consideration. Thus if the ends of the wires H, J
are free and have no capacity, the current along them must vanish at H
and J, which must be in opposite electric condition. Hence half the
wave length must be an odd submultiple of the length of the circuit
HLMJ. If H and J are connected together the wave length must be a
submultiple of the length of this circuit. When the capacity at the
ends is appreciable the wave length of the circuit is determined by a
somewhat complex expression. To facilitate the determination of the
wave length in such cases, Lecher introduced a second bridge L'M', and
moved this about until the deflection of the detector was a maximum;
when this occurs the wave length is one of those corresponding to the
closed circuit LMM'L', and must therefore be a submultiple of the
length of the circuit. Lecher showed that if instead of using a single
wire LM to form the bridge, he used two parallel wires PQ, LM, placed
close together, the currents in the further circuit were hardly
appreciably diminished when the main wires were cut between PL and QM.
Blondlot used a modification of this apparatus better suited for the
production of short waves. In his form (fig. 9) the exciter consists
of two semicircular arms connected with the terminals of an induction
coil, and the long wires, instead of being connected with the small
plates, form a circuit round the exciter.
As an example of the use of Lecher's arrangement, we may quote Drude's
application of the method to find the specific induction capacity of
dielectrics under electric oscillations of varying frequency. In this
application the ends of the wire are connected to the plates of a
condenser, the space between whose plates can be filled with the
liquid whose specific inductive capacity is required, and the bridge
is moved until the detector at the end of the circuit gives the
maximum deflection. Then if [lambda] is the wave length of the waves,
[lambda] is the wave length of one of the free vibrations of the
system HLMJ; hence if C is the capacity of the condenser at the end in
electrostatic measure we have
2[pi]l
cot --------
[lambda] C
------------ = ---
2[pi]l C'l
--------
[lambda]
where l is the distance of the condenser from the bridge and C' is the
capacity of unit length of the wire. In the condenser part of the
lines of force will pass through air and part through the dielectric;
hence C will be of the form C0+KC1 where K is the specific inductive
capacity of the dielectric. Hence if l is the distance of maximum
deflection when the dielectric is replaced by air, l' when filled with
a dielectric whose specific inductive capacity is known to be K', and
l" the distance when filled with the dielectric whose specific
inductive capacity is required, we easily see that--
2[pi]l 2[pi]l'
cot -------- - cot --------
[lambda] [lambda] 1 - K'
--------------------------- = ------
2[pi]l 2[pi]l" 1 - K
cot -------- - cot --------
[lambda] [lambda]
an equation by means of which K can be determined. It was in this way
that Drude investigated the specific inductive capacity with varying
frequency, and found a falling off in the specific inductive capacity
with increase of frequency when the dielectrics contained the radicle
OH. In another method used by him the wires were led through long
tanks filled with the liquid whose specific inductive capacity was
required; the velocity of propagation of the electric waves along the
wires in the tank being the same as the velocity of propagation of an
electromagnetic disturbance through the liquid filling the tank, if we
find the wave length of the waves along the wires in the tank, due to
a vibration of a given frequency, and compare this with the wave
lengths corresponding to the same frequency when the wires are
surrounded by air, we obtain the velocity of propagation of
electromagnetic disturbance through the fluid, and hence the specific
inductive capacity of the fluid.
[Illustration: FIG. 9.]
S 10. _Velocity of Propagation of Electromagnetic Effects through
Air._--The experiments of Sarasin and De la Rive already described
(see S 5) have shown that, as theory requires, the velocity of
propagation of electric effects through air is the same as along
wires. The same result had been arrived at by J.J. Thomson, although
from the method he used greater differences between the velocities
might have escaped detection than was possible by Sarasin and De la
Rive's method. The velocity of waves along wires has been directly
determined by Blondlot by two different methods. In the first the
detector consisted of two parallel plates about 6 cm. in diameter
placed a fraction of a millimetre apart, and forming a condenser whose
capacity C was determined in electromagnetic measure by Maxwell's
method. The plates were connected by a rectangular circuit whose
self-induction L was calculated from the dimensions of the rectangle
and the size of the wire. The time of vibration T is equal to
2[pi][root](LC). (The wave length corresponding to this time is long
compared with the length of the circuit, so that the use of this
formula is legitimate.) This detector is placed between two parallel
wires, and the waves produced by the exciter are reflected from a
movable bridge. When this bridge is placed just beyond the detector
vigorous sparks are observed, but as the bridge is pushed away a place
is reached where the sparks disappear; this place is distance
2/[lambda] from the detector, when [lambda] is the wave length of the
vibration given out by the detector. The sparks again disappear when
the distance of the bridge from the detector is 3[lambda]/4. Thus by
measuring the distance between two consecutive positions of the bridge
at which the sparks disappear [lambda] can be determined, and v, the
velocity of propagation, is equal to [lambda]/T. As the means of a
number of experiments Blondlot found v to be 3.02 X 10^10 cm./sec.,
which, within the errors of experiment, is equal to 3 X 10^10
cm./sec., the velocity of light. A second method used by Blondlot, and
one which does not involve the calculation of the period, is as
follows:--A and A' (fig. 10) are two equal Leyden jars coated inside
and outside with tin-foil. The outer coatings form two separate rings
a, a1; a', a'1, and the inner coatings are connected with the poles of
the induction coil by means of the metal pieces b, b'. The sharply
pointed conductors p and p', the points of which are about 1/2 mm.
apart, are connected with the rings of the tin-foil a and a', and two
long copper wires pca1, p'c'a'1, 1029 cm. long, connect these points
with the other rings a1, a1'. The rings aa', a1a1', are connected by
wet strings so as to charge up the jars. When a spark passes between b
and b', a spark at once passes between pp', and this is followed by
another spark when the waves travelling by the paths a1cp, a'1c'p'
reach p and p'. The time between the passage of these sparks, which is
the time taken by the waves to travel 1029 cm., was observed by means
of a rotating mirror, and the velocity measured in 15 experiments
varied between 2.92 X 10^10 and 3.03 X 10^10 cm./sec., thus agreeing
well with that deduced by the preceding method. Other determinations
of the velocity of electromagnetic propagation have been made by Lodge
and Glazebrook, and by Saunders.
[Illustration: FIG. 10.]
On Maxwell's electromagnetic theory the velocity of propagation of
electromagnetic disturbances should equal the velocity of light, and
also the ratio of the electromagnetic unit of electricity to the
electrostatic unit. A large number of determinations of this ratio
have been made:--
Observer. Date. Ratio 10^10 X.
Klemencic 1884 3.019 cm./sec.
Himstedt 1888 3.009 cm./sec.
Rowland 1889 2.9815 cm./sec.
Rosa 1889 2.9993 cm./sec.
J.J. Thomson and Searle 1890 2.9955 cm./sec.
Webster 1891 2.987 cm./sec.
Pellat 1891 3.009 cm./sec.
Abraham 1892 2.992 cm./sec.
Hurmuzescu 1895 3.002 cm./sec.
Rosa 1908 2.9963 cm./sec.
The mean of these determinations is 3.001 X 10^10 cm./sec., while the
mean of the last five determinations of the velocity of light in air
is given by Himstedt as 3.002 X 10^10 cm./sec. From these experiments
we conclude that the velocity of propagation of an electromagnetic
disturbance is equal to the velocity of light, and to the velocity
required by Maxwell's theory.
In experimenting with electromagnetic waves it is in general more
difficult to measure the period of the oscillations than their wave
length. Rutherford used a method by which the period of the vibration
can easily be determined; it is based upon the theory of the
distribution of alternating currents in two circuits ACB, ADB in
parallel. If A and B are respectively the maximum currents in the
circuits ACB, ADB, then
A / S^2 + (N - M)^2p^2 \
-- = [root]( ------------------ )
B \ R^2 + (L - M)^2p^2 /
when R and S are the resistances, L and N the coefficients of
self-induction of the circuits ACB, ADB respectively, M the
coefficient of mutual induction between the circuits, and p the
frequency of the currents. Rutherford detectors were placed in the two
circuits, and the circuits adjusted until they showed that A = B; when
this is the case
R^2 - S^2
p^2 = ---------------------.
N^2 - L^2 - 2M(N - L)
If we make one of the circuits, ADB, consist of a short length of a
high liquid resistance, so that S is large and N small, and the
other circuit ACB of a low metallic resistance bent to have
considerable self-induction, the preceding equation becomes
approximately p = S/L, so that when S and L are known p is readily
determined. (J. J. T.)
ELECTROCHEMISTRY. The present article deals with processes that involve
the electrolysis of aqueous solutions, whilst those in which electricity
is used in the manufacture of chemical products at furnace temperatures
are treated under ELECTROMETALLURGY, although, strictly speaking, in
some cases (e.g. calcium carbide and phosphorus manufacture) they are
not truly metallurgical in character. For the theory and elemental laws
of electro-deposition see ELECTROLYSIS; and for the construction and use
of electric generators see DYNAMO and BATTERY: _Electric_. The
importance of the subject may be gauged by the fact that all the
aluminium, magnesium, sodium, potassium, calcium carbide, carborundum
and artificial graphite, now placed on the market, is made by electrical
processes, and that the use of such processes for the refining of copper
and silver, and in the manufacture of phosphorus, potassium chlorate and
bleach, already pressing very heavily on the older non-electrical
systems, is every year extending. The convenience also with which the
energy of waterfalls can be converted into electric energy has led to
the introduction of chemical industries into countries and districts
where, owing to the absence of coal, they were previously unknown.
