We have already stated that soon after Coulomb's law had been established, electrostatics and magnetostatics were brought into the form of pseudocontiguous action. Maxwell now under-took to fuse this theory with Faraday's ideas, and to elaborate it so that it also included the newly discovered phenomena of dielectric and magnetic polarization, of electromagnetism and magnetic induction.
    
Alizzed substituted * and  letter for the symbols used by Brother Born.
Must we said the scribe needs must said Zed Aliz.
Maxwell took as the starting point of his theory the idea already mentioned above that an electric field E is always accompanied by an electric displacement D = *E not only in matter, for which * is different for one, but also in the ether, where *  = 1. We explained how the displacement can be visualized as the separation and flowing of electric fluids in the molecules. And we have found a differential law, which connects the charge density p in every space point with the divergence of D =*E:



                                             Div *E= 4 pi p                                                                                                                              (58)



Exactly the same considerations apply to magnetism, but with one important difference:  According to Ampere no real magnets exist, no magnetic quantities, but only electromagnets.  The magnetic field is always to be produced by electric currents, whether they be conduction currents in wires or molecular currents in the molecules. From this it follows that the magnetic lines of force never end, that is they are either closed or stretch to infinity. This is so in the case of an electromagnet, a coil through which a current is flowing (Fig 97a,b); the magnetic lines of force are straight lines in the in-terior of the coil, but outside they are partly closed and partly going off into infinity. If we consider the coil between two planes A and B,  

/ Page 182  /

Formal agreement of this kind is by no means a matter of indiffer-ence. It exhibits the underlying simplicity  of phenomena in nature, which remains hidden from direct perception because of the limitations of our senses and reveal itself only to our analytical faculty.
     In general a conduction and a displacement current will be present simultaneously. For the former, Ohm's law, jc = o E,
Holds (52) p162; for the latter, Maxwell's law, jd = *     E   If both are present simultaneously
                                                                                   4 pi  t
we thus have  J = *   E    E  +  o E.
                                 4 pi  t



There is no conduction current for magnetism, so we always have  
                                                                                                         I = u    H
                                                                                                             4 pi  t



If we insert this in our symbolic equations (58) to (61) we get:      
(a)                 div *E = 4 pi p,
(b)                 div  u H = O,



(c)                 c curl  H   = * E + 4 pi  o E,(62)
                                           t
(d)                 c curl E = u H .  
                                         t



These are Maxwell's laws which have remained the foundation of all electromagnetic and optical theories up to our own time. To the mathematician they are precise differential equations. To us they are precise differential equations. To us they are mnemonics which state:



(a)   Wherever an electric charge occurs an electric field arises of such a kind that in every volume the charge is exactly compensated by the displacement.
(b)   Through every closed surface Just as much magnetic displace-ment passes outwards as comes inwards there are no free magnetic charges).
(c)   Every electric current, be it a conduction or a displacement current is surrounded by a magnetic field.
(d)   A magnetic displacement current is surrounded by an electric field in the reverse sense. " /



The Alizzed reminded those who needed to know, of the needs must, symbol changes that had had to be made.
These yonder scribe had in the main emphasised,.advising consulting the original oracle Brother Born, for missing hieroglyphics and total accuracy of interruption.
Then in a sort of apology the scribe writ. That there wasn't much call for that sort of thing in our part of the world.
Then out of the blue the scribe writ the words Karmic magnet.
You are a caution scribe said Alizzed.
And you Zed Aliz said the scribe, adding, and you.

