MAGNETISM 265 It is convenient, following the analogy of physical optics, to divide magnetically teolotropic bodies into (a) "uniaxal" bodies, i.e., those that are symmetrical about one principal axis of magnetic susceptibility, or, in other words, have two of the principal coefficients of magnetic susceptibility equal ( Ko = K. S ) ; and (6) "biaxal" bodies, i.e., those that have the three principal susceptibilities unequal. Class (a) naturally divides itself into those in which the susceptibility parallel to the axis of symmetry is greater and those in which it is less than that in the plane perpen dicular to it. The former (where K 1 >K. 2 ) are said to be positive, the latter (KJ<KO) negative uniaxals. We have also to attend to the distinction which arises according as the mass of the crystal is paramagnetic or diamagnetic (KJ and K O both + , or both - ). We have then the follow ing experimental behaviour in uniaxal bodies : Sets the Axis of Symmetry Positive Negative Paramagnetic Diamagnetic i Paramagnetic | Diamagnetic Parallel to lines of force. Perpendicular to lines of force. Perpendicular to lilies of force. Parallel to lines of force. Faraday found for example that a crystal of bismuth suspended with its plane of smoothest cleavage vertical set with this plane perpendicular to the lines of force, but was indifferent when suspended with this plane horizontal. The axis of magnetic symmetry is therefore perpendicular to the plane of smoothest cleavage, and, since the substance is diamagnetic, it is a negative uniaxal. When suspended in any other way the crystal set so that the magnetic axis rested in a vertical plane through the direction of the lines of force. The difference between the behaviour of magnetic and diamagnetic uniaxals is beautifully illustrated by the behaviour of pure Iceland spar, which is a positive diamagnetic uniaxal, and sets the optic axis, which is the magnetic axis, equatorially ; when, however, as sometimes happens, the calcium is partly replaced by iron, its physical properties (optical included) being thereby unchanged, except that the mass of the crystal becomes magnetic, it sets the optic axis axial. 1 ttagne- All these cases are of course included in the single rule
- rystallic t na fc th e body sets the axis of greatest permeability parallel
to the lines of force. Since the setting of weakly magnetic seolotropic bodies depends merely on the differences between the principal magnetic susceptibilities, it follows that it is independent of the medium in which the body is placed, medium, f^is was established experimentally by Faraday, 2 who found the magnecrystallic couple exerted on a crystal of bismuth to be the same whether it was surrounded by air, by water, or by a saturated solution of protosulphate of iron. Pliicker gives the following list of uniaxal seolotropic bodies : MAGNETIC. iur- .oiindin Positive. Spathic iron ore. Scapolite. Green uranite. Ferruginous sulphate of mag nesia. Negative. Tourmaline. Beryl. Dioptase. Vesuvian. Sulphate of nickel. Ammouiochloride of copper. DlAMAC Positive. Calc-spar. Antimony. Molylxlate of lead. Arsenide of lead. Sulphate of potash. Nitrate of potash. NETIC. Negative. Bismuth. Arsenic. Ice. Zircon. Mellite. Cyanide of mercury. Arseniate of ammonium. 1 Tyndall and Knoblauch, Phil. Mag., 1850. 2 Exp. Res., 2498 sq., 1848. A later but much more extensive series of experiments led to the same result (Exp. Res., ser. xxx., 1855). The phenomena in the case of biaxal aeolotropics are naturally more complicated ; but they are all comprehended in the simple rule given above (page 244) that the axis of greatest paramagnetic or of least diamagnetic resultant susceptibility in the horizontal plane tends to set itself parallel to the lines of force, or, in the words of Faraday, Faraday s the body tends to set so as to allow the greatest number experi- of lines of magnetic induction to pass through it. In the mental azimuth just mentioned the body is in stable equilibrium, aw< in the perpendicular azimuth in unstable equilibrium. There are two axes of suspension in the plane of the axes Pliicker of least and greatest susceptibility, viz., the normals to the two ma g* circular sections of the ellipsoid K^- + * 2 y 2 + * 3 2 2 = constant, f etK such that the body behaves indifferently; these axes were as called by Pliicker the " magnetic axes" of the body. If we observe the times of vibration T 1? T 2 , T 3 of a sphere of the substance, when the axes K I( K.,, /c 3 respectively are vertical, then we have at once by the theory already given T! : T 2 : T 3 : : l/V/cT^": l/V^-^ : lM^~^; whence 1/TJ + 1/TJ = 1/T*, and tanco = T 3 /T 1 , o> being the angle between either magnetic axis and the axis of greatest magnetic susceptibility. These results were veri fied experimentally by Pliicker. 3 Maynecrystallic phenomena of the second kind were Pheno- looked for by Faraday very early in the history of the meim of subject, but at first he was unsuccessful in detecting them. 4 ^ j 1 * 1 lie seems, however, to have understood and clearly repre sented to himself in his own way their close connexion with the phenomena of the first kind, for he alluded to the subject more than once, and finally in the twenty-sixth series of his experimental researches, where he explained at length his magnetic theory, he showed that such an effect ought to exist, and actually succeeded in observing it in the case of a crystal of bismuth, which he found to be less repelled from places of stronger to places of weaker force when its First dis- axis was parallel to the lines of force than when it was OV( ^ ed perpendicular to them. He concluded that with Iceland J m ia spar the translational force ought to be greatest when the bismuth, axis is parallel to the lines of force, and least when it is perpendicular to them ; but his apparatus was not sufficiently delicate to show the effect. Unlike the magnecrystallic phenomena of the first kind, Pheno- those of the second kind depend on the difference between mena the susceptibilities of the body and of the surrounding 1C , medium. Faraday 5 demonstrated this conclusion experi- j cill(i mentally by covering crystals of the red prussiate of depend potash with a thin layer of wax to prevent dissolution, and on the immersing them in solution of sulphate of iron of various sur " strengths between the pointed poles of an electromagnet. rae( ii un In water the crystal was attracted to places of stronger force in all positions, in concentrated solution of sulphate of iron repelled in all positions, while in a solution of 14 or 15 volumes of the concentrated solution to 6 volumes of water it was attracted when the axis of symmetry was parallel to the lines of force and repelled about as strongly when the axis was perpendicular to them. Here then the crystal actually behaved paramagnetically in one direction and diamagnetically in the other. Similar results can be ob tained with Iceland spar in a mixture of alcohol and water. The prediction of the second class of magnecrystallic Faraday phenomena is one of the most extraordinary instances of and the theoretic insight which formed so large a part of the genius of Faraday. The laws of the phenomena of the first class might be regarded as merely a skilful classifica tion of observed facts, but the passage therefrom to the second class was a step of the first magnitude ; it constitutes in fact the root of the whole matter. To Sir William 3 Phil. Trans., 1858. 5 Exp. Res., ser. xxx., 1855. 4 Exp. Res., 2552, October 1848.
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