72 to it. We do not propose to go into detail respecting Weber s experiments, but merely to indicate their general character and give some of the results. Those desiring further information will find it in 1-9 of the Electro- dynamische Maasbeatimmungen. Weber first showed that the electrodynamic action between two parts of a piece of apparatus traversed by the same current varies as the square of the current. Apparatus A was arranged with the plane of its fixed coil in the magnetic meridian. The movable coil was concentric with the fixed one, but its plane was perpendicular to the magnetic meridian. The current of 1, 2, or 3 Grove s cells was sent through the fixed coil and tlirough the suspended coil; but as the deflection with this arrangement was too great, the latter was shunted by connecting its terminals by a wire of small but known resistance. A measurement of the first power of the strength of the current was found by observing the deflection produced by the current in the fixed coil on a magnet suspended in its plane at a convenient distance north of it. After the necessary corrections were applied, the following results were obtained : n D H M Diff. 3 440-038 108-426 108-144 -0-282 2 198-255 72-398 72-589 + 0-191 1 50-915 36-332 36-786 + 0-454 where n is the number of cells, D the electrodynamic force on the suspended coil, expressed in an arbitrary unit, M the force on the magnet, M the force on the magnet calculated from VD by means of a constant multiplier. The agreement between M and M is within the limits of experimental error. In another series of experiments Weber used the apparatus B described above. The suspended coil was arranged with its axis in the magnetic meridian, and the fixed coil set up with its axis perpendicular to the magnetic meridian. Experiments were made with the centres of the two coils coincident, and with the centres in the same horizontal plane, at distances of 300, 400, 500, and 600 millimetres, the fixed coil being, in one set of experiments, east or west from the suspended coil ; in another set, north or south. In the present series of experiments the strength of the current was measured by means of a magnet acted on, not by the fixed coil, but by another coil in circuit with it. After proper corrections, the following results were arrived at : (1 P P Q Q
22960 22680 22960 22680 300 189-93 189-03 77-11 77-17 400 77-45 7779 34-77 34-74 500 39-27 39-37 18-24 18-31 600 2-2-46 22-04 where d is the distance between the centres of the coils, P the couple 1 exerted on the movable coil when the direction of that distance is perpendicular to the meridian, Q the couple when it is in the meridian. P and Q are the values of the same couples cal culated from the theory of Ampere. The agreement here again is as near as could be expected. Weber further showed that the deflections (v, w) of the suspended coil, calculated by means of the formulae tan v = ad~ 3 + f}d~ 6 tan w in the two cases where the centres of the coils were at a considerable distance apart, agreed with observation within the limits of experi mental error. Now these formula are identical with those estab lished by Gauss for two magnets with their axes placed like the axes of the coils. This agreement therefore is an experimental proof that the. coils are replaceable by magnets. On the whole, therefore, the experiments of Weber 2 confirm the theory of Ampere, as far as experiment can test it. They form, therefore, a sufficient basis for the proposition on which we founded our theory ; for this proposition leads to the same result for closed circuits as the theory of Ampere. Experi- The action of any current on a magnetic pole, and hence on any meats of magnet, may be calculated either by replacing the circuit by an Biot and equivalent shell or by means of formula (19). We have already Snvart. found this action in the particular case of an infinitely long straight current. This result was originally found experimentally by Biot 1 Reduced to a standard current strength by means of the magnet deflections. 8 Fcr another verification by Cazin, seeWiedemann,u aZr > ., Bd. ii. 44. Y [ELECTROMAGKETISM. and Savart, and Laplace showed that it followed from their result that the force exerted by an element of the current varies inversely as the square of the distance. The fact that a circular current acts on a msignetic pole at its centre in the same way as a zig-zag cur rent which is everywhere very nearly coincident with it, leads, when properly interpreted, to the conclusion that the force varies as siaO In this way formula ^16) was originally arrived at, inde pendently of Ampere s theory. A great variety of instances might be given of the action of a Earth s magnet on a current. The earth, for instance, acts on a circular action, current, hung up on Ampere s stand : the current, being movable about a vertical axis, will turn until the maximum number of the earth s lines of magnetic force pass through it i.e., it will set with its plane perpendicular to the magnetic meridian, in such a way that the current, looked at from the north side, goes round in the opposite direction to the hands of a watch. A very simple way of showing the action between magnets and De la currents was devised by De la Rive. A small plate of copper and a Rive s small plate of zinc are connected together by a wire passing through floatin a cork and making a circuit of several turns ; the cork is placed in batter a vessel containing dilute sulphuric acid, and floats on the surface, carrying the little circuit about with it. Such a circuit will set under the earth s action, and may be chased and turned about, &c., by a magnet. After what has been already said, however, such experiments offer no new point of interest. Electromagnetic Rotations. It is obvious that no On rot invariable system of electric currents can produce con- tlons tinuous rotation of a magnetized body. For, suppose an gen elementary magnet, whose action may be represented by two poles of strengths m, to describe any path and to return exactly to its former position ; either it has or has not embraced the circuit in its path; if it has not, no work has been done on either pole ; if it has embraced the circuit n times, an amount of work ^nmiri has been done on the north pole, and an amount - knrmri on the south; on the whole, therefore, no work has been done on the magnet. As any magnetized body may be conceived to be made up of such elementary magnets, it is obvious that it is impos sible for such a body to rotate continuously, doing work against friction, 3 &c. The same is obviously true if we replace the magnet by an invariable system of electric currents. If, however, part of the electric circuit is movable with respect to the rest, and communicates therewith by means of sliding contacts or the like, continuous rotation of part of the circuit may occur. Again, if by any artifice the magnet can be transferred every revolution from one side of the current to the other, continuous rotation of the magnet may result. Lastly, if the direction of the current in some part of the apparatus be always reversed at a certain stage of the revolution, continuous motion may ensue. Rotations of the first and second class were first dis- Fara- covered by Faraday, and the ground principle of most of da > r s the pieces of apparatus used in demonstrating them is that * >ar originally used by him. One of the simplest cases is the rotation under the action of the vertical component of the earth s magnetic force. Let ABC (fig. 39) be a horizontal .circular conduc tor, OP a conductor pivoted at 0, having sliding contact at F with ABO. Let a current i enter ABC at A, and }eave it at P, flowing through PO to and thence to the battery again. The magnetic force at any eleinent dr of OP is perpendicular to OP and to the plane of ABC, hence the electro magnetic force on the element will be in the plane of ABC, in the direction of the arrow p, 4 and will be equal to idr (R. = vertical component of earth s force). Hence the moment about of the forces acting on OP is fiRrdr, i.e. $OP 2 R7 , which is independent cf the position of OP. OP will therefore rotate about 0, with an angular velocity which will go on increasing until the work lost by friction, &c., during each revolution is equal to 7rOP a Rt. 3 Maxwell, vol. i., 486 and 491. j * We are here supposed to be in southern latitudes.
Fig. 39.