certain distance; if the second unlike half be now brought near, the ball will approach again, and take up its original position. The question therefore appears to concentrate itself into the following:--Is this "approach" due to the fact that the magnetic forces of the two halves annul each other before they reach the ball, or is it the result of a compensation of inductions in the diamagnetic body itself? If a sphere of soft iron be suspended from a thread, the north pole of a magnet will draw it from the plumb-line; if the south pole of an exactly equal magnet be brought close to the said north pole, the sphere will recede to the plumb-line. Is this recession due to a compensation of inductions in the sphere itself, or is it not? If the former, then, by all parity of reasoning, we must assume a similar compensation on the part of the bismuth.'

That bismuth, and diamagnetic bodies generally, suffer induction, will, I think, appear evident from the following considerations. The power of a magnet is practically ascertained by the mechanical effect which it is able to produce upon a body possessing a constant amount of magnetism,-a hard steel needle, for instance. The action of a magnet in pulling such a needle from the magnetic meridian may be expressed by a weight which acts at the end of a lever of a certain length. By easy practical rules we can ascertain when the pull of one magnet is twice or half the pull of another, and in such a case we should say that the former possesses twice or half the strength of the latter. If, however, these two magnets, with their powers thus fixed, be brought to bear upon a sphere of soft iron, the attraction of the one will be four times or a quarter that of the other. The strengths of the magnets being, however, in the ratio of 1:2, this attraction of 1: 4 can only be explained by taking into account the part played by the iron sphere. We are compelled to regard the sphere as an induced magnet, whose power is directly proportional to the inducing one. Were the magnetism of the sphere a constant quantity, a magnet of double power could only produce a double attraction; but the fact of the magnetism of the sphere varying directly as the source of induction leads us inevitably to the law of squares; and conversely, the law of squares leads us to the conclusion that the sphere has been induced.

These sound like truisms; but if they be granted, there

is no escape from the conclusion that diamagnetic bodies are induced; for it has been proved by M. E. Becquerel and myself, that the repulsion of diamagnetic bodies follows precisely the same law as the attraction of magnetic bodies; the law of squares being true for both. Now were the repulsion of bismuth the result of a force applied to the mass alone, without induction, then, with a constant mass, the repulsion must be necessarily proportional to the strength of the magnet. But it is proportional to the square of the strength, and hence must be the product of induction.

In order to present magnetic phenomena intelligibly to the mind, a material imagery has been resorted to by philosophers. Thus we have the 'magnetic fluids' of Poisson and the lines of force' of Mr. Faraday. For the former of these Professor W. Thomson has recently substituted an 'imaginary magnetic matter.' The distribution of this matter' in a mass of soft iron, when operated on by a magnet, has attraction for its result. We have the same necessity for an image in the case of bismuth. If we imagine the two magnetic matters which are distributed by induction on a piece of iron to change places, we have a distribution which will cause the phenomena of bismuth. Hence it is unnecessary to assume the existence of any new matter in the case of diamagnetic bodies, the deportment being accounted for by reference to a peculiarity of distribution. Further, the experiments of Reich, which prove that the matter evoked by one pole will not be repelled by an unlike pole, compel us to assume the existence of two kinds of matter, and this, if I understand the term aright, is polarity.

[The foregoing slight paper could have very little influence on the decision of so weighty a question. In the autumn of 1854 I therefore resumed the investigation with a desire to exhaust, if possible, the experimental portion of it. The following memoir contains an account of the inquiry. I had previously been examining the influence of organic structure upon the display of magnetism; and had also been engaged with certain laws deduced by M. Plücker from his experiments as to the diminution of magnetism and diamagnetism with the distance. The account of these experiments precedes the real inquiry into the relations of magnetism to diamagnetism, and ought, perhaps, to have been published by itself.-J. T., 1870.]

89

FOURTH MEMOIR.

ON THE NATURE OF THE FORCE BY WHICH BODIES ARE REPELLED FROM THE POLES OF A MAGNET.*

Introduction.

FROM the published account of his researches it is to be inferred, that the same heavy glass, by means of which he first produced the rotation of the plane of polarisation of a luminous ray, also led Mr. Faraday to the discovery of the diamagnetic force. A square prism of the glass, 2 inches long and 0.5 of an inch thick, was suspended with its length horizontal between the two poles of a powerful electro-magnet: on developing the magnetism the prism moved round its axis of suspension, and finally set its length at right angles to a straight line drawn from the centre of one pole to that of the other. A prism of ordinary magnetic matter, similarly suspended, would, as is well known, set its longest dimension from pole to pole. To distinguish the two positions here referred to, Mr. Faraday introduced two new terms, which have since come into general use he called the direction parallel to the line joining the poles, the axial direction, and that perpendicular to the said line, the equatorial direction.