Norway and Switzerland have become important producers of chemicals, and
pastoral districts such as those in which Niagara or Foyers are situated
manufacturing centres. In this way the development of the
electrochemical industry is in a marked degree altering the distribution
of trade throughout the world.
_Electrolytic Refining of Metals._--The principle usually followed in
the electrolytic refining of metals is to cast the impure metal into
plates, which are exposed as anodes in a suitable solvent, commonly a
salt of the metal under treatment. On passing a current of electricity,
of which the volume and pressure are adjusted to the conditions of the
electrolyte and electrodes, the anode slowly dissolves, leaving the
insoluble impurities in the form of a sponge, if the proportion be
considerable, but otherwise as a mud or slime which becomes detached
from the anode surface and must be prevented from coming into contact
with the cathode. The metal to be refined passing into solution is
concurrently deposited at the cathode. Soluble impurities which are more
electro-negative than the metal under treatment must, if present, be
removed by a preliminary process, and the voltage and other conditions
must be so selected that none of the more electro-positive metals are
co-deposited with the metal to be refined. From these and other
considerations it is obvious that (1) the electrolyte must be such as
will freely dissolve the metal to be refined; (2) the electrolyte must
be able to dissolve the major portion of the anode, otherwise the mass
of insoluble matter on the outer layer will prevent access of
electrolyte to the core, which will thus escape refining; (3) the
electrolyte should, if possible, be incapable of dissolving metals more
electro-negative than that to be refined; (4) the proportion of soluble
electro-positive impurities must not be excessive, or these substances
will accumulate too rapidly in the solution and necessitate its frequent
purification; (5) the current density must be so adjusted to the
strength of the solution and to other conditions that no relatively
electro-positive metal is deposited, and that the cathode deposit is
physically suitable for subsequent treatment; (6) the current density
should be as high as is consistent with the production of a pure and
sound deposit, without undue expense of voltage, so that the operation
may be rapid and the "turnover" large; (7) the electrolyte should be as
good a conductor of electricity as possible, and should not, ordinarily,
be altered chemically by exposure to air; and (8) the use of porous
partitions should be avoided, as they increase the resistance and
usually require frequent renewal. For details of the practical methods
see GOLD; SILVER; COPPER and headings for other metals.
_Electrolytic Manufacture of Chemical Products._--When an aqueous
solution of the salt of an alkali metal is electrolysed, the metal
reacts with the water, as is well known, forming caustic alkali, which
dissolves in the solution, and hydrogen, which comes off as a gas. So
early as 1851 a patent was taken out by Cooke for the production of
caustic alkali without the use of a separate current, by immersing iron
and copper plates on opposite sides of a porous (biscuit-ware) partition
in a suitable cell, containing a solution of the salt to be
electrolysed, at 21 deg.-65 deg. C. (70 deg.-150 deg. F.). The solution
of the iron anode was intended to afford the necessary energy. In the
same year another patent was granted to C. Watt for a similar process,
involving the employment of an externally generated current. When an
alkaline chloride, say sodium chloride, is electrolysed with one
electrode immersed in a porous cell, while caustic soda is formed at the
cathode, chlorine is deposited at the anode. If the latter be insoluble,
the gas diffuses into the solution and, when this becomes saturated,
escapes into the air. If, however, no porous division be used to prevent
the intermingling by diffusion of the anode and cathode solutions, a
complicated set of subsidiary reactions takes place. The chlorine reacts
with the caustic soda, forming sodium hypochlorite, and this in turn,
with an excess of chlorine and at higher temperatures, becomes for the
most part converted into chlorate, whilst any simultaneous electrolysis
of a hydroxide or water and a chloride (so that hydroxyl and chlorine
are simultaneously liberated at the anode) also produces oxygen-chlorine
compounds direct. At the same time, the diffusion of these compounds
into contact with the cathode leads to a partial reduction to chloride,
by the removal of combined oxygen by the instrumentality of the hydrogen
there evolved. In proportion as the original chloride is thus
reproduced, the efficiency of the process is of course diminished. It is
obvious that, with suitable methods and apparatus, the electrolysis of
alkaline chlorides may be made to yield chlorine, hypochlorites
(bleaching liquors), chlorates or caustic alkali, but that great care
must be exercised if any of these products is to be obtained pure and
with economy. Many patents have been taken out in this branch of
electrochemistry, but it is to be remarked that that granted to C. Watt
traversed the whole of the ground. In his process a current was passed
through a tank divided into two or three cells by porous partitions,
hoods and tubes were arranged to carry off chlorine and hydrogen
respectively, and the whole was heated to 120 deg. F. by a steam jacket
when caustic alkali was being made. Hypochlorites were made, at ordinary
temperatures, and chlorates at higher temperatures, in a cell without a
partition in which the cathode was placed horizontally immediately above
the anode, to favour the mixing of the ascending chlorine with the
descending caustic solution.
The relation between the composition of the electrolyte and the
various conditions of current-density, temperature and the like has
been studied by F. Oettel (_Zeitschrift f. Elektrochem._, 1894, vol.
i. pp. 354 and 474) in connexion with the production of hypochlorites
and chlorates in tanks without diaphragms, by C. Haussermann and W.
Naschold (_Chemiker Zeitung_, 1894, vol. xviii. p. 857) for their
production in cells with porous diaphragms, and by F. Haber and S.
Grinberg (_Zeitschrift f. anorgan. Chem._, 1898, vol. xvi. pp. 198,
329, 438) in connexion with the electrolysis of hydrochloric acid.
Oettel, using a 20% solution of potassium chloride, obtained the best
yield of hypochlorite with a high current-density, but as soon as
1-1/4% of bleaching chlorine (as hypochlorite) was present, the
formation of chlorate commenced. The yield was at best very low as
compared with that theoretically possible. The best yield of chlorate
was obtained when from 1 to 4% of caustic potash was present. With
high current-density, heating the solution tended to increase the
proportion of chlorate to hypochlorite, but as the proportion of water
decomposed is then higher, the amount of chlorine produced must be
less and the total chlorine efficiency lower. He also traced a
connexion between alkalinity, temperature and current-density, and
showed that these conditions should be mutually adjusted. With a
current-density of 130 to 140 amperes per sq. ft., at 3 volts, passing
between platinum electrodes, he attained to a current-efficiency of
52%, and each (British) electrical horse-power hour was equivalent to
a production of 1378.5 grains of potassium chlorate. In other words,
each pound of chlorate would require an expenditure of nearly 5.1
e.h.p. hours. One of the earliest of the more modern processes was
that of E. Hermite, which consisted in the production of
bleach-liquors by the electrolysis (according to the 1st edition of
the 1884 patent) of magnesium or calcium chloride between platinum
anodes carried in wooden frames, and zinc cathodes. The solution,
containing hypochlorites and chlorates, was then applied to the
bleaching of linen, paper-pulp or the like, the solution being used
over and over again. Many modifications have been patented by Hermite,
that of 1895 specifying the use of platinum gauze anodes, held in
ebonite or other frames. Rotating zinc cathodes were used, with
scrapers to prevent the accumulation of a layer of insoluble magnesium
compounds, which would otherwise increase the electrical resistance
beyond reasonable limits. The same inventor has patented the
application of electrolysed chlorides to the purification of starch by
the oxidation of less stable organic bodies, to the bleaching of oils,
and to the purification of coal gas, spirit and other substances. His
system for the disinfection of sewage and similar matter by the
electrolysis of chlorides, or of sea-water, has been tried, but for
the most part abandoned on the score of expense. Reference may be made
to papers written in the early days of the process by C.F. Cross and
E.J. Bevan (_Journ. Soc. Chem. Industry_, 1887, vol. vi. p. 170, and
1888, vol. vii. p. 292), and to later papers by P. Schoop
(_Zeitschrift f. Elektrochem._, 1895, vol. ii. pp. 68, 88, 107, 209,
289).
E. Kellner, who in 1886 patented the use of cathode (caustic soda) and
anode (chlorine) liquors in the manufacture of cellulose from
wood-fibre, and has since evolved many similar processes, has produced
an apparatus that has been largely used. It consists of a stoneware
tank with a thin sheet of platinum-iridium alloy at either end forming
the primary electrodes, and between them a number of glass plates
reaching nearly to the bottom, each having a platinum gauze sheet on
either side; the two sheets belonging to each plate are in metallic
connexion, but insulated from all the others, and form intermediary or
bi-polar electrodes. A 10-12% solution of sodium chloride is caused to
flow upwards through the apparatus and to overflow into troughs, by
which it is conveyed (if necessary through a cooling apparatus) back
to the circulating pump. Such a plant has been reported as giving
0.229 gallon of a liquor containing 1% of available chlorine per
kilowatt hour, or 0.171 gallon per e.h.p. hour. Kellner has also
patented a "bleaching-block," as he terms it, consisting of a frame
carrying parallel plates similar in principle to those last described.
