From William Thomson   Aug 14, 1850

Row, Helensburgh | Dumbartonshire | Aug 14, 1850

Dear Sir

I regret not to have been able to answer your letter¹ of the 7^th sooner. I received it last week in passing through Glasgow, and I should have written to you immediately if I could have put down the titles of some works, as a sufficient answer. In reality however I cannot give you any satisfactory reference for an account of Poisson’s Theory of Magnetism except his own Mémoires which are published in the Mémoires de l’Institut,² if I remember right between the years 1810 and 1815. There are two, I believe published in the same volume, on the Theory of Magnetism, and one, published in a later volume (I believe consecutive to that which contains the first two) on Magnetism in Motion. In the last mentioned Mémoire, Poisson makes a brief statement to nearly the following effect. If, as we may conceive to be the case in crystalline substances, the magnetic elements are non-spherical and are symmetrically arranged, the induction of magnetism would follow different laws from those which have been obtained in the first two Mémoires, on the supposition that the elements are spherical or destitute of symmetrical arrangement. It would result that a spherical portion of such a substance would experience different inductive action according to the way in which it is turned when placed near a magnet ‘but such circumstances not having been observed I confine my present researches to the cases in which the magnetic elements are spherical, or if not spherical, non-symmetrically arranged’.

The preceding statement and quotation are, as nearly as I can recollect, all that Poisson says regarding the theory of the phenomena which might possibly be presented by crystals, in his third memoir. I know that in one or both of the first memoirs the same idea is started but passed over in a similar cursory manner.

It may be added to Poisson’s statement that, according to his theory of magnetic elements, the phenomena which he hints at as to be expected from non-spherical magnetic elements, symmetrically arranged, would also result from an arrangement of spherical elements such as you produce of the particles of powder by the compression of the dough containing them; that is, an arrangement in which a finite line drawn in a certain direction will cut across a greater number of the small spheres, than a line of equal length in any other direction. A ball of such substance, if free to turn round its centre of gravity would, if in the neighbourhood of a magnet, only be in stable equilibrium with the direction mentioned above (underlined in the preceding page) along the lines of force. If this direction were inclined to the lines of force at any oblique angle, there would be a directive ‘couple’ exerted upon the ball tending to bring this direction to be parallel to the lines of force, in virtue of the magnetism induced in it, by the magnet acting on the magnetism which it has induced.

Regarding the ‘magnetic elements’ the existence of which is the hypothesis adopted by Poisson, they will differ essentially from the particles of powder enclosed in dough which you use as an illustration, in this important respect. In each magnetic element there are two magnetic fluids (I make use of the language of Poisson’s hypothesis of the falseness of w^h, however, I am convinced) capable of moving about freely within the element but incapable of leaving it and passing to another element or into a space of the body external to the magnetic elements. Each element contains an enormous quantity of the northern fluid, and an equal quantity of the southern fluid. Hence a single magnetic element, if it could be detached from the body of which it is a part, would be susceptible of magnetic induction, by the actual separation of the fluids within it which the presence of a magnet would produce. The law which the separation of the elements within it w^d follow is this – The resultant magnetic force at any point P within the element due to the separated fluids at the surface of the magnetic element,

must balance the resultant force at the same point due to the influencing magnet. – (so that a small compass needle placed within the element would experience no directive action) From this inductive magnetic action the detached magnetic element would exhibit a ‘capacity for magnetic induction’ greater than that which is possessed by any real substance; & the phenomena of magnetic induction observed in actual substances result from the separation in this way of the magnetic fluids within the infinitely small elements, but are not dependent on any separation of the fluids through finite distances in the substance. In considering analogous electrical problems, I convinced myself a long time ago that a row of such spherical magnetic elements (corresponding precisely to insulated, naturally non-electrified conducting spheres) if placed in a uniform field of magnetic force, would, by their mutual actions when subjected to magnetic influence, produce a greater magnetization when their line is parallel to the lines of force than when it is perpendicular to them, and that when it is oblique to the lines of force there would be a resultant couple acting on the group w^h would tend to turn their line towards the direction of the lines of force. If the diameters of the balls be very small compared with their distances asunder, this directive action will be excessively feeble. If instead of imaginary detached magnetic elements we conceive balls of soft iron to be substituted, similar phenomena will be presented, to nearly an equal degree, since the capacity for induction of a ball of soft iron is so intense that it does not fall far short of what it would be if the magnetic fluids were freely separable throughout its entire extent. But if instead of balls of soft iron, we have a row of balls of a very feeble ferromagnetic substance (balls containing very weak solutions of sulphate of iron for instance) their mutual action when subjected to the influence of a magnet would be so slight that any directive tendency that would result (although it would certainly be towards the lines of force, if the field be uniform) would be practically inappreciable.

I have also convinced myself that a row of balls of a diamagnetic substance, placed in a uniform field of magnetic force, would experience a directive tendency of such a kind that there would be a stable equilibrium with the line joining their centres parallel to the lines of force; and, generally, that a long bar of a diamagnetic substance, free to move round its centre of gravity, would take the same direction as a bar of ferromagnetic substance, that is, the length of the bar parallel to the lines of force, provided the field be absolutely uniform; but the capacity for inductive magnetization in all known substances which are diamagnetic being excessively feeble, this directive tendency would I believe be absolutely inappreciable in the most refined experiments that could possibly be made with the most powerful uniform field of force that could be obtained.

It has struck me that some of the very remarkable phenomena which you have discovered in your experiments upon the cakes of dough may have been due to a quasi-crystalline structure induced in the dough, or stiff from water, by compression, and become permanent when the substance has dried in that constrained state. This occurred to me in consequence of the curious optical experiments performed by Mr. Clerk Maxwell Jun^r having been noticed, and shown to some of the members in Section A. From these it appears that isinglass jelly³ dried in a state of constraint (very moderate forces having been sufficient) presents a permanent crystalline structure as far as optical properties can indicate; why not also for induced magnetism? I believe every transparent solid that has been magnetically experimented upon which has the optical properties of a crystal has been found to possess the peculiar properties regarding induced magnetism. It is therefore to be expected that a small sphere of Clerk Maxwell’s dried isinglass, when placed near a powerful magnet would experience a directive tendency. I have requested him to prepare some small spheres and discs with a view to having experiments of this kind made, but I fear my apparatus will not enable me to arrive at any satisfactory results by experimenting myself. I should be extremely glad if the suggestion I have made should induce you, or M^r Knoblauch if you communicate it to him, to make some such experiments. There are several distinct arrangements I could indicate which I think might lead to a complete elucidation of the very remarkable experiments you have already made. If you wish it I shall be glad to communicate all I could suggest. I shall conclude this rambling letter by mentioning that Poisson’s Theory of Induced Magnetism is briefly described in Lame’s Cours de Physique,⁴ and probably in many other similar treatises; & that the elementary mathematical treatment of the subject is given in Green’s Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism,⁵ Nottingham 1828 (now out of print unfortunately) and in Murphy’s Treatise on Electricity, Cambridge 1833.⁶

Believe me, Dear Sir, | Your’s very truly | William Thomson

P.S. I enclose a paper which I published some time ago in the Cambridge and Dublin Mathematical Journal,⁷ and which contains some remarks closely connected with the subject of this letter. | John Tyndall Esq.

RI MS JT/1/T/9

RI MS JT/1/TYP/5/1523–1526