]ect of 1 ipera- 16. 6. The permeability of any metal depends on the quality of the metal, on the amount of permanent magnetization, on the total magnetization, and on the temperature. 7. The permeability of nickel and cobalt varies very much with temperature. In nickel for a moderate amount of magnetization the permeability increases with rise of temperature, but for high magnetization it decreases. This is very well shown in fig. 36, where the permeability curves for 15 C. and 220 C. intersect each other. In cobalt, on the other hand, the permeability appears to be always increased. The permeability of iron is not much affected by moderate changes of temperature. 8. The maximum of magnetization of iron and nickel decreases with rise of temperature, at least between 10 C. and 220 C., the first very slowly, the second very rapidly. At 220 C. the maximum for iron is $J = 17200 or | = 13 GO, and for nickel = 4900 or | = 380. The researches of Stoletow and Rowland have undoubtedly made clear the main phenomena of magnetic induction ; but in so doing they have raised a host of other questions which have not as yet been settled. There is no lack of recent work bearing on them, but it would be a difficult matter to give succinctly a complete account of the con clusions arrived at. The results of the different experi menters are not seldom contradictory, and the circumstances of experiment are often so complicated that criticism with the view of reconciling them seems hopeless in the meantime. While, therefore, we shall give a fairly complete list of the literature, the reader must not expect in this article an exhaustive analysis of the different memoirs that have recently appeared. Any remarks we shall make have chiefly for their object to call attention to the prominent questions that have been raised by the different workers. Riecke 1 made a series of experiments on ellipsoids of soft iron ; he expresses his results in terms of p the magnetization function for a sphere, and finds, as he ought to do, that, for a considerable range of values of the magnetizing force, p is approximately constant. 2 In point of fact this method of representation is bad, for the quality of the metal only begins to affect p about the fourth or fifth decimal place. Similar experiments on spheres and ellipsoids of soft iron were made by Fromme ; 3 and a very extensive series by A. L. Holz 4 on ellipsoids of iron and steel, in which he gives tables and curves showing the values both of p (to a large number of decimals) and of K ; and the values of the temporary, permanent, and vanish ing magnetisms for a considerable range of magnetizing forces. The results, although wanting in regularity and smoothness for the harder kinds of steel, agree in the main with those of Stoletow and Rowland. Holz enters largely in this and in a former paper 5 into speculations concerning the effect of the molecular structure of the metal upon its magnetic properties. Relating more particularly to the phenomena of the per manent and temporary magnetization of steel we have important memoirs of recent date by Bouty, Fromme, and Auerbach. Bouty s papers, 6 besides copious references to the general literature of the subject and interesting critical discussions of magnetic theory, contain the results of careful investigations as to the permanent magnetization attained by repeated applications of magnetic force under various circumstances, and verifications of the formulae of be remembered that the maximum of permanent magnetization which a body can attain is essentially conditioned by its form ; since the more elongated the form the less the demagnetizing force arising from the existing magnetization. 1 Pogg. Ann., cxlix., 1873. 2 = 3/4ir = "2387. 3 Pogg. Ann., clii., 1873. This paper contains also some results as to the permanent magnetism of soft iron. 4 Pogg. Ann., Ergbd. viii., 1877. 5 Pogg. Ann., cli., 1873. 6 Comptes Rend., 1875; Jour. d. Vc. Norm. Sup., 1875, 1876. 257 Green for the magnetic distribution in thin needles and cylindrical bars of steel. Two points as to his methods are worthy _ of notice. He employs a very simple method of measuring the magnetic moment of small pieces of steel : a small needle of moment m attached to a stiff stem, which carries a mirror, is freely suspended and allowed to come to rest in the magnetic meridian; the needle whose moment x is to be measured is then inserted into a tube fixed to the stem with its axis at right angles to the former needle. The deviation a of the compound system being measured by means of the mirror, we have x = m tana. He studies the magnetic distribution in very thin hard needles by the method of rupture, finding that, if the needle be carefully broken, so that the distortion or shock caused by the bending does not extend far from the point of rupture, the magnetic moment of the different parts is little, if at all, affected. For thicker magnets he uses the ordinary method of deflexion. Bouty found, in agreement with Hermann Scholz and Frankenheim, 7 that, although the continued application of a magnetizing force does not increase the resulting per manent magnetization, the repetition* of its application will. He finds for the magnetic moment y of a thin needle passed x times through a magnetizing spiral the formula y = A - E/x, where A and B are constants : e.g., in one case, A = 57-78, and B = 6-32. The ratio A/(A- B), that is, the ratio of the moment attained by an infinite number of applications of the magnetizing force to that attained by one, decreases as the force increases ; on the other hand, if R be the force required to produce by a single application the same effect as R produces by an infinite number, he finds the ratio R /R fairly constant 9 (viz., from TOGO to 1 065 in his best experiments) for values of R ranging from 10 to 42. In certain cases where the magnetization was effected by in duced currents, he finds the formula y = A + B (1 -e~ a:t ) to represent the results better. 10 He found that Green s formula, Measure ment of small mo ments. Rupture of needles. Effect of repeated applica tion of magnet izing force. where = > a giving the moment of a cylinder of length x and diameter a, was sufficiently accurate both for temporary and for permanent magnetism, and for hard or soft tempered steel, whether saturated or not, provided the bars were in a virgin condition before magnetization. For example, in a saturated bar of soft steel (a = 7 mm.), for the temporary magnetism A = 4 081, B = l/7 142; for the permanent magnetism A = 2 34, B = l/17 857. In a non-saturated bar of soft steel (a 10 mm.), for temporary magnetism A = 9966, B=l/7 142; for permanent magnetism A = 723, B = l/17 857; so that B is independent of the magnetic force. With hard tempered bars, A was less, both for temporary and permanent magnetism, than with soft bars ; B was independent of the magnetizing force for temporary magnetism, but increased for permanent magnetism with large magnetizing forces. He calls the magnetic distribu tion long or short according as B is small or great, and 7 Pogg. Ann., cxxiii., 1864. 8 In a very interesting paper (Phil. Mag., 1869 and 1870) dealing with certain phenomena of induced currents, Lord Rayleigh incident ally arrives at the conclusion that the magnetizing force of a current depends on its maximum intensity more than on its duration, or on the whole quantity of electricity that passes. This observation has an important bearing on certain experiments of Bouty as to the effect of the "extra current," which it does not seem necessary to mention here. 9 This conclusion is not in agreement with the results of Fromme. 10 The formula y = B(l-e~ a;r ) was used by Quetelet for the moment induced in a steel bar by rubbing it x times with a magnet.
XV. 33