The following figure shows the same facts in a different way. The ordinates are specific susceptibility. Alpha iron, beta iron, gamma iron, and delta iron are limited by the temperatures 756°, 920°, 1280° C. When iron ceases to be strongly magnetic at 756° and its temperature is further raised, the susceptibility falls rapidly, as the curve shows. In the gamma state the decrease of susceptibility is very gradual. At 1280° C. there is a sudden rise, after which again a gentle decline occurs.

So far we have considered the connection between magnetization intensity and temperature. Let us give attention to the curve showing change of intensity with field strength. The

ordinates here represent the former quantity and the abscissæ the latter. When the temperature of the specimen of iron is even as near the Curie point as 740.5° there is considerable rise in intensity of magnetization as the field strength increases. An elevation of temperature of a few degrees brings down this increase to a very modest amount. Compare the intensities for H=320. An increase of 3.7° from 740.5° to 744.2° C. reduces the intensity to about half its value at the lower temperature, while the intensity for 820° is so small that it cannot be represented on the diagram. Notice further that the curve for 740.5° becomes a straight line for 749.9° and higher temperatures.

Curie pointed out the similarity in the form of the curves connecting, on the one hand, the density and temperature of a gas near the critical state and, on the other, the intensity of magnetism and temperature of iron near the Curie point. This analogy has been of use both in suggesting methods of expressing results and also in pointing to explanations of phenomena.

So far you must agree with me that I have failed to justify the title of this lecture as "Modern Theories of Magnetism." No theories, but only facts, obtained by experiment, have been presented.

In 1820, less than a month after Arago, before an audience of the French Academy including Laplace, Biot, and Ampère, had demonstrated Oersted's experiment proving an electric current to produce magnetic effects, one of that audience, Ampère, made the suggestion that magnetism might be due to currents

This theory in

of electricity circulating within the magnet. modern garb holds the field to-day. When it became accepted that the atom consists of electrons revolving about or in a charge of positive electricity it was very easy to make the guess that the cause of magnetism was to be sought in the motion of these electrons. They explain so much,-the conduction of both heat and electricity, the Zeeman effect, kathode rays, radioactivity,— that they tempted the theorist to impose one additional burden upon them, that is, the phenomena of magnetism. The first attempts were, however, not successful. Both Sir J. J. Thomson, in England, and W. Voigt, in Germany, discussed at length the motion of these negatively-charged electrons without finding an explanation for the facts of magnetism. It remained for a Frenchman, Langevin, to find the clue. In 1905, ten years after Curie's work appeared, he made public his solution of the problem of diamagnetic and paramagnetic substances.

It may perhaps be well for us to recognize how complicated the problem of magnetism is in order that too much may not be expected at first of any explanation. I quote here from G. A. Schott 1:

"1. Effects due to the mutual interactions of the molecules of the substance; these are usually taken to include hysteresis and coercive force, and the numerous interactions between strain and magnetism.

"2. Effects due to the actions between the atoms of a molecule. The smallness of the magnetism of oxides and salts of iron and cobalt in proportion to the amounts of iron or cobalt contained in them is an effect of this kind.

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3. Effects due to the constitution of the atom itself. The fact that the amalgams of iron and cobalt are as strongly magnetic in proportion to their concentration as the pure metals, coupled with the usual supposition, made on chemical grounds, that the molecule of a metal is monatomic, can hardly be explained except by supposing that magnetism is, in the last resort, an atomic property, and that the largeness of the magnetism of iron and its congeners is due to some peculiarity of atomic structure. This conclusion is supported by the experiments of St. Meyer and others, from which it results that atomic magnetism is a periodic function of the atomic weight, and is in some very close connection with the atomic volume."

As specific instances of phenomena in magnetism difficult to explain let these suffice:

1. The formation of Heusler's ferromagnetic alloys from copper, manganese, and aluminum, no one of which by itself is usually more than slightly magnetic, either positively or negatively.

