An ordinary alternating current machine has a period of 0.02 sec, whence it only can excite the characteristic oscillation of a circuit if in it 2p(LC)1/2 = 0.02 sec. The capacity and inductivity of such a circuit are enormous - also its period of oscillation. However, we are only interested in oscillations, which are millions times shorter. A circuit with a Leyden jar of ordinary size (0.001 Microfarad capacity, that is, C = 10-9 Farad) and an about 1 m long connecting wire (about L= 10-6 Henry) has the characteristic period T = 2p(10-9·10-6)1/2 = about 1/5·106 sec. How can it be excited? Answer: By letting the circuit discharge itself by means of a spark. In fact, a spark discharge is not a single current shock, but a set of short duration currents, which flow to and fro in rapid succession in mutually opposite directions or, in the words of Hertz: Similarly to the striking of a bell, it is composed of a large number of oscillations, that is, to and fro moving discharges, which follow each other after exactly identical periods. And this also explains that, while the spark discharge acts like a stationary current, electrolyzing, magnetizing and inducting, during the electrolysis of water both gases - hydrogen and oxygen - develop at both electrodes; also, during the magnetization of a needle, around which the discharge is conducted, the needle has now the North pole at the one end, then at the other end (Henry 1842). Helmholtz 1847 drew from the law of conservation of energy the conclusion that a spark discharge must be an oscillatory process; experimentally, this was first demonstrated by Feddersen 1857. (In Fig. 593, obtained by means of a fast rotating mirror alternate [side by side and simultaneously facing each other] lighter and less light spots. The lighter ones are the discharges from the anode; you thus see that the electrodes change their polarity all along.) However, the most convincing proof of the fact that the discharge of a Leyden jar consists of oscillations, is supplied by the fact: The circuit of a Leyden jar, which discharges itself, generates in a similar circuit (Fig. 594), on which it acts inducting, under certain conditions a phenomenon, similar to resonance. If you let it act on another circuit, the inductivity and capacity of which must have almost the same period and change steadily the capacity C or the inductivity L, and hence also the period T = 2p(LC)1/2 of one of the two circuits, then resonance must manifest itself by the inductive action of the one circuit on the other, which is for certain values of C and L much stronger than for other values of C and L. And indeed, this is what happens.
The resonance of electric oscillations
yields for the detection of
electric oscillations (presence of which is suspected) a
tool which is simple as well as sensitive. Hertz's resonator (Fig. 595) is a wire bent into a rectangle or circle with a very
short spark gap f. If the inducting circuit - the
radiator - is active, you see under certain conditions - relating
to the relative position to the inducting circuit (its distance
and the orientation of its plane in space) - small sparks at f.
They indicate a resonant action similar to that described by Fig. 594. They are explained by the fact that
the oscillations, radiating from the inducing circuit, induct in
the wire frame electro-motoric forces, which are large enough to
compensate themselves across the spark gap. An ordinary
alternating current could never provoke such an action in the
resonator, because the induction emanating from it on a simple
wire, and in addition over a large distance, is much too small.
In contrast, in Hertz's inducting circuit (Fig. 596), the direction of the current changes many ten
thousand times faster; this makes the EMF so large - the
important thing after all is the rate at which the inducting
current changes.
The to and fro motion of the discharge is an action of self-induction. The quantity of electricity, which is shifted during the discharge, and the rate, at which the tension (and with it the intensity of the current) drops, depend also on the capacity of the discharging conductor. Following the theory of William Thomson (Lord Kelvin), also here is the period of the oscillation (one to and fro) T=2p(LC)1/2, where C is the capacity of the discharging conductor and L the coefficient of self-induction. The fact that the electric charge in this phenomenon flows so fast to and fro is demonstrated by Braun's tube (Fig. 519), if you connect the coatings of a Leyden jar to the plates FF. The cathode ray is then deflected according to the instantaneous direction of the electrical discharge, whence the motion of the phosphorescent spot reflects the oscillation (Fig 520).
Similarity between electric oscillations and light
Experiments concerning the effects of dielectrics, containing inducting and inducted circuits, on induction phenomena guided Faraday to the view that the fields, caused by electric charges and magnetic poles in surrounding media, demand a certain amount of time for their propagation. If we could suddenly generate at a location in space a magnetic pole, the interaction between this pole and a distant magnetic needle would not occur at the same instant; there would elapse a certain (although very short) time until the needle responds to the newly installed pole. In fact, the magnetic field of the pole requires a certain time before it reaches the magnetic needle. The same applies to the electric field of an electric charge.
