Faraday & Maxwell

Faraday Maxwell

Reference: A Logical Approach to Theoretical Physics

Faraday’s prime concern was resolution of the problem of gravitation. The explanation for gravity given by Newton in terms of distance did not fully explain the generation and disappearance of gravitational force as two bodies were moved.

Faraday saw “lines of force” as the substance that filled space with varied substantialness. He was looking for a way to explain gravitation with his concept of force as “the source of all possible changes amongst the particles of the universe.”

But this concept was not fully understood by Maxwell, who saw force merely as “the tendency of the body to pass from one place to another”. Maxwell then went on to formulate the concept of electromagnetic field that was based on a mechanical view of force. But he never addressed the problem of gravitation that Faraday was trying to resolve through the principle of conservation of force.

Here is Faraday’s original paper, On the Conservation of Force that he sent to Maxwell.  Here is Maxwell’s response, followed by Faraday’s answer.

This correspondence is presented below with my comments in colored text.



129 Union Street,
Aberdeen, 9th November 1857.

DEAR SIR—I have to acknowledge receipt of your papers on the Relations of Gold to Light, and on the Conservation of Force. Last spring you were so kind as to send me a copy of the latter paper, and to ask what I thought of it.

That question silenced me at that time, but I have since heard and read various opinions on the subject, which render it both easy and right for me to say what I think. And first I pass over some who have never understood the known doctrine of conservation of force, and who suppose it to have something to do with the equality of action and reaction.

Conservation of force is not the same thing as Newton’s third law of motion, which says, “To every action there is always opposed an equal reaction; or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.”

Now, first, I am sorry that we do not keep our words for distinct things more distinct, and speak of the “Conservation of Work or of Energy” as applied to the relations between the amount of “vis viva” and of “tension” in the world; and of the “Duality of Force” as referring to the equality of action and reaction.

“Vis viva” (Latin for “living force”) is a historical term used for the first known description of what we now call kinetic energy in an early formulation of the principle of conservation of energy.

Maxwell thinks that, to be clearer, the title of Faraday’s paper should be more like “Conservation of Work or Energy”. He doesn’t see that the use of the word “Force” by Faraday is much deeper because it includes the substance of space and matter in the equation of conservation. Maxwell excludes space and matter from the equation of conservation.

Energy is the power a thing has of doing work arising either from its own motion or from the “tension” subsisting between it and other things.

Force is the tendency of a body to pass from one place to another, and depends upon the amount of change of “tension” which that passage would produce.

In his letter Maxwell defines force as, “the tendency of a body to pass from one place to another”. This is not what Faraday meant. In his desire to interpret Faraday mathematically, Maxwell did not quite understand what Faraday was saying.

NOTE: Objects in space have inherent motion, and inherent mass. The source of that motion, and the mass, is not accounted for by the law of conservation of energy. Faraday’s notion of force accounts for them. The Kinetic energy term accounts only for the relative motion.

Now, as far as I know, you are the first person in whom the idea of bodies acting at a distance by throwing the surrounding medium into a state of constraint has arisen, as a principle to be actually believed in. We have had streams of hooks and eyes flying around magnets, and even pictures of them so beset; but nothing is clearer than your descriptions of all sources of force keeping up a state of energy in all that surrounds them, which state by its increase or diminution measures the work done by any change in the system. You seem to see the lines of force curving round obstacles and driving plump at conductors, and swerving towards certain directions in crystals, and carrying with them everywhere the same amount of attractive power, spread wider or denser as the lines widen or contract.

Maxwell did not see force as the source of all possible changes in the universe. He saw force only in limited mechanical terms as described by Newton. Thus he interpreted Faraday’s ideas as a force field of a mechanical nature filling the space. He did not see the effect taking time to travel through the medium as Faraday saw.

You have also seen that the great mystery is, not how like bodies repel and unlike attract, but how like bodies attract (by gravitation). But if you can get over that difficulty, either by making gravity the residual of the two electricities or by simply admitting it, then your lines of force can “weave a web across the sky,” and lead the stars in their courses without any necessarily immediate connection with the objects of their attraction.

