and are known as the B.A. units. More recent measurements made by the same method, as well as by several different methods, have shown that the B.A. units are not exactly 1 ohm, the true value being, 1 B.A. unit=0.9866 ohm.

Experiment has also shown that the resistance of a column of pure mercury 106.3 cm. long and one square millimetre in cross-section, when at a temperature of o° C., is equal to one ohm. As the resistance of a solid is dependent on the physical state, such as the hardness, &c., there is some doubt whether a standard resistance composed of a wire may not alter in time, due to a change in the molecular state of the metal. In the case of a liquid, however, such a molecular change is not to be feared, for liquids are not able to take up a state of strain. For this reason the final standards of resistance are composed of tubes of glass, of which the dimensions can be accurately measured, filled with pure mercury, and the wire standards used in ordinary work are compared with these mercury standards.

522. Determination of the Value of the Volt.-If the absolute value of a current and of a resistance is known from the measurements made by the methods described in §§ 515, 521, then, by passing the current through the resistance, the absolute value of the E.M.F. between the terminals of the resistance will be known. Hence of the three electrical quantities, ampere, ohm, and volt, the knowledge of the absolute value of any two enables us to obtain, by means of Ohm's law, the value of the third.

The values for the E. M.F. of the Clark and cadmium standard cells, given in §§ 554, 555, have been determined by comparing their E.M.F. with that developed between the terminals of a wire of known resistance when a current is passed, the value of the current being obtained from the indications of a current balance.

523. Arago's Experiment - Foucault Currents. — Arago discovered that if a copper disc is rotated about a vertical axis below a pivoted magnetic needle, the needle is deflected in the direction in which! the disc is rotating, and if the speed of rotation is fairly great the needle is dragged completely round, so that it is set in rotation. The inverse experiment can also be performed, that is, if a magnet is rotated near the face of a copper disc which is free to turn, the disc is set in rotation, the direction of rotation being the same as that in which the magnet is being rotated. The explanation of this experiment was given by Faraday, who showed that it was due to the reaction between the electric currents induced in the copper disc and the magnet.

Let AB (Fig. 501) be the copper disc which is rotated in the direction shown by the arrow, and let NS be a magnet suspended or pivoted above the surface of the disc. The tubes of induction of the magnet pass from the north pole N to the south pole s, spreading out in the air. Some of these tubes will pass down below the copper disc near the pole N,

D

FIG. 501.

B

and will come up through the disc near s. Hence when the disc is set in rotation we have the portions of the conducting disc near N and s moving so as to cut through the tubes of induction, and hence an E.M.F. will be set up which will cause currents to circulate in the disc. Now by Lenz's law the direction of the induced currents must be such as to tend to check the motion, that is, such that the force which will be called into play A between these induced currents and the inducing magnet will be so directed as by their action to check the motion which causes the induced currents. Hence, since action and reaction must always be equal and opposite, a force will act on the magnet tending to move it in the same direction as that in which the disc is rotating. The direction in which the currents must flow, so as to tend to turn the magnet in the same direction as that in which the disc is rotating, can be obtained by making use of the rule given in § 471. If we imagine a man in the disc near N facing the pole so that he must be on his back, then, in order that the pole N may be urged towards his left hand, he must lie with his head towards the circumference of the disc and his feet towards the centre. If when he is in this position a current is flowing from his feet to his head, the magnet pole N will be urged towards his left hand, that is, in the same direction as that in which the disc is rotating. In the same way it can be shown that, in order to produce a force between the magnet and the disc tending to check the motion of the disc, the currents in the portion of the disc near s must flow from the circumference towards the centre of the disc. Hence the path of the induced currents in the disc is somewhat as shown by the dotted curves.

Of course, we could have arrived directly at the same result by making use of the rule given in § 519 for the connection between the direction in which a conductor is moved through a magnetic field and the direction of the induced E.M.F. Thus the portion of the disc under the pole N is moving in a magnetic field where the tubes of induction are running downwards, and hence, if the right hand is placed palm downwards with the fingers pointing in the direction the portion of the disc below N is moving, the outstretched thumb will give the direction of the induced E.M.F., and this will act from the centre of the disc towards the circumference.

The effects of the currents induced in a mass of metal when it is moved in a magnetic field was very strikingly shown by Foucault, who arranged a copper disc so that it could be rotated by means of a handle and a train of wheels between the poles of a powerful electro-magnet. Although it was easy, when the magnet was not excited, to rotate the disc at a rapid rate, on starting the current in the electro-magnet

the reaction on account of the induced currents was so enormous that the disc was immediately brought almost to rest, and it could only be rotated at a comparatively slow speed. These currents, which are induced within a mass of metal when it is in a changing magnetic field or is in motion in a steady field, are generally called Foucault currents. The circulation of the currents is of course accompanied by the conversion of electrical energy into heat according to Joule's law, so that the mechanical energy which has to be spent in moving the conductor appears as heat developed in it.