Faraday's contemporaries believed in an unmediated
distant action of electric and magnetic forces. Only Maxwell 1864 was
able to follow the new ideas and - by far outdistancing Faraday -
to formulate them mathematically. Maxwell's equations - the
foundation of the new theory - express the interaction between
magnetic and electric fields: Wherever a magnetic
field experiences a change in time - disappears or arises -
a definite redistribution of the electric force field
arises thereby in the neighbourhood; conversely, if an electric field
of force changes in time, it brings about a definite distribution
of the magnetic field of force. From his equations, Maxwell drew
mathematically a number of fundamental conclusions, which could
be checked by experiments. They culminated in the result that
changes in magnetic and electric fields propagate through empty
space at the same
velocity as waves of light. This
result suggested the possibility that electric waves, which
according to their mode of generation have to comprise electric
and magnetic fields, could be similar to the waves emitted by a
source of light. Transversality of the oscillations and velocity
of propagation of 300,000 km/sec are common to both kinds of
waves. However, only after one had succeeded to reproduce
with electric waves those phenomena, which proved that light
had wave nature, and use them to measure their lengths, all
doubts could be removed. This was the achievement of Hertz.
Prior to a discussion of Hertz's experiments, we will try to obtain an image of an electromagnetic wave. For this purpose, we must understand the forces which cause in sparks the to and fro motion and ask to start with: Why does not the balancing of charges occur simply by the electricity flowing through the spark gap from the condenser layer to the other until both have the same tension? Compare the situation with the oscillating pendulum! The raised pendulum returns as it is released to its equilibrium position - its lowest location; when it arrives there, it has large kinetic energy- due to its fall -and it rises again on the other side - due to its inertia. If we arrange complete absence of friction, the pendulum rises as far as it has fallen, and goes on to repeat this process in the same manner. The pendulum's initial purely potential energy is converted by the fall into kinetic energy, which attains its maximum value as the pendulum passes through the lowest point. As it rises again, the kinetic energy reconverts into potential energy, which attains its maximum value when the pendulum starts to return. Thus, in a pendulum, a certain constant amount of energy is intermittently converted from the one form into the other.
In an electric oscillation, which occurs without losses - heat development and radiation - we are concerned with an amount of energy, which is conserved, but changes all along its kind in a definite rhythm. The change between magnetic and electric field energy in electric oscillations corresponds to the change between the potential and kinetic energy in the pendulum. At the instant when the spark starts, the entire energy is obviously electric - it consists of the charge of the condenser. The condenser discharges itself by the spark: There arises a current, which generates a magnetic field. However, the current cannot stop suddenly at the instant, when the tension is equilibrated, because the fading magnetic field continues to conduct the current. This phenomenon is nothing else but self-induction. We have seen that an electric current, as it is switched off, does not suddenly cease, but gradually fades out (excess current). In a circuit without condenser, this excess current is used to heat the wires. However, in the case of an oscillator, it serves above all for recharging the condenser, of course, in the opposite direction. If no losses of energy have occurred, the condenser also attains apart from the sign the same state of charge as before, and the cycle continues; the current now flows in the opposite direction through the spark gap. Thus, like the pendulum, the current has, while passing through the equilibrium state (that is, at the instant of voltage adjustment), inertia which advances the present motion of the electricity. The inertia is conditioned by the magnetic field, which is always linked to flowing electricity, and which as the current ceases generates a direct current - Faraday's excess current.
Systematic generation of faster possible electric oscillations (Hertz 1887)
For an experimental examination of the Faraday-Maxwell theory - one of the most important tasks of experimental Physics - the discharges of a Leyden jar are much too slow; it requires at least 1000 times as fast oscillations. This is where the work of Hertz entered: He discovered in 1887 how to excite characteristic oscillations in quite short metallic conductors and generated oscillations with periods of the order of magnitude of 10-9 sec. He confirmed in this way the Faraday-Maxwell theory and thereby removed the concept of remote forces from the theory of electricity; in 1888, he showed that the electric force spreads out in space like light and thereby confirmed the hypothesis that light is an electric phenomenon. He thus gave industry the foundation for wireless telegraphy and telephony.
What is the main point during the generation of so fast electric oscillations? In order to make T as small as possible, you must, according to the formula T=2p(LC)1/2, make the capacity C as small as possible. However, if you make the capacity of the conductors - which are to discharge over the spark gap - very small, the energy stored in them is not sufficient to pierce the spark distance. (By experience, this distance cannot be arbitrarily small (cf. below). This is the main point: "If the capacity of the conductor ends is very large - say, they are the layer of a battery - , the discharge current of these capacities itself can reduce the resistance of the spark gap sufficiently; however, with smaller capacities this function must be undertaken by an outside discharge (Hertz)." Hertz made a spark inductor perform this outside discharge (Fig. 596). The inductor A charges to start with the capacities C and C' and the conductors L and L' (they represent the inductivity of the circuit). When the discharge tension of the inductor is reached, a spark jumps across F and closes the circuit. This inductor spark - and this is important! - heats up and ionizes the air of the spark track and thereby reduces its resistance; the condenser circuit's discharges now oscillate. In fact, the energy in the circuit oscillates only when its resistance R < 2(LC)1/2 Ohm.
