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The 1855 Weber-Kohlrausch Experiment

(The Speed of Light)

Frederick David Tombe,

Northern Ireland, United Kingdom,

sirius184@hotmail.com

14th April 2019

Abstract. In the year 1855, German physicists Wilhelm Weber and Rudolf Kohlrausch

performed an experiment involving the discharge of a Leyden jar, from which they

established the ratio between electrostatic and electrodynamic units of charge. This

ratio became known as Weber’s constant and it is numerically equal to c√2, where c is

very close to the speed of light. In 1857, another German physicist, Gustav Kirchhoff,

used Weber’s constant to conclude that electric signals travel along a wire at the speed

of light. A few years later in 1861, Scottish physicist James Clerk Maxwell was working

on the physical medium responsible for magnetic lines of force and he established a

linkage between its transverse elasticity and Weber’s constant. On converting

electrodynamic units to electromagnetic units, Maxwell exposed the speed of light

directly and he connected it to the transverse elasticity of the luminiferous medium.

This paper sets out to establish the fundamental origins of the speed of light.

Electric Permittivity

I. Electric permittivity, ε, is a constant that is associated with dielectrics through

James Clerk Maxwell’s electric elasticity equation, D = −εE, where D is the

electric displacement vector, and E is an externally applied electric force. A

form of this equation first appeared in the preamble to Part III of Maxwell’s

1861 paper, “On Physical Lines of Force”, [1], in connection with the concept

of displacement current. Electric permittivity can be measured experimentally

by discharging a capacitor. The ensuing electric current is measured, and the

electric permittivity is established through the standard electromagnetic

relationships. For details, see the appendix after the reference section at the end.

Electric permittivity is related to the speed of light through the equation,

µε = 1/c² (1)

Unlike electric permittivity, however, magnetic permeability, µ, has always

been a defined quantity. Even though Maxwell attributed the physical

significance of µ to the density of the sea of molecular vortices which he

believed constituted the luminiferous medium, he had no way of knowing its

absolute value. This however didn’t matter for his purpose since he was only

working with ratios, and in electrodynamic and electromagnetic units, µ is

unity.

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The origins of equation (1) can be traced back to the year 1855 to an

experiment carried out by Wilhelm Eduard Weber and Rudolf Hermann Arndt

Kohlrausch, [2]. The experiment involved transferring a quantity of electricity

from a charged Leyden jar to a 13-inch ball that was coated with tin foil, and

then discharging the remainder through a conducting channel. The electrostatic

force generated by the charged ball was measured using a torsion balance, while

the magnetic force induced by the current due to the discharge of the Leyden

jar, was measured by the deflection of a compass needle in a galvanometer. The

purpose of the experiment was to determine the numerical value of the constant,

Cw, in Weber’s 1846 force law,

F = kq1q2/r2[1 − ṙ2/Cw2 + 2rr/Cw2] (2)

The idea was, that since the electrostatic force was measured using

electrostatic units of charge, while the magnetic force was measured using

electrodynamic units of charge, then the numerical ratio between the two forces

would yield the value of Cw, which was known as Weber’s constant.

The only term of major interest in equation (2) is the middle term on the

right-hand-side. This term, ṙ2/Cw2, is the convective term, where ṙ = Vw. It’s a

magnetic force which is a kind of centrifugal force, [3], because it opposes an

electrostatic force of attraction. Weber considered Vw to be the mutual speed

between two charged particles, q1, and q2, distance r apart, and he saw Cw as a

reducing speed such that when Vw = Cw, then the electrostatic force would be

completely cancelled.

Because the experiment begins with two unknowns, Vw, and Cw, it follows

therefore that there will be a corollary to the discovery of the numerical value of

Cw. This corollary was never noticed though, perhaps due to the conviction that

electric current consisted in the equal and opposite flow of charged particles.

But while that may well be the case, especially when a current is flowing

through an electrolyte, equation (2) above tells us that when the electrostatic

and magnetic forces are equal, then Vw must be equal to Cw, and so something

must be travelling in the discharge wire at speed Cw. Had Weber and

Kohlrausch used electromagnetic units of charge for the magnetic force, instead

of electrodynamics units, they would have concluded that the reducing speed,

Cw, was in fact very close to the speed of light. Instead, they thought that the

reducing speed was significantly greater than the speed of light.

In 1857, Gustav Robert Kirchhoff, while studying the motion of electricity

in conducting wires, [4], identified, in German miles, what appeared to be the

speed of light, c, in the relationship Cw = c√2, and he linked this to the speed of

electric signals in the wire, although he did not suggest that this speed

represented the actual flow speed of electric current, but only that it represented

the propagation speed of any changes in the electric current. Kirchhoff was

attempting to link the signal speed to wave theory.

