To William Thomson   4th February 1851

Marburg 4^th February 1851

Dear Sir.

I very gladly respond to the request contained in your last letter¹ which reached me immediately before my departure from England that is to write to you during the winter – the subject of my communication is not immediately connected with that which was brought before the British Association² nevertheless I believe it will interest you – setting aside all further preface I will at once plunge into it – I may remark that an account of the investigation will accompany this letter to the office of the philosophical Magazine.

The subject of the memoir³ is embraced by the following 4 propositions –

1. ‘To determine the general relation between 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 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 mass 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 the mass of soft iron is increased.’

4. ‘To determine the general relation between the strength of an electro 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 and as you are well aware has been the subject of manifold investigation. The results heretofore obtained have howev[er] defied reduction to a common law.

To avoid the causes of divergence complained of by previous experimenters I have applied a sphere of soft iron. This, combined with a peculiar mode of experiment has given results the coincidence of which is really surprising.

The reply to the 1^st proposition is that the force with which Magnet and sphere cling together is directly proportional to the strength of the magnet.

The ‘strength of the magnet’ is expressed by the intensity of the stream which circulates in the surrounding helix –⁴ This has been proved by Lenz and Jacobi⁵ – The dimensions of the magnet render the recent objections of Müller⁶ to this law inapplicable.

The reply to the 2^nd proposition is, that when the distance between magnet and sphere varies and a constant force opposed to the magnet is applied to the sphere, to hold this force in equilibrium the strength of the magnet must vary as the square root of the distance. Calling the strength of the magnet m and the distance d we have the equation – m [= n√d] where n is a constant. From this we see, that, if [the] magnet have double the strength of another and if the latter exert a certain force at a certain distance the former will exert an equal force at four times the distance; & so on.⁷

I ought to mention that the distances I have chosen are very small: the unit of distance is of an inch being the thickness of a sheet of foreign post paper by means of which the distances were regulated.

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

You will perhaps find some little difficulty in separating the 2^nd prop. from the 3^rd 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 fourth proposition embraces a law which in Germany is considered celebrated. It has been solved by direct experiment by Lenz and Jacobi. <It> follows, however [simply] as a corollary from the 2^nd and 3^rd propositions just noticed – The experimental proof and the deduction exhibit a surprising coincidence⁸

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

This latter law is true when an interval of little more than of an inch separates sphere and magnet – Is it not 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 –

You will doubtless detect a remarkable analogy between some of these results and the formulae which Poisson has developed for electrified balls. I am not at all astonished that Barlow arrived at the notion that magnetism was a surface phenomenon⁹ – The memoir will I hope¹⁰ appear on the 1^st of march.

I remain dear Sir | very sincerely yours | John Tyndall

Professor W^m Thomson &c &c

RI MS JT/1/T/1440

RI MS JT/1/TYP/5/1527–1529 Transcript