The gap of air
acts like an instantaneous lock, which opens or closes the path
between C and C'. You must
1. open and close the lock like lightening and
2. far enough. This means: The spark must
1. start and stop very suddenly and
2. its intensity must be large.
The first is required so that also the discharge starts suddenly, because that
increases self-induction (lightening like behaviour of the spark
implies maximum change
of current in unit time)
and favours thereby the oscillation of the discharge. The second is required so that the resistance
drops immediately and far enough
(below the value 2(LC)1/2) and remains low during the oscillating
discharge. The spark distance has per mm a considerable
resistance, but, according to experience (Hertz), the spark must not be too short. The air gap must
therefore not exceed a certain resistance, and yet not be shorter than a certain distance. When
the spark ceases, the air tends immediately to return to its
initial state. - Not every type of spark has all these
properties, but the discharge of a strong Rühmkorff inductor has; according to Hertz, it assumes
(at F in Fig. 596) the following functions: It charges the condenser to a
high potential, it brings a suddenly starting spark, and after
starting the discharge holds the resistance of the air gap below
the critical value. In this way, it enables the condenser to
discharge itself oscillatorily, even when its capacity is very small.
Formation and propagation of electromagnetic wave
The energy in the oscillator commutes periodically from that of the electric field into that of the magnetic field and conversely. How are the electromagnetic waves generated in which the vibrations propagate from the oscillator into space? First of all, we will answer the question: How do the vibrations escape from the oscillator?
During the periodic conversion of the oscillator's energy arise magnetic induction lines, which surround the conductor in rings, and electric lines of force, which run from the one half of the condenser to the other (and interconnect corresponding charges). This applies to the closed as well as to the open oscillatory circuit (Fig. 597). The closed circuit is mainly a magnetic oscillator; it acts also electrically due to its magnetic oscillations. In contrast, the open circuit is the electric oscillator. The electric lines of force, radiating from it far into space, determine its character: It thus stimulates the ether electrically. After a quarter period, the electrostatic charges of its condenser half - and with it also its lines of force - have disappeared, that is, the EMF is zero; however, at that stage, the electric current with the magnetic induction lines, ringing the conductor, has reached its maximum intensity. According to Hertz, the EMF and the magnetizing force in the oscillator are mutually delayed by a quarter period; the one has its maximum, the other its zero value. It is just in this way that the oscillation occurs; however, the electric and magnetic force are only out of phase in and close to the oscillator - at points away from the oscillator by a quarter wave length or more, the electric field and the magnetic field strengths are in phase and remain so: Both attain from then on simultaneously their maximum values and pass simultaneously through zero, that is, both reverse their direction simultaneously. However, this coincidence is only in time, not also locally (except where both pass through zero), for the oscillations of the electric and magnetic field strengths occur in two different planes, which are mutually perpendicular; Fig. 294 shows how the intensities of the two fields strengthen and weaken and reverse their directions simultaneously.
The fact that the electric and magnetic forces are in and out of phase decides the motion of the energy in a electromagnetic field, that is, whether it oscillates as in the case of a pendulum or whether it flows like in a river. John Henry Poynting 1852-1914 1884 has computed the change of the energy content of a space under the assumption that the energy passes like a substance through the surface, bounding the space. According to him, the energy flows in a variable electro-magnetic field in a direction, which is perpendicular to the directions of the electric and magnetic force; it reverses the direction of its flow whenever only one of them changes its direction, but retains its direction of flow, if both forces reverse their direction simultaneously. According to Hertz, inside and close to the oscillator the energy flows quite differently as at the points which are l/4 or further away from it. In the region, the points of which are less than l/4 from it, the electric and magnetic field strengths are in phase at some points, out of phase at others and at some even diametrically opposite. At some points, only one of the two reverses its direction, at others both reverse their direction together, whence the energy oscillates only partly in this region, but goes to the other part, and indeed to the larger one outwards. According to Hertz, this is explained by the fact that the developing wave does not owe its generation merely to the processes in the oscillator, but also arises from the circumstances in the total space surrounding it, and this is the real source of the energy. - Beyond that region (sphere of radius l/4), the electric and magnetic field strengths grow and drop simultaneously at each point: If the one reverses its direction, so does the other, whence the flow of energy is from that border always directed outwards - nothing returns, all radiates outward into space.
