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Maxwell's Original Equations
Posted on Saturday, February 04, 2012 @ 18:05:44 EST by vlad

Science FDT writes: The four equations that are presented in modern textbooks under the title of 'Maxwell's Equations' did indeed appear throughout Maxwell's 1861 paper "On Physical Lines of Force". They did not however appear as a distinct grouping. A distinct grouping of eight equations did however appear in Maxwell's 1865 paper "A Dynamical theory of the Electromagnetic Field" and this group contained more information about electromagnetism than the group of four that appears in modern textbooks. One of these eight equations ironically appears today in modern textbooks as a supplement to Maxwell's equations, as if it had never been one of Maxwell's equations in the first place. This original Maxwell equation appeared as equation (77) in his 1861 paper, and as equation (D) in the original list of eight equations in the 1865 paper, but it is nowadays introduced in modern textbooks under the misnomer of 'The Lorentz Force'. 

See "Maxwell's Original equations" at http://www.wbabin.net/Science-Journals/Essays-Mechanics%20/%20Electrodynamics/Download/3889

Another important feature of the original list of eight Maxwell's equations is that it includes the equation curl A = B, whereas the modern list uses the lesser informative divergence of this equation, div B = 0, hence missing out on the full physical significance of the electromagnetic momentum vector A which corresponds to Faraday's electrotonic state. The equation curl A = B when understood in the context within which it was derived by Maxwell, reveals the underlying fine-grained fly-wheel nature of the medium for the propagation of light.

David Tombe



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"Maxwell's Original Equations" | Login/Create an Account | 14 comments | Search Discussion
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Re: Maxwell's Original Equations (Score: 1)
by RBM on Sunday, February 05, 2012 @ 16:46:00 EST
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First let me say thanks for bringing this up. I'll be looking diligently at the links provided to see if they are of bookmark quality.

I first learned of the 4 versus 4 formulations through Tom Bearden's work several years ago.

Is there a particular reason you felt posting it was worthwhile ? Was it new information to you ?

Re: Maxwell's Original Equations (Score: 1)
by RBM on Sunday, February 05, 2012 @ 16:50:57 EST
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typo correction - '4 versus 8'


Re: Maxwell's Original Equations (Score: 1)
by FDT on Monday, February 06, 2012 @ 01:58:46 EST
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RBM, There were a number of reasons for bringing this matter up. One of these reasons was to try and highlight the fact that the so-called "Lorentz Force" was actually one of Maxwell's original equations. There are alot of people out there trying to rationalize that the Lorentz force should be one of Maxwell's equations, without realizing that it actually was one of Maxwell's equations. Another reason for bringing this issue up was to remind readers that the speed of light entered Maxwell's original works through the 1856 Weber/Kohlrausch experiment and not through Maxwell's mathematical manipulations. There are alot of people out there who do not realize these important facts.

David Tombe


Re: Maxwell's Original Equations (Score: 1)
by RBM on Monday, February 06, 2012 @ 14:46:33 EST
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Good points, and no argument from me.


Re: Maxwell's Original Equations (Score: 1)
by Koen on Monday, February 06, 2012 @ 12:05:08 EST
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FD, excellent article, I like it.  I agree  Maxwell's displacement current is in fact an aether current.  Equation C  should state   curl H = J,total   (not just 'J').

Modern textbooks don't mention equation D at all,  however, equation D is not the Lorentz force law.  Equation D  is a riddle:  what is it that has speed v (either relative speed to a motionless lab-observer frame, or relative speed between two objects) ?
I don't know how to understand this equation at all.

Another riddle:  the Lorentz force, and its less general derivative, the Grassmann force law,  does NOT satisfy Newton's third principle of colinear action-reaction forces, in general.
The older Weber force law (and the less general Ampere force law)  DOES satisfy Newton's third principle in general.
For this reason Maxwell's theory is not complete, because a 'longitudinal Ampere force is missing, in case of static currents'.   And according to Weber's law there can be a form of electric field induction that does not involve the time differential of the magnetic field (Faraday's law).