The block is immersed in the solution to be bleached, and may be
lifted in or out as required. O. Knofler and Gebauer have also a
system of bi-polar electrodes, mounted in a frame in appearance
resembling a filter-press.
_Other Electrochemical Processes._--It is obvious that electrolytic
iodine and bromine, and oxygen compounds of these elements, may be
produced by methods similar to those applied to chlorides (see ALKALI
MANUFACTURE and CHLORATES), and Kellner and others have patented
processes with this end in view. _Hydrogen_ and _oxygen_ may also be
produced electrolytically as gases, and their respective reducing and
oxidizing powers at the moment of deposition on the electrode are
frequently used in the laboratory, and to some extent industrially,
chiefly in the field of organic chemistry. Similarly, the formation of
organic halogen products may be effected by electrolytic chlorine, as,
for example, in the production of _chloral_ by the gradual introduction
of alcohol into an anode cell in which the electrolyte is a strong
solution of potassium chloride. Again, anode reactions, such as are
observed in the electrolysis of the fatty acids, may be utilized, as,
for example, when the radical CH3CO2--deposited at the anode in the
electrolysis of acetic acid--is dissociated, two of the groups react to
give one molecule of _ethane_, C2H6, and two of carbon dioxide. This,
which has long been recognized as a class-reaction, is obviously capable
of endless variation. Many electrolytic methods have been proposed for
the purification of _sugar_; in some of them soluble anodes are used for
a few minutes in weak alkaline solutions, so that the caustic alkali
from the cathode reaction may precipitate chemically the hydroxide of
the anode metal dissolved in the liquid, the precipitate carrying with
it mechanically some of the impurities present, and thus clarifying the
solution. In others the current is applied for a longer time to the
original sugar-solution with insoluble (e.g. carbon) anodes. F. Peters
has found that with these methods the best results are obtained when
ozone is employed in addition to electrolytic oxygen. Use has been made
of electrolysis in _tanning_ operations, the current being passed
through the tan-liquors containing the hides. The current, by
endosmosis, favours the passage of the solution into the hide-substance,
and at the same time appears to assist the chemical combinations there
occurring; hence a great reduction in the time required for the
completion of the process. Many patents have been taken out in this
direction, one of the best known being that of Groth, experimented upon
by S. Rideal and A.P. Trotter (_Journ. Soc. Chem. Indust._, 1891, vol.
x. p. 425), who employed copper anodes, 4 sq. ft. in area, with
current-densities of 0.375 to 1 (ranging in some cases to 7.5) ampere
per sq. ft., the best results being obtained with the smaller
current-densities. Electrochemical processes are often indirectly used,
as for example in the Villon process (_Elec. Rev._, New York, 1899, vol.
xxxv. p. 375) applied in Russia to the manufacture of alcohol, by a
series of chemical reactions starting from the production of acetylene
by the action of water upon calcium carbide. The production of _ozone_
in small quantities during electrolysis, and by the so-called silent
discharge, has long been known, and the Siemens induction tube has been
developed for use industrially. The Siemens and Halske ozonizer, in form
somewhat resembling the old laboratory instrument, is largely used in
Germany; working with an alternating current transformed up to 6500
volts, it has been found to give 280 grains or more of ozone per e.h.p.
hour. E. Andreoli (whose first British ozone patent was No. 17,426 of
1891) uses flat aluminium plates and points, and working with an
alternating current of 3000 volts is said to have obtained 1440 grains
per e.h.p. hour. Yarnold's process, using corrugated glass plates coated
on one side with gold or other metal leaf, is stated to have yielded as
much as 2700 grains per e.h.p. hour. The ozone so prepared has numerous
uses, as, for example, in bleaching oils, waxes, fabrics, &c.,
sterilizing drinking-water, maturing wines, cleansing foul beer-casks,
oxidizing oil, and in the manufacture of vanillin.
For further information the following books, among others, may be
consulted:--Haber, _Grundriss der technischen Elektrochemie_ (Munchen,
1898); Borchers and M'Millan, _Electric Smelting and Refining_
(London, 1904); E.D. Peters, _Principles of Copper Smelting_ (New
York, 1907); F. Peters, _Angewandte Elektrochemie_, vols. ii. and iii.
(Leipzig, 1900); Gore, _The Art of Electrolytic Separation of Metals_
(London, 1890); Blount, _Practical Electro-Chemistry_ (London, 1906);
G. Langbein, _Vollstandiges Handbuch der galvanischen
Metall-Niederschlage_ (Leipzig, 1903), Eng. trans. by W.T. Brannt
(1909); A. Watt, _Electro-Plating and Electro-Refining of Metals_
(London, 1902); W.H. Wahl, _Practical Guide to the Gold and Silver
Electroplater, &c._ (Philadelphia, 1883); Wilson, _Stereotyping and
Electrotyping_ (London); Lunge, _Sulphuric Acid and Alkali_, vol. iii.
(London, 1909). Also papers in various technical periodicals. The
industrial aspect is treated in a Gartside Report, _Some
Electro-Chemical Centres_ (Manchester, 1908), by J.N. Pring.
(W. G. M.)
ELECTROCUTION (an anomalous derivative from "electro-execution"; syn.
"electrothanasia"), the popular name, invented in America, for the
infliction of the death penalty on criminals (see CAPITAL PUNISHMENT) by
passing through the body of the condemned a sufficient current of
electricity to cause death. The method was first adopted by the state of
New York, a law making this method obligatory having been passed and
approved by the governor on the 4th of June 1888. The law provides that
there shall be present, in addition to the warden, two physicians,
twelve reputable citizens of full age, seven deputy sheriffs, and such
ministers, priests or clergymen, not exceeding two, as the criminal may
request. A post-mortem examination of the body of the convict is
required, and the body, unless claimed by relatives, is interred in the
prison cemetery with a sufficient quantity of quicklime to consume it.
The law became effective in New York on the 1st of January 1889. The
first criminal to be executed by electricity was William Kemmler, on the
6th of August 1890, at Auburn prison. The validity of the New York law
had previously been attacked in regard to this case (_Re Kemmler_, 1889;
136 U.S. 436), as providing "a cruel and unusual punishment" and
therefore being contrary to the Constitution; but it was sustained in
the state courts and finally in the Federal courts. By 1906 about one
hundred and fifteen murderers had been successfully executed by
electricity in New York state in Sing Sing, Auburn and Dannemora
prisons. The method has also been adopted by the states of Ohio (1896),
Massachusetts (1898), New Jersey (1906), Virginia (1908) and North
Carolina (1910).
The apparatus consists of a stationary engine, an alternating dynamo
capable of generating a current at a pressure of 2000 volts, a
"death-chair" with adjustable head-rest, binding straps and adjustable
electrodes devised by E.F. Davis, the state electrician of New York. The
voltmeter, ammeter and switch-board controlling the current are located
in the execution-room; the dynamo-room is communicated with by electric
signals. Before each execution the entire apparatus is thoroughly
tested. When everything is in readiness the criminal is brought in and
seats himself in the death-chair. His head, chest, arms and legs are
secured by broad straps; one electrode thoroughly moistened with
salt-solution is affixed to the head, and another to the calf of one
leg, both electrodes being moulded so as to secure good contact. The
application of the current is usually as follows: the contact is made
with a high voltage (1700-1800 volts) for 5 to 7 seconds, reduced to 200
volts until a half-minute has elapsed; raised to high voltage for 3 to 5
seconds, again reduced to low voltage for 3 to 5 seconds, again reduced
to a low voltage until one minute has elapsed, when it is again raised
to the high voltage for a few seconds and the contact broken. The
ammeter usually shows that from 7 to 10 amperes pass through the
criminal's body. A second or even a third brief contact is sometimes
made, partly as a precautionary measure, but rather the more completely
to abolish reflexes in the dead body. Calculations have shown that by
this method of execution from 7 to 10 h. p. of energy are liberated in
the criminal's body. The time consumed by the strapping-in process is
usually about 45 seconds, and the first contact is made about 70 seconds
after the criminal has entered the death-chamber.
When properly performed the effect is painless and instantaneous death.
The mechanism of life, circulation and respiration cease with the first
contact. Consciousness is blotted out instantly, and the prolonged
application of the current ensures permanent derangement of the vital
functions beyond recovery. Occasionally the drying of the sponges
through undue generation of heat causes desquamation or superficial
blistering of the skin at the site of the electrodes. Post-mortem
discoloration, or post-mortem lividity, often appears during the first
contact. The pupils of the eyes dilate instantly and remain dilated
after death.
