Page 146

     "The fact that a certain kind of ore, magnetite, attracts iron, and that rubbed amber (elektron in Greek) attracts and holds light bodies was already known to the ancients. But the science of magnetism and electricity are products of more recent times which had been trained by Galileo and Newton to ask rational questions of nature with the help of experiment.
    The fundamental facts of electrical phenomena, which we shall now recapitulate briefly, were established after the year 1600. At that time friction was the exclusive means of producing electrical effects. Gray discovered (1729) that metals, when brought into contact with bodies that had been electrified by friction, themselves acquire similar properties. He showed that electricity can be conducted in metals. This led to the classification of substances as conductors and nonconductors (insulators) It was discovered by du Fay (1730) that electrical action is not always attraction but may also be repulsion
To account for this fact he assumed the existence of two fluids (nowadays we call them positive and negative electricity), and he established that similarly charged bodies repel each other, while oppositely charged bodies attract each other.
     We shall define the concept of electric charge quantitatively. In doing so we will not follow the oftentimes very circuitous steps of argument that led historically to the enunciation of the concepts and laws, but rather we shall select a series of definitions and experiments in which the logical sequence emerges most clearly.
      Let us imagine a body M that has some how been electrified by friction. This now acts attractively or repulsively on other electrified  

/ Page 147  /  

bodies. To study this action we shall take small test bodies, say spheres, whose diameters are very small compared with the distance of their closest approach to the body M. If we bring a test body P near the body M, P experiences a statistical force of definite magnitude and direction which may be measured by the methods of mechanics, say, by balancing it against a weight with the help of levers and threads. It is found qualitevely that the force decreases with increasing distance P M.
     We next take two such test bodies P1 and P 2, bring them in turn to the same point in the vicinity of M, and measure in each case the forces K1 and K2 as regards size and direction. We shall henceforth adopt the convention that opposite forces are to be regarded as being in the same direction and having opposite signs. Experiment shows that the two forces have the same direction but that their values may have different signs.
      Now let us bring the two test bodies to a different point near M and let us again measure the forces K1' and K2' as regards value and direction. Again they have the same direction, but in general they have different values and different signs



                                                       K1 = K1'.
                                                       K2    K2'
From this result we may conclude:
       1.  The direction of the force exerted by an electrified body M on a small test body P does not depend at all on the nature and the amount of electrification of the test body, but only on the properties of the body M
       2  The ratio of the forces exerted on two test bodies brought to the same point in turn is quite independent of the choice of the point, that is, of the position, nature, and electrification of the body M. It depends only on the properties of the test bodies.
       We now choose a definite test body, electrified in a definite way, and let its charge be the unit of charge or amount of electricity q. With the aid of this test body we measure the force that the body M exerts at many places.  this force be denoted by Kq.  Then  

/ Page 148   /

this also determines the direction of the force K exerted on any other test body p. The ratio K: Kq, however, depends only on the test body P and defines the ratio e of the electric charge of P  and the unit of charge q. This may be positive or negative depending upon whether K and Kq are in the same or in opposite directions. Thus we have in any position:  K = Kq .
                E      q

From this one concludes that K depends only on the electrical nature of the body M.
                                             e
Therefore we call the quotient  K = Kq  the electrical field strength E. This quantity E determines the electrical
                                               e      q
  
action of M in the surrounding space, or as we usually say, its electric field. From K= E follows
                                                                                                                                    e



                                                                                                                                K = e E.                                                     (45)


The scribe puzzling, enquired as to the inclusion of diagrams and formula references supplied by good brother Born.
On advice from the only one who knows, Zed Aliz Zed,a being guided towards right action. asked the scribe to omit those of the suggested formulae and diagram references that had to be omitted and to include any that ought to be included betwixt and between pages 146 and 224 of Brother Born's work.
Not altogether puzzled by such an answer as that, the far yonder scribe would do just that, to the best of that's scribes abilities. Nevertheless, understanding its importance within the creator schema of rings, the scribe wondered aloud az to the Zed Aliz Zed's hieroglyphics conundrum, and not believing in working piecemeal had a mite to eat.  
After which the Zed Aliz Zed The Far Yonder Scribe, the shadows on my shoulder and attendant mirror images re-affirmed their golden thread, and did each enter, as spiritual glow worms, the cave of the Minotaur.