The lines of Force from the Sun spread out from him, and when they come near a planet curve out from it, so that every planet diverts a number depending on its mass from their course, and substitutes a system of its own so as to become something like a comet, if lines of force were visible.

Lines of Force

The lines of the planet are separated from those of the Sun by the dotted line. Now conceive every one of these lines (which never interfere but proceed from sun and planet to infinity) to have a pushing force instead of a pulling one, and then sun and planet will be pushed together with a force which comes out as it ought, proportional to the product of the masses and the inverse square of the distance.

Maxwell’s force field does seem to act as a substance filling the space, but it is assumed to be of mechanical nature. This is pretty much the same idea as that of aether, which was prevalent at that time. Faraday did not agree with the idea of mechanical aether, because his idea of force was not mechanical.

The difference between this case and that of the dipolar forces is, that instead of each body catching the lines of force from the rest, all the lines keep as clear of other bodies as they can, and go off to the infinite sphere against which I have supposed them to push.

Maxwell supposed the lines of force going around the bodies and pushing against an infinite sphere; but Faraday saw lines of force originating and terminating at each atom.

Here then we have conservation of energy (actual and potential), as every student of dynamics learns, and besides this we have conservation of “lines of force” as to their number and total strength, for every body always sends out a number proportioned to its own mass, and the pushing effect of each is the same.

Maxwell saw mechanical force field filling the space, while Faraday saw substance of varying force (inertia) extending out from the bodies.

All that is altered when bodies approach is the direction in which these lines push. When the bodies are distant the distribution of lines near each is little disturbed. When they approach, the lines march round from between them, and come to push behind each, so that their resultant action is to bring the bodies together with a resultant force increasing as they approach.

Maxwell’s lines of force push two objects towards each other from behind, with the resultant force increasing as they approach each other. Faraday saw substance of the bodies extending toward each other and thickening as the two bodies approached.

 Now the mode of looking at Nature, which belongs to those who can see the lines of force, deals very little with “resultant forces,” but with a network of lines of action of which these are the final results, so that I, for my part, cannot realise your dissatisfaction with the law of gravitation, provided you conceive it according to your own principles. It may seem very different when stated by the believers in “forces at a distance,” but there can be only differences in form and conception, not in quantity or mechanical effect, between them and those who trace force by its lines.

Maxwell could not comprehend Faraday’s dissatisfaction with the law of gravitation. He saw lines of forces as a mathematical device that provided an alternative explanation to action at a distance, but nothing more.

But when we face the great questions about gravitation—Does it require time? Is it polar to the “outside of the universe” or to anything? Has it any reference to electricity? or does it stand on the very foundation of matter, mass or inertia? — then we feel the need of tests, whether they be comets or nebulæ, or laboratory experiments, or bold questions as to the truth of received opinions.

But Maxwell did agree with Faraday in terms of greater questions that needs to be resolved in the understanding of inertia, mass, electricity, magnetism, etc., and effect taking time to travel, and that would require more experimentation, and could not be resolved by lines of force.

I have now namely tried to show you why I do not think gravitation a dangerous subject to apply your methods to, and that it may be possible to throw light on it also by the embodiment of the same ideas, which are expressed mathematically in the functions of Laplace and of Sir W. R. Hamilton in Planetary Theory.

Maxwell resolved the issue of aether in electromagnetic terms but he couldn’t come up with the explanation for gravitation that was missing per the principle of Faraday’s conservation of force.

But there are questions relating to the connection between magneto-electricity and certain mechanical effects which seems to me opening up quite a new road to the establishment of principles in electricity, and a possible conformation of the physical nature of magnetic lines of force. Professor W. Thomson seems to have some new lights on this subject.

I can see how Faraday must have been disappointed by this response from Maxwell.

—Yours sincerely,





Royal Institution: November 13, 1857

My dear Sir,—If on a former occasion I seemed to ask you what you thought of my paper, it was very wrong, for I do not think anyone should be called upon for the expression of their thoughts before they are prepared and wish to give them. I have often enough to decline giving an opinion, because my mind is not ready to come to a conclusion, or does not wish to be committed to a view that may by further consideration be changed. But having received your last letter, I am exceedingly grateful to you for it; and rejoice that my forgetfulness of having sent the former paper on conservation has brought about such a result. Your letter is to me the first intercommunication on the subject with one of your mode and habit of thinking. It will do me much good, and I shall read and meditate on it again and again.