The post-mortem examination of "electrocuted" criminals reveals a number
of interesting phenomena. The temperature of the body rises promptly
after death to a very high point. At the site of the leg electrode a
temperature of over 128 deg. F. was registered within fifteen minutes in
many cases. After the removal of the brain the temperature recorded in
the spinal canal was often over 120 deg. F. The development of this high
temperature is to be regarded as resulting from the active metabolism of
tissues not (somatically) dead within a body where all vital mechanisms
have been abolished, there being no circulation to carry off the
generated heat. The heart, at first flaccid when exposed soon after
death, gradually contracts and assumes a tetanized condition; it empties
itself of all blood and takes the form of a heart in systole. The lungs
are usually devoid of blood and weigh only 7 or 8 ounces (avoird.) each.
The blood is profoundly altered biochemically; it is of a very dark
colour and it rarely coagulates. (E. A. S.*)
ELECTROKINETICS, that part of electrical science which is concerned with
the properties of electric currents.
_Classification of Electric Currents._--Electric currents are classified
into (a) conduction currents, (b) convection currents, (c) displacement
or dielectric currents. In the case of conduction currents electricity
flows or moves through a stationary material body called the conductor.
In convection currents electricity is carried from place to place with
and on moving material bodies or particles. In dielectric currents there
is no continued movement of electricity, but merely a limited
displacement through or in the mass of an insulator or dielectric. The
path in which an electric current exists is called an electric circuit,
and may consist wholly of a conducting body, or partly of a conductor
and insulator or dielectric, or wholly of a dielectric. In cases in
which the three classes of currents are present together the true
current is the sum of each separately. In the case of conduction
currents the circuit consists of a conductor immersed in a
non-conductor, and may take the form of a thin wire or cylinder, a
sheet, surface or solid. Electric conduction currents may take place in
space of one, two or three dimensions, but for the most part the
circuits we have to consider consist of thin cylindrical wires or tubes
of conducting material surrounded with an insulator; hence the case
which generally presents itself is that of electric flow in space of one
dimension. Self-closed electric currents taking place in a sheet of
conductor are called "eddy currents."
Although in ordinary language the current is said to flow in the
conductor, yet according to modern views the real pathway of the energy
transmitted is the surrounding dielectric, and the so-called conductor
or wire merely guides the transmission of energy in a certain direction.
The presence of an electric current is recognized by three qualities or
powers: (1) by the production of a magnetic field, (2) in the case of
conduction currents, by the production of heat in the conductor, and (3)
if the conductor is an electrolyte and the current unidirectional, by
the occurrence of chemical decomposition in it. An electric current may
also be regarded as the result of a movement of electricity across each
section of the circuit, and is then measured by the quantity conveyed
per unit of time. Hence if dq is the quantity of electricity which flows
across any section of the conductor in the element of time dt, the
current i = dq/dt.
[Illustration: FIG. 1.]
[Illustration: FIG. 2.]
Electric currents may be also classified as constant or variable and as
unidirectional or "direct," that is flowing always in the same
direction, or "alternating," that is reversing their direction at
regular intervals. In the last case the variation of current may follow
any particular law. It is called a "periodic current" if the cycle of
current values is repeated during a certain time called the periodic
time, during which the current reaches a certain maximum value, first in
one direction and then in the opposite, and in the intervals between has
a zero value at certain instants. The frequency of the periodic current
is the number of periods or cycles in one second, and alternating
currents are described as low frequency or high frequency, in the latter
case having some thousands of periods per second. A periodic current may
be represented either by a wave diagram, or by a polar diagram.[1] In
the first case we take a straight line to represent the uniform flow of
time, and at small equidistant intervals set up perpendiculars above or
below the time axis, representing to scale the current at that instant
in one direction or the other; the extremities of these ordinates then
define a wavy curve which is called the wave form of the current (fig.
1). It is obvious that this curve can only be a single valued curve. In
one particular and important case the form of the current curve is a
simple harmonic curve or simple sine curve. If T represents the periodic
time in which the cycle of current values takes place, whilst n is the
frequency or number of periods per second and p stands for 2[pi]n, and i
is the value of the current at any instant t, and I its maximum value,
then in this case we have i = I sin pt. Such a current is called a "sine
current" or simple periodic current.
In a polar diagram (fig. 2) a number of radial lines are drawn from a
point at small equiangular intervals, and on these lines are set off
lengths proportional to the current value of a periodic current at
corresponding intervals during one complete period represented by four
right angles. The extremities of these radii delineate a polar curve.
The polar form of a simple sine current is obviously a circle drawn
through the origin. As a consequence of Fourier's theorem it follows
that any periodic curve having any wave form can be imitated by the
superposition of simple sine currents differing in maximum value and in
phase.
_Definitions of Unit Electric Current._--In electrokinetic
investigations we are most commonly limited to the cases of
unidirectional continuous and constant currents (C.C. or D.C.), or of
simple periodic currents, or alternating currents of sine form (A.C.). A
continuous electric current is measured either by the magnetic effect it
produces at some point outside its circuit, or by the amount of
electrochemical decomposition it can perform in a given time on a
selected standard electrolyte. Limiting our consideration to the case of
linear currents or currents flowing in thin cylindrical wires, a
definition may be given in the first place of the unit electric current
in the centimetre, gramme, second (C.G.S.) of electromagnetic
measurement (see UNITS, PHYSICAL). H.C. Oersted discovered in 1820 that
a straight wire conveying an electric current is surrounded by a
magnetic field the lines of which are self-closed lines embracing the
electric circuit (see ELECTRICITY and ELECTROMAGNETISM). The unit
current in the electromagnetic system of measurement is defined as the
current which, flowing in a thin wire bent into the form of a circle of
one centimetre in radius, creates a magnetic field having a strength of
2[pi] units at the centre of the circle, and therefore would exert a
mechanical force of 2[pi] dynes on a unit magnetic pole placed at that
point (see MAGNETISM). Since the length of the circumference of the
circle of unit radius is 2[pi] units, this is equivalent to stating that
the unit current on the electromagnetic C.G.S. system is a current such
that unit length acts on unit magnetic pole with a unit force at a unit
of distance. Another definition, called the electrostatic unit of
current, is as follows: Let any conductor be charged with electricity
and discharged through a thin wire at such a rate that one electrostatic
unit of quantity (see ELECTROSTATICS) flows past any section of the wire
in one unit of time. The electromagnetic unit of current defined as
above is 3 X 10^10 times larger than the electrostatic unit.
In the selection of a practical unit of current it was considered that
the electromagnetic unit was too large for most purposes, whilst the
electrostatic unit was too small; hence a practical unit of current
called 1 ampere was selected, intended originally to be 1/10 of the
absolute electromagnetic C.G.S. unit of current as above defined. The
practical unit of current, called the international ampere, is, however,
legally defined at the present time as the continuous unidirectional
current which when flowing through a neutral solution of silver nitrate
deposits in one second on the cathode or negative pole 0.001118 of a
gramme of silver. There is reason to believe that the international unit
is smaller by about one part in a thousand, or perhaps by one part in
800, than the theoretical ampere defined as 1/10 part of the absolute
electromagnetic unit. A periodic or alternating current is said to have
a value of 1 ampere if when passed through a fine wire it produces in
the same time the same heat as a unidirectional continuous current of 1
ampere as above electrochemically defined. In the case of a simple
periodic alternating current having a simple sine wave form, the maximum
value is equal to that of the equiheating continuous current multiplied
by [root]2. This equiheating continuous current is called the effective
or root-mean-square (R.M.S.) value of the alternating one.
_Resistance._--A current flows in a circuit in virtue of an
electromotive force (E.M.F.), and the numerical relation between the
current and E.M.F. is determined by three qualities of the circuit
called respectively, its resistance (R), inductance (L), and capacity
(C). If we limit our consideration to the case of continuous
unidirectional conduction currents, then the relation between current
and E.M.F. is defined by Ohm's law, which states that the numerical
value of the current is obtained as the quotient of the electromotive
force by a certain constant of the circuit called its resistance, which
is a function of the geometrical form of the circuit, of its nature,
i.e. material, and of its temperature, but is independent of the
electromotive force or current. The resistance (R) is measured in units
called ohms and the electromotive force in volts (V); hence for a
continuous current the value of the current in amperes (A) is obtained
as the quotient of the electromotive force acting in the circuit
reckoned in volts by the resistance in ohms, or A = V/R. Ohm established
his law by a course of reasoning which was similar to that on which
J.B.J. Fourier based his investigations on the uniform motion of heat in
a conductor. As a matter of fact, however, Ohm's law merely states the
direct proportionality of steady current to steady electromotive force
in a circuit, and asserts that this ratio is governed by the numerical
value of a quality of the conductor, called its resistance, which is
independent of the current, provided that a correction is made for the
change of temperature produced by the current. Our belief, however, in
its universality and accuracy rests upon the close agreement between
deductions made from it and observational results, and although it is
not derivable from any more fundamental principle, it is yet one of the
most certainly ascertained laws of electrokinetics.
Ohm's law not only applies to the circuit as a whole but to any part of
it, and provided the part selected does not contain a source of
electromotive force it may be expressed as follows:--The difference of
potential (P.D.) between any two points of a circuit including a
resistance R, but not including any source of electromotive force, is
proportional to the product of the resistance and the current i in the
element, provided the conductor remains at the same temperature and the
current is constant and unidirectional. If the current is varying we
have, however, to take into account the electromotive force (E.M.F.)
produced by this variation, and the product Ri is then equal to the
difference between the observed P.D. and induced E.M.F.