However, the beauty of Maxwell's theory (to me) is the aether as expressed by the 'displacement current'  which allows for a an "electrodynamical force wave" with a phase velocity c  that can propagate through the aether, and that has not been described before by for instance Weber & Gauss & Ampere.  For many years the German physicsts thought of Maxwell's aether wave as pure science fiction. Then Hertz proved Maxwell right, and this was a big shock to many.

Both theories (the Maxwell theory and the Weber theory) are essentially incomplete, therefore classical electrodynamics theory is still unfinished business, despite of all the "relativity" mambo jumbo. Official relativity theory is a travesty and wrong for many reasons,  Einstein played little or no part in this history, despite of the worship of saint Einstein by his kosher family.

Re: Maxwell's Original Equations (Score: 1)
by FDT on Monday, February 06, 2012 @ 17:07:44 EST
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Koen, The Lorentz force often appears in modern textbooks in the form F = q[E + vxB]. We know that the full expression for E is the sum of the electrostatic term and the time varying term that arises in electromagnetic induction and which is expressed as the partial time derivative of the magnetic vector potential A. Hence if we expand the Lorentz force by opening up the contents within the E term, then we will have an equation which is identical to equation (D) in Maxwell's original eight equations. From the original Maxwell text, as appears in the immediate vicinity of equation (D), one should be left in no doubt that the velocity term v refers to an electric current relative to the luminiferous medium. In fact Maxwell actually drops this convective vxB term when he derives the electromagnetic wave equation, because he is considering the electromagnetic wave equation from the perspective of a point that is stationary relative to the luminiferous medium.

In Weber's force law, two of the terms clearly correspond to the electrostatic term and the convective vxB term in Maxwell's equation (D). But as you correctly point out, there is a third term in Weber's force law that does not correspond to the time varying electromagnetic induction term in the equivalent Maxwell equation (D). The Maxwell term is perfectly compatible with Faraday's law whereas the Weber term is not, and so the only conclusion that I can draw from this is that Maxwell got it right where Weber got it wrong.

On Newton's third law, we would need to see the entire context in which Maxwell's equation (D) was being applied before we would conclude that Newton's third law was breaking down. You will almost certainly find that all the forces come in pairs.

On displacement current, although Maxwell got us looking in the right place, he wavered between the displacement mechanism being a rotatory phenomenon and it being a linear phenomenon, and in the end it seems that he settled for linear. I believe that this was a big mistake on Maxwell's part. I believe that the displacement current has to be a transverse effect with zero divergence, and hence it has to be an angular displacement in his tiny molecular vortices. Maxwell's focus on linear polarization and hence the subsequent focus on events in the space between the plates of a capacitor led us all in the wrong direction. Displacement current, as is used in the derivation of the electromagnetic wave equation needs to be something that is not confined to the space between the plates of a capacitor.

And that's why I don't like Maxwell's first equation (A) for total currents. It's the only one that I don't like. And that's why I was silent on the issue of 'totality' in equation (C). As far as I am concerned, current is current. It's merely a question of the context. And for electromagnetic radiation, the context is a fine-grained transverse current in a tiny molecular vortex.

David Tombe


Re: Maxwell's Original Equations (Score: 1)
by eye on Wednesday, February 08, 2012 @ 08:49:53 EST
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just out of interest on this subject, I came upon a little paper on the Weber Force in which it is shown how the Weber Force is  actually subsumed within the Maxwell Theory.  The author shows  how the Weber force emerges as an averaged effect under certain conditions of charge neutrality and closed current loops.  So I took this to mean that in conclusion the more general theory can be credited to Maxwell with both theories being identical only under certain conditions.


Re: Maxwell's Original Equations (Score: 1)
by eye on Wednesday, February 08, 2012 @ 08:51:28 EST
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Sorry, forgot to include the link. Here it is:



Re: Maxwell's Original Equations (Score: 1)
by FDT on Wednesday, February 08, 2012 @ 16:01:18 EST
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You can see Weber's force law at equation (1) in this paper here by Professor A.K.T. assis http://www.ifi.unicamp.br/~assis/Commun-Theor-Phys-V18-p475-478(1992).pdf [www.ifi.unicamp.br]

The problem with it is that we can't pin any of the terms down to specific electromagnetic effects, the way we can with Maxwell's equation (D). For example, what electromagnetic effect is being described by the third term on the right hand side of Weber's force law equation? If we can't answer that question, then we need to ask ourselves whether or not Weber's force law is accurately describing electromagnetic forces.

