or other arrangement so as to have a measurable free period of vibration.*

The following method, which has been frequently used in the Physical Laboratory of the University of Glasgow, is very convenient and useful in many cases. It consists in exploring the magnetic field by means of the induced current in a wire moved quickly across the lines of force over a definite area in the field. The wire is in circuit with a reflecting "ballistic" galvanometer— that is, a galvanometer the system of needles of which has so great a moment of inertia that the whole induced current due to the motion of the wire has passed through the coil before the needle has been sensibly deflected. The deflection thus obtained is noted, and compared with the deflection obtained when, with the same or a smaller resistance in circuit, a portion of the conductor is made to sweep across the lines of force over a definite area of a uniform field of known intensity, such as that of the earth or its horizontal or vertical component.

In performing the experiments, it is necessary to take precautions to prevent any action except that between the definite area of the field selected and the wire cutting its lines of force. For this purpose the conducting-wire, which is covered with insulating material, is bent so as to form three sides of a rectangle, the middle one of which is of the length of the portion of field to be swept over. This side is placed along one side of the space over which it is about to be moved so that the connecting wires lie along the ends of the space; and the open rectangle is then moved in the direction of its two sides

* The method just described gives (theoretically) a means of determining the ohm. For suppose the coil hung in a sufficiently intense and uniform field, the intensity of which has been measured by another method, and the decrement of the oscillatory motion produced by the induction observed. Then the resistance could be calculated.

until the opposite side of the space is reached. The connecting wires thus do not cut the lines of force, and the induced current is wholly due to the closed end of the rectangle.

Instead of a single wire cutting the lines of force, a coil of proper dimensions (for many purposes conveniently of rectangular shape), the mean area of which is exactly known, may be suspended in the field with its plane parallel to the lines of force, and turned quickly round through a measured angle of convenient amount not exceeding 90°; or it may be suspended with its plane at right angles to the lines of force and turned through an angle of 180°. If n be the number of turns, A their mean area, and I the mean intensity of the field over the area swept over in each case, then, in the first case, if be the angle turned through, the area swept over is n A sin and the number of lines cut is n I A sin 0; in the second, the area is 2 n A, and the number of lines cut is 2 n I A.

In order that with the feeble intensity of the earth's field a sufficiently great deflection for comparison may be obtained, it is necessary that a relatively large area of the field should be swept over by the conductor. One convenient way is to mount on trunnions a coil of moderately fine wire of a considerable number of turns wound round a ring of large radius, like the coil of a standard tangent galvanometer, and arranged with stops so that it can be turned quickly round a horizontal axis through an exact half-turn, from a position in which its plane is exactly at right angles to the dip. This coil, if the ballistic galvanometer is sensitive enough, may always remain in the circuit. The change in the number of lines of force passing through the coil in the same direction relatively to the coil, produced by the half-turn, is plainly equal to twice as many

times the area of the turn of mean area as there are turns in the coil (the effective area swept over) multiplied by the total intensity of the earth's magnetic force at the place of experiment. Or, and preferably when the horizontal component of the earth's magnetic force has been determined by experiment, the coil may be placed in an east and west (magnetic) vertical plane, and turned through an exact half-turn. The magnetic field intensity by which the effective area is to be multiplied is in this case the value of H.*

A sufficiently large area of the earth's field for comparison may, in some cases, be obtained very readily by carrying the wire along a rod of wood, say two or three metres long, and suspending this rod in a horizontal position by the continuations of the conductor at its ends from two fixed supports in a horizontal line at a distance apart equal to the length of the rod, and securing the remaining wires in circuit so that they may not cause disturbance by their accidental motion. The rod will thus be free to swing like a pendulum by the two suspending wires. The pendulum thus made is slowly deflected from the vertical until it rests against stops arranged to limit its motion. When the needle is at zero, the rod is quickly thrown to the other side against similar stops there, and caught. The straight conductor thus sweeps over an area of the vertical component of the earth's field equal to the product of the length of the rod into the horizontal distance between the two positions of the conductor at the extremities of its swing. The rod may be placed at any azimuth, as the suspending portions of the conductor in

* The method of reducing results of observations to absolute measure by means of an earth inductor was used by Professor H. A. Rowland in his experiments on the magnetic permeability of iron, steel, and nickel.—Phil. Mag., vol. 46, 1873.

circuit, moving in vertical planes, can cut only the horizontal lines of force; and the induced currents thus produced have opposite directions and neutralize one another.

The calculation of the results is very simple. By the theory of the ballistic galvanometer* (the same mutatis mutandis as that of the ballistic pendulum), if q be the whole quantity of electricity which passes through the circuit, and if be the angle through which the needle has been deflected, or the "throw," we have, neglecting air resistance, &c.,

where μ is the moment of inertia of the needle and attachments, m the magnetic moment of the needle, H the earth's horizontal magnetic force, and G the constant of the galvanometer. If be small, as it generally has been in these experiments, we have

and the quantities of electricity produced by sweeping over two areas, A and A', are directly as the deflections. Let A be the total area swept over in the field or portion of field the mean intensity I of which is being measured, A' and l' the same quantities for the known field, R, R' the respective total resistances in circuit, q, q' the quantities of electricity generated in the two cases, 0,

For further particulars see the author's Theory and Practice of Absolute Measurements in Electricity and Magnetism, vol. ii.

6' the corresponding deflections supposed both small; we have

If convenient, and e' may be taken as proportional to the number of divisions of the scale traversed by the spot of light in the two cases.

The error caused by neglecting the effect of air resistance, &c., in diminishing the deflection will be nearly eliminated if R and R' be chosen so that 0 and e' are nearly equal.

The following new method of reducing ballistic observations to absolute measure has been given by Sir William Thomson. A short induction coil wound round the centre of an ordinary magnetizing helix, whose length is great compared with its diameter, is kept in circuit with the galvanometer. A measured current is sent through the wire of the helix, and when the needle is at rest the circuit of the helix is broken, and the galvanometer deflection read off. If N be the number of turns of wire per cm. on the helix, C the current in electromagnetic C.G.S. units, the magnetic force within it is 4 πn C parallel to the axis; and if A' be the proper mean area of the cross-section of the helix, and n' the number of turns in the induction coil, the number of lines (unit tubes) of force passing out of the galvanometer circuit when the current is stopped is 4π N n' A' C.*

See the author's Theory and Practice of Absolute Measurements in Electricity and Magnetism, vol. ii.