Page 124  

"Since the bible says, " The Lord our God is a consuming fire," the Divine presence is properly represented by the Lion and Fire. Furthermore, in the Qabalah, the element of fire is attributed to the Holy letter ,Shin, because the numeral value is 300, and 300 is the value of RVCh ALHIM, Ruach Elohim - literally, "The Breath of the Creative Powers", or as the English Bible puts it, The Spirit of God. "

Page 90  

"The number 27 is important in occultism as the second cube, or 3 x 3 x 3. Qabalists would have recognized it as the number of the Hebrew adjective ZK, zak, meaning "clean" or "pure"..."
"...Furthermore, though it designated  by another adjective, the idea of purity is associated with the aspect of the Life Power that Qabalists call Yesod, meaning "Basis" or "Foundation." Yesod is the ninth Sephirah, corresponding to the ninth circle on the Tree of Life. Note that 9 is the sum of the three 3s, which, multipled together, produce 27, and that the digits of 27 also add up to 9.

The quote "3 x 3 x 3" occurs on the 36 th, line up of page 90

Page 103

"The square root of 9 is 3. So we know that the third side"
This occurs on the 33^rd line down  of page 103

Page 809  8 x 9 + 72  7 + 2 = 9

Chapter 33  Verse 3  x  33 = 99

       "Call unto me, and I will answer thee, and shew thee great and mighty things which thou know-est not."

Page 165 continued

"Faraday came from no learned academy his mind was not burdened with traditional ideas and theories His sensational rise from a bookbinder's apprentice to the world famous physicist..." "... is well known."
"...The world of his ideas, which arose directly and exclusively from the abundance of his experiments, was just as free from conventional schemes as his life. We discussed already his researches on electrolytic dissociation.
His method of trying all conceivable changes in the experimental conditions led him (1837) to insert nonconductors like petroleum and turpentine between the two metal plates (electrodes) of the electro-lytic cell in place of a conducting fluid (acid or a solution of a salt). These nonconductors did not dissociate, but they were not without influence on the electrical process. For it was found that when the two metal plates were charged by a voltaic battery with a definite  

/ Page 166   1 x 6 x 6 = 36  3 + 6 = 9    /  

potential difference, they took up different charges according to the substance that happened to be between them( Fig. 85). The non-conducting substance thus influences the power of taking up elec-tricity or the capacity of the system of conductors composed of two plates, which is called a condenser
      The discovery impressed Faraday so much that from that time on he gave up the usual idea that electrostatics was based on the direct action of electric charges at a distance, and developed a peculiar new interpretation of electric and magnetic phenomena, a theory of contiguous action. What he learned from the experiment

         Fig.85 A condenser is charged up by a voltaic cell     Fig.86 The lines of force in a condenser

described above was the fact that the charges on the two metal plates do not simply act on each other through the intervening space but that this intervening space plays an essential part in the action. From this he concluded that the action of this medium is propagated from point to point and is therefore an action by contact, or a contiguous action. We are familiar with the contiguous action of elastic forces in deformed rigid bodies. Faraday, who always kept to empirical facts, did indeed compare the electric contiguous action in non-conductors with elastic tensions, but he took care not to apply the laws of the latter to electrical phenomena. He used the graphical picture of  "lines of force" that run in the direction of the electric field from the positive charges through the insulator to the negative  

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charges. In the case of a plate condenser, the lines of force are straight lines perpendicular to the planes of the plate"(Fig.86 ) Faraday regarded the lines of force as the true substratum of electrical phenomena; for him they are actually material configurations that move about, deform themselves, and thereby bring about electrical effects. For Faraday the charges play a quite subordinate part, as the place, as the places at which the lines of force start out or end. He was confirmed in this view by those experiments which proved that in con-ductors the total electric charge resides on the surface while the interior remains quite free. To give a dramatic proof of this, he built a large cage fitted all around with metal, into which he entered with sensitive electrical measuring instruments. He then had the cage very bly charged and found that in the interior not the slightest influence of the charges was to be detected. We used this fact earlier (V,1) to derive Coulomb's law of action at a distance. But Faraday concluded from it that the charge was not primary element of electrical phenomena and that it must not be imagined as a fluid exerting forces at a distance. Rather, the primary element is the state of tension of the electric field in the nonconductors which is represented by the picture of lines of force. The conductors are in a sense holes in the electric field, and the charges in them are only fictions invented to explain the pressures and tensions arising through the strains in the field as actions at a distance. Among the nonconductors or die-lectric substances there is also the vacuum, the ether, which we here again encounter in a new form.
     This strange view of Faraday's at first found no favour among the physicists and mathematicians of his own time. The view of action at a distance was maintained; this was possible even when the "dielectric" action of nonconductors discovered by Faraday was taken into account. Coulumb's law only needed to be altered a little:to every conductor there is assigned a peculiar constant..." "...its dielectric constant, which is defined by the fact that the force acting between two charges e1, e2 embedded in the nonconductor is smaller in the ratio 1:.." "..than that acting in vacuo:.."