Faraday is disappointed at not being understood by Maxwell on his principle of the conservation of force. Nevertheless, he seems pleased to hear back from a mathematician like Maxwell.

I dare say I have myself greatly to blame for the vague use of expressive words. I perceive that I do not use the word “force” as you define it, “the tendency of a body to pass from one place to another.” What I mean by the word is the source or sources of all possible actions of the particles or materials of the universe, these being often called the powers of nature when spoken of in respect of the different manners in which their effects are shown.

Faraday was an experimentalist and not a theoretician versed in mathematics. He struggled to get his ideas across that were based on experiments only. Maxwell interpreted Faraday’s intent as conservation of work and energy, which was limited to a mechanical interpretation only. Much later, only Einstein could see that Faraday’s ideas went beyond a simple mechanical interpretation.

In a paper which I have received at this moment from the “Phil. Mag.,” by Dr. Woods, they are called the forces, “such as electricity, heat, &c.” In this way I have used the word “force” in the description of gravity which I have given as that expressing the received idea of its nature and source, and such of my remarks as express an opinion, or are critical, apply only to that sense of it. You may remember I speak to labourers like myself; experimentalists on force generally who receive that description of gravity as a physical truth, and believe that it expresses all and no more than all that concerns the nature and locality of the power,—to these it limits the formation of their ideas and the direction of their exertions, and to them I have endeavored to speak, showing how such a thought, if accepted, pledged them to a very limited and probably erroneous view of the cause of the force, and to ask them to consider whether they should not look (for a time, at least), to a source in part external to the particles. I send you two or three old printed papers with lines marked relating to this point.

Faraday explains further that he was speaking of the ‘force of gravity’ in a broad sense and not in a local sense as implied by the inverse square law. He wanted other experimentalists to consider if the source of gravity could be broader than just being limited to material particles.

 To those who disown the definition or description as imperfect, I have nothing to urge, as there is then probably no real difference between us.

Faraday intuitively felt that reality went beyond the mechanical view of Newton, but he struggled to express it clearly.

I hang on to your words, because they are to me weighty; and where you say, “I, for my part, cannot realise your dissatisfaction with the law of gravitation, provided you conceive it according to your own principles,” they give me great comfort. I have nothing to say against the law of the action of gravity. It is against the law which measures its total strength as an inherent force that I venture to oppose my opinion; and I must have expressed myself badly (though I do not find the weak point), or I should not have conveyed any other impression. All I wanted to do was to move men (not No. 1, but No. 2), from the unreserved acceptance of a principle of physical action which might be opposed to natural truth. The idea that we may possibly have to connect repulsion with the lines of gravitation-force (which is going far beyond anything my mind would venture on at present, except in private cogitation), shows how far we may have to depart from the view I oppose.

Faraday had no problem with the law of action of gravity as expressed by Newton. He only objected to the fact that this law did not fully explain the total measure of inherent forces involved. He simply wanted others to see that something was missing from the natural truth.

There is one thing I would be glad to ask you. When a mathematician engaged in investigating physical actions and results has arrived at his own conclusions, may they not be expressed in common language as fully, clearly, and definitely as in mathematical formula? If so, would it not be a great boon to such as we to express them so—translating them out of their hieroglyphics that we also might work upon them by experiment. I think it must be so, because I have always found that you could convey to me a perfectly clear idea of your conclusions, which, though they may give me no full understanding of the steps of your process, gave me the results neither above nor below the truth, and so clear in character that I can think and work from them.

Faraday feels that mathematical results should be expressed in clear and useful working terms so that non-mathematicians can understand and work with them experimentally.

If this be possible, would it not be a good thing if mathematicians, writing on these subjects, were to give us their results in this popular useful working state as well as in that which is their own and proper to them?

It seems that Faraday’s purpose was to inspire Maxwell to look beyond ‘action at a distance’ as coded in the inverse square law. Maxwell did just that as his life’s work. What a wonderful teamwork.

Ever, my dear Sir, most truly yours,

M. Faraday.


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