We may otherwise define the resistance of a circuit by saying that it is
that physical quality of it in virtue of which energy is dissipated as
heat in the circuit when a current flows through it. The power
communicated to any electric circuit when a current i is created in it
by a continuous unidirectional electromotive force E is equal to Ei, and
the energy dissipated as heat in that circuit by the conductor in a
small interval of time dt is measured by Ei dt. Since by Ohm's law E =
Ri, where R is the resistance of the circuit, it follows that the energy
dissipated as heat per unit of time in any circuit is numerically
represented by Ri^2, and therefore the resistance is measured by the heat
produced per unit of current, provided the current is unvarying.
_Inductance._--As soon as we turn our attention, however, to alternating
or periodic currents we find ourselves compelled to take into account
another quality of the circuit, called its "inductance." This may be
defined as that quality in virtue of which energy is stored up in
connexion with the circuit in a magnetic form. It can be experimentally
shown that a current cannot be created instantaneously in a circuit by
any finite electromotive force, and that when once created it cannot be
annihilated instantaneously. The circuit possesses a quality analogous
to the inertia of matter. If a current i is flowing in a circuit at any
moment, the energy stored up in connexion with the circuit is measured
by 1/2Li^2, where L, the inductance of the circuit, is related to the
current in the same manner as the quantity called the mass of a body is
related to its velocity in the expression for the ordinary kinetic
energy, viz. 1/2Mv^2. The rate at which this conserved energy varies with
the current is called the "electrokinetic momentum" of this circuit (=
Li). Physically interpreted this quantity signifies the number of lines
of magnetic flux due to the current itself which are self-linked with
its own circuit.
_Magnetic Force and Electric Currents._--In the case of every circuit
conveying a current there is a certain magnetic force (see MAGNETISM) at
external points which can in some instances be calculated. Laplace
proved that the magnetic force due to an element of length dS of a
circuit conveying a current I at a point P at a distance r from the
element is expressed by IdS sin [theta]/r^2, where [theta] is the angle
between the direction of the current element and that drawn between the
element and the point. This force is in a direction perpendicular to the
radius vector and to the plane containing it and the element of current.
Hence the determination of the magnetic force due to any circuit is
reduced to a summation of the effects due to all the elements of length.
For instance, the magnetic force at the centre of a circular circuit of
radius r carrying a steady current I is 2[pi]I/r, since all elements
are at the same distance from the centre. In the same manner, if we take
a point in a line at right angles to the plane of the circle through its
centre and at a distance d, the magnetic force along this line is
expressed by 2[pi]r^2I/(r^2 + d^2)(3/2). Another important case is that
of an infinitely long straight current. By summing up the magnetic force
due to each element at any point P outside the continuous straight
current I, and at a distance d from it, we can show that it is equal to
2I/d or is inversely proportional to the distance of the point from the
wire. In the above formula the current I is measured in absolute
electromagnetic units. If we reckon the current in amperes A, then I =
A/10.
It is possible to make use of this last formula, coupled with an
experimental fact, to prove that the magnetic force due to an element of
current varies inversely as the square of the distance. If a flat
circular disk is suspended so as to be free to rotate round a straight
current which passes through its centre, and two bar magnets are placed
on it with their axes in line with the current, it is found that the
disk has no tendency to rotate round the current. This proves that the
force on each magnetic pole is inversely as its distance from the
current. But it can be shown that this law of action of the whole
infinitely long straight current is a mathematical consequence of the
fact that each element of the current exerts a magnetic force which
varies inversely as the square of the distance. If the current flows N
times round the circuit instead of once, we have to insert NA/10 in
place of I in all the above formulae. The quantity NA is called the
"ampere-turns" on the circuit, and it is seen that the magnetic field at
any point outside a circuit is proportional to the ampere-turns on it
and to a function of its geometrical form and the distance of the point.
[Illustration: FIG. 3.]
[Illustration: FIG. 4.]
There is therefore a distribution of magnetic force in the field of
every current-carrying conductor which can be delineated by lines of
magnetic force and rendered visible to the eye by iron filings (see
Magnetism). If a copper wire is passed vertically through a hole in a
card on which iron filings are sprinkled, and a strong electric current
is sent through the circuit, the filings arrange themselves in
concentric circular lines making visible the paths of the lines of
magnetic force (fig. 3). In the same manner, by passing a circular wire
through a card and sending a strong current through the wire we can
employ iron filings to delineate for us the form of the lines of
magnetic force (fig. 4). In all cases a magnetic pole of strength M,
placed in the field of an electric current, is urged along the lines of
force with a mechanical force equal to MH, where H is the magnetic
force. If then we carry a unit magnetic pole against the direction in
which it would naturally move we do _work_. The lines of magnetic force
embracing a current-carrying conductor are always loops or endless
lines.
The work done in carrying a unit magnetic pole once round a circuit
conveying a current is called the "line integral of magnetic force"
along that path. If, for instance, we carry a unit pole in a circular
path of radius r once round an infinitely long straight filamentary
current I, the line integral is 4[pi]I. It is easy to prove that this
is a general law, and that if we have any currents flowing in a
conductor the line integral of magnetic force taken once round a path
linked with the current circuit is 4[pi] times the total current
flowing through the circuit. Let us apply this to the case of an
endless solenoid. If a copper wire insulated or covered with cotton or
silk is twisted round a thin rod so as to make a close spiral, this
forms a "solenoid," and if the solenoid is bent round so that its two
ends come together we have an endless solenoid. Consider such a
solenoid of mean length l and N turns of wire. If it is made endless,
the magnetic force H is the same everywhere along the central axis and
the line integral along the axis is Hl. If the current is denoted by
I, then NI is the total current, and accordingly 4[pi]NI = Hl, or H =
4[pi]NI/l. For a thin endless solenoid the axial magnetic force is
therefore 4[pi] times the current-turns per unit of length. This holds
good also for a long straight solenoid provided its length is large
compared with its diameter. It can be shown that if insulated wire is
wound round a sphere, the turns being all parallel to lines of
latitude, the magnetic force in the interior is constant and the lines
of force therefore parallel. The magnetic force at a point outside a
conductor conveying a current can by various means be measured or
compared with some other standard magnetic forces, and it becomes then
a means of measuring the current. Instruments called galvanometers and
ammeters for the most part operate on this principle.
_Thermal Effects of Currents._--J.P. Joule proved that the heat produced
by a constant current in a given time in a wire having a constant
resistance is proportional to the square of the strength of the current.
This is known as Joule's law, and it follows, as already shown, as an
immediate consequence of Ohm's law and the fact that the power
dissipated electrically in a conductor, when an electromotive force E is
applied to its extremities, producing thereby a current I in it, is
equal to EI.
If the current is alternating or periodic, the heat produced in any
time T is obtained by taking the sum at equidistant intervals of time
of all the values of the quantities Ri^2dt, where dt represents a small
interval of time and i is the current at that instant. The quantity
_
/ T
T^(-1) | i^2dt is called the mean-square-value of the variable
_/ 0
current, i being the instantaneous value of the current, that is, its
value at a particular instant or during a very small interval of time
dt. The square root of the above quantity, or
_ _ _
| / T | 1/2,
| T^(-1) | i^2dt |
|_ _/ 0 _|
is called the root-mean-square-value, or the effective value of the
current, and is denoted by the letters R.M.S.
Currents have equal heat-producing power in conductors of identical
resistance when they have the same R.M.S. values. Hence periodic or
alternating currents can be measured as regards their R.M.S. value by
ascertaining the continuous current which produces in the same time the
same heat in the same conductor as the periodic current considered.
Current measuring instruments depending on this fact, called hot-wire
ammeters, are in common use, especially for measuring alternating
currents. The maximum value of the periodic current can only be
determined from the R.M.S. value when we know the wave form of the
current. The thermal effects of electric currents in conductors are
dependent upon the production of a state of equilibrium between the heat
produced electrically in the wire and the causes operative in removing
it. If an ordinary round wire is heated by a current it loses heat, (1)
by radiation, (2) by air convection or cooling, and (3) by conduction of
heat out of the ends of the wire. Generally speaking, the greater part
of the heat removal is effected by radiation and convection.
If a round sectioned metallic wire of uniform diameter d and length l
made of a material of resistivity [rho] has a current of A amperes
passed through it, the heat in watts produced in any time t seconds is
represented by the value of 4A^2[rho]lt/10^9[pi]d^2, where d and l
must be measured in centimetres and [rho] in absolute C.G.S.
electromagnetic units. The factor 10^9 enters because one ohm is 10^9
absolute electromagnetic C.G.S. units (see UNITS, PHYSICAL). If the
wire has an emissivity e, by which is meant that e units of heat
reckoned in joules or watt-seconds are radiated per second from unit
of surface, then the power removed by radiation in the time t is
expressed by [pi]dlet. Hence when thermal equilibrium is established
we have 4A^2[rho]lt/10^9[pi]d^2 = [pi]dlet, or A^2 =
10^9[pi]^2ed^3/4[rho]. If the diameter of the wire is reckoned in mils
(1 mil = .001 in.), and if we take e to have a value 0.1, an
emissivity which will generally bring the wire to about 60 deg. C., we
can put the above formula in the following forms for circular
sectioned copper, iron or platinoid wires, viz.