Page 148 continued  

"As for the choice of unit charge, it would be almost impossible to fix this in a practical way by a decree concerning the electrification of a definite test body; a mechanical definition would be preferable. This can be arrived at as follows:
    We first give two test bodies equal charges. The criterion of equal charges is that they are subject to the same force from the same body M when placed at the same point near M. The two bodies will then repel each other with the same force. We now say that their charge equals the unit of charge q if this repulsion is equal to the unit of force when the distance between the two test bodies is equal to unit length. No assumption is made here about the dependence of the force on the distance.
      Through these definitions the amount of electricity or the electric charge becomes a measurable quantity just as length, mass or force may be measured.
      The most important law about amounts of electricity, which was enunciated independently in 1747 by Watson and Franklin, is that in every electrical process equal ammounts of positive and negative electricity are always formed. For example, if we rub a glass rod with a piece of silk, the glass rod becomes charged with positive electricity; an exactly equal negative charge is then found on the silk.  

/ Page 149  1 x 4 x 9 = 36    3 + 6 = 9   /  

This empirical fact may be interpreted by saying that the two kinds of electrification are not generated by friction but are only separated. They may be thought of as two fluids that are present in all bodies in equal quantities. In nonelectrified "neutral " bodies they are every-where present to the same amount so that their outward effects are counterbalanced. In electrified bodies they are separated. One part of the positive electricity, say, has flowed from one body to another; just as much negative has flowed in the reverse direction.
      But it is clearly sufficient to assume one fluid that can flow inde-pendently of matter. The we must ascribe to matter that is free of this fluid a definite charge say  positive, and to the fluid the opposite charge, that is, negative. Electrification consists of the flowing of negative fluid from one body to the other. The first body will then become positive because the positive charge of the matter is no longer wholly compensated; the other becomes negative because it has an excess of negative fluid.
      The struggle between the supporters of these two hypotheses, the one-fluid theory and the two fluid theory, lasted a long time, and of course remained futile and purposeless until it was decided by the discovery of new facts. We shall not enter further into these discussions, but shall only state briefly that characteristic differences were finally found in the behaviour of the two kinds of electricity; these differences indicated that positive electrification is actually firmly attached to matter but that negative electrification can move more or less freely. This doctrine still holds today. We shall revert to this point later in dealing with the theory of electrons.
                                         Another controversy arose  around the question of how the electri-cal forces of attraction and repulsion are transmitted                
through space. The first decades of electrical research came before the Newtonian theory of attraction. Action at a distance seemed unthinkable. Metaphysical theorems were held to be valid (for example, that matter can act only at points where it is present) and diverse hypotheses were evolved to explain electrical forces - for example, that emanations flowed from the charged bodies and exerted a pressure when they impinged on bodies, and similar assumptions. But after Newton's theory of gravitation had been established, the idea of a force acting directly at a distance gradually became a habit of thought. For it is, indeed, nothing more than a thought habit when an idea impresses  

/ Page 150  /

itself so bly on minds that it is used as the ultimate principal of explanation. It does not then take long for metaphysical speculation, often in the garb of philosophic criticism to maintain that the correct or accepted principle of explanation is a logical necessity and that its opposite cannot be imagined. But fortunately progressive empirical science does not as a rule trouble about this, and when new facts demand it, it often has recourse to ideas that have been condemned. The development of the doctrine of electric and magnetic forces is an example of such a cycle of theories. First came a theory of contiguous action based on metaphysical grounds, later a theory of action at a distance on Newton's model. Finally this became transformed, owing to the discovery of new facts, into a general theory of contiguous action again. The fluctuation is no sign of weakness. For it is not the pictures that are connected with the theories which are the essential features but the empirical facts and their conceptual relationships. Yet if we follow these we see no fluctuation but only a continuous development full of inner logical consistency. We may justifiably pass by the first theoretical attempts of pre-Newtonian times because the facts were known too incompletely to furnish really convincing starting points. But the rise of the theory of action at a distance in Newtonian mechanics is founded quite solidly on facts of observation. Research which had at its disposal only the experimental means of the eighteenth century was bound to come to the decision that the electric and magnetic forces act at a distance in the same way as gravitation. Even nowadays it is still permissible, from the point of view of the highly developed theories of contiguous action of Faraday and Maxwell, to represent electro- and magnetostatic forces by means of actions at a distance, and when properly used they lead to correct results.
      The idea that electric forces act like gravitation at a distance was first conceived by Aepinus (1759). He did not succeed in setting up the correct law for the dependence of electric actions on the dis-tance, but he was able to explain the phenomenon of electrostatic induction qualitively. This consists of a charged body acting attractively not only on other charged bodies but also on uncharged bodies, particularly on conducting bodies: a charge of the opposite sign is induced on the side of the influenced body nearest the acting body, whereas a charge of the same sign is driven to the farther side ( Fig 78 );  

