Page:Elementary Text-book of Physics (Anthony, 1897).djvu/367

§ 297] If now this wire be doubled on itself, so that near the frame there are two equal currents occupying practically the same position, but in opposite directions, then no motion of the frame can be observed when a current is set up in the wire. This is Ampère's first case of equilibrium. It shows that the forces due to two currents, identical in strength and in position, but opposite in direction, are equal and opposite.

If the portion of the wire which is doubled back be not left straight, but bent into any sinuosities, provided these be small compared with the distance between the wire and the frame, still no motion of the frame occurs when a current is set up in the wire. This is Ampère's second case of equilibrium. It shows that the action of the elements of the curved conductor is the same as that of their projections on the straight conductor.

To obtain the third case of equilibrium, a wire, bent in the arc of a circle, is arranged so that it may turn freely about a vertical axis passing through the centre of the circle of which the wire forms an arc, and normal to the plane of that circle. The wire is then free to move only in the circumference of that circle, or in the direction of its own length. Two vessels filled with mercury, so that the mercury stands above the level of their sides, are brought under the wire arc, and raised until conducting contact is made between the wire and the mercury in both vessels. A current is then passed through the movable wire through the mercury. Then if any closed circuit whatever, or any magnet, be brought near the wire, it is found that the wire remains stationary. The deduction from this observation is that no closed circuit tends to displace an element of current in the direction of its length.

In the fourth experiment three circuits are used, which we may call respectively $$A, B,$$ and $$C.$$ They are alike in form, and the dimensions of $$B$$ are mean proportionals to the corresponding dimensions of $$A$$ and $$C.$$ $$B$$ is suspended so as to be free to move, and $$A$$ and $$C$$ are placed on opposite sides of $$B,$$ so that the ratio of their distances from $$B$$ is the same as the ratio of the dimensions of $$A$$ to those of $$B.$$ If then the same current be sent through $$A$$ and $$C,$$