258 MAGNETIS M attc-r- efl uct. explains tlie phenomena of demagnetized or remaguetized bars by the superposition of long and short distributions. His final conclusion is that there is a greater independence between permanent and temporary magnetism than is usually admitted; and he starts a theory that magnetic bodies are composed of a mixture of two kinds of magnetic mulecules, one kind retaining all the induced magnetism, the other wholly devoid of coercive force. It is obvious, from the results of Wiedemann, Franken- heiui, and Bouty just alluded to, that the assumption made in the mathematical theory, that the effect of a magnetizing force is independent of the previous magnetic history of the body, is not even a first approximation to the actual truth. It becomes a matter of importance therefore to study the modification in the induced magnetism cor responding to any force produced by the forces that have preceded it. This effect has been called by German experimenters the magnetic after-effect (Magnetische 1 Nachwirkung). Fromme and Auerbach have recently occupied themselves with this subject, and it may be of some interest to the reader to indicate a few of their con clusions. Froninie. la his first paper l Fromme experiments with rotational ellipsoids of soft steel, using partly the method of Weber, Thalen, and Riecke, partly the ordinary method of deflexion. He found, in the first place, that the generalized theory of magnetic induction was applicable for values of |j) vary ing from 0061 to 132, K decreasing between these limits from 23 5 to 8 68. He attempted to find the maximum force for which permanent magnetism first appears, and fixes it with some reserve at from 2 to - 3. 2 The curve which he indicates for the temporary magnetization of soft fcteel has two points of inflexion, being first concave to the axis of *5> then convex, and finally concave again. He confirms the observation of Frankenheim that repeated applications of the magnetizing force increase the permanent magnetization up to a certain limit, and finds that when that limit is reached the body behaves towards all smaller forces having the same direction as if it were devoid of coercive force. Experimenting on ellipsoids permanently magnetized in this way, he found the mathematical theory of Kirchhoff to be inapplicable, it being impossible to fit the results obtained with the different ellipsoids together; and the discrepancy was greater with the softer than with the harder steel. For forces that are not sufficient to alter the permanent magnetization, K decreases with decreasing force, as is the case with soft iron, so long at all events as the forces are not very great ; and, again, for such forces the variation of K is more regular the greater the permanent magnetization. The number of impulses require d to saturate with per manent magnetism was greater the greater the ratio of the moment of saturation to the initial moment, e.g., greater for hard than for soft steel. It was found, in extension of a result of Frankenheim s, that, if U be the original moment, B 1 that produced by one and R that produced by an infinite number of impulses of the magnetizing force, then (U + Rj), (U + II) is tolerably constant ; but R L /R decreases with increasing magnetizing force. With reference to the non-permanent magnetism of a bar repeatedly magnetized by the same constant current, he concludes from his researches that it diminishes, but in such a way that the total induced magnetism remains con stant, so that what is lost in non-permanent is gained in permanent magnetism. In his second paper 3 Fromme experimented both with 1 Pogg. Ann., Ergbd. vii., 1875. 2 So far confirming Maxwell s conclusions from his modification of Weber s theory of molecular magnets, EL and Mag., vol. ii. 445 3 Wied Ann.,i., 1878. iron and with steel cylinders, pointed at the end, of lengths varying from 140 to 220 mm., and of thicknesses from 1 5 to 8 mm. The method of deflexion was used, the effect of the magnetizing spiral itself being compensated by an auxiliary spiral suitably placed. The cores were carefully introduced into the spiral after the current was established, removed before it was broken, and then replaced when the permanent magnetism was determined. In the following extract from his conclusions T,, denotes the total induced magnetization, R n the whole residual or permanent magnetization, V,, the non-permanent or vanish ing magnetization, after n impulses of a given magnetizing force, the suffix being dropped when the number of impulses is not in question, and replaced by GO when the number is so great that by further increasing it no altera tion iii the effect is produced. A constant force greater than all preceding induces a T which varies with successive impulses, sometimes increas ing, sometimes decreasing. If a bar previously heated white hot be subjected to a large force, successive impulses usually give a decrease of T. If, however, the force is preceded by one somewhat smaller, successive impulses usually give an increase. It depends merely on the magnitude and the number of impulses of the preceding force P whether the repeated impulses of a force p will give an increasing or a decreasing T. R always increases with successive impulses until the limit is reached, and always faster than T; hence increase of R and decrease of V go hand in hand ; the magnitude of this increase depends on P and j), and approaches zero with P-p. In order that the action of a force p may not be influenced by the after-effect of smaller forces preceding it, it must be applied so often that its further application ceases to increase R. When saturation for R is thus reached, then T, R, and V have the values corresponding to frequent impulses of p for a fresh bar. Rj/R^ , R^/RQQ , <fec., all starting from unity, decrease as the force p increases from zero, diverging more and more until they all reach minima for the same value of p ; they then converge again towards unity, which they all reach at the maximum of permanent magnetization. The values of p corresponding to the maxima of R^ , p, . . . . R 2 /p, RI/P are in ascending order of magnitude, and the first of them is the value corresponding to the minima of R/RSO , R^/ROQ , & c . What was stated for R x /R^ , R^/R^ , &c., holds word for word for T^ /T 15 T^ /T 2 , &c. Hence the decrease of T is conditioned solely by the increase of R ; so that it would appear that the after-effect of a preceding force P depends on the R which it produces. It would therefore be more correct to say that the after-effect depends on r - R than to say that it depends on p - P. When a bar has been magnetized by any force P, all smaller succeeding forces leave R unaltered, yet by repeated impulses of p (<P) T decreases until it reaches a certain limit. We may repeat the process as often as we please by always beginning with a new application of a larger force P; if we vary P, keeping p constant, T 1? T 2 , Ac., vary, but the limit T^ is always the same. In these experiments it was indifferent whether a few seconds or several hours elapsed between the applications of P and p ; time had no influence on the vanishing of this species of magnetic after-effect. On the other hand, several impulses of the greater force gave no more after-effect than a single impulse, of whatever duration. If N denote the after-efiect of a greater force P upon the action of a smaller p, the law of the phenomenon is Varying effect ol succes sive im pulses on tan- porury magnet ism. EfiVt on per manent matrnet Laws o after effect.
where c is a constant and a and b are constant positive