2. The existence of manganese as paramagnetic or ferromagnetic according to past treatment.

3. The change of tin from a diamagnetic to a paramagnetic When gray tin, which is diamagnetic, is heated its negative specific susceptibility grows greater and at 35° C. reaches zero. It continues to rise with the temperature up to 50°. A further increase of temperature fails to affect it until the tin melts at 232°, when it suddenly drops to a value below zero and

'Phil. Mag., Ser. 6, vol. xv, p. 172 (1908).

the liquid metal, a diamagnetic substance, retains this negative susceptibility as it rises still further in temperature.

4. The formation of iodide of mercury and potassium, a paramagnetic substance from three diamagnetic elements.

Surely no theory could hope to do more than explain the salient and general features of so complex a group of phenomena as magnetism presents to us.

LANGEVIN'S THEORY.

Every atom, according to current views of the constitution of matter, has a number of electrons revolving in closed orbits. within it or about its centre. All electrons have equal charges of negative electricity. Our fellow-countryman, Henry A. Rowland, proved that a charge of electricity in motion produces magnetic effects just as a current does. Accordingly each electron moving in its orbit is equivalent to a current of electricity flowing in the same orbit. One face of the orbit is a magnetic south pole, the other a north pole, and magnetic lines of force surround the moving electron.

Let us fix our mental gaze on one such electron revolving in a circular path. Let a magnetic field be set up perpendicular to the plane of the orbit,-that is, so that a magnetic pole would be urged by the field to move at right angles to the plane of the orbit. There will be an interaction between the field of force and the electron in motion, with the result that the electron continues to revolve at the same distance from the centre of its path, but makes a revolution in a different time. As any change in the velocity of the electron will cause a change in the electric current to which it is equivalent, and as a change in the current will carry with it a change in the magnetic effect, it follows that a change in the magnetic moment of the orbit follows upon the arrival of the external magnetic field which affects the electron. Calculation shows that no matter in which direction the electron is revolving, the change in magnetic moment of the orbit is always in the same direction. For example, let the external field be that existing between the north and the south pole of a horseshoe magnet. The effect of this field upon an electron revolving in an orbit whose plane is at right angles to the line joining the poles of the magnet is to cause the orbit to strive to develop a north pole on its side toward the north pole of the magnet and a south VOL. CLXXX, No. 1076-14

pole on the other side. This kind of induction effect is characteristic of diamagnetic substances. Even if the electron is at rest when the magnetic field is applied, the result is about the same, for Lorentz has shown that the electron will be made to rotate about an axis parallel to the direction of the field and in such a direction as to make its lines of force oppose those of the external field.

Perhaps enough has been said to show how closely the modern theory is in fundamental agreement with the ideas of Ampère and of Weber. In 1896 Zeeman, in Holland, discovered that a yellow sodium flame put in a strong magnetic field suffers a change in the character of the light which it emits. As the motion of the electrons is regarded as the source of radiation, it will be noted that the Zeeman effect is allied with the diamagnetic effect of a magnetic field outlined above. Since the Zeeman effect is found to occur in nearly all spectral lines of nearly all substances which have been examined, we are led to think that the diamagnetic effect of a magnetic field is very general; that it occurs in substances classed as paramagnetic or ferromagnetic as well as in diamagnetic bodies. Let us see how Langevin accounts for this.

Each atom has several electrons revolving in orbits. These orbits may be in distinct planes or may differ in other ways. The total magnetic moment of the atom will be found by summing up, with proper regard to direction and magnitude, the magnetic moments of the separate orbits. The result of this integration must give one of two results, either zero or some significant quantity. Langevin investigated the effect of the external magnetic field on an atom having no initial resultant magnetic moment. As the magnetic effects of the various electrons neutralized each other the atom as a whole would not rotate when an external field was applied, as it would tend to rotate were there a single orbit, in an endeavor to set the axis of the orbit in coincidence with the direction of the magnetic field. Even if the orbits were not perpendicular to the direction of the field the general effect would be unaltered. Although the total magnetic moment of the atom was zero before the imposition of the magnetic field, this does not cause to follow that the total change in the magnetic moment would be zero. On the contrary, the changes in the various electronic circuits are in the same