/ Page 151  /  

hence, since the forces decrease with increasing distance, the attraction outweighs the repulsion.
     The exact law of this decrease was presumably first found by Priestly, the discoverer of oxygen (1767). He discovered the law in an ingenious indirect way which was more convincing than a direct measurement would have been. Independently Cavendish (1771) derived the law by similar  reasoning. But it received its name from the physicist who first proved it by measuring the forces directly, Coulomb (1785)..."
 
            Fig. 78  A charged body M in-fluences charges             Fig. 79 Derivation of Cou-lomb's law.
                      on an originally uncharged body



  "The argument of Priestly and Cavendish ran somewhat as follows: If an electric charge is given to a conductor, then it cannot remain in equilibrium in the interior of the conducting substance, since particles of the same charge repel each other. Rather, they must tend to the outer surface where they distribute themselves in a certain way so as to be in equilibrium. Now experiment teaches very definitely that no electric field exists within a space that is enclosed on all sides by metallic walls, no matter how bly the envelope is charged The charges on the outer surface of the empty space must thus distribute themselves so that the force exerted at each point in the interior vanishes. Now, if the empty space has the particular form of a sphere, the charge for reasons of symmetry, can only be distributed uniformly over the surface..."

Page 153  

"...In conformity with our convention about the unit of electric charge we must set C= 1 x unit of forcex (unit of length) 2; then we define the dimensions of charge by putting C=q2. Now the force between two unit charges a unit distance apart is to be equal to one unit of force. With this convention the force that two bodies carrying charges e1 and e2 and at a distance r apart exert on each other is
                                    K=e1e2 .                                                                                                                                               (46)
                                            r2



This is Coulombs law. In its formulation we assume, of course, that the greatest diameter of the charged bodies is small compared with their distances apart. This restriction means that we have to do, just as in the case of gravitation, with an idealized elementary law. To deduce from it the action of bodies of finite extent we must consider the electricity distributed over them to be divided into small parts, then calculate the effects of all the particles of the one body on all those of the others in pairs and sum them.

Page 154    

"After Coulomb's law had been established, electrostatics became a mathematical science. Its most important problem is this: Given the total quantity of electricity on conducting bodies, to calculate the distribution of charges on them under the action of their mutual influence, and also the forces due to these charges. The develop-ment of this mathematical problem is interesting in that it very soon became changed from the original formulation based on the theory of action at a distance to a theory of pseudocontiguous action, that is, in place of the summations of Coulomb forces there were obtained differential equations in which the field E or a related quantity called potential occurred as the unknown. However we cannot discuss these purely mathematical questions any further here but only mention the names of Laplace (1782), Poisson (1813), and Gauss (1840) who have played a prominent role in their solution. We shall emphasize only one point. In this treatment of electrostatics, which is usually called the theory of potential, we are not dealing with a true theory of contiguous action in the sense which we attached to this expression before..." "...for the differential equations refer only to the change in the intensity of field from place to place and contains no term that expresses a change in time. Hence they entail no transmission of electric force with finite velocity but, in spite of their differential form, they represent an instantaneous action at a distance.
    The theory of magnetism was developed in the same way as that of electrostatics. We may, therefore express ourselves briefly.
    A lozenge-shaped magnetized body, a magnet needle, has two poles, that is, point from which the magnetic force seems to start out, and the law holds that like poles repel, unlike poles attract one another. If we break a magnet in half, the two parts do not carry opposite magnetic charges, but each part shows a new pole near the new surface and again represents a complete magnet with two equal but opposite poles. This holds, no matter into how many parts the magnet be broken.
   From this it has been concluded that there are indeed two kinds of magnetism as in the case of electricity except that they cannot move freely, and that they are present in the smallest particles of matter, molecules, in equal quantities, but separated by a small distance. Thus each molecule is itself a small magnet with a north and a south  

/ Page 155   /

pole (Fig. 80). In a body that is not magnetized all the elementary magnets are in complete disorder. Magnetization consists of bring-ing them into the same direction. Then the effects of the alternate north (+) and south (- ) poles counterbalance, except at the two ends which therefore seem to be the sources of the magnetic effects..."
 