Page 183   /

"Maxwell's "field equations," as they are called, constitute a true theory of contiguous action or action by contact, for, as we shall presently see, they give a finite velocity of propagation for electro-magnetic forces
      At the time they were set up, however, faith in direct action at a distance, according to the model of Newtonian attraction, was still so deeply rooted that a considerable interval elapsed before they were accepted, for the theory of action at a distance had also suc-ceeded in mastering the phenomena of induction by means of formulae. This was done by assuming that moving charges exert, in addition to the Coulomb attraction, certain actions at a distance that depend on the amount and direction of the velocity. The first hypo-theses of this kind were due to Neumann (1845). Another famous law is that set up by
Wilhelm Weber (1846); similar formulae were given by Riemann (1858) and Clausius (1877). These theories have in common the idea that all electrical and magnetic actions are to be explained by means of forces between elementary electrical charges, or as we say nowadays, "electrons." They were thus precursors of the present-day theory of electrons, with however an essential factor omitted: the finite velocity of propagation of the forces. These theories of electrodynamics, based on action at a distance, gave a complete explanation of the electromotive forces and induc-tion currents that occur in the case
Of closed conduction currents. But in the case of "open" circuits that is, condenser charges and discharges, they were doomed to failure, for here the displacement currents come into play, of which the theories of action at a distance know nothing. It is to Helmholtz that we are indebted for appro-priate experimental devices allowing us to decide between the theories of action at a distance and action by contact. He succeeded in carrying out the experiment with a certain measure of success, and he himself became one of the most zealous pioneers of Maxwell's theory. But it was his pupil Hertz who secured the victory for Maxwell's theory by discovering electromagnetic waves.

 

 

9 The Electromagnetic Theory of Light

" We have already mentioned (V, 4 p. 163 ) the impression which the coincidence, established by Weber and Kohlrausch, of the electro  

/ Page 184  /

magnetic constant c with the velocity of light made upon the physicists of the day. And there were still further indications that there is an intimate relation between light and electromagnetic phenomena. This was shown most strikingly by Faraday's
discovery ( 1834 ) that a polarized ray of light which passes through a magnetized transparent substance is influenced by it. When the beam is parallel to the magnetic lines of force, its plane of polarization becomes turned. Faraday concluded from this that the luminiferous ether and the carrier of electromagnetic lines of force must be identical. Although his mathematical powers were not sufficient to allow him to convert his ideas into quantitative laws and formulae, his ideas were of a most abstract type and far surpassed the trivial view which accepted as known what was familiar. Faraday's ether was no elastic medium. He derived its properties, not by analogy from the apparently known material world, but from exact experiments and systematic deductions from them. Maxwell's talents were akin to those of Faraday, but they were supplemented by a complete mastery of the mathematical means available at the time.
       We shall now show how the propagation of electromagnetic forces with finite velocity arises out of Maxwell's field laws (62). In doing so we shall confine ourselves to events that occur in vacuo or in the ether. The latter has no conductivity, that is,  o = O, and no true charges, that is p = O and its dielectric constant and permeability are equal to 1, that is, * = 1, u = 1. The first two field equations (62) then assert that
                       div E = O,      div H = O                                                                           (63)
 
or that all lines of force are either closed or run off to infinity. To obtain a rough picture of the processes we shall imagine individual, closed lines of force.
      The other two field equations are then        
                       (a)  E = c curl H,            (b)  H = c curl E.                                              (64)
                            t                                      t
 
We now assume that, somewhere in a limited space, there is an elec-tric field E which alters by the amount E in the small interval of time
T; then E   is its rate of change. According to the first equation, a  /                
            t

Page 185  /  

magnetic field immediately coils itself around this electric field, and its strength is proportional to  E  
                                                                                                                                                 t
The magnetic field, too, will alter in time, say by H during each successive small interval  t                                          
Again, in accordance with the second equation, its rate of change  H                                                                        
             t
immediately induces an interwoven electric field. In the following interval of time the latter again induces an encircling magnetic field, according to the first equation, and so this chainlike process con-tinues with finite velocity (Fig. 98)



Fig. 98  Electric and magnetic fields linked by induction.