If you view the oscillator as the launching site of the magnetic wave, it appears as if that of the electric wave lies a quarter wave length ahead, so that the magnetic wave passes it only one quarter period after its generation, and, as if from this point on both waves travel together in phase, in order to carry the energy away, that is, the radiation centre of the electro-magnet wave were lying l/4 away from the oscillator. - Whether it is a lot or little, which radiates from this border outwards and is lost for the oscillator, depends on the wave length.. For long waves, the radiation centre lies a quarter wave length away from the oscillator, whence the disturbance is only insignificant; the largest part of the energy returns then to the oscillator and its damping is only determined by the Ohm resistance. For example, it is like this in an ordinary alternating current machine of 50 periods, the quarter wave length of which is 750 km. But a small Hertz-oscillator with a quarter wave length of only a few centimetres radiates enormously and the rapid fading of its oscillations (due to the loss of energy during the duration of one spark) can be almost completely ascribed to this cause. In order to maintain permanently excited oscillations in spite of the radiation at the same intensity, you must replacer the loss by radiation by a continuous supply of energy to the oscillator.
The electric oscillation of the radiator acts inducing on its neighbourhood. The thus aroused disturbance advances from point to point in the space around the radiator in co-operation with the alternating electric and magnetic excitation of the ether. In the form of a wave, advancing freely in space, it spreads with the velocity of light. In order to demonstrate graphically the mechanism of the formation of waves, Hertz has computed for a special case the forces involved and reproduced the distribution of the forces. The curves in Fig. 598 represent the lines of electric force, their instantaneous density corresponds to the field strength in Volt/cm. The lines of force leave the poles of the oscillator and expand into the surrounding space. Their number grows to a maximum after which they start to contract again into the oscillating conductor. They vanish there as electric lines of force, but their energy converts there into magnetic energy. In this process, something very strange occurs : The lines of force, which have reached the greatest distance from their origin, while they contract, bend sidewards; this bending inwards increases and eventually a closed line of force separates from each of the outer lines of force, which travels away on its own into space. The remainder of the line of force returns to the oscillating conductor. (The number of returning lines of force is thus equal to the number of emitted ones, but their energy is reduced by that of the separated part. This loss of energy corresponds to the radiation into space.)
Far away from the radiator, the wave is perfectly spherical; it advances like, for example, the sound wave . However, the distribution of energy at the individual points is quite different: A sound wave contains at each point of the same spherical surface equally large energy, that is, the energy at any point depends only on its distance from the sound source. It is different in the case of an electro-magnetic spherical wave: The energy at a given point depends on its distance from the radiator and moreover on the azimuth and the height of the point, referred to the radiator as centre. It is largest in the equatorial plane of the transmitter and decreases to zero as the direction of the transmitter is approached. Fig. 599 demonstrates this schematically for a quadrant of the meridianal plane; the density of the lines of force has a maximum perpendicularly to the radiator; it vanishes in the direction of the radiator.
Experimental proof of the equality of the character of electromagnetic and light waves
According to Hertz, the fact that induction really spreads in the air space as waves is proved without difficulty by the assumption that there form (by interference) standing waves in space - in Optics and Acoustics these are the strongest arguments for the wave nature of light and sound. Standing waves always form when two wave trains interfere, which have the same wave length and amplitude, and propagate in a mutually opposite direction. Standing electric waves with nodes and bulges can also form in this way. The spark distance F of the inductor (Fig. 600) emits the waves. Place perpendicularly to the line bF between the oscillator and resonator (visible on the left hand side between bb) a large metal screen A. The distance between the oscillator and screen is fixed, the resonator can be slid along bF. If you take the resonator close to A, it displays no sparks; if you move it gradually along bF away from the screen, sparks arise, which strengthen steadily until they again start to weaken at a certain distance. This increase and decrease of the sparks repeats itself at regular distances from the screen (maxima at the points a, minima at the points b). This suggests interference: The waves which apparently come from the oscillator meet the screen and are reflected; the arriving and reflected waves interfere and form bulges and nodes (Fig. 298). However, while in an organ pipe or in Kundt's tube the air, that is, matter oscillates, in the case of electromagnetic waves, magnetic and electric fields of force oscillate and generate through their rapid changes the character of oscillations. Moreover: While in the case of sound the direction of motion of the air particles coincides with direction of propagation of the wave, in the case of the electric wave the direction of the fields of force is perpendicular to the direction of propagation (Fig. 294).
After Hertz disvovered that metal surfaces reflect electric waves, it suggested an experiment in which the waves are concentrated by a parabolic, concave mirror and thereby parallel rays of electric force are produced. The oscillator is installed in the parabolic mirror (out of metal sheet) in such a way that its spark track coincides with the focal line (Fig. 601). The radiated oscillations are reflected as shown and form a wave train, which a second parabolic mirror can capture. If the mirrors, like A and B, face each other, the resonator R in the focal line of B addresses the mirror strongly also at a large distance. However, if you shift B to B', the sparks in the resonator R' expire, which is a proof that the electric waves can be held together by suitable reflectors in parallel bundles of rays.
With the same experimental layout, Hertz was able to find yet other fundamental properties of electric waves: The sparks in R expired as soon as a metal screen was placed in their course, but a wooden board or a glass plate did not exhibit the same phenomenon. Thus, metals absorb, respectively, reflect electric waves, insulators let them pass, both in agreement with Maxwell's theory.
