again the same disposition of two bar magnets, with like poles adjacent to one another, just as they were used for the production of fig. 16. The lines of force, however, have not been developed (by tapping the paper) as far as the indifferent points J' and J." But it will be seen, especially on comparison with the diagram corresponding to a single bar magnet, how the lines of force have been driven away from the space between the two bars. Thus the stresses are seen to be present, even when our chains of filings do not extend to the points J, J."

FIG. 17

38. Transverse effects; rotatory displacements.-We must now examine the disposition of the lines of force when two bar magnets are laid in the grooves a and c of the board (fig. 9) so as to have their axes at right angles to one another, an extremity of one being not far removed from the middle of the other. The line-of-force diagram in a horizontal plane (i.e. in a plane parallel to the axes of the magnets) is shown in fig. 18.

The lines of force proceeding from the pole n, of the magnet m, pass mostly to the unlike pole s, of the other magnet. From the pole n, of this magnet they are driven away by the issuing lines of force which they encounter. Between n, and n, there is an indifferent point, where the magnetic force vanishes. Under the influence of the pressures and tensions in the field, the bar m, in the figure is urged towards the right, as indicated by the arrow. On the right hand, the lines of force with both ends attached to the magnet are striving to become shorter, and thus exerting a pull; while on the left hand a thrust is exerted by mutual repulsion between the lines of force, which encounter and turn away from one another. At the left side there is an indifferent zone, or region of small magnetic force, extending obliquely upwards towards the right.

Experiment 29.-The mechanical forces.-Over one end of one of the magnets let a tightly-fitting collar be passed, the collar being provided with a hook so that the magnet may be able to hang vertically from a suspending thread. This magnet, on bringing near to it the middle of another magnet held in a horizontal position, will be attracted towards one pole, in accordance with the course followed by the lines of force.

Experiment 30.-One of the magnets m,, being supported at its middle upon a needle-point, or hung by a thread so

as to turn freely in a horizontal plane, will come to rest pointing north and south.

magnet m2.

Now bring near the other

(a) From the east or the west with one or other pole foremost, its axis being always kept perpendicular to the position of rest of m1, and passing through the axis about which m, rotates. First theorem (GAUSS and WEBER): a rotation akes place. This is easily explained by reference to the actions between the ends of the two magnets.

(b) From the south or the north, with its axis perpendicular to the position of rest of m,, which should pass

through the middle of m. Second theorem: rotations also take place. They are less (by about half) than in the previous case (a), for the same distance between the centres of the magnets, and as before their sense is determined by the disposition of the poles.

These rotatory displacements are not to be referred to the mutual action of separate point-poles; for, as fig. 18 shows, it is not only the extreme ends of the magnets that take part in this effect, but nearly all parts of the bars, provided we do not restrict ourselves to the employment of very long and thin bar magnets, whose distance apart is considerable.

CHAPTER III

MAGNETISM AS A TERRESTRIAL AND ASTRONOMICAL

PHENOMENON

THE lodestone is almost the only natural body which is found to have magnetic properties, but these in turn can be communicated to pieces of steel by rubbing with the lodestone. It might seem as if magnetic effects were restricted to a very narrow range; and so, before attempting to enter further into the essential nature of the phenomena, we shall show that they are of far greater interest and importance than our first observations would lead us to suppose. The earth itself is a magnet, and we live in its magnetic field. This field is not constant, but is subject to periodic variations, is convulsed by sudden changes of conditions, and is slowly and progressively altering its distribution. In the variations of the field we can recognise the influence of astronomical events, so that there would seem to be magnetic lines of force connecting our planet with other worlds. The knowledge of this fact gives to magnetic forces a universal interest and significance.

A.-Magnetism as a terrestrial phenomenon

39. The magnetic elements. We have already mentioned (Chap. I., D) the north and south direction of a magnetic needle at rest, and as an effect of this kind is to be observed at nearly all places on the earth's surface, we must attribute it to some property of the planet, to some magnetic force which the earth as such calls into play. So far, we have only made use of this terrestrial magnetism for determining

and specifying the polarity of our magnets, but it is now time to investigate more closely the course of the lines of force in terrestrial magnetic fields, and the data needed for their determination. For this purpose we make use of a magnetic needle freely movable in all directions.

Experiment 31.-Let a good unmagnetised steel needle be suspended in such a way that the weights of the two parts on either side of the point of suspension balance one another. Then magnetise the needle by stroking it with another magnet, and having duly observed its polarity, let it turn freely in a place far enough removed from all artificial magnetic fields. One end of the needle is found to dip downwards-in our part of the world, the north-seeking end-the angle of dip being determinate, and the axis of the needle lying in a determinate vertical plane. If we take the needle to different parts of the room, keeping it sufficiently far from considerable masses of iron, such as stoves, etc., the various positions taken up by the needle are parallel to one another, so that the field is sensibly uniform throughout the space which we have examined.

(a) Direction of the lines of force in the earth's magnetic field. Our freely movable needle sets itself in the direction of the lines of force, for the complete specification of which direction we require to know two angular magnitudes.

Experiment 32.-Let the needle be suspended over a horizontal plane, on which a north-and-south line (geographical meridian) has been marked out,' while a sheet of paper supported in a vertical plane is to be brought quite close to the needle, so as to be parallel to its length. The vertical plane thus determined has roughly, but by no

The meridian may be found with sufficient accuracy for our present purpose as follows: a pin, which is stuck in an upright position into a horizontal plane, has attached to it a card through which a small hole has been bored. About the point vertically beneath the hole as centre, a number of circles are drawn upon the horizontal plane, and marks are made at those points where the circles are intersected by the path of the sun's image, as it moves over the plane. On any given day, each circle will be intersected twice, once before noon, and once after, and the line drawn from the centre of the circles so as to bisect the corresponding arc is the meridian line required.