(55)

Page 168

"... With this addition the phenomena of electrostatics could all be explained even when the dielectric properties of nonconductors were taken into account.  We have already mentioned that electrostatics had previously passed over into a theory of pseudocontiguous action, the so-called theory of potential. This likewise easily succeeded in assimilating the dielectric constant..." "...Nowadays we know that this actually was already equivalent to a mathematical formulation of

Fig 87 "... The magnetic field of a magnetized bar is made visible by iron filings on a paper above the bar.

Faraday's concept of lines of force. But as this method of potential was then regarded only as a mathematical artifice, the antithesis between the classical theory of action at a distance and Faradays idea of contiguous action still remained.
     Faraday developed similar views about magnetism. He discovered that the forces between two magnetic poles likewise depend on the medium that happens to lie between them, and this again led him to the view that the magnetic forces, just as with the electric forces, are produced by a peculiar state of tension in the intervening  

/ Page 169

media. The lines of force serve to represent these tensions. They can as it were, be made visible by scattering iron filings over a sheet of paper and holding the latter closely over a magnet (Fig 87).
     The theory of action at a distance leads to the formal introduction of a constant characteristic of the substance, the magnetic pene-trability or permeability..." "...and gives Coulomb's law in the altered form

 (55a)



Physicists have not, however, remained satisfied with this formal procedure, but have devised a molecular mechanism that makes the magnetic and dielectric power of polarization intelligible. We have already seen that the properties of magnets lead us to regard their molecules as small elementary magnets made to point in parallel directions by the process of magnetization. It is assumed that they retain this parallelism by themselves, say, through frictional resis-tances. Now it may be assumed that in the case of most bodies that do not occurr as permanent magnets this friction is wanting. The parallel position is then indeed produced by an external magnetic field, but will at once disappear if the field is removed. Such a substance will then be a magnet only as long as an external field is present. But it need not even be assumed that the molecules are permanent magnets that are forced into parallel positions. If each molecule contains the two magnetic fluids, then they will separate under the action of the field and the molecule will become a magnet of itself. But this induced magnetism must have exactly the effect that the formal theory describes by introducing the permeability. Between the two magnetic poles (N,S) in such a medium there are formed chains of molecular magnets called magnetic dipoles, whose opposite poles everywhere compensate each other in the interior but end with opposite poles at Nand S and hence weaken the actions of N and S (Fig.88). (The converse effect strengthening, also occurs, but we shall not enter into its interpretation.)
       Exactly the same as has been illustrated for magnetism may be imagined for electricity. A dielectric, in this view, is composed of molecules that are either electric dipoles of themselves and assume a parallel position in an external field or that becomes dipoles through  

/ Page 170   /

the separation of the positive and negative electricity under the action of the field. Between two plates of a condenser (Fig.89) chains of molecules again form whose charges compensate each other in the interior but not on the plates. Through this a part of the charge on the plates is itself neutralized, and a new charge has to be imparted to the plates to charge them up to a definite tension or potential. This explains how the polarizable dielectric increases the receptivity or capacity of the condenser.


Fig. 88  Molecular magnetic di-poles                       Fig. 89  Electric dipoles between the plates of a
Between the poles of a magnet                               condenser are directed along the lines of force.