Use is often made of Foucault currents to check the oscillations of a suspended magnetic needle, such as a galvanometer needle, which are often a source of considerable loss of time, since the needle takes some time in coming to rest after it has been deflected. If the needle is surrounded by a thick copper box made to fit as near the needle as possible, when the needle is in oscillation induced currents will be produced in the copper, which will tend to check the motion of the needle. Under these circumstances the motion of the needle is said to be damped.

524. The Induction Coil.-By means of electro-magnetic induction, it is possible to produce in a secondary circuit an induced E. M.F. which is higher than the E.M.F. employed to produce the current in the primary circuit. If, on account of the current passing in a primary circuit, tubes of induction pass through a secondary which consists of a single turn, the induced E.M.F. produced when the current in the primary is varied is equal to the rate of change of n. If, how ever, the secondary circuit consists of two turns, so that the # tubes of force due to the primary thread through both turns, the E.M.F. induced in each turn will be equal to the rate of change of n, and hence the total E. M.F. produced in the circuit will be the sum of the E.M.F.'s produced in the two portions of the circuit, that is, will be equal to twice the rate of change of the number of tubes of induction which pass through the secondary. Thus, by increasing the number of turns of the secondary circuit, the induced E.M.F. produced by a given rate of change of n can be made very great. One of the best known arrangements for obtaining a very high E.M.F. by means of electro-magnetic induction is the induction coil which, since it was first employed by Ruhmkorff, is often called Ruhmkorff's coil. The primary of these coils consists of a comparatively few number of turns of fairly thick wire, which is wound on a core composed of soft iron wires. The object of the iron core is to increase the induction through the primary produced by any given current, as was explained in § 513. The reason why wires are used instead of a solid rod is to prevent, as much as possible, the formation of Foucault currents in the mass of the iron, since these currents would not only waste the electrical energy used to work the coil, but would also, by their reaction on the primary current, tend

to keep this current from changing rapidly. For they would produce tubes of induction in such a direction as to keep the total induction through the primary constant when the strength of the primary current is altered. The iron used must be of a very soft quality, so that the hysteresis and residual magnetism which it possesses may be as small as possible, for the effect of hysteresis is to convert some of the electrical energy into heat as well as to make the changes in the induction through the coil slower. Round the outside of the primary coil is wound a secondary coil consisting of a very large number of turns of fine wire, each turn being very well insulated by means of a covering of silk and shellac. The ends of the secondary are generally connected to two insulated brass rods, the ends of which form a spark-gap of adjustable length. The current in the primary circuit being alternately made and broken, the induction through the secondary changes and an induced E.M.F. is produced in the secondary, which is in one direction when the current is made and in the opposite direction when the current is broken. Various arrangements are employed for automatically making and breaking the primary current. In some of these a small electric motor makes and breaks the current by dipping a rod of platinum into a mercury-cup. The more usual arrangement, at any rate on small coils, is to have a small piece of iron fixed to the end of a spring, so that when the current passes and magnetises the iron core the piece of iron is attracted. When no current is passing, the spring keeps the iron away from the end of the core, and makes contact between a piece of platinum fixed to the back of the iron and a platinum point which is attached to a pillar carried by the base of the coil. The primary current passes between the platinum point and the spring, and hence when the iron hammer is attracted by the core the primary current is interrupted. The interruption of the current causes the core to lose its magnetism, so that it no longer attracts the hammer, and hence the spring forces it back against the platinum point, thus again completing the primary circuit.

Since the magnitude of the induced E.M.F. depends on the rate at which the number of tubes which thread through the secondary change, it is of importance to make the starting and stopping of the primary current as sudden as possible. Now it has been shown in § 518 that, on account of the self-induction of a circuit in which a current is stopped or started, the current does not reach its full value at once, nor does it die away instantaneously. The effect of self-induction is shown very markedly by the spark which is produced every time the primary current is broken. It has been found that the intensity of the spark formed at the break can be considerably decreased, and hence the rapidity with which the primary current stops increased, so that the induced E.M.F. is also increased, by using a condenser, formed by a number of sheets of tinfoil separated the one from the other by sheets of

paraffined paper, one armature being connected with the spring of the interrupter and the other with the platinum point. In this way the condenser and the primary coil are connected in parallel, and it can be shown that connecting a condenser in this way has the same effect as if the self-induction of the coil were reduced.

By means of such a coil it is possible to produce a spark between the terminals up to about 20 inches in length, and this when the E.M.F. used to produce the primary current is only a few volts, and would be quite unable to produce a spark of a hundredth of an inch in length. Although the E.M.F. of the induced current is very great, the quantity of electricity which traverses the secondary is excessively small, for, on account of the great length of the secondary wire and its small diameter, the resistance of the secondary is very great.