CHAPTER II.

PROGRESS OF MAGNETIC THEORY.

THEORY of Magnetic Action. The assumption of a fluid, as a mode of explaining the phenomena, was far less obvious in magnetic than in electric cases, yet it was soon arrived at. After the usual philosophy of the middle ages, the 'forms' of Aquinas, the 'efflux' of Cusanus, the vapours' of Costæus, and the like, which are recorded by Gilbert, we have his own theory, which he also expresses by ascribing the effects to a formal efficiency;'-a 'form of primary globes; the proper entity and existence of their homogeneous parts, which we may call a primary and radical and astral form:'-of which forms there is one in the sun, one in the moon, one in the earth, the latter being the magnetic virtue.

Without attempting to analyse the precise import of these expressions, we may proceed to Descartes's explanation of magnetic phenomena. The mode in which he presents this subject is, perhaps, the most persuasive of his physical attempts. If a magnet be placed among iron filings, these arrange themselves in curve lines, which proceed from one pole of the magnet to the other. It was not difficult to conceive these to be the traces of currents of ethereal matter which circulate through the magnet, and which are thus rendered sensible even to the eye. When phenomena could not be explained by means of one vortex, several were introduced. Three Memoirs on Magnetism, written on such principles, had the prize adjudged by the French Academy of Sciences in 1746.

But the Cartesian philosophy gradually declined; and it was not difficult to show that the magnetic curves, as well as other phenomena, would, in fact,

1 Gilb. lib. ii. c. 3, 4.

2 Prin. Phil. pars c. iv. 146.

3 Coulomb, 1789, p. 482.

result from the attraction and repulsion of two poles. The analogy of magnetism with electricity was SO strong and clear, that similar theories were naturally proposed for the two sets of facts; the distinction of bodies into conductors and electrics in the one case, corresponding to the distinction of soft iron and hard steel, in their relations to magnetism. Epinus published a theory of magnetism and electricity at the same time (1759); and the former theory, like the latter, explained the phenomena of the opposite poles as results of the excess and defect of a magnetic fluid,' which was dislodged and accumulated in the ends of the body, by the repulsion of its own particles, and by the attraction of iron or steel, as in the case of induced electricity. The Epinian theory of magnetism, as of electricity, was recast by Coulomb, and presented in a new shape, with two fluids instead of one. But before this theory was reduced to calculation, it was obviously desirable, in the first place, to determine the law of force.

In magnetic, as in electric action, the determination of the law of attraction of the particles was attended at first with some difficulty, because the action which a finite magnet exerts is a compound result of the attractions and repulsions of many points. Newton had imagined the attractive force of magnetism to be inversely as the cube of the distance; but Mayer in 1760, and Lambert a few years later, asserted the law to be, in this as in other forces, the inverse square. Coulomb has the merit of having first clearly confirmed this law, by the use of his torsion-balance. He established, at the same time, other very important facts, for instance, that the directive magnetic force, which the earth exerts upon a needle, is a constant quantity, parallel to the magnetic meridian, and passing through the same point of the needle whatever be its position.' This was the more important, because it was necessary, in the first place, to allow for the effect of the terrestrial force, before the mutual action of the magnets

Mem, A. P. 1784, 2d Mem. p. 593.

could be extricated from the phenomena.5 Coulomb then proceeded to correct the theory of magnetism.

Coulomb's reform of the Epinian theory, in the case of magnetism, as in that of electricity, substituted two fluids (an austral and a boreal fluid,) for the single fluid; and in this way removed the necessity under which pinus found himself, of supposing all the particles of iron and steel and other magnetic bodies to have a peculiar repulsion for each other, exactly equal to their attraction for the magnetic fluid. But in the case of magnetism, another modification was necessary. It was impossible to suppose here, as in the electrical phenomena, that one of the fluids was accumulated on one extremity of a body, and the other fluid on the other extremity; for though this might appear, at first sight, to be the case in a magnetic needle, it was found that when the needle was cut into two halves, the half in which the austral fluid had seemed to predominate, acquired immediately a boreal pole opposite to its austral pole, and a similar effect followed in the other half. The same is true, into however many parts the magnetic body be cut. The way in which Coulomb modified the theory so as to reconcile it with such facts, is simple and satisfactory. He supposes the magnetic body to be made up of 'molecules or integral parts,' or, as they were afterwards called by M. Poisson, 'magnetic elements.' In each of these elements, (which are extremely minute,) the fluids can be separated, so that each element has an austral and a boreal pole; but the austral pole of an element which is adjacent to the boreal pole of the next, neutralizes, or nearly neutralizes, its effect; so that the sensible magnetism appears only towards the extremities of the body, as it would do if the fluids could permeate the body freely. We shall have exactly the same result, as to sensible magnetic force, on the one supposition and on the other, as Coulomb showed.7 The theory, thus freed from manifest incongruities,

