John Tyndall to Faraday   4 February 1851

Marburg | Feb. 4th. 1851

Dear Sir,

Your last kind letter informed me that you were occupied with terrestrial magnetism¹. I had however read with deep interest previously that you had arrived at the probable origin of that hitherto enigmatical phenomenon - the variation of the needle².

During the last three or four months I have worked at the hem of the same great garment. My belief in the living interest you feel in the progress of science encourages me to lay a brief abstract of my investigation before you. It relates however, not to terrestrial magnetism but to electro-magnetism.

The subject of the investigation embraces the following four propositions:-

1. To determine the general relation of the strength of an electro-magnet and the mutual attraction of the magnet and a mass of soft iron when both are in contact.

2. A constant force, being opposed to the pull of the magnet being applied to the mass of soft iron, to determine the conditions of equilibrium between this force and magnetism, when the distance between the magnet and the force varies.

3. To determine the general relation between force and distance, that is to say, the law according to which the magnetic force decreases when the distance between the magnet and mass of soft iron is increased.

4. To determine the general relation between the strength of a magnet and the mutual attraction of the magnet and a mass of soft iron, when both are separated by a fixed distance.

The first proposition relates to the so called “lifting power” of the magnet which, as you are well aware, has been the subject of manifold investigation. The results however heretofore obtained are incapable of being reduced to anything like law.

To avoid the causes of divergence complained of by previous experimenters a peculiar method of experiment has been adopted, and instead of irregular masses of iron I have made use of spheres. The coincidence of the results is truly surprising.

The reply to the first proposition is, that the force with which the magnet and the sphere cling together is directly proportioned to the strength of the magnet.

The “strength of the magnet” is measured by the intensity of the current which circulates in the surrounding helix and the current was measured by means of a galvanometer of tangent[.] In the investigation the tangent of the angle of deflection is taken as the measure of the strength of the magnet.

The reply to the 2nd. proposition is, that when the distance between the magnet and the sphere varies, and a constant force opposed to the magnet is applied to the latter, to hold this force in equilibrium the strength of the magnet must vary as the square root of the distance.

I ought to mention that the “distances” are very small - the unit of distance is 1/1000 of an inch being the thickness of a leaf of foreign post paper; by placing a number of such leaves between the sphere and magnet the distance could be varied at pleasure.

The reply to the 3rd. proposition is, that the force varies inversely as the distance.

You may perhaps find some little difficulty in separating the 2nd. proposition from the 3rd. This will vanish when you consider, that, in the former case a constant force (a weight) operated against the magnet, and the question was one between magnetism and distance:- in the latter case, the magnetism is preserved constant, and the question is one between weight and distance.

The 4th. proposition embraces the rather celebrated law of Lenz³ and Jacobi⁴ - who solved it by direct experiment⁵. It can however be deduced á priori from the 2nd. and 3rd. proposition just noticed - I have submitted the deduction to experimental test and found the coincidence remarkably close.

The answer to the 4th. proposition is, that the attracting force is directly proportional to the square of the strength of the magnet.

This latter law holds good when a distance of little more than 1/1000 of an inch separates sphere and magnet. Is it not most singular that this small distance should so entirely change the nature of the law? In contact, as before remarked, the attracting force is proportional to the strength of the magnet simply.

A most remarkable analogy exists between some of the results established and the formulae which Poisson has developed for electrified balls⁶. I am not at all surprised that Prof. Barlow⁷ arrived at the notion, that magnetism is a surface phenomenon⁸. As far as I am able to judge at present the whole might be explained on this supposition.

A memoir containing an account of the investigation accompanies this letter to the office of the Philosophical Magazine. The memoir will, I trust, appear on the 1st. March⁹.

When Science is a Republic as you say it gains, and yet I dare affirm that no living man knows better than yourself how little benefit is to be derived in this way in comparison with that which results from the solitary communion of the individual with nature. There are people in the world who are very fond of what they call “composite ideas”. They imagine, if six men come together and talk on a matter, that more will be elicited than if one man held his tongue and simply thought over it. I must say that I have little faith in the proceeding, and if I needed an authority to confirm me in my scept[ic]ism I should without hesitation turn to Professor Faraday.

I remain dear Sir | Most faithfully yours, | John Tyndall.

Professor Faraday | etc. etc.