An elementary optical experiment shows that light rays are refracted from their initial direction as they pass a prism. Hertz performed a similar experiment with electric waves. He placed in the path of the ray of the oscillator O a prism P with an about 1 m long edge, made out of asphalt which lets electric waves pass well (Fig. 602). The resonator did not respond when it was at B on the axis of the parabolic mirror A, but only when it was rotated by a considerable angle from this direction (to the position B'): This means that electric waves also refract like light rays.
Successful
experiments with the refraction and polarization of electric
waves have removed all 
doubts regarding the similarity of the character of
light and electric waves. The only difference are the lengths of
their waves: Hertz's waves measure in metres, light waves
in ten thousands of millimetres. - Hertz's work has
caused innumerable experiments to generate faster and shorter
electric waves.The shortest wave is probably that of 0.22 mm
produced by Nichols and Tear.
The nodes and bulges, moreover the coincidence of the direction of the field at points of the same half wave and the opposite nature of neighbouring half waves, are visually observable at the resonator with the arrangement of Fig. 600. Hertz has discovered by means of it that the action of the primary oscillation propagates starting from the oscillator from point to point: He conducted them by a wire away from the oscillator and discovered thus along the wire the bulges and nodes with his resonator.. These days (1935), you employ for their detection the set-up of Ernst Lecher 1856-1926 1890 (Fig. 603) with two plates C1 and C2, which face at a few centimetres distance the plates B1 and B2, and with the two 7 - 8 m long, parallel, bare wires; they are connected by wire bridge which can be pushed along them and let you delimit arbitrarily long segments (D1D2D3). The wires C1 and C2 charge intermittently themselves positively and negatively as well as the plates connected to them . If the action of the oscillation were instantaneous, all points of the same wire would at a given instant simultaneously have the same potential like the plates connected to them, and the field between the wires would oscillate as a whole. Between two opposite points along the wire, there would everywhere at a given instant be the same potential difference as between the plates. However, something quite different occurs. This is shown by the tube of Heinrich Johann Wilhelm Geissler 1815-1879, by which, following Lecher, the wires are bridged - it lights with different intensity at different locations along the wire, strongly, weakly and even not at all. In this way, it indicates the bulges and nodes of the standing electric wave. If you surround the wires by a glass tube (Arons), which is made air tight and evacuated like a Geissler tube, the entire space between C1 and C2 lights up with similar changes in light intensity.
This observation reminds us of the oscillating column of air and the locations of maximal and minimal brightness of the flame of Rudolf König 1832-1901 (Fig.337), even of the open and closed pipe (Figs. 332,333), depending on whether the wires are connected or not: The locations of the largest and smallest brightness lie both times in different places. The points of strongest brightness are those, at which the voltage difference oscillates most strongly - electric oscillation bulges; there several of them along the wires. At the centre between two bulges lies a node; it arises from the interference of two waves: One from the radiator, another reflected at the end of the wire system. If you connect two opposite points by a bridge (short circuit), you force there a node, if the ends of the wires are free, a bulge. If you short circuit the ends of the wires, you force there a node, if the ends are free, a bulge. If you place a Geissler tube between the bridge and the short circuited end of the wires across them and displace the bridge, you detect those locations of the space between the wires which light brightest at short circuiting - a bulge. Displacement of the bridge lengthens or shortens the oscillation circuit of the oscillator and shortens (lengthens) the part behind the bridge. In this way, you can cause the wire system to resonate with the exciter. It has a characteristic oscillation which depends on its length and can be caused to resonate with the oscillator by a changing its length; due to the smallness of the inductivity and capacity, is has a very short period. (This circuit is coupled by the bridge with the oscillator - you say: Galvanically coupled in contrast to the inductive coupling during which only the lines of force of two circuits are interconnected.) The distance between two neighbouring nodes is half the wave length, whence you can measure the wave length at the wires with the aid of a Geissler tube.
Wire waves are very significant for the development of the Faraday-Maxell theory. The system of wires displays immediately the length l of the electric wave; if you compute also the period T of the oscillation by computation (Hertz) or Lecher's set-up (Mercier 1922), l/T yields the velocity of propagation of the electric wave: In this way, it yielded the velocity of light in air (v = 299790 +/- 20 km/sec).
If a wire sends the action of the primary oscillation into the distance, its inside knows nothing about this; all the changes yielding the wave occur close to it and only on its surface. Its action penetrates it hardly more than the light, which meets its surface and is reflected. This is the result of self-induction: A constant current in a cylindrical wire fills every part of its cross-section equally strongly, a changing one prefers the edges, alternating current does the more, the larger is its frequency. According to the theory, this preference should be detectable already at several hundred changes per second and increase rapidly with the number of changes. At several millions changes per second, the flow must be confined to the surface of the wire (skin effect). Hertz has confirmed this theory: The fast oscillations of his oscillator are then almost static loads. Like these, they also are located on the surface of the conductor: They generate an electro-dynamic counter piece to Faraday's electro-static cage experiment .