      This is, of course, only a rough description of the process, which actually propagates itself in all directions continuously. Later we shall sketch a better picture.
       What particularly interests us here is the following: We know from mechanics that the finite velocity of propagation of elastic waves is due to the delays that occur as a result of the inertia which comes into play when the forces are transmitted in the body from point to point. We have formulated this in equation  (36)  pb = pf and with  (37)  c2 =  p
                                                                                                                                                                  p
b = c2 f.                                                                                                                                                                                   (36a)



Here c2 means the square of the velocity of the elastic waves, b the acceleration of the mass particles in the elastic body
(i.e., the second-order differential coefficient with respect to time), and f is the second-order differential coefficient with respect to space.
       Now, in the electromagnetic field, the case is nearly the same. The only difference is that instead of the dependency of the displace-ment on space and time in the elastic case we have two quantities  

/ Page 186  /

E and H depending on space and time. The rate of change of the electric field E
                                                                                                                    t



first determines the magnetic field H, and then the rate of change  H  of the latter determines the electric field E at a
                     t
neighbouring point. The equations (64) contain only differential quantities of the first order, for instance E ,                                                                                                                                                            t
a first-order differential coefficient with respect to time, and curl H, a first order differential coefficient with respect to space. One gets an equation similar to (36) by the following procedure: To begin with, take the first-order differential coefficient of equation (64a) with respect to time. Then we have on the left-hand side the second-order differential coefficient of E with respect to time which is analogous to b in (36a) and which we will call  bE.  On the right-hand side we have a mixed second order differential coefficient (forming first the difference in space and then in time or vice versa).  One gets the same mixed coefficient from (64b) by forming the first-order differential coefficient with respect to space. Then one sees that the mixed coefficient is equal to the product of c into the second-order differential coefficient in space of E, which is analogous to f in (36a)  and may therefore be called fe. Now one can eliminate the mixed coefficient in the equations and
one gets  bE = c2 f E.                                                                                                                                                               (65)



This equation is in complete analogy with (36a) and shows the existence of electric waves with velocity  c. By the same method one may derive a corresponding equation for the magnetic field  H(bH=c2fH). If one of the two partial effects would happen without loss of time, no propagation of the electric force in the forms of waves would occur. This helps us to realize the importance of Maxwell's



displacement current, for it provides just this rate of change E  of the electric field."
                                                                                          t
 
And so, guided by the good brother Born, and the intermittent company of Elders. The Alizzed, Scribe, and shaded glow of those so-called,  followed the good brother to the best of their abilities, through the trick and treat of the hear, there, and everywhere, of that long subterranean nights journey into light. Holding within that minds eye the golden thread of eventual escape.
The page continued to read.
 
      "We shall now give a description of the propagation of an electro-magnetic wave  which is somewhat nearer to the actual process. Let two metal spheres have large, opposite, equal charges + e and - so that a b electric field exists between them Next let a  

/ Page 187  /  

spark occur between the spheres. The charges then neutralize each other; the field collapses at a great rate of change E .  The figure shows how the magnetic and electric lines of force then encircle each other alternately (Fig. 99).
             t
In our diagram the magnetic lines of



Fig 99  The electromagnetic field surrounding a discharge spark between two spheres. This field expands with velocity c of light in all directions.



force are drawn only in the median plane between the spheres, the electric lines of force only in the plane of the paper, perpendicular to the median plane. The whole figure is, of course, radially sym-metrical about the line connecting the centre of the spheres. Each successive loop of the lines of force is weaker than its immediate pre-decessor because it lies further outwards and has a larger circum-ference. Accordingly, the inner part of a loop of electric force does not quite counterbalance the outer part of its predecessor, especially since it enters into action a little late.
     If we pursue the process along a straight line which is perpendicular to the line connecting the centers of the spheres, say along the x-axis, then we see that the electric and magnetic forces are always perpen-dicular to this axis; moreover, they are perpendicular to each other.  

/ Page 188  /

The Alizzed had yonder scribe count in descending order of a kind , the number of the lines on which dances the following words  "light waves are nothing other than electromagnetic waves."
The scribe noted in passing, that if the title of the Chapter v, counted as line 1 then the phrase occupied  lines 9 and 10 or alternatively if the heading be discounted az iz usually the case Edgar, then lines 8 and 9 carry the crown.
Either way the reference contains 9 lines
And we all know what that means, writ the scribe, wonderingly wandering.


