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340
[STRESS AND MAGNETIZATION
MAGNETISM


magnetized under very heavy loads, the wire was indeed found to undergo slight contraction. Honda subjected tubes of iron, steel and nickel to the simultaneous action of circular and longitudinal fields, and observed the changes of length when one of the fields was varied while the other remained constant at different successive values from zero upwards. The experimental results agreed in sign though not in magnitude with those calculated from the changes produced by simple longitudinal magnetization, discrepancies being partly accounted for by the fact that the metals employed were not actually isotropic. Heusler's alloy has been tested for change of length by L. Austin, who found continuous elongation with increasing fields, the curves obtained bearing some resemblance to curves of magnetization.

As regards the effect of magnetization upon volume there are some discrepancies. Nagaoka and Honda, who employed a fluid dilatometer, found that the volume of several specimens of iron, steel and nickel was always slightly increased, no diminution being indicated in low fields; cobalt, on the other hand, was diminished in volume, and the amount of the change, though still very small, was greater than that shown by the other metals. Various nickel-steels all expanded under magnetization, the increase being generally considerable and proportional to the field; in the case of an alloy containing 29% of nickel the change was nearly 40 times greater than in soft iron. C. G. Knott, who made an exhaustive series of experiments upon various metals in the form of tubes, concluded that in iron there was always a slight increase of volume, and in nickel and cobalt a slight decrease. It is uncertain how far these various results are dependent upon the physical condition of the metals.

Attempts have been made to explain magnetic deformation by various theories of magnetic stress,1 notably that elaborated by G. ~R. Kirchhoff (Wied. Ann., 1885, 24, 52, and 1885, 25, 601), but so far with imperfect success. E. Taylor jones showed in 1897 that only a small proportion of the contraction exhibited by a nickel wire when magnetized could be accounted for on Kirchhoff's theory from the observed effects of pulling stress upon magnetization; and in a more extended series of observations Na aoka and Honda found wide quantitative divergences between the results of experiment and calculation, though in nearly all cases there was agreement as to quality. They consider, however, that Kirchhof'f's theory, which assumes change of magnetization to be simply proportional to strain, is still in its infancy, the present stage olp its evolution being perhaps comparable with that reached by the theory of magnetization at the time when the ratio I /H was supposed to be constant. In the light of future researches further development may reasonably be expected.

It has been suggested 2 that an iron rod under magnetization may be in the same condition as if under a mechanically applied longitudinal stress tending to shorten the iron. If a long magnetized rod is divided transversely and the cut ends placed nearly in contact, the magnetic force inside the narrow air gap will be B=H+41rI. The force actin on the magnetism of one of the faces, and urging this face towarcis the other, will be less than B by 21rl, the part of the total force due to the first face itself; hence the force per unit of area with which the faces would press against each other if in Contact is

P = (B -21rI)l =2-fri'-I-HI = (B2-H?) =/81r. The width of the gap may be diminished until it is no greater than the distance between two neighbouring molecules, when it will cease to be distinguishable, but, assuming the molecular theory of magnetism to be true, the above statement will still hold good for the intermolecular gap. The same pressure P will be exerted across any imaginary section of a magnetized rod, the stress being sustained by the intermolecular springs, whatever their physical nature may be, to which the elasticity of the metal is due. The whole of the rod will therefore be subject to a compressive longitudinal stress P, the associated contraction R, expressed as a fraction of the original length, being

R = P/M = (B2-HZ)/81rM,

where M is Y0ung's modulus. This was found to be insufficient to account for the whole of the retraction exhibited by iron in strong fields, but it was pointed out by L. T. M0re3 that R ought to be 1 For a discussion of theories of magnetic stress, with copious references, see Nagaoka, Rap. du Congrés International de Physique (Paris, 1900), ii. 545. Also Nagaoka and jones, Phil. Mag., 1896, 41, 454-

