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curve can not be explained by the presence of iron, as the positive susceptibility of the iron would become less with temperature increase.
We come now to the second case, in which the magneton has a true axis of figure and an essentially permanent angular momentum about this axis, and therefore a magnetic moment in the direction of this axis, un
Fig. 6. changeable by collisions. On account of this permanent magnetic moment and angular
shown in Fig. 7. Thus while diamagnetism momentum, paramagnetism results very much
may exist without paramagnetism, paramagas in the theory of Voigt already presented;
netism is always accompanied by diamagand on account of the slight diminution of this angular momentum in the magnetic field and on account of the rotation of the magneton about the other axes brought about or modified by the thermal agitation in accordance with the law of equipartition, diamagnetism results and is superposed upon the paramagnetism.
This diamagnetism does not appear in Langevin's theory, because instead of a permanently rotating magneton he assumed a permanent magnet without angular momentum about the axis except as produced by thermal collisions. Langevin, however, assumed that Weber's diamagnetism was super
Fig. 7. posed upon the paramagnetism, and this corresponds in part to the diamagnetism of netism, as on all other theories. In weak Gans's theory.
fields and at low temperatures the paramagReturning to the results of Gans's statis- netism may prevail; but as the temperature tical treatment for the case of the magneton and field strength increase it goes over into in permanent rotation about a unique axis, diamagnetism. we find that the susceptibility is a function A transition from paramagnetic to diamagof both field strength and temperature. It netic susceptibility, whatever may be the ex
planation, has been observed by Weber and tures when equipartition exists, and the rigorOverbeck13 in the case of copper-zinc alloys, ous theories agree well with experimental reand by Honda in the case of indium. Weber sults obtained at low temperatures, where and Overbeck, who have taken great precau
Langevin's theory completely fails. The next tions and believe their alloys free from iron, step should be the rigorous application of the have called the phenomenon metamagnetism. quantum theory to the case in which the The downward trend of paramagnetic sus- magneton has a permanent angular momenceptibility with increase of field strength is tum,, with gyroscopic properties, as required apparent in some of the curves obtained by by the electron theory. Honda.
According to experiment hydrogen and For weak fields at low temperatures, but
helium are diamagnetic although according to with H/T finite, Gans's formula approaches
Bohr's models their molecules have strong that of Langevin as a limit. Here the para
magnetic moments. This is apparently con: magnetic rotations are prominent in compari- sistent with the theory of Gans, but inconson with diamagnetic thermal rotations about sistent with the theory of Weber and Langethe other axes. As the field intensity ap
vin. Honda and Okubo,20 in a part of a paper proaches zero with finite values of the tem- dealing more generally with the kinetic theory perature the susceptibility approaches a limit of magnetism, have proposed the following exwhich is the sum of two terms, a paramagnetic planation of this diamagnetic effect. Suppose term identical with that of Langevin and a the magnetic axis to be rotating about one of diamagnetic term independent of the tem- the other axes in a plane parallel to the mag. perature like that of Weber.
netic intensity. On account of the presence The theory of Gans thus covers a wide of the field, the velocity of rotation, which range of cases, but so far has been applied in
would be uniform without the field, is now detail to but few. By taking account of the variable, the motion being more rapid when molecular field, and by applying the quantum the moment points in the direction of the field theory, although not in the most thorough than when it points the other way. Hence way, he has more recently extended his theory the time mean of its directions is opposite to to cover more accurately the paramagnetism
that of the field and the mean effect is diaexhibited by dense bodies and at low tempera
magnetic. If the magnetic axis is rotating in tures. 14 In a similar way the quantum theory a plane not parallel to the direction of the has been set into the theory of Langevin by field, we must resolve the effect in the diOesterhuis15 and Keesom16; and it has been
rection of the field. Doing this for all the thoroughly applied, for the case of rotation elementary magnets, originally pointing uniwith one degree of freedom, by Weyssenhoff,17 formly in all directions, we get a resultant and for the case of rotation with two degrees
diamagnetic effect. This, however, is only a of freedom by Reichels and by Rotzajn,19 to
part of the total effect found in Langevin's the system of elementary magnets, without
theory to be paramagnetic, though it is only permanent angular momentum, assumed by
implicit in his treatment, unless we assume Langevin. These theories are thus not elec- permanent rotations, independent of the temtron theories, like that of Gans. They reduce
perature, about an axis normal to the magto the theory of Langevin at high tempera
netic axis. This assumption they have made.
From what we have seen there seems to be 13 Ann. der Phys. (4), 46, 1915, p. 677. 14 Ann. der Phys. (4), 50, 1916, p. 163.
no way to account satisfactorily for para16 Phys. Zeit., 14, 1913, p. 862
magnetism and ferromagnetism except on the 16 Phys. Zeit., 15, 1914, p. 8.
assumption of an elementary magnet which 17 Ann. der Phys. (4), 51, 1916, p. 285,
is a permanent electrical whirl, as Ampère 18 Ann. der Phys. (4), 54, 1917, p. 401.
assumed; which has also mass, as Weber as19 Ann, der Phys. (4), 57, 1918, p. 81.