David Tombe


Re: Maxwell's Original Equations (Score: 1)
by eye on Wednesday, February 08, 2012 @ 23:51:33 EST
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I get the feeling that Weber's force does not describe the 'actual' force acting between current  elements but only an averaged force empirically obtained from the measurements of the total force between CLOSED current loops, as was originally performed by Ampere. On the other hand I think the Lorentz force provides the 'actual' force acting between current elements. In other words if you average the Lorentz force between closed current loops the result will be in agreement with the Weber force. In light of this I would be lead to infer that the Weber force should break down when applied to a force description between elements in an open circuit, which can only be described by the Lorentz and Maxwell equations 


Re: Maxwell's Original Equations (Score: 1)
by FDT on Thursday, February 09, 2012 @ 11:11:04 EST
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I would take the attitude that Weber's force law is either correct or it's not correct, and I'm inclined to believe that the latter is the case. As regards the second term on the right hand side of Weber's force equation, it is certainly very similar to the vxB term in Maxwell's equation (D). It is undoubtedly centrifugal force, but in the Weber force there is a factor of 1/2 which I can't account for in the circumstances. [Interestingly, JJ Thomson seems to have made that same error with the factor of 1/2. It might be something to do with not having appreciated the subtle difference between a simple centrifugal force on the one hand and a compound centrifugal force on the other hand.] As regards the third term on the right hand side of Weber's equation, I can't relate it to any electromagnetic effect. I think it is a faulty version of the -(partial)dA/dt term that appears in Maxwell's equation (D), and that Weber's version is faulty by virtue of the fact that the second time derivative term is a radial effect rather than an angular effect.

As regards the Lorentz force, it is pretty well the same thing as Maxwell's equation (D), and that fact was one of the main purposes of this news item in the first place.

I think we just have to accept that Weber got it wrong, whereas Maxwell got it right, and that Lorentz was only repeating what Maxwell had already derived.

David Tombe


by nanotech on Saturday, February 11, 2012 @ 06:37:58 EST
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Read this paper on Scribd, everyone:


by FDT on Wednesday, February 15, 2012 @ 12:19:27 EST
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              It strikes me that Tesla was focusing on the electromagnetic wave propagation mechanism itself, which involves a coherent flow of energy, whereas Hertz was focusing on the large scale wavelengths associated with the emission mechanism.

             For example, a radio wave has a very long wavelength. That wavelength has no bearing however on the wavelength involved in the tiny vortices that comprise the electromagnetic wave carrying medium. Maxwell and Tesla both believed that space is densely packed with such tiny vortices. Maxwell's equations are all about those tiny vortices. The coordinate origin for the equations is ideally at the centre of such a tiny vortex. Hence applying Maxwell's equations to the large scale cycles of a radio wave is an indication that Hertz entirely missed the point of Maxwell's equations.

             That might answer your question as to why you have a non-Hertzian phenomenon that is in agreement with Maxwell's equations.

David Tombe


by FDT on Saturday, February 18, 2012 @ 01:50:24 EST
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              Yes, having now studied your Tesla paper more carefully, I am convinced that a Hertzian wave and a Tesla wave are one and the same thing. The only difference is that with the Hertzian wave we are focused on the wave mechanics of the emission source, whereas in the case of Tesla, it seems that he had insight into the actual electromagnetic wave propagation mechanism itself, and he could see the flow of positive pulses of aether pressure. The Hertzian approach would be appropriate for large wavelengths such as occur at radio frequency, whereas Tesla's insights would become more relevant when analyzing the nature of light. Maxwell's equations of course deal with the propagation mechanism and not with the emission frequencies, and it would seem that many modern textbooks have overlooked this fact.

David Tombe



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