Page 188 continues  

" One of the inferences which Maxwell drew was soon confirmed experimentally to a certain extent, for he calculated the velocity of light c1 for the case of an insulator (o = O) and no free charge (p = O). Maxwell's equations (62c and d) show that we get nearly the same equations as (64) but with other c-values. In (64a) c is to be released by c
                                                                                                                                                                                             *
and in (64b) by c . The same reasons which led us to equation (65) show now that the square of the velocity  c 1  2 of the electro-magnetic waves must be equal to the product of c and  c : c 1 2 = c2 .
                         u                                                                                                *         u               *u
Many materials are not noticeably magnetizable, so we can set u = 1, which means that the velocity of light in an insulator with dielectric constant * is given by c1 = c.     This leads to the value n = c  =  / *
                                                                   / *                                                c1
for the refractive index.
    Thus it should be possible to determine the refrangibility of light from the dielectric constant as given by purely electrical measure-ments. For some gases-for example, hydrogen, carbon dioxide, air-this is actually the case, as was shown by L Boltzmann. For other substances Maxwell's relation n = / * is not correct, but in all these cases the refractive index is not constant but depends on the colour (frequency) of the light. This shows that dispersion of the light introduces a disturbing effect.  We shall return to this fact later and deal with it from the point of view of the theory of electrons. At any rate, it is clear that the slower the vibrations or the longer the waves of light that is used, the more closely the dielectric constant as determined statically, agrees with the square of the refractive index. Waves of an infinite time of vibration are, of"  /
 
The nightmare transition of mind realization that out is in within the womb of the mother.
 
The scribe recorded the 7 lettered name
 
Page 189   1 x 8 x 9 = 72  7 + 2 = 9  1+ 8 + 9 = 18   1 + 8 = 9

"course identical with a stationary state. Researches into the region of long waves (lengths of the order of centimeters) have completely confirmed Maxwell's formula.
      Concerning the more geometrical laws of optics, reflection, refraction, double refraction, and polarization in crystals and so forth, the electromagnetic theory of light resolves all the difficulties that were quite insuperable for the theories of the elastic ether. In the latter, the greatest obstacle was the existence of longitudinal waves which appeared when light crossed theboundary between two media and which could be removed only by making quite probable hypotheses about the constitution of the ether. The electromagnetic waves are always strictly transversal. Thus this difficulty vanishes.
Maxwell's theory is almost identical formally with the ether theory of MacCullagh, as we mentioned above (IV,6. P 117); without repeat-ing the calculations we can take over most of his deductions.
      We cannot here enter into the later development of electro-dynamics. The bond between light and electromagnetism became ever closer. New phenomena were continually being discovered which showed that electric and magnetic fields exerted an influence on light. Everything proved to be in accordance with Maxwell's laws, the certainty of which continued to grow.
       But the striking proof of the oneness of optics and electrodynamics was given by Henrich Hertz (1888) when he showed that the velocity of propogation of electromagnetic waves was finite and when he actually produced electromagnetic waves. He made sparks jump across the gaps between two charged spheres and by this means generated waves such as are represented by our diagram (Fig 99 ). When they encountered a circular wire with a small gap in it, they produced in it currents which manifested themselves by small sparks at the gap. Hertz succeeded in reflecting these waves and in making them interfere. This enabled him to measure their wave length. He knew the frequency of the oscillations and thus could calculate the velocity of the waves which came out equal to c, that of light. This directly confirmed Maxwell's hypothesis. Nowadays the Hertzian waves of wireless stations travel over the earth without cessation and bear their tribute to the two great scientists Maxwell and Hertz, one of whom predicted the existence of electromagnetic waves while the other actually produced them.  

Page 190   1 x 9 x 0 = 9     1 + 9 = 10

From this time on there was only one ether, which was the carrier of all electric, magnetic, and optical phenomena."


Either or either, either or neither, writ yon scribe.
 