5 p. 603.

6 Mem. A. P. 1789, p. 488.

7 Mem. A. P. p. 492.

was to be reduced to calculation, and compared with theory; this was done in Coulomb's Seventh Memoir.8 The difficulties of calculation in this, as in the electric problem, could not be entirely surmounted by the analysis of Coulomb; but by various artifices, he obtained theoretically the relative amount of magnetism at several points of a needle,9 and the proposition that the directive force of the earth on similar needles saturated with magnetism, was as the cube of their dimensions; conclusions which agreed with experi

ment.

The agreement thus obtained was sufficient to give a great probability to the theory; but an improvement of the methods of calculation, and a repetition of experiments, was, in this as in other cases, desirable, as a confirmation of the labours of the original theorist. These requisites, in the course of time, were supplied. The researches of Laplace and Legendre on the figure of the earth had (as we have already stated,) introduced some very peculiar analytical artifices, applicable to the attractions of spheroids; and these methods were employed by M. Biot in 1811, to show that on an elliptical spheroid, the thickness of the fluid in the direction of the radius would be as the distance from the center. 10 But the subject was taken up in a more complete manner in 1824 by M. Poisson, who obtained general expressions for the attractions or repulsions of a body of any form whatever, magnetized by influence, upon a given point; and in the case of spherical bodies was able completely to solve the equations which determine these forces.11

Previously to these theoretical investigations, Mr. Barlow had made a series of experiments on the effect of an iron sphere upon a compass needle; and had obtained empirical formulæ for the amount of the deviation of the needle, according to its dependence upon the position and magnitude of the sphere. He afterwards deduced the same formulæ from a theory

8 A. P. 1789.

9

p. 485.

10 Bull. des Sc. No. li. 11 A. P. for 1821 and 2, published 1826.

which was, in fact, identical with that of Coulomb, but which he considered as different, in that it supposed the magnetic fluids to be entirely collected at the surface of the sphere. He had indeed found, by experiment, that the surface was the only part in which there was any sensible magnetism; and that a thin shell of iron would produce the same effect as a solid ball of the same diameter.

But this was, in fact, a most complete verification of Coulomb's theory. For though that theory did not suppose the magnetism to be collected solely at the surface, as Mr. Barlow found it, it followed from the theory, that the sensible magnetic intensity assumed the same distribution, (namely, a surface distribution,) as if the fluids could permeate the whole body, instead of the 'magnetic elements' only. Coulomb, indeed, had not expressly noticed the result, that the sensible magnetism would be confined to the surface of bodies; but he had found that, in a long needle, the magnetic fluid might be supposed to be concentrated very near the extremities, just as it is in a long electric body. The theoretical confirmation of this rule among the other consequences of the theory,-that the sensible magnetism would be collected at the surface,-was one of the results of Poisson's analysis. For it appeared that if the sum of the electric elements of the body was equal to the whole body, there would be no difference between the action of a solid sphere and a very thin shell.

We may, then, consider the Coulombian theory to be fully established and verified, as a representation of the laws of magnetical phenomena. We may add, as a remarkable and valuable example of an ulterior step in the course of sciences, the application of the laws of the distribution of magnetism to the purposes of navigation. It had been found that the mass of iron which exists in a ship produces a deviation in the direction of the compass-needle, which was termed 'local attraction,' and which rendered the compass an erroneous guide. Mr. Barlow proposed to correct this by a plate of iron placed near the compass; the plate being of comparatively small mass, but, in consequence of its