Einstein's
Theory Of
Relativity
Max
Born
Chapter
V
THE FUNDAMENTAL LAWS OF ELECTRODYNAMICS
Page
146
1.Electroand
Magnetostatics
"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
reaffirmed 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 everywhere 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
independently 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 onefluid 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 electrical 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
preNewtonian 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 distance, 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 influences
charges
Fig. 79
Derivation of Coulomb'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 development 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 lozengeshaped 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 bringing 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 socalled 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 onefluid or the
twofluid 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 continually 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 farreaching consequences 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
completed.
/
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 apparatus for storing
electricity, socalled 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 dissociation,
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 crosssection 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
crosssection of the conductor per unit time.
Page 160 1 + 6 = 7
3.
Resistance and Heat of Current
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 gravitation 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 crosssection 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 complete
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 (contrary 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 midpoint 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 perpendicular 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 completely 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 crosssection 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 electromagnetic 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 dimensional
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 memorable achievements of
precise physical measurement not only on account of their
difficulty but also on account of the farreaching
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 physicists, 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 wonderful 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.
The
Expanding Universe
Sir Arthur Eddington 1932
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
Cassell's
English Dictionary 1974
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
The
True And Invisible Rosicrucian
Order
Paul Foster Case 1884  1954.
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
Stephen
Hawking
Quest For A Theory Of Everything
Kitty Ferguson
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
Holy
Bible
Scofield References
Jeremiah B.C. 590
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 knowest not."
Einstein's
Theory Of Relativity
Max Born
5.
Faraday's Lines of Force
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 electrolytic 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
nonconducting substance thus influences the power of taking
up electricity 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 nonconductors 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
/
Page 167 /
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 conductors 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
dielectric 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 socalled
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 penetrability
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
resistances. 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
dipoles
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
/
Page 171 /
dielectrics.
For the ether the dielectric constant..." "...=1, for other
insulators..." "..differs from 1.
If the graphical picture of electric displacement 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.
b The displacement of the two opposite charge
distributions through a small distance a produces
two thin
opposite
layers of charge on corresponding surfaces f of the
cube.
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. Imagine a rectangular
block of space filled with a continuous positive charge
density, p
and then the same part of space filled with a negative
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
corresponding 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 produces 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 concept 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 pseudocontiguous 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 propagation. 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 however 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 displacement 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
7
Magnetic Induction
"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 electricity.
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 conducting 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 current 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
constitute 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
/
Page 178 /
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.