                                         Fig 80 A magnetized body consisting of elementary magnets.
 
     "... By using a very long, thin magnetized needle one can be sure that in the vicinity of the one pole the force of the other becomes negligible. Hence in magnetism, too we may operate with test bodies, namely with the poles of very long, thin magnetic rods. These allow us to carry out all the measurements that we have already discussed in the case of electricity..."      "...Clearly the dimensions of magnetic quantities are the same as those of the corresponding electric quantities, and their units have the same notation in the C.G.S. system.
    The mathematical theory of magnetism runs almost parallel with that of electricity. The most essential difference is that magnetism is attached to the molecules, and that the measureable accumulations  

/ Page 156  /

that condition the occurrence of poles in the case of finite magnets arise only owing to the summation of molecules that point in the same direction. One cannot separate the two kinds of magnetism and make a body, for example a north pole.



                                                                 2 Voltaic Electricity and Electrolysis
    The discovery of so-called contact electricity by Galvani (1780) and Volta (1792) is so well known that we may pass by it here. However interesting Galvani's experiments..." "...and the resulting discussion about the origin of electric charges may be, we are here more concerned with formulating concepts  and laws. Hence we shall recount only the facts..."
                                                                                                          Fig.81  Voltaic cell
 
    "...If two different metals are dipped into a solution (Fig. 81), say, copper and zinc into dilute sulphuric acid, the metals manifest electric charges that have exactly the same properties as frictional electricity. According to the fundamental law of electricity, charges of both signs occurr on the metals (poles) to the same amount. The system composed of the solution and the metals, which is called a voltaic element or cell, thus has the power of separating the two kinds of electricity. Now, it is remarkable that this power is apparently inexhaustible, for if the poles are connected by a wire so that their charges flow around and neutralize each other, as soon as the wire is  

/ Page157  /

again removed, the poles are still charged. Thus the element continues to keep up the supply of electricity as long as the wire connection is maintained. Hence a continuous flow of electricity must be taking place. How this is to be imagined in detail depends on whether the one-fluid or the two-fluid theory is accepted. In the former case only one current is present: in the latter, two opposite currents, one of each fluid, flow.      Now, the electric current manifests its existence by showing very definite effects. Above all it heats the connecting wire. Everyone knows this fact from the metallic filaments in our electric bulbs. Thus the current continually produces hear energy. From what does the voltaic element derive the power of producing electricity con-tinually and thereby indirectly generating heat? According to the law of conservation of energy, wherever one kind of energy appears during a process, another kind of energy must disappear to the same extent.    
      The source of energy is the chemical process in the cell. One metal dissolves as long as the current flows; at the same time a constituent of the solution separates out on the other. Complicated chemical processes may take place in the solution itself. We have nothing to do with these but content ourselves with the fact that the voltaic element is a means of generating electricity in unlimited quantities and of producing considerable electric currents.
      We shall now have to consider, however, the reverse process, in which the electric current produces a chemical decomposition. For example, if we allow the current between two indecomposable wire leads (electrodes), say of platinum, to flow through slightly acidified water, the latter resolves into its components, hydrogen and oxygen, the hydrogen coming off at the negative electrode (cathode), the oxygen at the positive electrode (anode), The quantitative laws of this process of "electrolysis," discovered by Nicholson and Carlisle (1800) were found by Faraday (1832). The far-reaching conse-quences of Faraday's researches for the knowledge of the structure of matter are well known; it is not the consequences themselves that lead us to discuss these researches but the fact that Faraday's laws furnished the means of measuring electric currents accurately, and hence allowed the structure of electromagnetic theory to be com-pleted.  