Page 190  

"We know its laws, Maxwell's field equations, but we know little of its constitu-tion. Of what do the electromagnetic fields actually consist, and what is it that executes vibrations in the waves of light ?
       We recall that Maxwell took the concept of displacement as the foundation of his argument, and we interpreted this visually as meaning that in the smallest parts or molecules of the ether, just as in the molecules of matter, an actual displacement and separation of the electric (or magnetic) fluid occur. So far as this idea con-cerns the process of electric polarization of matter, it is well founded: it is also adopted in the modern modifications of Maxwell's theory, the theory of electrons, for numerous experiments have rendered certain that matter has a molecular structure and that every molecule carries displaceable charges. But this is by no means the case for the free ether: here Maxwell's idea of displacement is purely hypothetical, and its only value is that it provides a visualizable image for the abstract laws of the field.
     These laws state that with every change of displacement in time there is associated an electromagnetic field of force. Can we form a mechanical picture of this relationship ?
    Maxwell himself designed mechanical models for the constitution of the ether and applied them with some success.  "...Kelvin was particularly inventive in this direction and strove unceasingly to comprehend electromagnetic phenomena as actions of concealed mechanisms and forces."
 
Good Lord! exclaimed the scribe at all this activity.



Page 190

"The rotational character of the relationship between electric currents and magnetic fields, and its reciprocal character, suggests that we regard the electric state of the ether as a linear displacement, the magnetic state as a rotation about an axis, or conversely. In this way we arrive at ideas that are related to MacCullagh's ether theory. According to this the ether was not to generate elastic resistences against distortions in the ordinary sense, but resistances against the absolute rotation of its elements of volume. It would take us too far to count the numerous and sometimes very fantastic hypotheses that have been put forward about the constitution of the ether. If  

/ Page 191  /

we were to accept them literally, the ether would be a monstrous mechanism of invisible cogwheels, gyroscopes, and gears inter-gripping in the most complicated fashion, and of all this confused mass nothing would be observable but a few relatively simple features which would present themselves as an electronic field.
       There are also less cumbersome, and in some cases, ingenious theories in which the ether is a fluid whose rate of flow represents, say, the electric field, and whose vortices represent the magnetic field. Bjerknes has sketched a theory in which the electric charges are imagined as pulsating spheres in the ether fluid, and he has shown that such spheres exert forces on one another which exhibit con-siderable similarity with the electromagnetic forces.
     If we inquire into the meaning and value of such theories, we must grant them the credit of having suggested (though rather seldom) new experiments and of having led to the discovery of new phenomena. More often, however, elaborate and laborious experimental researches have been carried out to decide between two ether theories equally improbable and fantastic. In this way much effort has been wasted. Even nowadays there are people who regard a mechanical explanation of the electromagnetic ether as something demanded by reason. Such theories continue to crop up, and naturally they became more and more abstruce as the abundance of facts to be explained grows; hence the difficulty of the task increases without cessation. Heinrich Hertz deliberately turned away from all mechanistic speculations. We give the substance of his own words:
"The interior of all bodies, including the free ether, can, from an initial state of rest, experience some disturbances which we call electrical and others which we call magnetic. We do not know the nature of these changes of state, but only the phenomena which their presence calls up." This definite renunciation of a mechanical explanation is of great importance from the methodical point of view. It opens up the avenue for the great advances which have been made by Ein-stein's researches. The mechanical properties of solid and fluid bodies are known to us from experience, but this experience con-cerns only their behaviour in a crude sense. Modern molecular researches have shown that these visible, crude properties are a sort of appearance, an illusion, due to our clumsy methods of observation,  

/ Page 192   1 x 9 x 2 + 18  1 + 8 = 9   /  

whereas the actual behaviour of the smallest elements of structure, the atoms, molecules, and electrons follows quite different laws. It is therefore, naïve to assume that every continuous medium, like the ether, must behave like the apparently continuous fluids and solids of the crude world accessible to us through our coarse senses. Rather, the properties of the ether must be ascertained by studying the events that occur in it independent of all other experiences. The result of these researches may be expressed as follows: The state of the ether may be described by two directed magnitudes, which bear the names electric and magnetic strength of field, E and H, and whose changes in space and time are connected by Maxwell's equations. Under certain circumstances such an ether phenemon produces mecha-nical, thermal, and chemical actions in matter that are capable of being observed.
     Everything that goes beyond these assertions is superfluous hypo-thesis and fancy. It may be objected that such an abstract view undermines the inventive power of the investigator, which is stimulated by visual pictures and analogies, but Hertz's own example contradicts this opinion, for rarely has a physicist been possessed of such wonderful ingenuity in experiment, although as a theorist he recognized only pure abstraction as valid."
 

