250 MAGNETISM small number of principles drawn from observation. He enters more fully than Poisson had done into the specifica tion of magnetic distribution. He gives simple synthetic solutions of the induction problem for spheres and ellipsoids in a uniform field. He gives for the first time with full generality the theory of induction in seolotropic media, and shows that Poisson s theory thus fully developed leads to all the laws of paramagnetic and diamagnetic action discovered by Faraday, and also to the laws of magnecrystallic action discovered by Pliicker and Faraday. The value of his Pliicker. theory was fully recognized by Pliicker, 1 and apparently also by Faraday ; indeed one of its ablest expositors was Beer. Beer 2 the friend and coadjutor of Pliicker. The experi menters who followed these -masters were less intelligent, and the theory of Thomson was for a number of years mis understood or neglected, the result being much fruitless discussion in which the true issues were often confused. Of late the theory has obtained wide currency and the adhesion of every physicist worthy of the name. Quite recently Thomson s theory has been further developed in Helm- an interesting paper by Helmholtz, 3 chiefly with a view to holtz. j(; g application to the phenomena of dielectric polarization. For the benefit of the mathematical reader we append a list of the more important papers on the mathematical theory of magnet ism that have appeared recently, and are not quoted above : Plana, " Memoire sur la theorie du magnetisme," Ast. Naefi., xxxix., 1851 ; F. Neumann, Vorlesungen ilber die Thcoric dcs Magnetismus, delivered 1857, edited by C. Neumann, 1881 ; Eiemann, Schwerc, Electricitdt, iind Magnetismus, lectures de livered in 1861, edited by Hatteudorf, 1876; Lamont, " Beitrag _ zu einer mathematischen Theorie des Magnetismus," Sitzber. d. Bayer. Akad., 1862 ; L Weber, Zur Theorie dcr Magnetischen Induction, Kiel, 1877, see Wied. Beibl., 1878 ; Rowland, Silli- man s Jour., 1879 (calculation of couple on a body suspended in a heterogeneous magnetic . field) ; Boltzmann, " Magnetisirung eines Eisenringes," Wied. Beibl., 1879; Id., " TJeber die auf Diamagnete wirkende Kraft," Wien. Bcr., 1879 ; Riecke, Wicd. Ann., 1881 (approximative solutions of the problem of magnetic induction). INDUCTION IN STRONGLY MAGNETIC BODIES. Experi- The earliest experiments bearing on the mathematical ments of theory of magnetic induction are those of Barlow 4 and Barlow Christie, who determined the deflexion of a compass needle Christie P^ ace( l in various positions relatively to splieres of cast iron inductively magnetized by the earth s force. They found that the deflexion a of the compass could be repre sented by tana = Asin$cos$sin</r 3 , wherefl is the angle between the line of dip and the line joining the centres of the sphere and compass, and < the angle between the plane of these two lines and the plane of the magnetic meridian. It was also found that the deflexion produced by a hollow sphere was as great as that produced by a solid sphere so long as the thickness of the former was not less than the Y^th of its radius. Magnetic All these results of Barlow and Christie are in agreement screens, with the theory of Poisson. 5 Another consequence of great practical importance follows from the mathematical theory, viz,, that inside a hollow iron sphere of any considerable thickness the magnetic force is very small in comparison with the external inducing force. Sir William Thomson takes advantage of this principle to render his marine galvanometers independent of external magnetic force by surrounding them with a tube of soft iron. * Along with the experiments of Barlow we may rank 1 See Phil. Trans., 1858, p. 587. 2 See his Einleitung in die Electrostatik, die Lchre vom Magnetismus, und die Electrodynamik, published after the death of its accomplished author, under the editorship of Pliicker. This is one of the best works on the subject. 3 Monatsber. d. Ber. Akad., 1881. 4 Barlow, An Essay on Magnetic Attractions, London, 1820. 5 See Poisson s first memoir, or Maxwell, El. and Mag. , vol. ii. 433. those of Pliicker 6 and Dronke 7 as affording us the means Piucker of testing the general applicability of the mathematical and theory to the magnetization of soft iron. In Pliicker s Dronke> ! experiments an ellipsoid of soft iron was fixed in a gradu ated brass ring with its longest and shortest axes (a and c) in the plane of the ring. When the ring was suspended with the longest axis a vertical in the nearly uniform field between the two flat vertical faces of the poles of an electro magnet, the mean axis b set itself parallel to the horizontal line of force ; as the point of suspension was moved along the circumference of the ring a point was reached at which the plane of b and a ceased to set parallel to the lines of force, and the plane of a and c began to do so ; to, the number of degrees between this point and the end of the axis a, was observed. The times of vibration, T a and T,,. of the ellipsoid, when suspended so that a and c were vertical. were then observed. By the theory we ought to have tan 2 * = T=(6 2 + c 2 )/T>( 2 + Z> 2 ) . The value of w calculated by means of T,. and T a from this formula was 30 13 ; the value observed was about 29. The relation connecting T n , Tj,, T c according to the theory is (a 2 + Z> 2 )/T e 2 + (6 2 + c 2 )/Tf - (c 2 + a 2 )/T| = ; and the observed values of T a , T 6 , T c did, in fact, satisfy this equation very nearly. Dronke s experiments on ellip soids of iron and nickel were of a similar character. Deviation of the Compass. One of the earliest and First ol; certainly the most important of the applications of the serva- mathematical theory of magnetic induction was the discus- *j ons of . sion of the deviation of the compass caused by the magnet- a ti 0n . ism of the iron in ships. This disturbance seems to have been first noticed by Wales the astronomer, who accom panied Cook on his voyages of discovery (1772 to 1779). The same thing was noticed during the voyage of D Entre- casteaux in search of La Perouse; .and Beautemps-Beaupre, who accompanied him, calls attention to the errors thence arising in the surveying of coasts by means of the compass. Flinders, 8 using the numerous observations made by Wales and by himself, endeavoured without success to construct empirical formula} for correcting the errors of the compass. He also attempted to correct the errors partially by means of a vertical bar of soft iron placed near the binnacle. Barlow 9 and Scoresby 10 also occupied themselves with the problem. The unusually great deviations observed during the Arctic voyage of the "Isabella " and " Alexander" in 1818 attracted the attention of Poisson, and gave rise to his memoir on the subject already alluded to. Important as the matter then appeared, it became still more so after the introduction of iron ships. Investigations both theoretical and experimental were made in England by Johnson, 11 Airy, 12 Evans, 13 Smith, 13 &c. It is to Smith that the mathematical theory as it now stands is mainly due. The cause of the deviation of the compass is twofold ; Causes it arises partly from the permanent magnetism of the ship, devia- partly from the temporary or induced magnetism. The tlou> permanent magnetism of the ship is acquired for the most part during the process of building. The earth s force acts on the iron, and the constant jarring in the process of con struction enables it to induce a considerable permanent magnetization, which the ship carries with her to sea. The quantity and distribution of this magnetism will depend greatly on the build of the ship (whether of wood or of 7 Pogg. Ann., 1862. 9 Ib., 1831. 11 II}., 1836. 6 Phil. Trans., 1858, p. 555. 8 Phil. Trans., 1805. 10 Ib., 1819 and 1832, &c. 12 P>., 1839, &c. 13 See> Admiralty Manual for the Deviation of the Compass, 4th ed,, 1874 ; also a very interesting obituary notice of Smith by Sir W.
Thomson, Proc. Roy. Soc. Lond., 187 4.