James Clerk Maxwell to Faraday   19 October 1861

8 Palace Gardens Terrace | Kensington W. | 19 Oct. 1861

Dear Sir

I have been lately studying the theory of static electric induction, and have endeavoured to form a mechanical conception of the part played by the particles of air, glass or other dielectric in the electric field, the final result of which is the attraction and repulsion of “charged” bodies¹.

The conception I have hit on has led, when worked out mathematically to some very interesting results, capable of testing my theory, and exhibiting numerical relations between optical, electric and electromagnetic phenomena, which I hope soon to verify more completely.

What I now wish to ascertain is whether the measures of the capacity for electric induction of dielectric bodies with reference to air have been modified materially since your estimates of them in “Series XI,” either by yourself or others².

I³ wish to get the numerical value of the “electric capacity” of various substances especially transparent ones, if formed into a thin sheet of given thickness and coated on both sides with tinfoil[.] Sir W. Snow Harris has made experiments of this kind⁴ but I do not know whether I can interpret them numerically.

Another question I wish to ask is whether any experiments similar to those in Series XIV on crystalline bodies have yet led to positive results⁵. I expect that a sphere of Iceland spar, suspended between two oppositely electrified surfaces would point with its optic axis transverse to the electric force, and I expect soon to calculate the value of the force with which it should point.

Again, I have not yet found any determination of the rotation of the plane of polarisation by magnetism in which the absolute intensity of magnetism at the place of the transparent body was given. I hope to find such a statement by searching in libraries, but perhaps you may be able to put me on the right track⁶.

<-><->

My theory of electrical forces is that they are called into play in insulating media by slight electric displacements, which put certain small portions of the medium into a state of distortion which, being resisted by the elasticity of the medium, produces an electromotive force. A spherical cell would, by such a displacement be distorted thus- where the curved lines represent diameters originally straight, but now curved.

I suppose the elasticity of the sphere to react on the electrical matter surrounding it, and press it downwards.

From the determination by Kohlrausch⁷ and Weber⁸ of the numerical relation between the statical and magnetic effects of electricity⁹, I have determined the elasticity of the medium in air, and assuming that it is the same with the luminiferous ether I have determined the velocity of propagation of transverse vibrations. The result is

193088 miles per second

(deduced from electrical & magnetic experiments)¹⁰[.] Fizeau¹¹ has determined the velocity of light = 193118 miles per second, by direct experiment¹².

This coincidence is not merely numerical. I worked out the formulae in the country, before seeing Webers number, which is in millimetres; and I think we have now strong reason to believe, whether my theory is a fact or not, that the luminiferous and the electromagnetic medium are one.

Supposing the luminous and the electromagnetic phenomena to be similarly modified by the presence of gross matter, my theory says that the inductive capacity (static) is equal to the square of the index of refraction, divided by the coefficient of magnetic induction (air = 1).

I have also examined the theory of the passage of light through a medium filled with magnetic vortices, and find that the rotation of the plane of polarisation is in the same direction with that of the vortices, that it varies inversely as the square of the wave length (as is shown by experiment)¹³ and that its amount is proportional to the diameter of the vortices.

The absolute diameter of the magnetic vortices, their velocity and their density, are so involved, that though as yet they are all unknown, the discovery of a new relation among them would determine them all.

Such a relation might be obtained by the observation of a revolving electromagnet if our instruments were accurate enough. I have had an instrument made for this purpose, but I have not yet overcome the effects of terrestrial magnetism in masking the phenomena.

When I began to study electricity mathematically, I avoided all the old traditions about forces acting at a distance, and after reading your papers as a first step to right thinking, I read the others, interpreting as I went on, but never allowing myself to explain anything by these forces. It is because I put off reading about electricity till I could do it without prejudice, that I think I have been able to get hold of some of your ideas, such as the electrotonic state¹⁴, action of contiguous parts¹⁵ &c and my chief object in writing to you is to ascertain if I have got the same ideas which led you to see your way into things, or whether I have no right to call my notions by your names.

I remain | yours truly | J.C. Maxwell

Professor Faraday