  A more important question than the pseudo problem of the mechanical interpretation of the ether is that concerning the influence of the motions of bodies (among which must be counted, besides matter, the ether) on electromagnetic phenomena.
This brings us back, but from a more general standpoint, to the investigations which we made earlier (IV,7)into the optics of moving bodies. Optics is now a part of electrodynamics, and the luminiferous ether is identical with the electromagnetic ether. All the inferences that we made earlier from the optical observations with regard to the behaviour of the luminiferous ether must retain their validity since they are obviously quite independent of the mechanism of light vibrations; for our investigation concerned only the geometrical characteristics of a light wave, namely, frequency (Doppler effect), velocity (convection), and direction of propagation (abberation).  

/ Page 193     /

We have seen that up to the time when the electromagnetic theory of light was developed only quantities of the first order in B = v
                               c
were open to measurement. The result of these observations could be expressed briefly as the "optical principle of relativity":
Optical events depend on the relative motions of the involved material bodies that emit, transmit or receive the light. In a system of reference moving with constant velocity relative to the ether all inner optical events occur just as if it were at rest.
      Two theories were proposed to account for this fact. That of Stokes assumed that the ether inside matter was completely carried along by the latter; the second, that of Fresnel, assumed only a partial convection, the amount of which could be derived from experi-ments. We have seen that Stoke' theory, when carried to its logical conclusion, became involved in difficulties, but that Fresnel's represented all the phenomena satisfactorily.
       In the electromagnetic theory the same two positions are possible, either complete convection, as advocated by Stokes, or the partial convection of Fresnel. The question is whether purely electro-magnetic observations will allow us to come to a decision about these two hypotheses.
       Hertz was the first to apply the hypothesis of complete convection to Maxwell's field equations. In doing so, he was fully conscious that such a procedure could be only provisional, because the appli-cation to optical events would lead to the same difficulties as those which brought Stoke's theory to grief. But the simplicity of a theory which required no distinction between the motion of ether and that of matter led him to develop and to discuss it in detail. This brought to light the fact that the induction phenomena in moving conductors, which are by far the most important for experi-mental physics and technical science, are correctly represented by Hertz's theory. Disagreements with experimental results occur only in finer experiments in which the displacements in nonconductors play a part. We shall investigate all possibilities in succession:

              1. Moving conductors (a) in the electrical field.
                                                   (b) in the magnetic field.
              2. Moving insulators    (a) in the electrical field
                                                   (b) in the magnetic field.

/ Page 194

1a. A conductor acquires surface charge in an electric field. If it is moved, it carries them along with itself. But moving charges must be equivalent to a current, and hence must produce a surrounding magnetic field according to the law of Biort and Savert. To pic-ture this to ourselves we imagine a plate condenser whose plates are parallel to the xz-plane (Fig.100).
Let them be be oppositely charged
 
Fig.100  A charged plate of a condenser moving with velocity v perpendicular to the electric field.        