According to the theory of action at a distance, the effect of the dielectric is an indirect one. The field in the vacuum is only an abstraction. It signifies the geometrical distribution of the force that is exerted on an electric test body carrying a unit charge. But the field in the dielectric represents a real physical change of the substance consisting of the molecular displacement of the two kinds of electricity.
    Faraday's Theory of contiguous action knows no such difference between the field in the ether and in insulating matter. Both are

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dielectrics. For the ether the dielectric constant..." "...=1, for other insulators..." "..differs from 1.
If the graphical picture of electric dis-placement is correct for matter, it must also hold for the ether. This idea plays a great part in the theory of Maxwell, which is essentially the translation of Faraday's idea of lines of force into the exact language of mathematics. Maxwell assumes that in the ether, too, the production of an electric or a magnetic field is accompanied by "displacements" of the fluids. It is not necessary for this purpose to imagine the ether to have an atomic structure, yet Maxwell's idea comes out most clearly if we imagine ether molecules which become



        Fig. 90 a   Two opposite but equal charge distributions in a cubic volume and their neutralization by superposition.

dipoles just like the material molecules in the field. The field is not the, however the cause of the polarization, but is the displacement which is the essence of the state of tension that we call electric field. The chains of ether molecules are the lines of force and the charges at the surface of the conductors are nothing but the end charges of these chains. If there are material molecules present besides the ether particles, the polarization becomes strengthened and the charges at the end become greater.
    We shall now discuss these ideas in more detail. We have just

/ Page 172 /

explained how magnetization and electrification can be illustrated by chains of dipole molecules (Fig. 88, 89).
However the idea of molecules in the ether has no empirical foundation. Therefore it is preferable to represent the situation by a continuous model. Imag-ine a rectangular block of space filled with a continuous positive charge density, p and then the same part of space filled with a nega-tive charge density, - p. If both kinds of charges are present simultaneously the space is uncharged (Fig. 90a) The establishment of an electrical field E is, according to Faraday and Maxwell, nothing but a displacement of the two blocks of charge (see Fig 90b) through a small distance a.  The whole interior remains uncharged, although there is a shift of charges at each point; only on two opposite faces there appear opposite equal charges,
For if f is the area of the face, there are two rectangular sheets of volume fa which contain only one kind of charge. As a is small one can speak of surface charges pfa and  pfa - The surface charge per unit area liberated by the little shift a is pa; it represents a measure of the electric displacement D. However, one does not simply equate these two quantities, but must add a numerical factor for the following reason.
Consider a point charge e in a dielectric (see Fig. 91). The law of force (55) requires that the field E produced by it is..."

(56)
"...If one describes the same situation in Faraday's language one has to assume a displacement which is constant on spheres around the centre and diminishes with distance r (Fig 92). If a spherical shell with the outer radius r and the inner radius r' is imagined to be filled with mutually cancelling charge densities p and - p and if these are displaced in the radial direction by a
there appears the charge -f'ap at the inner sphere and the charge fap at the outer sphere. Both of these must be equal to the given central point charge; for if the inner radius is contracted to nothing the corres-ponding charge must just cancel the central charge e. Therefore e = fap..."

(57)



One can say that the displacement D diverges from the central charge e in all directions.



Fig. 91 A point charge e pro-duces a field E directed

Fig 92  The displacement on two spheres with charge e in the center:."

radially and having a concentric sphere.

"...or r2 D=r'2D' = e.

    This expression is also used in the general case where the true charge is not concentrated in one point but continuously distributed with a density p (which is not to be mistaken for the fictional density denoted by the same letter that we used to illustrate Maxwell's con-cept of displacement).One writes symbolically



                                                            Div D= 4..."  here the scribe writ pi, with a p.
(58)



But this is more than a mnemonic help. Maxwell has managed to give the symbol div a definite meaning as a differential operation performed on the components of D Thus to the mathematician (60) signifies a differential equation, a law of contiguous action.  

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Are Faraday' and Maxwell's ideas or those of the theory of action at a distance right?
   So long as we confine ourselves to electrostatic and magnetostatic phenomena both are equivalent. For the mathematical expression of Faradays idea is what we have called a theory of pseudocont-iguous action, because it does, indeed operate with differential equations but recognizes no finite velocity of propagation of tensions. Faraday and Maxwell, however themselves disclosed those phenomena which, in a way analgous to the inertial effects of mechanics, effect the delay in the transference of an electromagnetic state from point to point and hence bring about the finite velocity of propaga-tion. These phenomena are the displacement current and the magnetic induction."