Earth's Horizontal Magnetic Force

Consider a magnet which is free to turn about a vertical axis, and which can be inverted on this axis, so that after the inversion the side which was the top comes to the bottom, and vice versa. Then we have seen (p. 348) that a certain straight line in the body will set itself in a certain direction, namely, that of the earth's horizontal force. We wish to determine this direction. It may of course be found approximately by the use of a compass needle. Find it thus . and make two marks on the magnet such that the line joining them is approximately in the required direction, and at the same time is horizontal.

Let A, B (fig. 54) be the two marks, O the point in the axis round which the magnet turns which is in the same horizontal plane as A B, and OH the required direction. Take the magnet off its support, and turn it over top to bottom through 180°; replacing it, we will suppose, in such a manner on the support that the point o is brought back into its former position. When the magnet again comes to rest, the line in the magnet which originally coincided with OH will clearly do so again; the effect of the change might have been attained by keeping this line fixed and turning the magnet about it through 180°. Hence, clearly if A'B' be the new position of AB, AB and A'B' meet on OH at K, say, and are equally inclined to it. But AB, A'B' being visible marks on the material of the magnet, the directions of these two lines can be identified: the line which bisects them is the direction required, and is thus readily determined.

Moreover, it is not necessary that the point o should, when the magnet is turned round, be brought exactly into its old position. The line OH will in any case after the reversal remain parallel to itself, and A'B' will represent not the new position of AB, but its projection on the horizontal plane OAB. The plane of the magnetic meridian will be a vertical plane bisecting the angle between the vertical planes through the old and new positions of any line A B fixed in the magnet. The experiment then in its simplest form may be performed as follows:

Fasten a sheet of white paper down on to the table, and suspend over it a magnet of any shape whatever, hanging freely in a stirrup, as already described, by a fibre which has been carefully freed from torsion (p. 368). The magnet should be as close down to the paper as is possible.

Make two marks on the magnet, one at each end, and looking vertically down on it, make two dots on the paper with a fine-pointed pencil, or some other point, exactly under the two marks; join these two dots by a straight line. Reverse the magnet in its stirrup, turning the top to the bottom, and let it again come to rest. Make two dots as before on the paper vertically below the new positions of the marks, and join these two. The line bisecting the angle between the two lines thus drawn on the paper gives the direction of the horizontal component of the earth's force. In performing the experiment thus, serious error is introduced if the observer's eye be not held vertically over the magnet in each case. This is best ensured by placing a piece of plane mirror on the table below the magnet, leaving the part of the paper which is just below the mark uncovered, and placing the eye at some distance away, and in such a position that the image of the magnet, formed by reflection in the mirror, is exactly covered by the magnet itself; then if the dot be made on the paper in such a manner as to appear to the observer to be covered by the mark on the magnet, it is vertically below that mark.

If the position of true geographical north at the place of observation be known, we can obtain the angle between the true north and the magnetic north from this experiment. This angle is known as the magnetic declination.

The declinometer, or apparatus used to measure the declination, is constructed on exactly the same principles as those made use of in the foregoing experiment, more delicate means being adopted to determine the position of the two marks on the magnet with reference to some fixed direction. For an account of these more delicate methods, see Maxwell's 'Electricity and Magnetism', vol. ii. part iii. chap, vii., and Chrystal, 'Ency. Brit,' article Magnetism.