With density of charge o on the surface. This means e = of is the amount of electricity on an area f of the plate. Now let one plate be moved with respect to the ether in the direction of the x-axis with the velocity v. Then a convection current arises.
The moving plate is displaced with velocity v, that is, by a length vr in the time t . If its width in z-direction is a, then an amount of electricity e = oavt  passes in time t through a plane that is parallel to the yz-plane,
 
Hence a current  J = e = oav  flows. This must exert exactly the same
                               t
magnetic action as a conduction current of magnitude J flowing through the plate when it is at rest.
      This was confirmed experimentally in Helmholtz's laboratory by H. A. Rowland (1875), and later, more accurately, by
A. Eichenwald. Instead of a plate moving rectilinearly, a rotating metal disk was used.
1b. When conductors are moved about in a magnetic field, electric fields arise in them, and hence currents are produced. This is the  

/ Page 195  /

phenomenon of induction by motion, already discovered by Faraday and investigated quantitatively by him. The simplest case is this: Let the magnetic field H produced, say by a horseshoe magnet be parallel to the z-axis (Fig. 101). Let there be a straight piece of wire of length l parallel to the y-axis,  and let this be moved with the velo-city  v in the direction of the x-axis. If the wire is now made part of

Fig.101  Motion of a wire of length 1, which is part of a closed circuit, in a magnetic field between the ends of a large horseshoe magnet.
 
A closed circuit by sliding it on the two opposite arms of a U-shaped piece of wire in such a way that the Utakes no part in the motion (seefigure). Then an induction current J flows in the wire. This is given most simply by stating Faraday's law of induction thus: The current induced in a wire which forms part of a closed circuit is proportional to the change per second of the number of lines of force enclosed by the wire loop. This number is measured by the magnetic displacement per unit area uH multipied by the area f of the loop fuH. In the section on magnetic induction (p.176) the change of this quantity was considered to be due to a change of H by H in the short time interval t Here it is due to a change of the area f produced by the movement of the wire. If its length is l and its velocity perpendicular to its extension is v, then it sweeps out the  

/ Page 196 /

area lv each second, and this is the change of f. The change of the number of lines of force per second is therefore vluH. According to Faraday's induction law an electric current  J is induced in the wire. Instead of speaking of the current J it is better to express the effect in terms of the potential difference V produced between the ends of the wire. The experiment gives V proportional to the quan-tity just discussed, vluH. Concerning the factor of proportionality, a remarkable law of symetry has been revealed. If one measures all quantities in units here used, this factor turns out to be 1 , so that
                                                                                                                                                                    c
one has the equation V=1 v l u H. Seen from the wire this corres-ponds to an electric field E= V = v
                                       c                                                                                                              l     c u H. If the same piece of wire were to move without being part of a closed circuit, there would appear charges at the end of the wire corresponding to this field as long as the movement went on.
      This law is the basis of all machines and apparatus of physics and electrotechnical science in which energy of motion is transformed by  induction into electromagnetic energy; these include, for example, the telephone, and dynamo machines of every kind. Hence the law may be regarded as having been confirmed by countless experiments.
 
Fig. 102    A charged condenser is filled with a disk-shaped insulator. In the insulator the displacement has induced charges on the surface of the disk. One part of the displacement (dipoles + ) is caused by the ether, the other part (dipoles + ) by the insulator. If the insulator is moved, only the insulator dipoles are moved with it..  

/ Page 197  /

2a. We suppose the motion of a nonconductor in an electric field to be realized thus: A moveable disk composed of the substance of the non-conductor is placed between the two plates of the condenser of Fig. 100 (see Fig. 102). The disk shall fill the space between the condenser plates so that the distance a marked in Fig. 100 measures also the corresponding width of the disk. If the condenser is now charged, an electric field E arises in the disk, and a displacement*E is induced which is perpendicular to the plane of the plates, that is, parallel to the y-direction. This causes the two boundary faces of the insulating disk to be charged equally and oppositely to the metal plates facing them respectively. The surface charge has a density o which is proportional to the displacement D in the insulator: 4 pio = D E.  D consists of two parts, De = E. the displacement of the ether, and D =D - e, the displacement of matter alone.
      If the insulating layer is now moved in the direction of the x-axis with the velocity v, then, according to Hertz, the ether in the layer will be carried along completely. Hence the field E and the charges of density o = *E produced by it on the bounding planes will also be carried along.                                                                                4pi
    Therefore the moving charge of a bounding surface again repre-sents a current *E av and must generate, according to Biot and Savert,s law, a magnetic field.                                                                           4pi
     W.C. Rontgen proved experimentally (1885) that this was the case, but the deflection of the magnet needle that he observed was much smaller than it should have been from Hertz's theory. Ront-gen's experiments show that only the excess of the charge density over the displacement of the ether alone (i.e, D - De = E (*-)1 = Dm, the displacement of the insulator alone) participates in the motion of the matter. We shall interpret this result later in a simple way. Here we merely establish that, as was to be expected according to the well known facts of optics, Hertz's theory of complete convection also fails to explain purely electromagnetic phenomena.
    Eichenwald (in 1903) confirmed Rontgen's result very strikingly by allowing the charged metal plates to take part in the motion.  These give a convection current of the amount oav = *E av; according  /
                                                                                                       4pi
 