1 S. Bidwell, Phil. Trans., 1888, 179a, 321. 3 Phil. Mag., 1895, 40, 345.

regarded as a “ correction ” to be applied to the results of experiments on magnetic change of length, the magnetic stress being no less an extraneous effect than a stress applied mechanically. Those who support this View generally speak of the stress as “ Maxwell's stress, ” and assume its value to be B2/8-/r. The stress in question seems, however, to be quite unconnected with the “stress in the medium " contemplated by Maxwell, and its value is not exactly B2/81r except in the particular case of a permanent ring magnet, when H=O. Further, Maxwell's stress is a tension along the lines of force, and is equal to B2/8-rr only when B=H, and there is no magnetization! Some writers have indeed contended that the stress in magnetized iron is not compressive, but tensile, even when, as in the case of a ring-magnet, there are no free ends. The point at issue has an important bearing upon the possible correlation of magnetic phenomena, but, though it has given rise to much discussion, no accepted conclusion has yet been reached.5 7. EFFECTS or MECHANICAL STRESS UPON MAoN1:T1zAT10N The effects of traction, compression and torsion in relation to magnetism have formed the subject of much patient investigation, especially at the hands of ]. A. Ewing, C. G. Knott and the indefatigable physicists of Tokyo University. The results of their experiments embrace a multiplicity of details of which it is impossible to give an adequate summary. Only a few of the most important can be mentioned here; the reader who wishes for fuller information should consult the original papers.”

It was first discovered by E. Villari in 1868 that the magnetic susceptibility of an iron wire was increased by stretching when the magnetization was below a certain value, but diminished when that value was exceeded; this phenomenon has been termed by Lord Kelvin, who discovered it independently, the “Villari reversal, ” the value of the magnetization for which stretching by a given load produces no effect being known as the “ Villari critical point” for that load. The Villari critical point for a given sample of iron is reached with a smaller magnetizing force when the stretching load is great than when it is small; the reversal also occurs with smaller loads and with weaker fields when the iron is soft than when it is hard. The following table shows the values of I and H corresponding to the Villari critical point in some of Ewing's experiments if

Soft Iron. Hard Iron.

H.

34

32

29

25

2-15 1220 7-3 27-6 1180

4-3 1040- 4-3 32-2 1150

8-6 840 3-4 37-3 1110

Kilos per sq. mm. I. H. Kilos per sq. mm. I. 12-9 690 3-05 42-5 1020

The effects of pulling stress may be observed either when the wire is stretched by a constant load while the magnetizing force is varied, or when the magnetizing force is kept constant while the load is varied. In the latter case the first application of stress is always attended by an increase—often a very great onwof the magnetization, whether the field is weak or strong, but after a load has been put on and taken off several times the changes of magnetization become cyclic. From experiments of both classes it appears that for a given field there is a certain value of the load for which the magnetization is a maximum, the maximum occuring at a smaller load the stronger the field. In very strong fields the maximum may even disappear altogether, the effect of the smallest stress 4 ]. C. Maxwell, Treatise, § 643.

5 See correspondence in Nature, 1896, 53, pp. 269, 316, 365, 462,533; 1906, 74, pp. 317, 539; B. B. Brackett, loc. cit., quotes the opinion of H. A. Rowland in support of compressive stress. 6 J. A. Ewing, Phil. Trans., 1885, 176, 580; 1888, 179, 333; Magnetic Induction, 1900, ch. ix.; ]. A. Ewing and G. C. Cowan, Phil. Trans., 1888, 179a,325; C. G. Knott, Trans. Roy. Soc. Ed., 1882-1883, 32, 193; 1889, 35, 377; 1891, 36, 485; Proc. Roy. Soc. Ed., 1899, 586; H. Nagaoka, Phil. Mag., 1889, 27, 117; 1890, 29,123;H. Nagaoka and K. Honda, Journ. Coll. Sci. Tokyo, 1900, 13, 263; 1902, 16, art. 8; Phil. Mag., 1898, 46, 261; 1902, 4, 45; K. Honda and S. Shimizu, Ann. d. Phys., 1904, 14, 791; Tokyo Physica-Math. Soc. Rep., 1904, 2, No. 13; K. Honda and T. Terada, Journ. Coll. Sci. Tokyo, 1906, 21, art. 4.,