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While we all know that the electric particles that are involved in an electric

current travel at nowhere remotely near to the speed of light, the implication of

the Weber-Kohlrausch experiment is nevertheless that something much more

subtle must be the fundamental basis of electric current, and that even if

changes in electric current propagate in a wave-like form along a conducting

wire at a speed close to the speed of light, that this is only because they are

carried by the movement of a fluid which is itself flowing at that same speed.

As to what exactly this fluid is, we should look to the electrostatic field that

surrounds charged particles and consider that the inflowing or outflowing

aethereal electric fluid, which is the basis of this field, is the prime candidate.

A few years later, in 1861, in the paper already mentioned, [1], Maxwell

developed a model for the luminiferous medium based on the idea that space is

filled with tiny aethereal vortices that press against each other with centrifugal

force while striving to dilate, [5], [6]. Equation (77) in Part II is an electromotive

force equation containing a convective term, µv×H, which is nowadays unduly

credited to Lorentz. Then in Part III in a section on elasticity and electrostatics,

Maxwell set out to link the Weber-Kohlrausch ratio, Cw, to the transverse

elasticity of his sea of tiny vortices. When he converted this ratio from

electrodynamic units to electromagnetic units in order to get it into a workable

form, he explicitly isolated c, and like Kirchhoff before him, he noticed that c

was very close to the measured speed of light. But rather than linking this speed

to the circumferential speed of his vortices, Maxwell was focused on elasticity

and displacement, and he applied c to Newton’s equation for the speed of a

wave in an elastic solid. The full derivation is found in Part III, where he begins

by demonstrating the linkage between the dielectric constant and the transverse

elasticity. Equations (132) to (135) in this paper should leave nobody in any

doubt that Newton’s equation is the equivalent of both E = mc² and c² = 1/µε,

which are in effect one and the same equation.

In Part III, Maxwell does not resort to the specifics of the sea of molecular

vortices that he postulated in Part I of the same paper. Had he done so; he could

have linked c directly to the circumferential speed in his vortices. See

“Radiation Pressure and E = mc2”, [7]. Nevertheless, Maxwell still established

that light is a transverse wave in the same medium that is the cause of electric

and magnetic phenomena.

Electric Current

II. Maxwell and Kirchhoff both used broadly the same equations of

electromagnetism in connection with the Weber-Kohlrausch numerical ratio,

but they came to different conclusions. In 1857, Kirchhoff concluded that an

electric signal travels along a conducting wire at the speed of light, whereas in

1861, Maxwell concluded that this speed is the speed of a wireless

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electromagnetic wave through space, and he believed space to be densely

packed with tiny aethereal vortices. The only way that these two seemingly

contradictory positions could be reconciled is if Maxwell’s aethereal vortices

constitute tiny electric circulations in which the circumferential speed is the

speed of light. See the paragraph below equation (5) in the next section. The

drift velocities of charged particles in an electric current are nowhere near the

speed of light, but the electric force field that drives them will have an

associated aethereal momentum field which will be. This will be the magnetic

vector potential A known to Maxwell as the electromagnetic momentum.

Maxwell identified A with Faraday’s electrotonic state. See “An Interpretation

of Faraday’s Lines of Force”, [8].

Centrifugal Force

III. Maxwell’s convective electromotive force is a centrifugal force of the form,

E = µv×H = F/q (3)

See equations (5) and (77) in his 1861 paper, [4]. It is a centrifugal force by

virtue of its origins in a sea of tiny aethereal vortices which are pressing against

each other while striving to dilate, as like the water presses on the walls of

Newton’s rotating bucket. The magnetic intensity H is a measure of the

vorticity or the angular momentum of the vortices. Electric particles at the edge

of the vortices have an angular momentum H = D×v where D is the

displacement of these particles from the polar origin in the centre, and where v

is their circumferential velocity. Substituting Maxwell’s electric elasticity

equation, D = −εE, into H = D×v, leads to,

H = εv×E (4)

If we then substitute (3) into (4) we obtain,

E = εµv×(v×E) (5)

Since εµ is equal to 1/c2 and since H, v, and E, are mutually perpendicular,

then it follows that the circumferential speed of Maxwell’s tiny vortices is what

determines the speed of light.

