ELECTRICITY [KLKCTK.OMOTIVE INDUCTION. When the charge has any of these maximum values, the current is zero. The current maxima form a similar descending geometric series, the times of occurrence being 9 6 + tr e + 2ir 6 + Sir where 9 is the acute angle tan _. m The interval between any positive and the next negative maxi mum, whether of charge or current, is therefore - . We need not insist on the evident importance of this result. Thomson, in his original paper, points out the various applications of which it is capable. He predicts the phenomena afterwards observed by Feddersen ; in fact, he suggests the use of "Wheatstone s mirror to detect it. Its bearing on the anomalous magnetization of steel needles by jar discharges, and on the anomalous evolution of gas by statical discharges, when electrodes of small surface are used (in Wollaston s manner), are also dwelt upon. Experi- Several physicists have taken up the experimental in- uieiits of vestigation of this matter. Feddersen s experiments realize Tedder- fa Q case a b ove discussed, if we abstract the disturbance sen, &c. QW j n g fco t k e air interval, of the effect of which it is not easy to give an accurate account. Feddersen s results are in good general agreement with theory. He finds, for in stance, that the critical resistance at which the discharge begins to assume the oscillatory character varies inversely as the square root of the capacity of the battery from which the discharge is taken. A good account of the researches of Paalzow, 1 Bernstein, 2 and Blaserna, and of the older researches of Helmholtz, 3 remarkable for thu use of his pendulum interruptor, will be found in Wiedemann, 801, &c. Schiller, in a very interesting paper, 4 describes a variety of measurements of the period of oscillation, and the damping of the alternating currents in a secondary coil, when the current of the primary is broken. By means of the pendulum interruptor of Helmholtz (for descrip tion of which see his paper) the primary is broken, and at a measured interval thereafter the secondary circuit, which contains a condenser and a Thomson s electrometer, is also broken. The deflection of the electrometer indicates the charge of the condenser at the instant when the secondary is broken. The interval between two null points sepa rated by a whole number of oscillations can thus be found, and hence the time of oscillation of the coil calculated. The agreement of Schiller s results with calculation is very remarkable, and must be regarded as a highly satisfactory proof of the validity of the theoretical principles involved. Indue Induction in Masses of Metal and Magnetism of Rota tion in tion. Hitherto we have dealt only with linear circuits ; masses of but it is obvious that currents will also be induced in a metal. mass O f me t a l present in a varying magnetic field. If the variation of the field be due to relative motion between the mass of metal and the system to which the field is due the electromagnetic action of the induced currents will oppose the motion. Many instances might be given ol this principle. If a magnot be suspended over a copper disc, or, better still, in a small cavity inside a mass o copper, its vibrations are opposed by a force due to the induced currents which for small motions varies as the angular velocity of the needle. Accordingly, it comes much sooner to rest than it would do if suspended in th air at a distance from conducting masses ; it moves beside the copper as if it were immersed in a viscous fluid Expert- Pliicker suspended a cube of copper between the poles of a ments of powerful electromagnet, and set it spinning about Pliicker ver tj ca | ax i s directly the magnet was excited it stoppec cault U ~ ^ ead - Foucault arranged a flat copper disc between th 1 Pogg. Ann., 1861. 3 Monatsber. der Deri. A had., 1874. 9 Pogg. Ann., 1871.
- Pogg. Ann., 1874.
flat poles of an electromagnet placed at such a distance part as just to admit it between them. The disc was set ti rotation by means of a driving gear. So long as the nagnet was not excited, the driver had comparatively little ivork to do ; but as soon as the magnet was excited, the vork required to keep up any considerable velocity greatlv ncreased. The additional work thus expended appears in he heat developed in the disc by the induced currents, . ynclall demonstrates this very neatly by causing a small ylindrical vessel of thin copper filled with fusible metal o rotate between the poles of an electromagnet, when enough heat is quickly developed to melt the metal. On the other hand, when a mass of metal moves in the Arag neighbourhood of a magnet, the electromagnetic action of ex P e! he induced currents will cause the magnet to move, if it " >e free to do so. Thus, if we suspend a magnet with its axis horizontal over a disc which can be set in rotation about a vertical axis, owing to the electromagnetic action of the induced current, the needle will tend to rotate in the same direction as the disc. If the velocity be great nough, or the needle be rendered astatic, it may be arried round and round continuously. This action was discovered by Arago, and excited the attention of many philosophers, till it was at last explained by Faraday (see Fare- Historical Sketch). Many of the observations made by day Faraday s predecessors, and some made by himself, are at ^. xp once seen to support the conclusion that the phenomenon is simply a case of Lenz s law. Thus Snow Harris found that the deflecting couple on a suspended needle varied approximately as the velocity of the disc directly, and as the square of the distance of the needle from the disc in versely. It was also found that the action of the disc vas directly proportional to the conductivity of the metal of which it was made, an exception occurring in the case of iron, whose action was disproportionately great. Cutting radial slits in the disc diminished the action very much. Besides the component tangential to the disc, it is found that there is a repulsive normal action on the pole of the magnet, and also a radial action, which may be towards or from the centre of the disc, according as the pole is nearer or farther from the centre of the disc. These actions look at first sight somewhat more difficult to explain; but a little consideration will show that the laws of induction account for these also. Let us first suppose the induced currents to appear and die away instantly after the small motion of the disc which produces them (we may suppose the motion of the disc to take place by an infinite number of small jumps). Thus the currents of induction arc obviously symmetrical with respect to the diameter through the foot of the perpendicular from the magnetic pole on the disc, and we may roughly re present the elec tromagnetic ac tion by a magnet placed perpendicu lar to the diameter at a certain dis tance from the centre of the disc, its south pole point ing in the direc tion of the disc s motion if the in ducing pole be a north pole. Let OX (fig. 52) be the direction of the diameter in the Fl &- 52 - same vertical plane as the pole, NS the representative magnet, OY being the direction of motion. By our present supposition the inducing pole M lies in the plane of ZOX, in which case it is obvious that the resultant action reduces to a tangential com ponent T parallel to OY. But, owing to the inductive action on each other of the currents in the disc, the induced currents do not rise and fu.1! instan
taneously, but endure for a sensible time. We may roughly represent