A = [root](d^3/500) for copper wires
A = [root](d^3/4000) for iron wires
A = [root](d^3/5000) for platinoid wires.
These expressions give the ampere value of the current which will
bring bare, straight or loosely coiled wires of d mils in diameter to
about 60 deg. C. when the steady state of temperature is reached. Thus,
for instance, a bare straight copper wire 50 mils in diameter (=0.05
in.) will be brought to a steady temperature of about 60 deg. C. if a
current of [root]50^3/500 = [root]250 = 16 amperes (nearly) is passed
through it, whilst a current of [root]25 = 5 amperes would bring a
platinoid wire to about the same temperature.
A wire has therefore a certain safe current-carrying capacity which is
determined by its specific resistance and emissivity, the latter being
fixed by its form, surface and surroundings. The emissivity increases
with the temperature, else no state of thermal equilibrium could be
reached. It has been found experimentally that whilst for fairly thick
wires from 8 to 60 mils in diameter the safe current varies
approximately as the 1.5th power of the diameter, for fine wires of 1 to
3 mils it varies more nearly as the diameter.
_Action of one Current on Another._--The investigations of Ampere in
connexion with electric currents are of fundamental importance in
electrokinetics. Starting from the discovery of Oersted, Ampere made
known the correlative fact that not only is there a mechanical action
between a current and a magnet, but that two conductors conveying
electric currents exert mechanical forces on each other. Ampere devised
ingenious methods of making one portion of a circuit movable so that he
might observe effects of attraction or repulsion between this circuit
and some other fixed current. He employed for this purpose an astatic
circuit B, consisting of a wire bent into a double rectangle round which
a current flowed first in one and then in the opposite direction (fig.
5). In this way the circuit was removed from the action of the earth's
magnetic field, and yet one portion of it could be submitted to the
action of any other circuit C. The astatic circuit was pivoted by
suspending it in mercury cups q, p, one of which was in electrical
connexion with the tubular support A, and the other with a strong
insulated wire passing up it.
[Illustration: FIG. 5.]
Ampere devised certain crucial experiments, and the theory deduced from
them is based upon four facts and one assumption.[2] He showed (1) that
wire conveying a current bent back on itself produced no action upon a
proximate portion of a movable astatic circuit; (2) that if the return
wire was bent zig-zag but close to the outgoing straight wire the
circuit produced no action on the movable one, showing that the effect
of an element of the circuit was proportional to its projected length;
(3) that a closed circuit cannot cause motion in an element of another
circuit free to move in the direction of its length; and (4) that the
action of two circuits on one and the same movable circuit was null if
one of the two fixed circuits was n times greater than the other but n
times further removed from the movable circuit. From this last
experiment by an ingenious line of reasoning he proved that the action
of an element of current on another element of current varies inversely
as a square of their distance. These experiments enabled him to
construct a mathematical expression of the law of action between two
elements of conductors conveying currents. They also enabled him to
prove that an element of current may be resolved like a force into
components in different directions, also that the force produced by any
element of the circuit on an element of any other circuit was
perpendicular to the line joining the elements and inversely as the
square of their distance. Also he showed that this force was an
attraction if the currents in the elements were in the same direction,
but a repulsion if they were in opposite directions. From these
experiments and deductions from them he built up a complete formula for
the action of one element of a current of length dS of one conductor
conveying a current I upon another element dS' of another circuit
conveying another current I' the elements being at a distance apart
equal to r.
If [theta] and [theta]' are the angles the elements make with the line
joining them, and [phi] the angle they make with one another, then
Ampere's expression for the mechanical force f the elements exert on
one another is
f = 2II'r^(-2) {cos [phi] - (3/2)cos [theta] cos [theta]'}dSdS'.
This law, together with that of Laplace already mentioned, viz. that
the magnetic force due to an element of length dS of a current I at a
distance r, the element making an angle [theta] with the radius vector
o is IdS sin [theta]/r^2, constitute the fundamental laws of
electrokinetics.
Ampere applied these with great mathematical skill to elucidate the
mechanical actions of currents on each other, and experimentally
confirmed the following deductions: (1) Currents in parallel circuits
flowing in the same direction attract each other, but if in opposite
directions repel each other. (2) Currents in wires meeting at an angle
attract each other more into parallelism if both flow either to or from
the angle, but repel each other more widely apart if they are in
opposite directions. (3) A current in a small circular conductor exerts
a magnetic force in its centre perpendicular to its plane and is in all
respects equivalent to a magnetic shell or a thin circular disk of steel
so magnetized that one face is a north pole and the other a south pole,
the product of the area of the circuit and the current flowing in it
determining the magnetic moment of the element. (4) A closely wound
spiral current is equivalent as regards external magnetic force to a
polar magnet, such a circuit being called a finite solenoid. (5) Two
finite solenoid circuits act on each other like two polar magnets,
exhibiting actions of attraction or repulsion between their ends.
Ampere's theory was wholly built up on the assumption of action at a
distance between elements of conductors conveying the electric currents.
Faraday's researches and the discovery of the fact that the insulating
medium is the real seat of the operations necessitates a change in the
point of view from which we regard the facts discovered by Ampere.
Maxwell showed that in any field of magnetic force there is a tension
along the lines of force and a pressure at right angles to them; in
other words, lines of magnetic force are like stretched elastic threads
which tend to contract.[3] If, therefore, two conductors lie parallel
and have currents in them in the same direction they are impressed by a
certain number of lines of magnetic force which pass round the two
conductors, and it is the tendency of these to contract which draws the
circuits together. If, however, the currents are in opposite directions
then the lateral pressure of the similarly contracted lines of force
between them pushes the conductors apart. Practical application of
Ampere's discoveries was made by W.E. Weber in inventing the
electrodynamometer, and later Lord Kelvin devised ampere balances for
the measurement of electric currents based on the attraction between
coils conveying electric currents.
_Induction of Electric Currents._--Faraday[4] in 1831 made the important
discovery of the induction of electric currents (see ELECTRICITY). If
two conductors are placed parallel to each other, and a current in one
of them, called the primary, started or stopped or changed in strength,
every such alteration causes a transitory current to appear in the other
circuit, called the secondary. This is due to the fact that as the
primary current increases or decreases, its own embracing magnetic field
alters, and lines of magnetic force are added to or subtracted from its
fields. These lines do not appear instantly in their place at a
distance, but are propagated out from the wire with a velocity equal to
that of light; hence in their outward progress they cut through the
secondary circuit, just as ripples made on the surface of water in a
lake by throwing a stone on to it expand and cut through a stick held
vertically in the water at a distance from the place of origin of the
ripples. Faraday confirmed this view of the phenomena by proving that
the mere motion of a wire transversely to the lines of magnetic force of
a permanent magnet gave rise to an induced electromotive force in the
wire. He embraced all the facts in the single statement that if there
be any circuit which by movement in a magnetic field, or by the creation
or change in magnetic fields round it, experiences a change in the
number of lines of force linked with it, then an electromotive force is
set up in that circuit which is proportional at any instant to the rate
at which the total magnetic flux linked with it is changing. Hence if Z
represents the total number of lines of magnetic force linked with a
circuit of N turns, then -N(dZ/dt) represents the electromotive force
set up in that circuit. The operation of the induction coil (q.v.) and
the transformer (q.v.) are based on this discovery. Faraday also found
that if a copper disk A (fig. 6) is rotated between the poles of a
magnet NO so that the disk moves with its plane perpendicular to the
lines of magnetic force of the field, it has created in it an
electromotive force directed from the centre to the edge or vice versa.
The action of the dynamo (q.v.) depends on similar processes, viz. the
cutting of the lines of magnetic force of a constant field produced by
certain magnets by certain moving conductors called armature bars or
coils in which an electromotive force is thereby created.
[Illustration: FIG 6.]
In 1834 H.F.E. Lenz enunciated a law which connects together the
mechanical actions between electric circuits discovered by Ampere and
the induction of electric currents discovered by Faraday. It is as
follows: If a constant current flows in a primary circuit P, and if by
motion of P a secondary current is created in a neighbouring circuit
S, the direction of the secondary current will be such as to oppose
the relative motion of the circuits. Starting from this, F.E. Neumann
founded a mathematical theory of induced currents, discovering a
quantity M, called the "potential of one circuit on another," or
generally their "coefficient of mutual inductance." Mathematically M
is obtained by taking the sum of all such quantities as ff dSdS' cos
[phi]/r, where dS and dS' are the elements of length of the two
circuits, r is their distance, and [phi] is the angle which they make
with one another; the summation or integration must be extended over
every possible pair of elements. If we take pairs of elements in the
same circuit, then Neumann's formula gives us the coefficient of
self-induction of the circuit or the potential of the circuit on
itself. For the results of such calculations on various forms of
circuit the reader must be referred to special treatises.