If we now consider H in equation (3) to be a vector field in the vicinity of

an electromagnet, we can substitute a form of the Biot-Savart law such that v

becomes the mutual velocity as between an element of electric current in the

wire, to which will be ascribed a charge q1, and a charged particle with charge

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q2 that is moving in the magnetic field. If, based on the Biot-Savart Law, we

take H to be,

H = q1v×r

/4πr2 (6)

then in the special case where v is perpendicular to r

, and multiplying top

and bottom by ε, equation (3) becomes,

F = q1q2εµv2r

/4πεr2 (7)

Substituting εµ = 1/c2 leads to,

F = v2/c2(q1q2/4πεr2)r

(8)

so, when v = c, the magnetic force will be equal to the electrostatic force.

This confirms that Weber and Kohlrausch should have used electromagnetic

units for the magnetic force in their experiment, so that Cw wouldn’t have been

clouded by the √2 factor, and hence Vw in Weber’s force law would indeed

represent a reducing speed.

Equation (8) also identifies the physical context in which the middle term

on the right-hand-side of Weber’s force law, at equation (2), begins to take on a

higher degree of accuracy, providing that the mutual speed v is transverse, and

not radial as is implied by this law. As regards an important example of where

this magnetic force simultaneously equates with the electrostatic force, we will

take a closer look at the stability mechanism within the rotating electron-

positron dipoles that fill all of space and form magnetic lines of force.

Magnetic Force

IV. In the 2006 article entitled “The Double Helix Theory of the Magnetic

Field”, [9], it was argued that the electric particles that surround Maxwell’s tiny

vortices are in fact just a single positron and a single electron. In the equatorial

plane, the escape velocity relative to the electrostatic force has been exceeded

and they are hemmed into their circular orbits by centrifugal force pressing

inwards from the surrounding vortices. This centrifugal pressure must be

counterbalanced by electrostatic tension in the axial direction channelled along

the double helix. If electrons and positrons are sources and sinks in a primary

aethereal fluid, it is proposed that the rate of inflow and outflow will be

proportional to the vorticity. The magnetic intensity H (angular momentum)

will therefore determine the electrostatic charge in the axial direction. As such,

we cannot simply use Coulomb’s Law to calculate the spacing between the

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individual vortices, because Coulomb’s Law assumes that electrons and

positrons have a fixed charge. In the bound state within the double helix

alignment, their electric charge, which determines their magnetic charge, will

not however be fixed. It will be determined by their vorticity and hence by the

magnitude of the electric current that causes the magnetic field.

Figure 1. A close-up view of a single magnetic tube of force. Attraction along the tube is

caused by electrostatic attraction between the electrons and positrons. Repulsion laterally

between adjacent magnetic tubes of force is caused by centrifugal force. Within each rotating

electron-positron pair, the orbital speed is what determines the speed of light.

Maxwell never knew the size of his molecular vortices, but it would be

reasonable to assume that they are small enough to flow through the interstitial

spaces between the atoms and molecules of ponderable matter, as like water

flows through a basket. We could assume that the circumference of these

dipolar vortices is equal to half of the Compton wavelength for an electron,

since gamma radiation of this wavelength, or lower, can resonate with the

dipoles and split them apart, as has just been explained above. This would make

their diameter 0.3863 picometres, hence setting them at about one thousandth

the size of the average atom. The density of the vortex sea will however be

difficult to calculate because the balance between the electrostatic force in the

axial direction and the centrifugal force in the equatorial plane would point to

inter-particle spacings between neighbouring vortices on the femtometre scale.

Since this is very much less than their actual diameters, the magnetic lines of

force will in effect become tubes of force. Then on the issue of the density, as an

absolute minimum, if we were to simply consider only the diameter of the

vortices, the density of the vortex sea will already be into the region of fourteen

hundred times denser than lead, but it will surely be many orders of magnitude

yet higher than that still.

The presence of this dense sea of electron-positron dipoles throughout all of

space, not only acts as the medium for the propagation of light, but it also

causes a compound centrifugal force to act upon all bodies in motion, [10], [11],

and this is what gives rise to Newton’s first law of motion and the inertial path.

The inertial forces on the large scale are a product of the inertial path and not, as

is wrongly taught in the modern literature, a product of making observations

from a rotating frame of reference. The electron-positron sea causes the inertial

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forces, and hence contributes to the shape of the planetary orbital paths, as

opposed to causing dissipative friction.

It’s only within the context of this dense sea of rotating electron-positron

dipoles that Maxwell and Kirchhoff can be reconciled, and Maxwell and Weber

partially reconciled. More specifically, it’s probably only on the scale of an

individual rotating electron-positron dipole that we can use an inverse square

law of distance in the Biot-Savart law, because it’s only on this scale where the

centrifugal force arises as a transverse interaction between two electric

monopoles. On the large scale, inertial centrifugal force obeys an inverse cube

law in distance, which is characteristic of a dipole field.