/ Page 158  /

This experiment of electrolytic dissociation can be carried out not only with a voltaic current, but just as well with a discharge current, which occurs when oppositely charged metallic bodies are connected by a wire. Care must be taken that the quantities of electricity that are discharged are sufficiently great. We have appara-tus for storing electricity, so-called condensers , whose action depends on the induction principle, and which give such powerful discharges that measurable amounts are decomposed in the electrolytic cell. The amount of the charge that flows may be measured by the methods of electrostatics discussed above. Now Faraday discovered the law that twice the charge produces twice the dissocia-tion, three times the charge three times the dissociation - in short that the amount m of dissociated substance (or of one of the products of dissociation) is proportional to the quantity e of electricity that has passed through the cell:
Cm= e.
The constant C depends on the nature of the substances and of the chemical process.
    A second law of Faraday regulates this dependence. It is known that chemical elements combine in perfectly definite proportions to form compounds. The quantity of an element that combines with 1 gm. of the lightest element, hydrogen, is called its equivalent weight. For example, in water (H 2 O) 8gm. of oxygen (O) are combined with 1 gm. of hydrogen (H), hence oxygen has the equivalent weight 8gm. Now Faraday's law states that the same quantity of electricity that seperates out 1 gm. of hydrogen is able to separate out 1 gm. of hydrogen is able to separate out an equivalent weight of every other element, for example, 8 gm. of oxygen.
       Hence the constant C need only be known for hydrogen, and then we get it for every other substance by dividing this value by the equivalent weight for the substance."
 
The scribe noted the appearance of Ra and the eight.
                  
Page 159

                                 (47)
 
             (48)  
...Thus electrolytic dissociation furnishes us with a very convenient measurement of the quantity of electricity e
That has passed through the cell during a discharge. We need only determine the mass m of a product of decomposition that has the equivalent weight..." "...and then we get the desired quantity of electricity from equation (48). It is of course a matter of indifference whether this electricity is obtained from the discharge of charged conductors (condensers) or whether it comes from a voltaic cell. In the latter case the electricity flows continuously with constant strength; this means that the charge = J x t passes through any cross-section of the conducting circuit and hence also through the decomposing cell in the time t Here the quantity
               (49)
is called the intensity of current or current strength, for it measures how much electrical charge flows through the cross-section of the conductor per unit time.
 
Page 160 1 + 6 = 7

We must next consider the process of conduction or current itself. It has been customery to compare the electric current with the flowing of water in a pipe and to apply the concepts there valid to the electrical process. If water is to flow in a tube there must be some driving force If it flows from a higher vessel through an inclined tube to a lower vessel, gravitation is the driving force (Fig. 82 ) This is greater, the higher the upper surface of the water
 
Fig 82 The current strength of the water is proportional to the potential difference V and therefore to the difference h in height of the two levels.
 
is above the lower. But the velocity of the current of water, or its current strength, depends not only on the forces exerted by gravi-tation but also on the resistance that the water experiences in the conducting tube. If this is long and narrow, the amount of water passing through per unit of time is less than in the case of a short wide tube. The currant strength J is thus proportional to the difference V of potential energy that drives the water (which is proportional to the difference in height h of the two levels;"
"...and inversely proportional to the resistance W. We set  

/ Page 161   /

     J = V   or  JW =V,                                   (50)
In which the unit of resistance chosen is that which allows one unit of current to flow when the difference of level is one unit of height.
     G.S. Ohm (1826) applied precisely the same ideas to the electric current. The difference of level that effects the flow corresponds to the electric force. We define the sign of the current as positive in the direction from the positive to the negative pole. For a definite piece of wire of length l we must set V=El, where E is the field strength, which is regarded constant along the wire. For if the same electric field acts over a greater length of wire, it furnishes a ber impulse to the flowing electricity. The force V is also called the electromotive force (difference of potential or level) It is, moreover, identical with the concept of electric potential which we mentioned above (p.154).
     Since the current strength J and the electrical intensity of field E, hence also the potential difference or electromotive force V = El, are measurable quantities, the proportionality between J and V expressed in Ohm's may be tested experimentally
     The resistance W depends on the material and the form of the conducting wire; the longer and thinner it is the greater is W. If l is the length of the wire and f the size of the cross-section then W is directly proportional to l, and inversely proportional to f.
               (51)
where the factor of proportionality..."  "...depends only on the material of the wire and is called the conductivity..."

