Professor Schwatt's papers were presented by Professor Dunham Jackson; Mr. MacDuffee was introduced to the society by Professor L. E. Dickson and Professor Wood by Professor Wilezynski; the papers of Professors Miller and Lane were read by title. Professor Bliss, president of the society, presided at the meeting of Friday afternoon. The other sessions were presided over by Professor R. D. Carmichael, chairman of the Chicago Section, relieved on Saturday by Professor Dunham Jackson, vice-president of the society.

ARNOLD DRESDEN, Secretary of the Chicago Section

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W. W. SARGEANT,

Secretary, Pacific Division

FRIDAY, MAY 20, 1921

THE ELECTRON THEORY OF

MAGNETISM1

EVER since the time of Faraday it has been known that all varieties of matter can be grouped in three classes on the basis of magnetic behavior, ferromagnetic, paramagnetic and diamagnetic.

It would be far too much to claim that the electron theory has as yet given anything like a complete account of the phenomena witnessed in connection with these three types of magnetism; but it is the only theory proposed which has been in any way satisfactory and which appears to hold out any hope for the future.

In accordance with the plans of this symposium I shall restrict myself to a consideration of the more general aspects of the theory and its simplest applications. For the sake of logical completeness I shall have to refer to many matters well known. The extension of the theory and its application to more special and complex cases, in so far as they can be handled on this occasion, will be treated by my colleagues.

The first electrical theory of ferromagnetism was proposed by Ampère just about one hundred years ago. On the basis of his own experiments on the behavior of electric circuits and magnets, and on the assumption, already justified, that magnetism is a molecular and not a molar phenomenon, he concluded that the molecule of iron is the seat of a permanent electrical whirl and thus essentially a permanent magnet with its axis perpendicular to the whirl. When the iron is fully magnetized, all the whirls are oriented alike, and

1 A paper read as a part of the symposium on recent progress in magnetism held at the joint meeting of the American Association for the Advancement of Science, Section B, and the American Physical Society, December, 1920. Revised, January, 1921.

the magnetic moment of the mass of iron is the sum of the moments of the elementary molecular magnets. Ampère undoubtedly considered that in a neutral mass of iron the molecular magnets are turned indiscriminately in all directions, but he did not enter into any discussion of the process by which their axes are made parallel by the field during magnetization, nor did he consider the nature of the electrical whirls themselves.

Ampère was the grandfather of the electron theory of magnetism. Wilhelm Weber was its father. In 1852 Weber2 published a paper in which he developed a theory which, slightly modified by Langevin, is still perhaps the most widely accepted theory of diamagnetism, together with a theory of ferromagnetism which formed the starting point for the wellknown theory of Ewing. Weber adopted the molecular whirls of Ampère, but assumed in addition that these whirls, always present in the molecules of magnetic substances, are also present in the molecules of diamagnetic substances when placed in a magnetic field. Further, he took the very important step of attributing mass or inertia to the electricity in the whirls, and he assumed that the electricity moves as if in fixed circular grooves in the molecule, so that each whirl maintains its diameter and its orientation with respect to the rest of the molecule as if rigidly constrained. According to Weber's conception, a substance is paramagnetic or ferromagnetic when the molecule, or magnetic element, contains a permanent whirl, with a definite magnetic moment, and so tends to set with its axis in the direction of any magnetic field in which it is placed; and a substance is diamagnetic when the molecule contains one or more frictionless grooves, with the mobile electricity at rest before the creation of the magnetic field. Langevin merely substitutes electrons moving in fixed orbits for Weber's electricity in grooves; and assumes that in a diamagnetic substance more than one orbit exists in the molecule and that the orbits are so constituted and grouped that the magnetic

2 W. Weber's Werke, III., p. 555.

8 Ann. chim. phys. (8), 5, 1905, p. 70.

moment of the whole molecule is zero in a neutral field.

In this case, which we shall consider in some detail, the complete molecule will suffer no change of orientation when introduced into a magnetic field, but the speed of the electricity in each orbit or groove will change on account of the electromotive force around the orbit or groove due to the alteration of the extraneous magnetic flux through it. Its magnetic moment u will thus increase (algeμ braically) by an amount Au, which can readily be calculated. If e denotes the charge of electricity circulating in an orbit (whether as a single electron, or a ring of electrons, or a continuous ring), m the mass associated with the moving charge, r the radius of the orbit, H the intensity of the extraneous magnetic field, and the angle between the axis of the orbit and the direction of the field,

but the agreement is in general far from close. The equation requires that K should be independent of the temperature, unless e, m, r and N depend upon it. As is well known, the susceptibilities of many diamagnetic substances are independent of the temperature over wide ranges, while in other cases there is a marked dependence.