The speed of electric current should not be confused with the drift velocity

of the charged particles in a conducting wire, which is many orders of

magnitude less. Electric current is fundamentally a flow of the primary aethereal

electric fluid from which everything is made, while the speed of light is tied up

with the circumferential speed of the rotating electron-positron dipoles, [7]. In

order to connect it all together, the general position is that the speed of electric

current is the average speed that the electric fluid flows between a source and a

sink, whether in the case of the electric current flowing between the two

terminals in a conducting circuit or between a positron and a neighbouring

electron in the all-pervading electron-positron sea, [12].

Conclusion

V. The speed of light, which arises in connection with both electromagnetic

radiation and electric current, is a product of the velocity field of the electric

field, [13], [14]. It is the average speed with which the ancient electric fluid flows

from positive source particles towards negative sink particles. This is so in the

case of the electric fluid emerging from one terminal of a battery and flowing

back into the other terminal, and it is also the case with electromagnetic

radiation in space where the electric fluid flows between neighbouring electrons

and positrons. Space is densely packed with tiny dipole pairs like two-pin power

points, each pair consisting of an electron in mutual orbit with a positron,

circulating at the speed of light.

The velocity field is more correctly the momentum field A known as the

magnetic vector potential, [8]. It is Maxwell’s displacement current. It exists

everywhere in space. In the steady state it is undergoing fine-grained circulation

such that ∇×A = B, where B is the local magnetic flux density. In the dynamic

state, angular acceleration of an electron-positron dipole leads to an overflow of

electric fluid into the neighbouring dipole at that same average speed, [12]. This

is the principle behind transverse electromagnetic waves.

In a conducting wire, where we normally denote A by the symbol J, the

electric fluid imparts its acceleration to charged particles, but not its velocity.

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When accelerating it would push positive particles along with it, while negative

particles would eat their way towards the source. The motion of charged

particles in an electric current is merely secondary to a more fundamental flow

of electric fluid at average speeds in the order of the speed of light. The idea of

the existence of such an electric fluid is not new, but it was abandoned in favour

of the belief that electric current is in fact a flow of charged particles. The two

ideas are not however mutually exclusive, but the absence of the electric fluid in

modern physics is a major omission.

References

[1] Clerk-Maxwell, J., “On Physical Lines of Force”, Philosophical Magazine, vol. XXI,

Fourth Series, London, (1861)

http://vacuum-physics.com/Maxwell/maxwell_oplf.pdf

[2] Weber, W., and Kohlrausch, R., “Elektrodynamische Maassbestimmungen insbesondere

Zurueckfuehrung der Stroemintensitaetsmessungen auf mechanisches Maass”, Treatises

of the Royal Saxon Scientific Society, Volume 5, Leipzig, S. Hirzel, (1856)

See chapters 5, 6, and 7 in this link,

https://www.ifi.unicamp.br/~assis/Weber-in-English-Vol-3.pdf

Prof. A.K.T Assis has written an excellent summary of this work in an article entitled “On

the First Electromagnetic Measurement of the Velocity of Light by Wilhelm Weber and

Rudolf Kohlrausch”.

https://www.ifi.unicamp.br/~assis/Weber-Kohlrausch(2003).pdf

Weber and Kohlrausch wrote a short precis of their paper, and this can be found in

Poggendorf’s Annalen, vol. XCIX, pp. 10-25. An English translation of this precis is

presented in the appendix at the end of Prof. Assis’s paper.

[3] Assis, A.K.T., “Centrifugal Electrical Force”, Communications in Theoretical Physics,

18, pp. 475-478 (1992)

http://www.ifi.unicamp.br/~assis/Commun-Theor-Phys-V18-p475-478(1992).pdf

[4] Kirchhoff, G.R., “On the Motion of Electricity in Wires”, Philosophical

Magazine, Volume XIII, Fourth Series, pp. 393-412 (1857)

https://www.ifi.unicamp.br/~assis/Weber-Kohlrausch(2003).pdf pages 280-282

[5] Whittaker, E.T., “A History of the Theories of Aether and Electricity”, Chapter 4, pages

100-102, (1910)

“All space, according to the younger Bernoulli, is permeated by a fluid aether, containing an

immense number of excessively small whirlpools. The elasticity which the aether appears to

possess, and in virtue of which it is able to transmit vibrations, is really due to the presence

of these whirlpools; for, owing to centrifugal force, each whirlpool is continually striving to

dilate, and so presses against the neighbouring whirlpools.”