Maxwell's relation n²= e (1860)
Electro-magnetic waves do not propagate inside a conductor, but slide in the dielectric along it (cf. above). But the velocity of propagation can then only depend on the nature of the dielectric and not the material of the conductor. This is indeed true. It depends apparently on the resistance by which the material opposes its dielectric polarization, that is, the electric and magnetic displacements. This resistance is characterized by the dielectric constant e (DC) and the magnetic permeability m. If we denote the velocity of the wave in empty space - in the ether - by c cm/sec and its velocity in substances, characterized by e and v , then, according to Maxwell, v = c/(e ·m)1/2 cm/sec. The number is almost 1 for all substances, whence v = c/(e)1/2 cm/sec. The validity of this equation is demonstrated by measurement of the velocity of propagation of electric waves in air, the dielectric constant of which is 1: It turned out to equal that of light (cf. above).
If a wave, which spreads in an isolator with dielectric constant e1, encounters an isolator with DC e2, say a plane wall, its velocity changes from v1 = c/(e1)1/2 to v2 = c/(e2)1/2. If it encounters the surface obliquely, its direction of propagation changes, it is refracted. You have between its velocities of propagation before and after refraction, on the one hand, and the velocities v1 and v2, on the other hand, Maxwell's important fundamental relation. Fig. 604 shows a perpendicular cut through the interface 1,2 between two dielectrics through a plane wave, which comes from e1 and hits obliquely the interface.(You can imagine aa', the cut perpendicularly to the plane of the drawing and the direction of propagation of the wave, to be a linear wave, travelling along two wires, which lie in the plane of the drawing and encounter 1,2 obliquely.) While the electro-magnetic disturbance in e1 still covers a'c, it has already advanced in e2 by ac' - where the ratio ac'/a'c is like that of the velocity of propagation of the disturbance in e2 to that in e1, that is, a'c/ac' = v1/v2; it advances in the same ratio from the points lying between a and c. Hence, the disturbance reaches also in e1 the point c, it has moved already in e2 to a plane, which, being perpendicular to the plane of the drawing, intersects it in c'c. You have then in e2 a plane wave, which forms with 1,2 the angle b. (Fig. 605). However, this means: When the plane enters e2 from e1, it changes its direction by its angle of inclination a becoming b. You call a the incidence angle, b the refraction angle. Between these angles and the velocities of propagation exists an important relationship. You have sin a = a'c/ac and sin b = ac'/ac, whence sin a/sin b = a'c/ac'. Moreover, from above, a'c/ac' = v1/v2, whence sin a/sin b = v1/v2 = (e2)1/2/(e1)1/2, since v = c/(e)1/2.
Hence this ratio is itself for the two substances, characterized by e2 and e1, a constant (n). However large is the angle of incidence, the corresponding angle of refraction is
sin (angle of incidence)/sin (angle of refraction) = (e2)1/2/(e1)1/2 = n.
This relationship is one of the fundamental supports of the electro-magnetic theory of light, for it holds for waves of light: Imagine instead of the electric wave a wave of light, the substances 1 and 2 to be transparent and 1,2 to be their interface; n is then the light refraction quotient - the refraction number. If there lies on the one side of the interface a vacuum or air, on the other side some material with DC e,, we have for the electro-magnetic wave sina/sinb = (e)1/2 and for the wave of light sina/sinb = ne, whence n² = e (replacing ne by n), which is the customary way of writing Maxwell's relation.
However, a substance has many light-refraction coefficients n (a different one for every colour), but, in contrast, only one dielectric constant, according to its definition. With which n are we to compare the so defined (e)1/2? The equation n² = e almost holds for gases (atmospheric air, hydrogen, carbonic acid, carbon oxide, nitrous oxide), the quotients of refraction of which change only little with colour, also for several hydrocarbons, for example, benzol, petroleum, carbon disulphide. But, in general, for water (e)1/2= 9, for ethyl alcohol 5.0, while their n, related to yellow light, is 1.33 - 1.34 - 1.36.
The contradiction between theory and experiment vanishes, if you expand the theory - hitherto only empty space (ether) has been taken into consideration - by certain assumptions, which also take matter into consideration. This expansion of the theory (Helmholtz) explains refraction by an interaction between the ether and the molecules of substances, or even more the ether and the electrons, linked to the molecules, that is, by an influence of the molecules on the oscillations of the ether. This interaction does not only manifest itself in the optical refraction coefficients n, but also in the DC e. The dielectric constant measures the shift of quantities of electricity if the substance, when it is polarized di-electrically in an electrostatic field. In this definition of the DC, its is assumed that the field does not change. However, when electromagnetic waves pass through it, it changes periodically. If its period of changes differs so much from the characteristic periods of the ionized molecules that the molecules do not covibrate, this change of the dielectric shift also does not affect the DC. However, if the period of changes causes the ions to covibrate, the quantity of electricity, shifted during the dielectric polarization, and thereby the DC depends on the wave length provoking the change in the field. - When you measure electrostatically the DC, you employ a constant field, that is, a field which changes infinitely slowly. It corresponds to a field, which is penetrated by an infinitely slow oscillation, that is, an infinitely long wave. The electrostatically measured e relates therefore almost to an infinitely long wave.