20 Phys. Rev., 13, 1919, p. 6.
sumed; and which has therefore the dynam- mind of Maxwell in 1861, and has occurred to ical properties of a gyroscope. It will now be a number of others since. shown how these gyroscopic properties have In an ordinary ferromagnetic. body in the made possible a complete and direct demon- usual state with which we are familiar only stration of the correctness of this theory. a slight change of orientation can occur on
accunt of the forces due to adjacent molecules, which perform the function of the springs in the case of our gyroscope. The rotation causes each molecule to contribute a minute angular momentum, and thus also a minute magnetic moment, parallel to the axis of impressed rotation; and thus the body, whose magnetons originally pointed in all directions equally, becomes magnetized along the axis of impressed rotation. If the revolving electrons, or rotating magnetons, are all positive, the body will thus become magnetized in the
direction in which it would be magnetized by FIG. 8.
an electric current flowing around it in the
direction of the angular velocity imparted to In Fig. 8 is shown a gyroscope whose wheel, it. If they are all negative, or if the action pivoted in a frame, can be rotated rapidly on the negative magnetons is preponderant, about its axis A. Except for the action of it will be magnetized in the opposite direction. two springs, the frame and the axis A are If R denotes the ratio of the angular free to move in altitude about a horizontal momentum of a magneton, or an electron axis B, making an angle with the vertical C; orbit, to its magnetic moment, it can readily and the axis B and the whole instrument can be shown that rotating a magneton or electron be rotated about the vertical axis C. If the orbit about any axis with an impressed wheel is spun about the axis A, and the in- velocity N revolutions per second, is equivastrument then rotated about the vertical C, lent to placing it in a magnetic field with the wheel tips up or down so as to make the intensity H directed along this axis such that direction of its rotation coincide more nearly
H = R2TN. with the direction of the impressed rotation If the electric density is proportional to about the vertical axis C. If it were not for the mass density throughout the volume of the springs, the wheel would tip until the axes the magneton this ratio is easily shown to be A and C became coincident. The greater the R=2m/e; so that in this case rotary speed about the vertical the greater is
H = 47" N. the tip of the wheel. When the wheel's speed
(16) about the axis A is zero, no tip occurs.
If all the magnetons in a body are alike, Now if the magnetic molecule is a gyro- therefore, rotating it at an angular velocity scope, it will behave like this wheel. If the of N r.p.s. will produce the same intensity of body of which it is a part is set into rotation magnetization in it as placing it in a field of about any axis, the molecule, or magneton, strength 45 (m/e) N gausses. will change its orientation in such a way as to For negative electrons of the ordinary type make its direction of rotation coincide more 47(m/e) = - 7.1 x 10-7 e.m.u. . according to nearly with the direction of the impressed well-known experiments. Hence, if orbital rotation; the coincidence will finally become motions of these electrons are responsible for exact if this is not prevented by the action of the magnetism of ferromagnetic substances, the rest of the body. This idea was in the rotating them at a velocity of N revolutions
per second should magnetize them as would a field of intensity H = - 7.1 x 10-7N gauss.
(17) Now in two investigations on cold-rolled steel by a method of electromagnetic induction, a third investigation principally on steel, nickel and cobalt by a magnetometer method, and a fourth investigation on steel, soft iron, cobalt, and Heusler alloy by another magnetometer method, Mrs. Barnett and I have found the above theory verified, except that in place of the number 7.1 we find smaller numbers; in the best work, which appears to be free from any serious systematic error, we find instead of 7.1 numbers about one half as great and even smaller.21 This work, however, , is still in progress.
If these results are correct, we seem to be driven to one of two conclusions: Either negative electrons or magnetons with a value of m/e or R for the motions involved different from that ordinarily accepted are responsible for magnetism; or positive electrons or magnetons, whose rotation we have seen must produce an opposite effect, are also involved. It does not seem impossible that a ring or other type of negative magneton, with R different for the permanent rotary motion from the value obtained from cathode ray experiments and otherwise, should be involved; but the presence of positive electron orbits, or rotating positive magnetons, is also possible, especially in view of the known expulsion of a particles with great velocities from the radioactive substances. Chemical evidence is often quoted in favor of the idea that superficial negative electrons alone are responsible for magnetism; but I do not think this evidence conclusive.
Not long after our first conclusive experiments on magnetization by rotation were communicated to this society, experiments on the converse effect, viz., rotation by magnetization, first suggested by Richardson, were performed by Einstein and deHaas.22 Mag
21 Phys. Rev., 6, 1915, p. 239; 10, 1917, p. 7; Proc. American Phys. Soc. for December, 1920; Proc. Phil. Soc. of Washington for October 9, 1920.