According to this theory also, effects of the same kind must exist in bodies which are ferromagnetic or paramagnetic superposed on effects of opposite sign, the resultant susceptibility being, as Larmor long ago pointed out, the sum of the two. The paramagnetic term may account for the variation of the resultant susceptibility with temperature in many diamagnetic bodies. From Weber's equation it may be shown that when =0

Thomson, Voigt, Lorentz, and others, including very recently H. A. Wilson. If a substance contains electrons either at rest or in plain rectilinear motion due to thermal agitation, and a magnetic field is created, an electrical intensity will evidently be developed with a curl equal to the negative rate of increase of the flux density, which will cause the electrons to move in paths curved in such a way as to produce a magnetic moment opposed to the direction of the applied field; and as the field becomes steady curvature will be maintained by the action of the field on the moving electrons normal to their velocities. Calculation on this hypothesis gives susceptibilities of the same order of magnitude as those given by the Weber-Langevin theory. This form of theory has the advantages over the other of greater freedom from assumptions and of giving, when applied to the optical case, a Zeeman effect with sharp lines. Weber does not attempt to justify his assumption that in a molecule the diameters of his orbital grooves remain constant, and that in a diamagnetic substance the grooves maintain their orientations independent of the applied magnetic intensity. With respect to the diameters, however, Langevin has shown that the magnetic field will produce no alteration provided the law of force is not precisely that of the inverse cube, which is quite improbable.

We shall return to the subject of diamagnetism later.

The first detailed theory of paramagnetism was given for perfect gases by Langevin in 1905. Following Langevin, I shall begin with a gravitational analogue. Let us consider an enclosure containing a gas at uniform temperature and let us suppose the gravitational field anulled. The density of the gas will then be uniform throughout the enclosure. If now the uniform gravitational field is brought into action every particle of gas will receive an acceleration downward, 4 Int. cong. phys., 1900, vol. 3, p. 138. * Ann. der Phys. (4), 9, 1902, p. 130. 6"The Theory of Electrons," p. 124. 7 Roy. Soc. Proc. A, 97, 1920, p. 321.

and the up and down velocities of the molecules will exceed the horizontal velocities, until after a short time involving many collisions, a redistribution, as required by the principle of equipartition, will have occurred, in which the component squared velocities are equalized and the whole mass of gas has a temperature greater than before. If Do denotes the density of the gas at the bottom of the enclosure, D the density at any height x, m the mass of one molecule, r the gas constant for one molecule, T the absolute temperature and g the acceleration of gravity, we have the relation

μ

Now suppose each molecule to have a magnetic moment and imagine a vertical magnetic field applied throughout the enclosure instead of the gravitational field. The molecules will be driven to set themselves with their magnetic axes parallel to the magnetic intensity just as before the molecules were driven downward, and rotational velocities about lines normal to the field intensity will be favored, but thermal agitation will redistribute them as before until the law of equipartition is satisfied. If now denotes the angle made by the axis of any molecular magnet with the (vertical) magnetic intensity H, p the number of molecules per unit volume with their axes between 0 and 0 + do, and the number between 0 and do, we have, Po by strict analogy with the gravitational case, mH (1― cos 0) rT

(9)

p/po =eStarting from this formula we can readily calculate the total change produced in the magnetic moment of the gas (0 before the application of the field) and thus the intensity of magnetization I. If a is written for

The susceptibility is thus independent of H, and inversely proportional to T. So far as temperature is concerned it expresses the law of Curie, which holds for the paramagnetic gas oxygen over a great range of temperatures, and which holds over a great range in many other cases in which the molecular magnets are so far apart as not to act appreciably on one another.

Inasmuch as r is known, and as N is known for any value of T at known pressure, we can calculate from the observed value of K. We μ thus obtain for oxygen, reckoning from 0° C. and 760 mm. pressure,

Langevin's theory of paramagnetism is not an electron theory, as it has been developed without regard to the permanent electrical rotations assumed on this theory to account for the permanent magnetic moment of the elementary magnet. Nevertheless, it has rendered great services and has important relations to the electron theory.

Investigation of the behavior of free electron orbits, as distinguished from the fixed orbits of Weber, in a magnetic field, have been made by Voigt" and J. J. Thomson,8 who independently, in 1902 and 1903, reached the conclusion that the existence, without damping, of such orbits in a substance would give it neither diamagnetic nor paramagnetic properties. The diamagnetic effects arising from change of velocities produced by the magnetic intensity are just balanced by the paramagnetic effects due to the change of orbital orientation. With suitable dissipation 8 Phil. Mag. (6), 6, 1903, p. 673.