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[6] O’Neill, John J., “PRODIGAL GENIUS, Biography of Nikola Tesla”, Long Island, New

York, 15th July 1944, Fourth Part, paragraph 23, quoting Tesla from his 1907 paper “Man’s

Greatest Achievement” which was published in 1930 in the Milwaukee Sentinel,

“Long ago he (mankind) recognized that all perceptible matter comes from a primary

substance, of a tenuity beyond conception and filling all space - the Akasha or luminiferous

ether - which is acted upon by the life-giving Prana or creative force, calling into existence,

in never ending cycles, all things and phenomena. The primary substance, thrown into

infinitesimal whirls of prodigious velocity, becomes gross matter; the force subsiding, the

motion ceases and matter disappears, reverting to the primary substance”.

http://www.rastko.rs/istorija/tesla/oniell-tesla.html

http://www.ascension-research.org/tesla.html

[7] Tombe, F.D., “Radiation Pressure and E = mc2” (2018)

http://www.gsjournal.net/Science-Journals/Research%20Papers-

Mathematical%20Physics/Download/7324

[8] Tombe, F.D., “An Interpretation of Faraday’s Lines of Force” (2019)

https://www.researchgate.net/publication/332249473_An_Interpretation_of_Faraday's_Lines

_of_Force

[9] Tombe, F.D., “The Double Helix Theory of the Magnetic Field” (2006)

Galilean Electrodynamics, vol. 24, Number 2, p.34 (March/April 2013)

http://gsjournal.net/Science-Journals/Research%20Papers-

Mathematical%20Physics/Download/6371

[10] Tombe, F.D., “The Coriolis Force in Maxwell’s Equations” (2010)

Galilean Electrodynamics, vol. 25, Number 2, p.22 (March/April 2014)

http://gsjournal.net/Science-Journals/Research%20Papers-Astrophysics/Download/3161

[11] Tombe, F.D., “Magnetic Repulsion and the Gyroscopic Force” (2015)

http://gsjournal.net/Science-Journals/Essays-

Mechanics%20/%20Electrodynamics/Download/5887

[12] Lodge, Sir Oliver, “Ether (in physics)”, Encyclopaedia Britannica,

Fourteenth Edition, vol. 8, pp. 751-755 (1937)

http://gsjournal.net/Science-

Journals/Historical%20PapersMechanics%20/%20Electrodynamics/Download/4105

In relation to the speed of light, “The most probable surmise or guess at present is that the

ether is a perfectly incompressible continuous fluid, in a state of fine-grained vortex

motion, circulating with that same enormous speed. For it has been partly, though as yet

incompletely, shown that such a vortex fluid would transmit waves of the same general nature

as light waves— i.e., periodic disturbances across the line of propagation—and would

transmit them at a rate of the same order of magnitude as the vortex or circulation speed”

[13] Tombe, F.D., “The Deeper Physical Nature of Electric Current” (2022)

https://www.researchgate.net/publication/363887411_The_Deeper_Physical_Nature_of_Elec

tric_Current

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[14] Tombe, F.D., “The Commonality between Light and Electric Current” (2022)

https://www.researchgate.net/publication/364337354_The_Commonality_between_Light_an

d_Electric_Current

Appendix

The Experimental Determination of Electric Permittivity

A capacitor is discharged using a vibrating switch unit at a frequency f. The discharge current

I is measured using a sensitive galvanometer. The capacitance equations are C = εA/d and Q

= CV, where ε is electric permittivity, C is capacitance, A is the area of the capacitor plates, d

is the separation distance between the plates, Q is charge, and V is the applied voltage. Since

Q = I/f, we can combine these equations into ε = Id/fVA, and since V is known, we can

numerically evaluate ε, which in SI units comes out to be 8.85 × 10−12 farad metre−1.

There has been a tendency since 1983 for the textbooks to avoid treating the

experimental determination of electric permittivity ε. In that year, the International Bureau of

Weights and Measures, BIPM, decided to define the metre in terms of the speed of light,

resulting in the fact that the speed of light itself has now become a defined quantity. This

tautology has resulted in the absurd situation whereby equation (1) in section I above

becomes an equation linking three defined quantities and hence loses all its physical

significance. It is not widely known that the speed of light only enters Maxwell’s equations

through the 1855 Weber-Kohlrausch experiment. In fact, it is a common error to believe the

complete opposite, which is that equation (1) is a consequence of Maxwell’s equations. In

modern textbooks, the significance of the speed of light has been shifted away from the

Weber-Kohlrausch experiment and placed within the realm of Einstein’s theories of relativity

instead. The decision on the part of BIPM to make the speed of light a defined quantity might

possibly be interpreted as a decision to consolidate Einstein’s theories of relativity within the

established system of units and to divert attention away from the involvement of a physical

medium in the propagation of light waves.

5th October 2022 amendment