which we may call magnetic parallels. These lines have the property of being everywhere perpendicular to the magnetic meridians; for, being drawn on the surface of the earth, which is supposed spherical, they are perpendicular to the vertical, and since they lie in the equipotential surfaces, they are perpendicular to the direction of the force. These lines are equipotential lines in reference to the horizontal component; at each point this component is normal to the line, and its mean value varies inversely as the distance between two adjacent lines. The magnetic equator corresponds to the surface V = o, which, unless the distribution is far from being symmetrical, will pass near the centre: the equator separates those points of the surface for which the potential is positive from those for which it is negative; the dip along this circle is not necessarily zero, nor the force constant. Thus, the magnetic parallels are not necessarily either lines of constant dip nor lines of constant force. The points of the surface where the force is vertical, and which are erroneously called the poles, are those in which the surface of the globe is a tangent to the equipotential surface which meets it; these are the points of the surface for which the absolute value of the potential is a maximum. Thus, in order to know the distribution of magnetism, it is sufficient to draw the equipotential lines for the surface of the globe. Gauss showed that in the most general case, and within the degree of accuracy of the observations, these lines may be algebraically expressed by formulæ containing twenty-four coefficients; so that when these coefficients have been calculated once for all, by means of an equal number of observations corrected for local disturbances, it is only needful to introduce the geographical co-ordinates of any given point into the formula to obtain the value of the magnetic elements at this point. The calculations of Gauss made for the year 1838 fix the following positions for those of the two so-called poles : North pole, 73° 35′ lat., 97° 59′ long. west from Greenwich. It will be seen that they are a long way from corresponding to the ends of one and the same diameter. 235. Variations of Terrestrial Magnetism.-The elements of the earth's magnetism are not constant at any given place, but undergo variations in the course of time. Among these variations $ 235.] Variations of Terrestrial Magnetism. 295 some appear to be accidental, while others, on the contrary, have a well-defined periodic character. 2114 Secular Variations.-Since the date of the earliest exact observations, slow changes have been found to be going on, which may be approximately represented by supposing a continuous uniform rotation of the magnetic axis about the terrestrial axis to be taking place in the direction of the hands of a watch, for an observer placed at the north pole, the period of a complete rotation being about 900 years (Fig. 200). Thus at Paris, which is represented in the figure by P, the declination, which was easterly when first recorded, was zero in 1666; since this time it has been westerly, and went on increasing until 1824, when it amounted to 24°; at present it is decreasing, and may be expected to become nothing again about the year 2114. The magnetic pole will then be on the other side of the north pole in respect to us. As to the dip, it has diminished steadily from 1666, and, on the same hypothesis, will continue to do so until about 2114. 1829 65° N 2400 E 2567 1666 FIG. 200. Daily Variations.—Other variations have a short period, and appear to be connected with the apparent motion of the sun, the moon, &c., and follow laws which are not yet known. These variations affect particularly the declination, which in one and the same place has a well-marked daily oscillation with two maxima and two minima. The amplitude of the excursion of the needle is greater during the day than during the night. The time at which the greatest deflection is reached differs in different places. At Kew the declination is greatest at about 1 or 2 P.M., and least at about 8 A.M., the difference being 12' or 14' in summer, and rather more than half as much in winter. Accidental Variations. — These variations are simultaneously produced over a great part of the surface of the earth, and always accompany the aurora borealis. They are called magnetic storms. Both daily and accidental variations are observed by special apparatus, known as registering magnetometers; the small move ments of suspended magnets, magnified by the method of reflexion, are registered continuously by photography. The variations commonly observed are those of declination and of the horizontal and vertical forces. The first is observed by means of a small bar suspended horizontally in the meridian by cocoon threads; the second is measured by means of a horizontal magnet suspended at right angles to the meridian by a twisted metal wire or by a bifilar suspension; the third, by a magnet that is movable like the beam of a balance about a knife-edge, and being exactly counterpoised for a given value of the vertical component, dips more or less as this value changes. CHAPTER XXII. ELECTRO-MAGNETISM. 236. Electro-Magnetism.-In studying the effects of electric currents, we have hitherto been concerned only with internal actions, that is to say, effects produced by the current in the conductors traversed by it. It now remains to investigate the actions produced outside the conductor, which, for this reason, are called the external actions. The part of Science which relates to these phenomena is called electro-magnetism; it originated in an experiment made by Oersted in July 1820, and it owes its principal developments to the researches of Ampère and of Faraday. 237. Oersted's Experiment-Ampère's Rule.-When a conductor through which a current is passing is brought near and parallel to a magnetic FIG. 201. needle, the latter is de- Y flected from its ordinary position (Fig. 201); this is the fact which Oersted observed. According to the relative positions of the needle and the circuit, the direction of the deflection is different. It may, however, be determined in each case by what is known as Ampère's Rule. Suppose an observer swimming in the direction of the current, so that it enters by his feet and emerges by his head if the observer has his face turned towards the needle, the north pole is always deflected to his left. We shall speak of this as the left of the current. 238. Ampère's Astatic Needle.-If it were not for the action of the earth, the needle would always set at right angles to the current. In order to show this, Ampère used a needle arranged like a dip-needle (§ 230), so that it moved only about a fixed axis passing through the centre of gravity, and he placed this axis parallel to the direction of the earth's force (Fig. 202). As the couple due to the earth acts in a plane containing the axis, it FIG. 202. dent of the degree has no effect on the position of the needle. The needle then always sets at right angles to the current, whatever be the strength of the latter. Hence it follows that the action of the current is exerted in a direction at right angles to the conducting wire, and that it acts oppositely on the two poles. 239. Galvanometer.-If we stretch the wire above a horizontal needle (Fig. 201) when it is at rest in the magnetic meridian, the needle is under the action of two systems of forces acting in planes at right angles to each other, and the needle takes up an intermediate position. Experiment shows that, other things being equal, the extent of the deflection is indepenof magnetisation of the needle, which proves that the two actions are in a constant ratio, and therefore that the force due to the current, like that due to the earth, is proportional to the strength of the pole upon which it acts. The deflection increases, moreover, with the strength of the current as measured by its chemical action, and may, therefore, serve as a measure of it. This is the principle of the electro magnetic measurement of the current, and of the apparatus which Ampère called a galvanometer (see Chapter xxviii.). The action of the current can be increased by coiling the conductor on a frame; the needle is put at the centre of the frame (Fig. 203), and the plane of the frame is placed in the magnetic meridian. It is easily seen from Ampère's rule that all parts of the current tend to deflect the needle in the same direction. Such a frame is known as Schweigger's Multiplier. |