Page 162  1 + 6 + 2 = 9

(52)
"... In this form Ohm's law is left only one constant whose value depends on the conducting material, namely, the conductivity, but in no other way depending on the form and size of the conducting body (wire).
    In the case of insulators..." "= 0. But ideal insulators do not exist. Very small traces of conductivity are always present except in a com-plete vacuum. There is an unbroken sequence leading from bad conductors (such as porcelain or amber) to the metals, which have enormously high conductivity.
      We have already pointed out that the current heats the conducting wire. The quantitative law of this phenomenon was found by Joule (1841). It is clearly a special case of the law of conservation of energy, in which electric energy becomes transformed into heat. Joule's law states that the heat developed per unit of time by the current J in traversing the potential difference V is
Q = JV,    (53)  
Where Q is to be measured not in calories but in mechanical units of work. We shall make no further use of this formula, and state it here merely for the sake of completeness.



By this time both the Zed Aliz Zed and far yonder scribes's Z's, were about ready to abandon their gyroscopes



Page 162  1 x 6 x 2 = 12  1 + 2 = 3   1 + 6 + 2 = 9
 
                                                                                4 Electromagnetism
Up to the early nineteenth century, electricity and magnetism were regarded as two regions of phenomena which was similar in some respects but quite separate and independent. A bridge was eagerly sought between the two regions, but for a long time without success. At last Oersted (1820) discovered that the magnetic needle is deflected by voltaic currents. In the same year Biot and Savart discovered the quantitive law of this phenomenon, which Laplace formulated in terms of action at a distance. This law is very important for us, for the reason that in it there occurs a constant peculiar to electromagnetism and of the nature of a velocity, which showed itself later to be identical with the velocity of light.
    Biot and Savart established that the current flowing in a straight wire neither attracts nor repels a magnetic pole, but strives to drive  

/ Page 163  1 x 6 x 3 = 18  1 + 8 = 9  /

it around in a circle about the wire (Fig. 83), so that the positive pole moves in the sense of a right handed screw turned from below (con-trary to the hands of a watch) about the positive direction of the current."



That's odd said the odd ones, at odds over whether the watch was showing the right time, or had it now taken a turn for the hearse. To which the scribe responded would you believe, by writing the words Spirit and Spiral.



"The quantitative law can be brought into the simplest form by supposing the conducting wire to be divided into a number of short pieces of length l and writing down the effects of these current elements, from which the whole current is obtained by summation. We shall state the lae of a current element only for the special case in which the magnetic pole lies in the plane that passes through the middle part of the element and is perpendicular"



         Fig 83 The magnetic field H surrounding a current J.         Fig. 84 The direction of H is perpendicular to the directions
                                                                                                                    of J and the radius vector r  
"to its direction (Fig 84). Then the force that acts on the magnet pole of unit strength, i.e., the magnetic intensity of field H in this plane is perpendicular to the line connecting the pole with the mid-point of the current element, and is directly proportional to the current intensity J and to its lengthl, and inversely proportional to the square of the distance r:"



                                                                                                 cH= J1
(54)
                                                                                                          r2  


"Outwardly this formula has again a similarity to Newton' law of attraction or Coulomb's law of electrostatics and magnetostatics, but the electromagnetic force has nevertheless a totally different  

/ Page 164   /

character. For it does not act in the direction of the connecting line but perpendicular to it. The three directions J,r H are  perpendi-cular to each other in pairs. From this we see that electrodynamic effects are intimately connected with the structure of Euclidean space; in a certain sense they furnish us with a natural rectilinear coordinate system..."
     The factor of proportionality c introduced in formula (54) is com-pletely determined since the distance r, the current strength J and the magnetic field H are measurable quantities. It clearly denotes the strength of that current which, flowing through a peiece of conducter of unit length, produces a unit of magnetic field at a unit distance. It is customary and often convenient to choose in place of the unit of current that we have introduced (namely, the quantity of static electricity that flows through the cross-section per unit of time and is called the electrostatic unit), this current of strength c (in electrostatic measure) as the unit of current; it is then called the electromagnetic unit of current. Its use has an advantage in that
                                                                       Jl           Hr2 ,
Equation (54) assumes the simple form  H= r2 or J =  l       so that measurement of the strength of a current is reduced to that of two lengths and of a magnetic field. Most practical instruments for measuring currents depend on the deflection of magnets by currents, or the converse, and hence give the current strength in electro-magnetic measure.
To express this in terms of the electrostatic measure of current first introduced the constant c must be known; for this, however, only one measurement is necessary.
     Before we speak of the experimental determination of the quantity c, we shall get an insight into its nature by means of a simple dimen-sional consideration. According to (54) it is defined by c = J l .
                                                                                                                     Hr 2
Page 165

