MAGNETISM 259 Zliet numbers, b being a proper fraction, and a possibly very near unity. This of course gives N = for p = and for p = P, and gives a maximum value of N for some value of p between and P. The interposition of a force P between P and p increases the after-elfect if P >P, diminishes it if P <P; and this holds irrespective of the sign of P - p. If we denote by ~k the susceptibility of a body for vanishing magnetism (V) induced by any force p, the question arises how far this is influenced by the permanent magnetism R induced by preceding greater forces. Jamin holds that k is approximately, and Chwolson that it is absolutely, independent of such permanent magnetism. Fromme finds that, when a force 2^ capable of itself producing a permanent magnetism r, acts on a bar already possessing a permanent magnetism R>r, then k is increased (by the presence of R) if R - r is small, but diminished when R - r is great. 1 The after-effect for small forces p may therefore be either increase or decrease of k ; but for large forces p it is always increase. At the conclusion of his paper Fromme points out the contrast between magnetic and elastic after-effect, and dwells upon the analogy between his results and those of Thale n 2 concerning the limits of elasticity in solid bodies. The experimental method followed by Auerbach 3 was much the same as that of Fromme, except that the core was left in the magnetizing spiral during the make and break of the current. The core was generally a hollow cylinder of soft iron 148 1 mm. long, IT S mm. in diameter, 1 G mm. thick, with end plates 1 5 mm. thick. He distinguishes two kinds of magnetic after-effect. The first kind consists in alteration of the magnetization of the body during the action of a constant force, or after it has ceased to act. The second kind is that already mentioned, in which the action of any force is influenced by preceding forces. It is this second kind of after-effect that is dealt with in the paper from which we are quoting. The leading peculiarity of his view of the phenomenon is the introduction of the force zero, both as a preceding and as a final force. The fundamental principle laid down is the following : When the force p, which, following immediately after the force 0, would produce a magnetization T , is preceded by a series of forces P 1? P 2 . . . .P H , the magnetization which results is T, differing from T by an amount N called the after-effect. N is wholly determined by the first of the preceding forces P 2 , which is such that all the forces that act between P z and p lie in magnitude between P 2 and p. This general law is, however, subject to exceptions. For example, let the whole series of forces acting be P 10 , p, P 9 , p (evidently an extreme case), then experience shows that neither T TO nor T 9 is the resulting magnetization, but something intermediate, much nearer to T 10 , however, than to T 9 . In order to obtain T 9 a force P <> must be interposed before P 9 ; even then the magnetization varies a little with P , but, if the stationary condition for P 9 , p be established by alternating P 9 , p many times after applying P , thus
- 10 Pi "()> 9> Pi 9 Pi 9 P
the limit is found to be independent of P , and is held to be the true value of T, In this way, for a given p, T can be determined as a function of P. It is necessary, however, to attend to the following principle, that, of two preceding forces lying in magnitude on different sides of p, the second determines 1 These conclusions are in agreement with the results of Herwig obtained from experiments on the longitudinal and circular magnetiza tion of iron tubes, Pogg. Ann., clvi., 1875. 2 Pogg. Ann., cxxiv., 1865. 9 Wied. Ann., xiv., 1881. the after-effect exclusively only when it differs more from p than the first ; in other cases both contribute to the after effect ; in no case does the first exclusively determine the after-effect. In the case where both preceding forces lie on the same side of p, the exceptions to the general law are far less marked; only where the second force is very nearly equal to p does it exercise a disturbing influence on the after-effect of the first. The process used for obtaining T as a function of P, for a given p, say 10, is therefore to cause the influencing forces to alternate with the influenced, the succession of the former being such that the one preceding p always differs less from p than the one following. The stationary con dition is supposed to be established for each pair as above explained; e.g., starting with P=ll, the series might be 11, 10, 8, 10, 13, 10, G, 10, 15, 10, 4, 10, &c. In this way T n , T 8 , T 13 , &c., can be determined. When the values of T are plotted against the values of Curves P, the curves corresponding to different values of p have of tem- all a similar character (see figure 37). They consist of r rarjr . two congruent parts lying on the two sides of a point of js inflexion, which is the only point that has any marked after- character. To the right of the inflexion the concavity effect. is towards the axis ^ of P, to the left in the opposite direction. The infinite branches appear to approach asymptotes parallel to the axis of P. The abscissa of the point of inflexion for any particular curve p is P =p ; the ordinate is T p , which may be called the normal magnetization corresponding to p when p alone has acted before. This of course is an ideal case ; but a process is indicated for determining T p directly. 4 The dotted curve in the figure is the curve of normal magnetization, whose abscissa and ordinate are p and T p . From the symmetry of the curves representing the after effect Auerbach concludes that the after-effect of forces on opposite sides of p as to magnitude, and equidifferent from it, is equal and opposite, and ascribes the failure to observe the after-effect of forces smaller than p to the interposition of the force zero. He further concludes that the after-effect depends in the same way on P-p as T p depends on p. There is one of the curves of after-effect, that, viz., for p = o, which has a special meaning. It is clearly the curve 4 A particular case of this process is interesting and practically important; viz., in order to demagnetize a core (i.e., to and T.) possessing a moment T. Apply in succession the forces - P, + (I -(P-2e), +(P-3), &c., down to 0, P being chosen of sufficient
magnitude, rather too great than too small (the smaller the better).