wires lie in the magnetic meridian. The greater the Fig. 80. But number of turns the more of this observation when he has read the chapter on Ohm's Law. 190. Astatic Combinations. The directive force exercised by the earth's magnetism on a magnetic needle may be reduced or obviated by one of two methods : (a.) By employing a compensating magnet. An ordinary long bar magnet laid in the magnetic meridian, but with its N.-seeking pole directed towards the north, will, if placed horizontally above or below a suspended magnetic needle, tend to make the needle set itself with its S.-seeking pole northwards. If near the needle it may overpower the directive force of the earth, and cause the needle to reverse its usual position. If it is far away, all it can do is to lessen the directive force of the earth. At a certain distance the magnet will just compensate this force, and the needle will be neutral. This arrangement for reducing the earth's directive force is applied in the reflecting galvanometer shown in Fig. 91, in which the magnet at the top, curved in form and capable of adjustment to any height, affords a means of adjusting the instrument to the desired degree of sensitiveness by raising or lowering it. (b.) By using an astatic pair of magnetic needles. If two magnetised needles of equal strength and size are bound together by a light wire of brass, or aluminium, in reversed positions, as N m shown in Fig. 81, the force urging one to set itself in the magnetic meridian is exactly counterbalanced by the force that acts on the other. Consequently this pair of needles will remain in any position in which it is set, and is independent of the earth's magnetism. Such a combination is known as an astatic pair. It is, however, difficult in practice to obtain a perfectly astatic pair, since it is not easy to magnetise two needles exactly to equal strength, nor is it easy to fix them perfectly parallel to one another. Fig. 81. Such an astatic pair is, however, readily deflected by a current flowing in a wire coiled around one of the needles; for, as shown in Fig. 82, the current which flows above one needle and below the other will urge both in the same direction, because they are already in reversed positions. It is even possible to go farther, and to carry the wire round both needles, Fig. 82. winding the coil around the upper in the opposite sense to that in which the coil is wound round the lower needle. Nobili applied the astatic arrangement of needles to the multiplying coils of Schweigger, and thus constructed a very sensitive instrument, the Astatic Galvanometer, Shown in Fig. 88. The special forms of galvanometer adapted for the measurement of currents are described in the next Lesson. Arago 191. Magnetic field due to Current. found that if a current be passed through a piece of copper wire it becomes capable of attracting iron filings to it so long as the current flows. These filings set themselves at right angles to the wire, and cling around it, but drop off when the circuit is broken. There is, then, a magnetic "field," around the wire which carries the current ; and it is important to know how the lines of force are distributed in this field. Let the central spot in Fig. 83 represent an imaginary cross-section of the wire, and let us suppose the current to be flowing in through the paper at that point. Then by Ampère's rule a magnet needle placed below will tend to set itself in the position shown, with its N. pole pointing to the left. The current will urge a needle above the wire into the reverse position. A needle on the right of the current will set itself at right angles to the current (i.e. in the plane of the paper), and with its N. pole pointing down, while the N. pole of a needle on the left would be urged up. In fact the tendency would be to urge the N. pole round the conductor in the same move; while the S. pole way as the hands of a watch would be urged in the opposite cyclic direction to that of the hands of a watch. If the current is reversed, and is regarded as flowing towards the reader, i.e. coming up out of the plane of the paper, as in the diagram of Fig. 1 If the student has any difficulty in applying Ampère's rule to this case and the others which succeed, he should carefully follow out the following mental operation. Consider the spot marked "in" as a hole in the ground into which the current is flowing, and into which he dives head-foremost. While in the hole he must turn round so as to face each of the magnets in succession, and remember that in each case the N.-seeking pole will be urged to his left. In diagram 84 he must conceive himself as coming up out of the hole in the ground where the current is flowing out. 84, then the motions would be just in the reverse sense. It would seem from this as if a N.-seeking pole of a magnet ought to revolve continuously round and round a current; but as we cannot obtain a magnet with one pole only, and as the S.-seeking pole is urged in an opposite direction, all that occurs is that the needle sets itself as a tangent to a circular curve surrounding the conductor. This is what Oerstedt meant when he described the electric current as acting "in a revolving manner," upon the magnetic needle. The field of force with its circular lines surrounding a current flowing in a straight conductor, can be examined experimentally with iron filings in the following way: A card is placed horizontally and a stout copper wire is passed vertically through a hole in it (Fig. 85). Iron filings are sifted over the card (as described in Art. 108), and a strong current from three Fig. 85. or four large cells is passed through the wire. On tapping the card gently the filings near the wire set themselves in concentric circles round it. 192. Equivalent Magnetic Shell: Ampère's Theorem. For many purposes the following way of regarding the magnetic action of electric currents is more convenient than the preceding. Suppose we take a battery and connect its terminals by a circuit of wire, and that a portion of the circuit be twisted, as in Fig. 86, into a looped curve, it will be found that the entire space enclosed by the loop possesses magnetic properties. In our figure the current is supposed to be flowing round the loop, as viewed from above, in the same direction as the hands of a clock move round; an imaginary man swimming round the circuit and always facing towards the centre would have his left side down. By Ampère's rule, then, a N. pole would be urged downwards through the loop, while a S. pole would be urged upwards. In fact the space enclosed by the loop of the circuit behaves Ꮓ Fig. 86. like a magnetic shell (see Art. 107), having its upper face of S.-seeking magnetism, and its lower face of N.-seeking magnetism. It can be shown in every case that a closed voltaic circuit is equivalent to a magnetic shell whose edges coincide in position with the circuit, the shell being of such a strength that the number of its lines of force is the same as that of the lines of force due to the current in the circuit. The circuit acts on a magnet attracting or repelling it, and being attracted or repelled by it, just exactly as its equivalent magnetic shell would do. Also, the circuit itself, when placed in a magnetic field, experiences the same force as its equivalent magnetic shell would do. 193. Maxwell's Rule. Professor Clerk Maxwell, who developed this method of treating the subject, has given the following elegant rule for determining the mutual action of a circuit and a magnet placed near it. Every portion of the circuit is acted upon by a force urging it in such a direction as to make it enclose within its embrace the greatest possible number of lines of |