"But we know that the electric charge e and the magnetic strength of pole p have the same dimensions because Coulomb's law for electric and magnetic force is exactly the same. Hence..."
"...c has the dimensions of a velocity.
   The first exact measurement of c was carried out by Weber and Kohlrausch (1856). These experiments belong to the most memor-able achievements of precise physical measurement not only on account of their difficulty but also on account of the far-reaching consequences of the result. For the value obtained for c was 3 x 10 10  cm. / sec., which is exactly the velocity of light.
      This equality could not be accidental. Numerous thinkers, including Weber himself and many other mathematicians and phy-sicists, felt the close relationship that the number c = 3 x 10  10 cm./sec established between two great realms of science, and they sought to discover the bridge that ought to connect electromagnetism and optics. This was accomplished by Maxwell after Faraday's wonder-ful and ingenious method of experimenting had brought to light new facts and new views..."



This has arrived said Zed Aliz, its for inclusion afore even the even deadline.

Page 113

                           "...and since the velocity of light c is 300,000 km per sec.,..."                  
9^th line down of main text.
Writ the scribe, counting on it
 

Page 69

"Augean (aw je an ) [L. Augeas, Gr. Augeias], a.Pertaining to Augeas (mythic king of Elis, whose stable, containing 3000 oxen, had not been cleaned

Page 70  /  

out for thirty years, till Hercules, by turning the river Alpheus through it, did so in a day) ;..."
 
 
At this most critical moment in the now of our passing. The Zed AlizZed took time out to address yon companies goodly mix of striven souls. And in manner gentle, this incantation sold .Dearest of dear friends, all iz one and one iz all, the GOD of the THAT, iz the GOD of MIND, THAT MIND hath always sparkling point with thee.THAT mind of thine, and THAT sparkle point of the THAT, iz the number NINE,and its dynastic progeny. NINE iz the number of the THAT. Listen to the call of thy                                                                                    GOD      
  
                                                                   '3000 Oxen  x   thirty years'
                                                                                     90000
                                                                               ' thirty years'
                                                                                     30 x 360                                                                                                  10800
                                                                             Ra + the eight gods
 

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  

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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.  

/ Page 174  

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."



                                                                    6 The Electrical Displacement Current
"Suppose the poles of a galvanic cell to be connected with the plates of a condenser by means of two wires, one of them containing a switch (Fig. 93). If the switch is pressed down , a current flows..."
 
Fig. 93  When the condenser is charged by a convection current Jc, the electric field inside the condensers changes and gives rise to a displacement current of the same amount as Jc
 
Page 175  

"...which charges the two plates of the condenser; an electric field E is thereby introduced between them. Before Maxwell's time, this phenomenon was regarde as an "open circuit." Maxwell how-ever realized that during the growth of the field E a displacement current flows between the condenser plates, and thus the circuit becomes closed. As soon as the condenser plates are completely charged, both currents, the conduction and displacement current cease..."                                                                  



Fig 94  Both the convection current Jc and the displacement current Jd produce a surrounding magnetic field.



    "...Now the essential point is Maxwell's affirmation that the displace-ment current just like the conduction current, produces a magnetic field according to Biot and Savart's law. That this is actually so has not only been proved by the success of Maxwell's theory in predicting numerous phenomena but was also later confirmed directly by experiment
    The magnitude of the displacement current can easily be computed...."
     "... Therefore, following Maxwell, the whole current density is the sum j = jc + jd where jc is the current density of the free moveable charges and jd is the displacement current. Both kinds of current are surrounded by a magnetic field in the usual way (Fig.94)