The difference between this new action and the ordinary magnetic action was further manifested when a fragment of the heavy glass was suspended before a single magnetic pole: the fragment was repelled when the magnetism was excited; and to the force which produced this repulsion Mr. Faraday gave the name of diamagnetism.

Numerous other substances were soon added to the heavy glass, and, among the metals, it was found that bismuth possessed the new property in a comparatively exalted degree. A fragment of this substance was forcibly repelled by either of the poles of a magnet; while a thin bar of the substance, or a glass

* Phil. Trans. 1855, p. 1: being the Bakerian Lecture.

tube containing the bismuth in fragments, or in powder, suspended between the two poles of a horseshoe magnet, behaved exactly like the heavy glass, and set its longest dimension equatorial.

These exhaustive researches, which rendered manifest to the scientific world the existence of a pervading natural force, glimpses of which merely had been previously obtained by Brugman and others, were made public at the end of 1845; and in 1847 M. Plücker announced his beautiful discovery of the action of a magnet upon crystallised bodies. His first result was, that when any crystal whatever was suspended between the poles of a magnet, with its optic axis horizontal, a repulsive force was exerted on the axis, in consequence of which it receded from the poles and finally set itself at right angles to the line joining them. Subsequent experiments, however, led to the conclusion, that the axes of optically negative crystals only experienced this repulsion, while the axes of positive crystals were attracted; or, in other words, set themselves from pole to pole. The attraction and repulsion, here referred to, were ascribed by M. Plücker to the action of a force, independent of the magnetism or diamagnetism of the mass of the crystal.*

Shortly after the publication of M. Plücker's first memoir,

The force which produces this repulsion is independent of the magnetic or diamagnetic condition of the mass of the crystal; it diminishes less, as the distance from the poles of the magnet increases, than the magnetic and diamagnetic forces emanating from these poles and acting upon the crystal.'-Prof. Plücker in Poggendorff's Annalen, vol. lvii. No. 10; Taylor's Scientific Memoirs, vol. v. p. 353.

The forces emanating from the poles of a magnet are thus summed up by M. Plücker:-

1st. The magnetic force in a strict sense.

2nd. The diamagnetic action discovered by Faraday.

3rd. The action exerted on the optic axes of crystals (and that producing the rotation of the plane of polarisation which probably corresponds to it). The second diminishes more with the distance than the first, and the first more than the third.— Taylor's Scientific Memoirs, vol. v. p. 380.

The crystal (cyanite) does not point according to the magnetism of its substance, but only in obedience to the magnetic action upon its optic axes.-Letter to Mr. Faraday, Phil. Mag. vol. xxxiv. p. 451. The italics in all cases are M. Plücker's own.

M. de la Rive states the view of M. Plücker to be :-'that the axis in its quality as axis, and independently of the very nature of the substance of the crystal, enjoys peculiar properties, more frequently in opposition to those possessed by the substance itself, or which at least are altogether independent of it.'-Treatise on Electricity, vol. i. p. 359.

Mr. Faraday observed the remarkable magnetic properties of crystallised bismuth; and his researches upon this, and other kindred points, formed the subject of the Bakerian Lecture before the Royal Society for the year 1849.

Through the admirable lectures of Professor Bunsen on Electro-chemistry in 1848, I was first made acquainted with the existence of the diamagnetic force; and in the month of November 1849 my friend Professor Knoblauch, then of Marburg, now of the University of Halle, suggested to me the idea of repeating the experiments of M. Plücker and Mr. Faraday. He had procured the necessary apparatus with the view of prosecuting the subject himself, but the pressure of other duties prevented him from carrying out his intention. I adopted the suggestion and entered upon the inquiry in M. Knoblauch's cabinet. Our frequent conversations upon the subject led naturally to our making a joint investigation.

We published our results in two papers, the first of which, containing a brief account of some of the earliest experiments, appeared in the Philosophical Magazine' for March 1850, and some time afterwards in Poggendorff's Annalen; while the second and principal memoir appeared in the Philosophical Magazine' for July 1850, and in Poggendorff's Annalen about January 1851.* I afterwards continued my researches in the private laboratory of Professor Magnus of Berlin, who, with prompt kindness and a lively interest in the furtherance of the inquiry, placed all necessary apparatus at my disposal. The results of this investigation are described in a paper published in the Philosophical Magazine' for September 1851, and in Poggendorff's Annalen, vol. lxxxiii.

In these memoirs it was shown that the law according to which the axes of positive crystals are attracted and those of negative crystals repelled, was contradicted by the deportment of numerous crystals both positive and negative. It was also proved that the force which determined the position of the optic axes in the magnetic field was not independent of the magnetism or diamagnetism of the mass of the crystal; inasmuch as two crystals, of the same form and structure, exhibited alto

* The memoirs in the Philosophical Magazine' were written by me, and the second one has, I believe, been translated into German by Dr. Krönig; the papers in Poggendorff's Annalen were edited by my friend and colleague.-J. T.