Return now to the relation n² = e. The DC, electro-statically measured (with an electrometer), applies effectively to infinitely long, electromagnetic waves. However, the refraction coefficient n is measured optically (with a spectrometer) in terms of the angles between rays of light, that is, electromagnetic waves with wave lengths of the order of ten-thousandth millimetres, that is, it applies only to very short waves. We have seen that for n measured in this way, in general, Maxwell's relations are not satisfied. Wherever Maxwell's relation holds only in an approximate manner, there arises a legitimate explanation for the deflection in the difference of the wave lengths, with which we operate, on the one hand, optically and, on the other hand, electrically. However, since Hertz's discoveries, we can generate electro-magnetic waves, which can be viewed in comparison with light waves to be infinitely long, which, however, are nevertheless so short, that we can operate with them as with waves of light. (A 50 cm long Hertz wave relates to a wave of green light of about 0.005 mm length like 1 km to 1 mm.) If we measure n directly (as in Fig. 602, where a prism of pitch performs on Hertz waves as a glass prism on waves of light) the deflection of refracted electro-magnetic rays, that is, with the aid of electro-magnetic waves, which we can view to be infinitely long waves of light, we obtain, for example, for water n = 9, that is, n² = 81; most accurate electrometric measurements yield e = 80. In facing electric waves, which are extremely long compared with those of light (by means of which, before Hertz, n could only be determined) water also obeys Maxwell's relation and so does every other substance, the refraction coefficient of which is determined be means of electric waves.
These measurements with especially short electric waves prove effectively Maxwell's relation from the electric side. We understand from the optical side its validity by measurements with residual rays - especially long waves of light, so long that they can be shown to have the properties of electrically generated ether waves (Dubois, Heinrich Rubens 1865-1922). The wave length l = 56m (isolated from the Welsbach burner by Rubens and E. Aschkinass) is 112 times as long as that of medium green light and still as long as the extreme, visible red light. For this wave, quartz has the unexpectedly large refraction coefficient n = 2.18, that is, n² = 4.75; its DC is 4.55 to 4.73. For middle green light (l = 0.5350m), n - 1.5466, that is, n² = 2.39, for extreme visible red light (l=0.7682m), n = 1.539, that is n² = 2.37, that is, hardly half the value of the DC. Hence the brief and clearly formulated prediction of Oliver Joseph Lodge 1851-1940 has been met thereby: "In order to compare appropriately the velocities of propagation of waves, we must find out either how to shorten the electric waves or to lengthen the waves of light, or both, and then compare them with each other, when they have the same wave length. There is no reason to doubt that they will turn out to be identical."
Wireless telegraphy and
telephony
Hertz's set-up (Fig. 596) offers a chance to transmit signals
into the distance and make them there perceptible, whence it
forms the foundation of wireless telegraphy, but only in
principle. Its details demanded large improvements for purposes
of technical applications. Wave telegraphy had to solve the four
tasks:
1. generation of high frequency oscillations at the transmitter,
2. radiation of electric waves by the transmitter,
3. reception of the electric waves by the receiver,
4. making the received oscillations perceptible.
(From the
transmitter to the receiver, the waves spread out on their own,
wave telegraphy only interferes here as directional telegraphy.) Above all, it has turned out to be
necessary to decompose the transmitter into two 
parts: One in which the oscillations are generated and another one which
radiates them into the space around and thereby causes the
electric waves in space. Hertz combined these two functions
(generation of oscillations, radiation) in a single oscillation circuit; so did Guglielmo Marconi 1874-1937. Only Braun separated these actions into two (coupled) circuits. However, his second circuit acts back on the first, a collision
occurs between them as is shown in Fig. 131 b(1). Wien succeeded to circumvent this defect by a
spark device which acts as is shown by Fig. 131 b(2). But damping of waves cannot be separated
from the sparks and the damping affects from the
sharpness of the resonance of the receiver, that is, the
possibility of tuning the receiver sharply to the transmitter.
Hence one attempts to produce undamped waves
- waves with constant amplitude. This became possible with the
arc lamp - with the high frequency, alternating current machine (Reginald Aubrey Fessenden, von
Arco, Goldschmidt) and more so with vacuum tubes.