Page 198 1 x 9 x 8 = 72  2 + 7 = 9    8 + 9 +1= 18  8 + 1 = 9     /

to Hertz this insulating layer ought, on account of the opposite and equal charges, exactly to compensate this current. But Eichenwald found that this was not the case. Rather, he obtained a current which was entirely independent of the material of the insulator. This is exactly what is to be expected according to Rontgen's results described above."
 
The Alizzed removes information for one reason or another.
Page 198 "he obtained a current which was entirely independent of the material of the insulator."
 
" For the current due to the insulator is (*E   -  E )  av, of which the first term is compensated by the convection of the plates,                       4pi   4pi
 
and so we are left with the current E  av, which is independent of the dielectric constant *.
                                                 4 pi
Fig. 103   A piece of an insulator is moved in a magnetic field to measure the induced displacement charges at the surface of the disk.
2b. We assume a magnetic field parallel to the z-axis, produced, say, by a horseshoe magnet, and a disk of non-conducting material moving through the field in the direction of the x-axis ( Fig. 103). Let the insulator be not magnetizable (u = 1).
Let the two bounding faces of the disk which are perpendicular to the y-axis be covered with metal, and let these surface layers be connected to an electro-meter by means of sliding contacts so that the charges that arise on them can be measured.

Page 199

This experiment corresponds exactly with the induction experiment discussed under (1b), except that a moving dielectric now takes the place of the moving conductor. The law of induction is applicable in the same way. It demands the existence of an electric field  E = H v ,  acting in the magnetic direction of the y-axis on the moving insulator. Hence, according to Hertz's                                       c
theory, the two superficial layers must exhibit opposite charges of surface density  *E = * H  v
                                                                                                                            4pi   4pi   c
 
which cause a deflection of the electrometer. The experiment was carried out by H.F. Wilson, in 1905, with a rotating dielectric, and it did, indeed, confirm the existence of the charge produced, but again to a lesser extent, namely, corresponding to a surface density (*- 1) H v .   Thismeans that there is only an effect of the moving matter and none of the ether. Here too, then Hertz's theory fails.
                                                                                                          4 pi c
     In all these four typical phenomena what counts is clearly only the relative motion of the field-producing bodies with respect to the conductor or insulator investigated. Instead of moving this in the x direction, as we have done, we could have kept it at rest and moved the remaining parts of the apparatus in the negative direction of the x-axis. The result would have been the same. For Hertz's theory recognisezes only relative motions of bodies, the ether being also reckoned as a body. In a system moving with constant velocity everything happens, according to Hertz, as if it were at rest; that is the classical principle of relativity holds.
      But Hertz's theory is incompatible with the facts, and it soon had to make way for another which took exactly the opposite point of view with regard to relativity."  
 
Hearing a sighting, on the nearside of an outside sounding wind the Zed Aliz Zed thanked, the me, mi'self, and I, of the far yonder scribe for the, az iz transcription, of Brother Born's most important exposition. Telling the wah scribe that reight or wrong it would be right az ninepence on the night, and not to hurry a worry.
 
Page 199
       1 x 9 x 9 = 81
             8 + 1 = 9
       1 + 9 + 9  = 19
                1 x 9 = 9
                 1 + 9 = 1
                   1 x 9 = 9
                    9 + 1 = One x the NINE of the that.