quantity of electricity is transferred across any section in one second. But as yet we have no definition of the unit quantity of electricity. To obtain this, we shall consider certain other properties of an electric current. A current flowing in a conductor is found to produce a magnetic field in its neighbourhood. Magnetic force is exerted by the current, and the pole of a magnet placed near the conductor will be urged by a force definite in direction and amount. If the conductor be in the form of a long straight wire, a north magnetic pole would tend to move in a circle round the wire, and the direction of its motion would be related to the direction of the current in the same way as the direction of rotation is related to that of translation in a right-handed screw. If instead of a magnetic pole we consider a compass needle placed near the wire, the needle will tend to set itself at right angles to the wire, and if we imagine a man to be swimming with the current and looking at the needle, then the north end will be turned towards his left hand. As to the intensity of the force, let us suppose that the length of the wire is / centimetres, and that it is wound into the form of an arc of a circle centimetres in radius; then when a current of intensity i circulates in the wire, it is found that the magnetic force at the centre is proportional to lir and acts in a direction at right angles to the plane. of the circle, and if i be measured in proper units, we may say that the magnetic force is equal to li/r2. Let the length of the wire be one centimetre, and the radius one centimetre, and let us inquire what must be the strength of the current in order that the force on a unit magnetic pole may be one dyne." See p. 500. See chap. ii. p 18. We have then in the equation F = 1, / = 1, † = 1, and it becomes therefore i = 1; that is, the strength of the current is unity, or the current required is the unit current. Thus, in order that the equation F= li may be true, it is necessary that the unit current should be that current which circulating in a wire of unit length, bent into the form of an arc of a circle of unit radius, exerts unit force on a unit magnetic pole placed at the centre. But we have seen already that the unit current is obtained when unit quantity of electricity crosses any section of the conductor. We have thus arrived at the definition of unit quantity of electricity of which we were in search. This definition is known as the definition of the electromagnetic unit of quantity. DEFINITION OF C.G.S. ELECTRO-MAGNETIC UNIT QUANTITY AND UNIT Current.-Consider a wire one centimetre in length bent into an arc of a circle one centimetre in radius. Let such a quantity of electricity flow per second across any section of this wire as would produce on a unit magnetic pole placed at its centre a force of one dyne. This quantity is the electro-magnetic unit of quantity of electricity, and the current produced is the electro-magnetic unit of current. With this definition understood then, we may say that if a current of strength i traverse a wire of length / bent into an arc of a circle of radius, the force on a magnetic pole of strength m placed at the centre of the circle will be mil/r2 dynes in a direction normal to the circle, and the strength of the magnetic field at the centre is il\r2. The magnetic field will extend throughout the neigh bourhood of the wire, and the strength of this field at any point can be calculated. Accordingly, a magnet placed in the neighbourhood of the wire is affected by the current, and disturbed from its normal position of equilibrium. It is this last action which is made use of in galvanometers. Let the wire of length / be bent into the form of a circle of radius r, then we have 1 = 2 πr, and the strength of the field, at the centre of the circle, is 2 π i|r. Moreover, we may treat the field as uniform for a distance from the centre of the circle, which is small compared with the radius of the circle. If then we have a magnet of moment м, whose dimensions are small compared with the radius of the circle, and if it be placed at the centre of the circle so that its axis makes an angle with the lines of force due to the circle, and therefore an angle of 90° - 0 with the plane of the circle, the moment of the force on it which arises from the magnetic action of the current is 2 Mi sin 0|r. π If, at the same time, & be the angle between the axis of the magnet and the plane of the meridian, the moment of the force due to the horizontal component H of the earth's magnetic force is м H sin ; if the small magnet be supported so as to be able to turn round a vertical axis, and be in equilibrium under these forces, we must have the equation if then we know the value of H, and can observe the angles and, and measure the distance r, the above equation gives us the value of i. Two arrangements occur usually in practice. In the first the plane of the coil is made to coincide with the magnetic meridian; the lines of force due to the coil are then at right angles to those due to the earth, and The instrument is then called a tangent galvanometer. In the second the coil is turned round a vertical axis until the axis of the magnet is in the position of equilibrium in the same plane as the circle; the lines of force due to the coil are then at right angles to the axis of the magnet, so that the effect of the current is a maximum, and 0=90°. In these circumstances, therefore, we have, if y be the deflection of the magnet, The instrument is in this case called a sine-galvanometer. We shall consider further on, the practical forms given to these instruments. Our object at present is to get clear ideas as to an electric current, and the means adopted to measure its strength. The current strength given by the above equation will, using C.G.S. units of length, mass, and time, be given in absolute units. Currents, which in these units are represented even by small numbers, are considerably greater than is convenient for many experiments. For this reason, among others, which will be more apparent further on, it is found advisable to take as the practical unit of current, onetenth of the C.G.S. unit. This practical unit is called an ampère. DEFINITION OF AN AMPÈRE.-A current of one ampère is one-tenth of the C.G.S. absolute unit of current. Thus, a current expressed in C.G.S. units may be reduced to ampères by multiplying by 10. EXPERIMENTS CHAPTER XIX. ON THE FUNDAMENTAL PROPERTIES OF ELECTRIC CURRENTS-MEASUREMENT OF ELECTRIC CUR- 71. Absolute Measure of the Current in a Wire. THE wire in question is bent into the form of a circle, which is placed approximately in the plane of the magnetic meridian. This is done by using a long magnet mounted as a compass-needle and placing the plane of the wire by eye parallel to the length of this magnet. The two ends of the wire are brought as nearly into contact as is possible, and then turned parallel to each other at right angles to the plane of the circle; they are kept separate by means of a small piece of ebonite, or other insulating material. A small magnet is fixed on to the back of a very light mirror, and suspended, by a short single silk fibre, in a small metal case with a glass face in front of the mirror, just as in a Thomson's mirror galvanometer. The case is only just large enough to allow the mirror to swing freely, so that the air enclosed damps the vibrations rapidly. The case is fixed to an upright stand and rests on levelling screws in such a way that the centre of the magnet can be brought into the centre of the circle. A scale parallel to the plane of the circle is fixed some little distance in front of the mirror, the level of the scale being very slightly above that of the mirror. Below the scale is a slit, and behind that a lamp, the light from which shines through the slit on to the K K |