An electric oscillation which is left to itself is always dampened. The amplitude of the oscillation, which arises during a discharge of a spark across a gap, decreases quickly to zero, because the supply of energy ends after the start of the discharge of the condenser . The oscillation is like that of a physical pendulum, the vibration of which has been started, which then moves on its own and comes to rest due to friction in its bearings and the friction of air. Undamped electric oscillations are therefore like those of a physical pendulum, the loss of energy due to friction (like in a clock by a weight or a spring) is all along compensated. But it is undamped only because the reduction of their amplitude is impeded by a lasting supply of energy.
The discharge over a spark gap is not the only method for causing characteristic oscillations of a circuit of large frequency. A direct current arc lamp can replace the spark gap (W. Duddell). Depending on the magnitude of the voltage and the resistance, on the one hand, the capacity inductivity, on the other hand, different kinds of oscillations arise.
Oscillations of the first kind are sine waves, supperimposed on the direct current; the amplitude of the current in the oscillation circuit (effective voltage) is smaller than the arc lamp direct current and the arc light is never extinguished. Oscillations of the second kind have the form shown in Fig. 606; every period is composed of the discharge interval T1, during which the arc burns, and the duration of the charge T2, during which the condenser is charged and the arc is extinguished. Only the oscillations of the second kind can be charged with practically sufficient energy (wireless telegraphy). One seeks to reduce as far as possible the duration of charging and to let ignition tension increase fast as is possible; then the gas between the electrodes must be deionized very fast. In order to effectively reduce the temperature, Valdemar Pulsen generates the arc in hydrogen between a copper anode and a carbon cathode; as the current passes, he lets a magnetic blower drive the gas from the closest gap between the electrodes, where the arc most readily would reignite Fig. 607. According to Duddell, the ordinary arc lamp is useless for wireless transmission of information due to the low energy of its oscillations in contrast to his own arc, which has become very important for wireless telegraphy: Its oscillations are not damped.
Neither a spark gap nor an arc closes the oscillatory circuit L1RC (Fig. 608) in the anode current circuit of the vacuum tube. It interacts alternatingly through back coupling (between L1 and L2) with the lattice circuit. One says: It begins to oscillate by means of back coupling (Walter Franz Meissner 1878-1968). As the anode circuit is closed, the developing current induces an EMF in the coil L1; it generates an alternating current in the circuit L1RC, which due to consumption of energy in the circuit fades immediately unless it receives energy from the outside. It induces in L1 and therefore also in between the lattice and the cathode an alternating tension of its own frequency. This alternating lattice tension causes fluctuations in the anode conductor, which then on their part by means of the coil L1 in L1RC create an EMF with the same frequency. If the coils L1 and L2 are given properly directed windings, this EMF is in phase with the alternating current already present in L1RC, that is, it feeds energy into the circuit. Hence the amplitude of the alternating current does not fade, it increases and eventually attains a constant value: There arises in the circuit an undamped oscillation - an action which increases itself like it happens during self excitation according to the dynamo electric principle. (If you introduce into the circuit a telephone, you hear a tone of constant height and strength, a proof that the circuit actually oscillates, and does so at constant strength and frequency.) By a suitable choice of the capacity C and the inductivity L, you can generate oscillations of any frequency according to Thomson's formula.This method of production of back coupled oscillations is of immense importance for industrial purposes.
The oscillations, generated in the transmitter, are transferred to the antenna, connected to it, and from there radiated into the surrounding space. In the process arise in it electromagnetic waves, which propagate in all directions, that is, also to the receiver station, where they generate in an antenna high frequency oscillations; they are made perceivable in the receiver station by means of certain tricks. They are converted by special attachments (detectors) into a direct current or rather into direct current pulses, which are as far as required amplified by vacuum tubes and either heard by telephone or fed into a printer. The technical details do not belong here.
The oscillations, generated in a transmitter, and the spreading of its radiated electric waves can also be used in telephony. For the transmission of sound, only undamped, continuous oscillations are suitable. If you superimpose on them oscillations of the current, which arise in a microphone, also these high frequency sound fluctuations are transmitted by radiation over Earth's surface and are reproduced by every ordinary wireless receiver (antenna with detector) quantitatively correctly and audibly. Fig. 609 demonstrates the principle of the simplest and oldest arrangement of wireless telephony.
The generation of the oscillations and their modulation by speech and music is perfected technically in the vacuum tube transmitter. It has brought about radio. (Introduction of the vacuum tube transmitter and the back coupling principle by Meissner 1913) - We still will refer to the high frequency telephony along transmission lines: On the same wire, you can transmit (apart from an ordinary long distance conversation) a number of conversations simultaneously, provided they come from vacuum tube transmitters. You then have to deal with high frequency alternating currents, whence you can separate at the receivers by resonance circuits the different alternating currents, which are present simultaneously in a wire, and thus separate the conversations. Hence the high frequency manifold telephony allows to utilize a telephone net with many more connections than otherwise would be possible.