22 Verh. d. D. Phys. Ges., 17, 1915, p. 152.
netizing a bar of iron, in turning the magnetons about until they all rotate in the same direction, produces angular momentum in this direction which must be compensated by an angular momentum within the molecules themselves, or in the bar, or in the magnetizing solenoid. If we assume that the reactions all take place upon the bar we can calculate 47(m/e) from the measurable angular momentum communicated to it when magnetized to a given intensity on the assumption that all the magnetons are alike. The result published by Einstein and deHaas agreed closely with the value to be expected on the hypothesis that only the common type of negative electron is involved; but the sign of the effect was not determined with certainty till much later, and errors in the value of the assumed intensity of magnetization and in the experiments themselves undoubtedly exist. The experiments have been repeated with great improvements by Emil Beck,23 and experiments on th subject but by a different method had already been made by J. Q. Stewart;24 both these investigations, on the basis of a single kind of electron and on the assumption made above with reference to the seat of the reaction to the electron momentum, give values of 47 (m/e) for iron and nickel similar to those which Mrs. Barnett and I have found by the method of magnetization by rotation, into the theory of which no assumptions appear to enter except such as can be justified completely.
If a magneton is sufficiently free it will, as stated above, when rotated about a given axis align itself with its axis completely parallel to the axis of impressed rotation. If in the unit volume there are N magnetons all alike, each with the moment of inertia C and initial angular velocity U about the magnetic axis, and if the effects of collisions and the demagnetizing field are negligible, the intensity of magnetization will be
(18) 2m The first term is independent of s, which is a measure of the intrinsic intensity of rota
23 Ann. der Phys. (4), 60, 1919, p. 109. 24 Phys. Rev. (2), 11, 1918, p. 100.
tion, just as, in Voigt's equation, the first term in the Cosmos Club, Washington, D. C., on is independent of H. The orientation is here the afternoon and evening of Sunday, April produced by the rotation, but only the time 24. The following paragraphs summarize taken to reach a steady state is affected by its items of business that were transacted. The magnitude. The second term, here added to personnel of the executive committee is as folthe first, corresponds to Voigt's diamagnetic lows: term. Here we have, except for the small sec- Simon Flexner (chairman), J. McK. Catond term, saturation for even very small values tell, H. L. Fairchild, L. O. Howard, W. J. of Ω.
Humphreys, B. E. Livingston (permanent sec· If collisions are not absent, or if the mag- retary of the association), D. T. MacDougal netic fields of adjacent molecules and the (general secretary of the association), E. H. demagnetizing field become appreciable, the Moore (president of the association), A. A. intensity of magnetization will not reach sat- Noyes, Herbert Osborn, H. B. Ward. All of uration; but it will increase with 1, being the members were present at this meeting, exgreater for a given value of the greater the cepting Messrs. Flexner, Moore, and Noyes. mean interval between collisions, the less their The meeting was called at 4.00 P.M. violence, and the weaker the field.
After the minutes of the last meeting of this It was suggested by Schuster in 1912 and by committee (Chicago, Dec. 29, 1920) had been Einstein and deHaas in 1915, and earlier by read and approved it was voted that the next myself, that the behavior of a magnetic mole- meeting of the executive committee “shall cule as a gyroscope might account for cos- occur in New York City on the first Sunday mical magnetism, as the direction of the mag- after November 1 that shall be convenient to netization of the earth and sun bear to the a majority of the members,” the exact date direction of the rotation the relation required to be arranged by the permanent secretary. by the theory. If the theory is quantitively It was voted that the action thus far taken sufficient, the interior of the earth and sun, as by the American Association committee on pointed out years ago, must be in a very conservation, be approved and that that comdifferent state from that of bodies with which
mittee be authorized to proceed with its plans. we are familiar. If m/e reaches enormous (The committee on conservation consists of values for magnetons within the earth and
J. C. Merriam (chairman), H. S. Graves, Barsun, which is not probable, or if the magneton
rington Moore, V. E. Shelford and Isaiah density is sufficiently high and the effects of
Bowman. It held a meeting in New York collisions and the molecular and demagnetizing
City on April 9, jointly with corresponding fields at the same time sufficiently small, it
committees of the National Academy of Sciis possible that even the small angular veloci
ences and the National Research Council, and ties of the earth and sun may be sufficient to
it was recommended that these three commitproduce the observed magnetizations.25
tees form a continuing joint committee on S. J. BARNETT
national conservation, representing the three DEPARTMENT OF TERRESTRIAL MAGNETISM,
organizations just mentioned, and that this CARNEGIE INSTITUTION
joint committee be authorized to set up an THE AMERICAN ASSOCIATION FOR executive and secretarial agency for the active THE ADVANCEMENT OF SCIENCE prosecution of its work.) SPRING MEETING OF THE EXECUTIVE
The executive committee ratified the action COMMITTEE
taken by the committee on honorary life memThe executive committee of the council of berships through the Jane M. Smith fund, in the association held its regular spring meeting placing the names of the distinguished sci25 See papers by Professor S. Chapman and by
entists, J. E. Clark and J. N. Stockwell, remyself in Nature, Nov. 25, 1920, and March 3, cently deceased, on the list of honorary life 1921.
members of the Association. (Both were ac