H. von Helmholtz, and later on Lord Kelvin, showed that the facts of
induction of electric currents discovered by Faraday could have been
predicted from the electrodynamic actions discovered by Ampere
assuming the principle of the conservation of energy. Helmholtz takes
the case of a circuit of resistance R in which acts an electromotive
force due to a battery or thermopile. Let a magnet be in the
neighbourhood, and the potential of the magnet on the circuit be V, so
that if a current I existed in the circuit the work done on the magnet
in the time dt is I(dV/dt)dt. The source of electromotive force
supplies in the time dt work equal to EIdt, and according to Joule's
law energy is dissipated equal to RI^2dt. Hence, by the conservation
of energy,
EIdt = RI^2dt + I(dV/dt)dt.
If then E = 0, we have I = -(dV/dt)/R, or there will be a current due
to an induced electromotive force expressed by -dV/dt. Hence if the
magnet moves, it will create a current in the wire provided that such
motion changes the potential of the magnet with respect to the
circuit. This is the effect discovered by Faraday.[5]
_Oscillatory Currents._--In considering the motion of electricity in
conductors we find interesting phenomena connected with the discharge of
a condenser or Leyden jar (q.v.). This problem was first mathematically
treated by Lord Kelvin in 1853 (_Phil. Mag._, 1853, 5, p. 292).
If a conductor of capacity C has its terminals connected by a wire of
resistance R and inductance L, it becomes important to consider the
subsequent motion of electricity in the wire. If Q is the quantity of
electricity in the condenser initially, and q that at any time t after
completing the circuit, then the energy stored up in the condenser at
that instant is 1/2q^2/C, and the energy associated with the circuit
is 1/2L(dq/dt)^2, and the rate of dissipation of energy by resistance
is R(dq/dt)^2, since dq/dt = i is the discharge current. Hence we can
construct an equation of energy which expresses the fact that at any
instant the power given out by the condenser is partly stored in the
circuit and partly dissipated as heat in it. Mathematically this is
expressed as follows:--
_ _ _ _
d | q^2 | d | /dq\^2 | /dq\^2
- -- | 1/2 --- | = -- | 1/2L ( -- ) | + R ( -- )
dt |_ C _| dt |_ \dt/ _| \dt/
or
d^2q R dq 1
---- + -- -- + -- q = 0.
dt^2 L dt LC
The above equation has two solutions according as R^2/4L^2 is greater
or less than 1/LC. In the first case the current i in the circuit can
be expressed by the equation
[alpha]^2+[beta]^2
i= Q ------------------ e^(-[alpha]t) [e^([beta]t) - e^(-[beta]t)],
2[beta]
________
/R^2 1
where [alpha] = R/2L, [beta] = / --- - --, Q is the value of q when
\/ 4L^2 LC
t = 0, and e is the base of Napierian logarithms; and in the second
case by the equation
[alpha]^2+[beta]^2
i = Q ------------------ e^(-[alpha]t) sin [beta]t
[beta]
_________
/1 R^2
where [alpha] = R/2L, and [beta] = / -- - ----.
\/ LC 4L^2
These expressions show that in the first case the discharge current of
the jar is always in the same direction and is a transient
unidirectional current. In the second case, however, the current is an
oscillatory current gradually decreasing in amplitude, the frequency n
of the oscillation being given by the expression
_________
1 /1 R^2
n = ----- / -- - ----.
2[pi] \/ LC 4L^2
In those cases in which the resistance of the discharge circuit is
very small, the expression for the frequency n and for the time period
of oscillation R take the simple forms n = 1, 2[pi][root]LC, or T =
1/n = 2[pi][root]LC.
The above investigation shows that if we construct a circuit consisting
of a condenser and inductance placed in series with one another, such
circuit has a natural electrical time period of its own in which the
electrical charge in it oscillates if disturbed. It may therefore be
compared with a pendulum of any kind which when displaced oscillates
with a time period depending on its inertia and on its restoring force.
The study of these electrical oscillations received a great impetus
after H.R. Hertz showed that when taking place in electric circuits of a
certain kind they create electromagnetic waves (see ELECTRIC WAVES) in
the dielectric surrounding the oscillator, and an additional interest
was given to them by their application to telegraphy. If a Leyden jar
and a circuit of low resistance but some inductance in series with it
are connected across the secondary spark gap of an induction coil, then
when the coil is set in action we have a series of bright noisy sparks,
each of which consists of a train of oscillatory electric discharges
from the jar. The condenser becomes charged as the secondary
electromotive force of the coil is created at each break of the primary
current, and when the potential difference of the condenser coatings
reaches a certain value determined by the spark-ball distance a
discharge happens. This discharge, however, is not a single movement of
electricity in one direction but an oscillatory motion with gradually
decreasing amplitude. If the oscillatory spark is photographed on a
revolving plate or a rapidly moving film, we have evidence in the
photograph that such a spark consists of numerous intermittent sparks
gradually becoming feebler. As the coil continues to operate, these
trains of electric discharges take place at regular intervals. We can
cause a train of electric oscillations in one circuit to induce similar
oscillations in a neighbouring circuit, and thus construct an
oscillation transformer or high frequency induction coil.
_Alternating Currents._--The study of alternating currents of
electricity began to attract great attention towards the end of the 19th
century by reason of their application in electrotechnics and
especially to the transmission of power. A circuit in which a simple
periodic alternating current flows is called a single phase circuit. The
important difference between such a form of current flow and steady
current flow arises from the fact that if the circuit has inductance
then the periodic electric current in it is not in step with the
terminal potential difference or electromotive force acting in the
circuit, but the current lags behind the electromotive force by a
certain fraction of the periodic time called the "phase difference." If
two alternating currents having a fixed difference in phase flow in two
connected separate but related circuits, the two are called a two-phase
current. If three or more single-phase currents preserving a fixed
difference of phase flow in various parts of a connected circuit, the
whole taken together is called a polyphase current. Since an electric
current is a vector quantity, that is, has direction as well as
magnitude, it can most conveniently be represented by a line denoting
its maximum value, and if the alternating current is a simple periodic
current then the root-mean-square or effective value of the current is
obtained by dividing the maximum value by [root]2. Accordingly when we
have an electric circuit or circuits in which there are simple periodic
currents we can draw a vector diagram, the lines of which represent the
relative magnitudes and phase differences of these currents.
A vector can most conveniently be represented by a symbol such as a +
ib, where a stands for any length of a units measured horizontally and
b for a length b units measured vertically, and the symbol i is a sign
of perpendicularity, and equivalent analytically[6] to [root]-1.
Accordingly if E represents the periodic electromotive force (maximum
value) acting in a circuit of resistance R and inductance L and
frequency n, and if the current considered as a vector is represented
by I, it is easy to show that a vector equation exists between these
quantities as follows:--
E = RI + [iota]2[pi]nLI.
Since the absolute magnitude of a vector a + [iota]b is [root](a^2 +
b^2), it follows that considering merely magnitudes of current and
electromotive force and denoting them by symbols (E) (I), we have the
following equation connecting (I) and (E):--
(I) = (E)[root](R^2 + p^2L^2),
where p stands for 2[pi]n. If the above equation is compared with the
symbolic expression of Ohm's law, it will be seen that the quantity
[root](R^2 + p^2L^2) takes the place of resistance R in the expression
of Ohm. This quantity [root](R^2 + p^2L^2) is called the "impedance"
of the alternating circuit. The quantity pL is called the "reactance"
of the alternating circuit, and it is therefore obvious that the
current in such a circuit lags behind the electromotive force by an
angle, called the angle of lag, the tangent of which is pL/R.
_Currents in Networks of Conductors._--In dealing with problems
connected with electric currents we have to consider the laws which
govern the flow of currents in linear conductors (wires), in plane
conductors (sheets), and throughout the mass of a material
conductor.[7] In the first case consider the collocation of a number
of linear conductors, such as rods or wires of metal, joined at their
ends to form a network of conductors. The network consists of a number
of conductors joining certain points and forming meshes. In each
conductor a current may exist, and along each conductor there is a
fall of potential, or an active electromotive force may be acting in
it. Each conductor has a certain resistance. To find the current in
each conductor when the individual resistances and electromotive
forces are given, proceed as follows:--Consider any one mesh. The sum
of all the electromotive forces which exist in the branches bounding
that mesh must be equal to the sum of all the products of the
resistances into the currents flowing along them, or [Sigma](E) =
[Sigma](C.R.). Hence if we consider each mesh as traversed by
imaginary currents all circulating in the same direction, the real
currents are the sums or differences of these imaginary cyclic
currents in each branch. Hence we may assign to each mesh a cycle
symbol x, y, z, &c., and form a cycle equation. Write down the cycle
symbol for a mesh and prefix as coefficient the sum of all the
resistances which bound that cycle, then subtract the cycle symbols of
each adjacent cycle, each multiplied by the value of the bounding or
common resistances, and equate this sum to the total electromotive
force acting round the cycle. Thus if x y z are the cycle currents,
and a b c the resistances bounding the mesh x, and b and c those
separating it from the meshes y and z, and E an electromotive force in
the branch a, then we have formed the cycle equation x(a + b + c) -
by - cz = E. For each mesh a similar equation may be formed. Hence we
have as many linear equations as there are meshes, and we can obtain
the solution for each cycle symbol, and therefore for the current in
each branch. The solution giving the current in such branch of the
network is therefore always in the form of the quotient of two
determinants. The solution of the well-known problem of finding the
current in the galvanometer circuit of the arrangement of linear
conductors called Wheatstone's Bridge is thus easily obtained. For if
we call the cycles (see fig. 7) (x + y), y and z, and the resistances
P, Q, R, S, G and B, and if E be the electromotive force in the
battery circuit, we have the cycle equations
(P + G + R)(x + y) - Gy - Rz = 0,
(Q + G + S)y - G(x + y) - Sz = 0,
(R + S + B)z - R(x + y) - Sy = E.
