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
we get b =c2f.                                                                                                                                                 (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."