Page 176

"After Oersted had discovered that a conduction current produces a magnetic field and Biot and Savart had formulated this fact as an action at a distance, Ampere discovered (1820) that two voltaic currents exert forces on each other, and he succeeded in expressing the law underlying this phenomenon again in terms of an action at a distance. This discovery had far- reaching consequences, for it made it possible to regard magnetism as an effect of moving elec-tricity. According to Ampere small closed currents are supposed to flow in the molecules of magnetized bodies. He showed that such currents behaved exactly like elementary magnets. This idea has stood the test of thorough examination; from his time on magnetic fluids became superfluous. Only electricity was left, which, when at rest, produced the electrostatic field, and when flowing, produced the magnetic field besides. Ampere's discovery may also be expressed in the following way: According to Oersted a wire in which the current J 1 is flowing produces a magnetic field in its neighborhood. A second wire in which the current
J 2 is flowing  is then pulled by forces due to this magnetic field. In other words, a field produced by one current  tends to deflect or accelerate flowing electricity.
     Hence the following question suggests itself: Can the magnetic field also set electricity that is at rest into motion? Can it produce or "induce" a current in the second wire which is initially without a current?
     Faraday found the answer to this question (1831)  He discovered that a static magnetic field is not able to produce an electric current  

/ Page 177  1 x 7 x 7 = 49   /

but that a field which varies in time is able to. For example, when he quickly brought a magnet close to a loop of wire made of conduct-ing material, a current flowed in the wire as long as the magnet moved. In particular, when he produced the magnetic field by means of a primary current, a short impulse of current occurred in the secondary wire whenever the first current was started or stopped.
     From this it is clear that the induced electric force depends on the velocity of alteration of the magnetic field in time. Faraday succeeded in formulating the quantitive law of this phenomenon with the help of his concept of lines of force. Using Maxwell's ideas we shall give it such a form that its analogy with Biot and Savert's law comes out clearly


    Fig. 95 A changing magnetic field which represents                     Fig. 96 Direction of the electric field E induced by a
   a magnetic cur-rent 1 is surrounded by an electric field.                          magnetic current 1 (compare with Fig. 84).


We imagine a bundle of parallel lines of magnetic force that con-stitute a magnetic field H. We suppose a circular conducting wire placed around this sheath (Fig 95). If the intensity of field H changes in the small interval of time..." "...by the amount H we call..."  "...its velocity of change or the change in the number of lines of force. If in analogy to the electrical displacement we represent the lines of force as chains of magnetic dipoles ( which, however, according to Amphere  

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then with the change of H a displacement of the magnetic quantities will occur in every ether molecule, or a magnetic displacement current" will flow whose current strength per unit of area or current density is given by I =..."
If the field H is not in the ether but ii a substance of permeability..." "...the density of the magnetic displacement current is
i =..." "...Thus the magnetic displacement current is I =..." Thus the magnetic displacement current is I =..." Thus the magnetic current I = fi = f ..." "...passes through the cross section f, that is, through the surface of the circle formed by the conducting wire.
        Now according to Faraday, this magnetic current produces all round it an electric field E, which encircles the magnetic current exactly as the magnetic field H encircles the electric current in Oersted's experiment but in the reverse
direction. It is this electric field E that drives the induced current around in the conducting wire; it is also present even if there is no conducting wire in which the current can form.
     We see that the magnetic induction of Faraday is a perfect parallel to the electromagnetic discovery of Oersted. The quantitative law too, is the same. According to Biot and Savert, the magnetic field H produced by a current element of length l and of strength j (compare fig. 84) in the middle plane perpendicular to the connecting line r and to the current direction, and has the value H = J1 (formula (54)).
                                   Cr2
Exactly the same holds when electric and magnetic quantities are exchanged and when the sense of rotation is reversed (Fig.96). The induced electric intensity of field in the central plane is given by
       E = I l .
       Cr2
       In it the same constant c, the ratio of the electromagnetic to the electrostatic unit of current, occurs which was found by Weber and Kohlrausch to be equal to the velocity of light. It can easily be seen from considerations about the energy involved that this must be so.
     A great number of the physical and technical applications of electricity and magnetism depend on the law of induction. The transformer, the induction coil, the dynamo and innumerable other  

/ Page 179  1 x 7 x 9 = 63  6 +3 = 9  /

apparatus and machines are appliances for inducing electric currents by means of changing magnetic fields. But however interesting these things may be, they do not lie on the road of our investigation, the final goal of which is to examine the relationship of the ether with the space problem. Hence we turn our attention at once to the theory of Maxwell, whose object was to combine all known magnetic phenomena into one uniform theory of contiguous action.