[Illustration: FIG. 7.]
From these we can easily obtain the solution for (x + y) - y = x,
which is the current through the galvanometer circuit in the form
x = E(PS - RQ)[Delta].
where [Delta] is a certain function of P, Q, R, S, B and G.
_Currents in Sheets._--In the case of current flow in plane sheets, we
have to consider certain points called sources at which the current
flows into the sheet, and certain points called sinks at which it
leaves. We may investigate, first, the simple case of one source and
one sink in an infinite plane sheet of thickness [delta] and
conductivity k. Take any point P in the plane at distances R and r
from the source and sink respectively. The potential V at P is
obviously given by
Q r1
V = -------------log_e --,
2[pi]k[delta] r2
where Q is the quantity of electricity supplied by the source per
second. Hence the equation to the equipotential curve is r1r2 = a
constant.
If we take a point half-way between the sink and the source as the
origin of a system of rectangular co-ordinates, and if the distance
between sink and source is equal to p, and the line joining them is
taken as the axis of x, then the equation to the equipotential line is
y^2 + (x + p)^2
--------------- = a constant.
y^2 + (x - p)^2
This is the equation of a family of circles having the axis of y for a
common radical axis, one set of circles surrounding the sink and
another set of circles surrounding the source. In order to discover
the form of the stream of current lines we have to determine the
orthogonal trajectories to this family of coaxial circles. It is easy
to show that the orthogonal trajectory of the system of circles is
another system of circles all passing through the sink and the source,
and as a corollary of this fact, that the electric resistance of a
circular disk of uniform thickness is the same between any two points
taken anywhere on its circumference as sink and source. These
equipotential lines may be delineated experimentally by attaching the
terminals of a battery or batteries to small wires which touch at
various places a sheet of tinfoil. Two wires attached to a
galvanometer may then be placed on the tinfoil, and one may be kept
stationary and the other may be moved about, so that the galvanometer
is not traversed by any current. The moving terminal then traces out
an equipotential curve. If there are n sinks and sources in a plane
conducting sheet, and if r, r', r" be the distances of any point from
the sinks, and t, t', t" the distances of the sources, then
r r' r" ...
----------- = a constant,
t t' t" ...
is the equation to the equipotential lines. The orthogonal
trajectories or stream lines have the equation
[Sigma]([theta] - [theta]') = a constant,
where [theta] and [theta]' are the angles which the lines drawn from
any point in the plane to the sink and corresponding source make with
the line joining that sink and source. Generally it may be shown that
if there are any number of sinks and sources in an infinite
plane-conducting sheet, and if r, [theta] are the polar co-ordinates
of any one, then the equation to the equipotential surfaces is given
by the equation
[Sigma](A log_er) = a constant,
where A is a constant; and the equation to the stream of current lines
is
[Sigma]([theta]) = a constant.
In the case of electric flow in three dimensions the electric
potential must satisfy Laplace's equation, and a solution is therefore
found in the form [Sigma](A/r) = a constant, as the equation to an
equipotential surface, where r is the distance of any point on that
surface from a source or sink.
_Convection Currents._--The subject of convection electric currents has
risen to great importance in connexion with modern electrical
investigations. The question whether a statically electrified body in
motion creates a magnetic field is of fundamental importance.
Experiments to settle it were first undertaken in the year 1876 by H.A.
Rowland, at a suggestion of H. von Helmholtz.[8] After preliminary
experiments, Rowland's first apparatus for testing this hypothesis was
constructed, as follows:--An ebonite disk was covered with radial strips
of gold-leaf and placed between two other metal plates which acted as
screens. The disk was then charged with electricity and set in rapid
rotation. It was found to affect a delicately suspended pair of astatic
magnetic needles hung in proximity to the disk just as would, by
Oersted's rule, a circular electric current coincident with the
periphery of the disk. Hence the statically-charged but rotating disk
becomes in effect a circular electric current.
The experiments were repeated and confirmed by W.C. Rontgen (_Wied.
Ann._, 1888, 35, p. 264; 1890, 40, p. 93) and by F. Himstedt (_Wied.
Ann._, 1889, 38, p. 560). Later V. Cremieu again repeated them and
obtained negative results (_Com. rend._, 1900, 130, p. 1544, and 131,
pp. 578 and 797; 1901, 132, pp. 327 and 1108). They were again very
carefully reconducted by H. Pender (_Phil. Mag._, 1901, 2, p. 179) and
by E.P. Adams (id. ib., 285). Pender's work showed beyond any doubt that
electric convection does produce a magnetic effect. Adams employed
charged copper spheres rotating at a high speed in place of a disk, and
was able to prove that the rotation of such spheres produced a magnetic
field similar to that due to a circular current and agreeing numerically
with the theoretical value. It has been shown by J.J. Thomson (_Phil.
Mag._, 1881, 2, p. 236) and O. Heaviside (_Electrical Papers_, vol. ii.
p. 205) that an electrified sphere, moving with a velocity v and
carrying a quantity of electricity q, should produce a magnetic force H,
at a point at a distance [rho] from the centre of the sphere, equal to
qv sin [theta]/[rho]^2, where [theta] is the angle between the direction
of [rho] and the motion of the sphere. Adams found the field produced by
a known electric charge rotating at a known speed had a strength not
very different from that predetermined by the above formula. An
observation recorded by R.W. Wood (_Phil. Mag._, 1902, 2, p. 659)
provides a confirmatory fact. He noticed that if carbon-dioxide strongly
compressed in a steel bottle is allowed to escape suddenly the cold
produced solidifies some part of the gas, and the issuing jet is full of
particles of carbon-dioxide snow. These by friction against the nozzle
are electrified positively. Wood caused the jet of gas to pass through a
glass tube 2.5 mm. in diameter, and found that these particles of
electrified snow were blown through it with a velocity of 2000 ft. a
second. Moreover, he found that a magnetic needle hung near the tube was
deflected as if held near an electric current. Hence the positively
electrified particles in motion in the tube create a magnetic field
round it.
_Nature of an Electric Current._--The question, What is an electric
current? is involved in the larger question of the nature of
electricity. Modern investigations have shown that negative electricity
is identical with the electrons or corpuscles which are components of
the chemical atom (see MATTER and ELECTRICITY). Certain lines of
argument lead to the conclusion that a solid conductor is not only
composed of chemical atoms, but that there is a certain proportion of
free electrons present in it, the electronic density or number per unit
of volume being determined by the material, its temperature and other
physical conditions. If any cause operates to add or remove electrons at
one point there is an immediate diffusion of electrons to re-establish
equilibrium, and this electronic movement constitutes an electric
current. This hypothesis explains the reason for the identity between
the laws of diffusion of matter, of heat and of electricity.
Electromotive force is then any cause making or tending to make an
inequality of electronic density in conductors, and may arise from
differences of temperature, i.e. thermoelectromotive force (see
THERMOELECTRICITY), or from chemical action when part of the circuit is
an electrolytic conductor, or from the movement of lines of magnetic
force across the conductor.
BIBLIOGRAPHY.--For additional information the reader may be referred
to the following books: M. Faraday, _Experimental Researches in
Electricity_ (3 vols., London, 1839, 1844, 1855); J. Clerk Maxwell,
_Electricity and Magnetism_ (2 vols., Oxford, 1892); W. Watson and
S.H. Burbury, _Mathematical Theory of Electricity and Magnetism_, vol.
ii. (Oxford, 1889); E. Mascart and J. Joubert, _A Treatise on
Electricity and Magnetism_ (2 vols., London, 1883); A. Hay,
_Alternating Currents_ (London, 1905); W.G. Rhodes, _An Elementary
Treatise on Alternating Currents_ (London, 1902); D.C. Jackson and
J.P. Jackson, _Alternating Currents and Alternating Current Machinery_
(1896, new ed. 1903); S.P. Thompson, _Polyphase Electric Currents_
(London, 1900); _Dynamo-Electric Machinery_, vol. ii., "Alternating
Currents" (London, 1905); E.E. Fournier d'Albe, _The Electron Theory_
(London, 1906). (J. A. F.)