11. Hertz's Theory of Moving Bodies

  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).  

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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
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.

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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 v
r 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
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  

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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  

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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
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..  

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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  /


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.

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"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.

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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
pi   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
pi c This means that there is only an effect of the moving matter and none of the ether. Here too, then Hertz's theory fails. 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.
     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.

12. The Electron theory of Lorentz
   "It is the theory of H.A. Lorentz (proposed in
1892) that signi-fied the climax and the final step of the physics of the material ether.
    It is a one-fluid theory of electricity that had been developed atomistically, and it is this feature which, as we shall presently see, determines the part allocated to the ether.
    The fact that electric charges have an atomic structure, that is,  

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occur in very small indivisible quantities, was first stated by Helm-holtz (in 1881) in order to make intelligible Faradays laws of eloctro-lysis (p.157)  Actually, it was only necessary to assume that every atom in an electrolytic solution enters into a sort of chemical bond with an atom of electricity or an electron in order to make intelligible the fact that a definite amount of electricity always separates out equivalent amounts of substances.
    The atomic structure of electricity proved of particular value for explaining the phenomena which are observed in the passage of the electric current through a rarefied gas. Here it was first discovered that positive and negative electricity behave quite differently. If two metal electrodes are introduced into a glass tube and if a current is made to pass between them
(Fig. 104). Very complicated pheno-mena are produced so long as gas is still present at an appreciable
Fig. 104   A tube to produce cathode rays.   K  cathode, A  anode.
Pressure in the tube. But if the gas is pumped out more and more, the phenomena becomes increasingly simple. When the vacuum is very high, the negative electrode, the cathode K, emits rays which pass through a hole in the positive pole, the anode A, and are observed behind   A   through fluorescence produced on a screen (as known from any television set). These rays are called cathode rays. It was shown that they could be deflected by a magnet in the manner of a stream of negative electricity. The greatest share in investigating the nature of cathode rays was taken by Sir J. J. Thomson and P.L. Lenard. The negative charge of the rays could also be directly demonstrated by collecting it in a hollow conductor. Furthermore, the rays are deflected by an electric field applied per  

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pendicular to their path, and this deflection is opposite to the direc-tion of the field, which again proves the charge to be negative.
     The conviction that the nature of cathode rays is corpuscular became a certainty when physicists succeeded in deducing quantita-tive conclusions concerning their velocity and their charge.
     If we picture the cathode ray as a stream of small particles of mass m
el, then clearly it will be the less deflected by a definite elec-tric or magnetic field the greater its velocity - just as the trajectory of a rifle bullet is straighter the greater its velocity. Now it is possible to produce cathode rays that can be bly deflected - that is, slow cathode rays - by using a small difference of potential between cathode and anode. If one chooses a b difference of potential between the two poles, the rays are bly accelerated by the field from K to A, which may be calculated from the fundamental equation of mechanics    
el b = K = e E,
where e is the charge and E is the field strength. We are here clearly dealing with a case analogous to that of "falling" bodies, in which the acceleration is not equal to that of gravity g but to e  E.  If the ratio e were known, the velocity v could be found                                                                                   m
el                  m el

from the laws for falling bodies. But there are two unknowns, e and v, and hence another measurement is necessary if they                                                                                     m

are to be determined. This is obtained by applying a lateral magnetic force. In discussing Hertz's theory (V,11, 1b, p. 194)
we saw that a magnetic field H sets up in a body moving perpendicular to H an electrical field E= v H,
which is perpendicular both to H and to v. Hence a deflecting force eE = e v H  will act on every cathode ray particle so that                                                                                                          c