meridian a magnetised steel wire, about 23 inches long, taking care that the north pole was turned downwards, the south pole of the wire being opposite to the north pole of the proof-needle, but at variable distances. The centre of the attractive action of this pole should be situated in the horizontal plane of the proof-needle, a necessary condition, in order that the needle should not run the risk of dipping, either below or above this plane. For this reason it would be necessary to place the south extremity of the magnetised steel wire at about an inch above the same plane. Things being thus arranged, at 4 inches from the wire, the needle made forty-one oscillations per minute instead of fifteen; at 8 inches it made twenty-four; at 16 it made seventeen. From the law of the pendulum that we have just mentioned as being applicable to the present case, we have, calling m the force of terrestrial magnetism, m' that which acts upon the needle at the distance of 4 inches, and m" that which acts at the distance of 8 inches, But, in order to obtain the law of the simple action of the magnet upon the movable needle, we must deduct from m' and m" the total force acting upon this needle, m, the force of terrestrial magnetism; the differences m'-m, m"-m express correctly the simple action of the magnet at the respective distances of 4 and 8 inches. Now we deduce from the two preceding propositions m'. ・m = 412-152 1456 = m" -m 242-152 351 =4.1. Thus the force that acts at 4 inches, namely, at a certain distance, is quadruple that which acts at a double distance. We should find for the distance of 16 inches, 172-152-64, a number a 1456 little too small; for =22, and it ought to be found to 64 be 16. This variation occurs because that, at the distance of 16 inches, the lower north pole of the fixed magnet acts upon the north pole of the movable needle, and diminishes, by its repulsive effect, the attractive action of the south pole which is above. It was with a view of avoiding this incon venience that we gave a considerable length to the vertical magnet; but this precaution, which fulfils the object in view, as we may easily conceive, when the movable needle is not too far off, is no longer sufficient as soon as the distance exceeds a certain limit. In fine, we may conclude equally from both methods that magnetic attractions and repulsions are inversely as the square of the distance. Distribution of Magnetism in a magnetised Bar. The same two methods that we have just employed to find the law of the inverse of the square, come to our aid also in determining the distribution of magnetism in a magnetised bar. We may too, by a very simple method, prove the inequality of this distribution: it is sufficient for this to hold a magnetised bar in a horizontal position, and to move under its lower surface and along its whole length a small piece of soft iron, sustaining a small scale-pan by three or four threads. We very quickly discover that the weight, which must be put in the pan to detach the soft iron, varies much with the position of the point of the magnet that acts upon the iron; hence we conclude that the magnetic force, which may be regarded as proportional to the weight, is very unequally distributed. Thus it is at its maximum at two points, distant a tenth of an inch or so from the two extremities of the bar. Setting out from these points, it goes on diminishing very rapidly, either in the interval by which they are separated, or from each of them to the same extremity of the bar. The manner in which iron filings are distributed around the bar, when they are attracted by it, confirms this result. We see them, in fact, accumulated in a large proportion about the poles, around which they seem to converge from all parts, as towards centres of action (Fig. 76.). The central portion of the bar attracts only a very small number of the particles of iron; it even sometimes happens that it does not attract any. However, if the bar is not very long, the filings are distributed around the central point, describing a species of curves which go from one pole to the other, and forming as it were an ellipse, having for its axis that of the bar, and for its foci its two poles. To make these figures evident, we should project the iron filings, after the manner of rain, upon a sheet of white paper or upon a pane of glass, covering the magnetised bar; by means of small taps given to the paper, the arrangement of the filings and the formation of the figures is facilitated. M. de Haldat succeeded in fixing these figures, which he termed magnetic phantoms; with this view, he applied to a pane of glass upon which the figure is formed, a sheet of stiff paper impregnated with starch glue prepared from gelatine; the powder of iron filings is thus obtained fixed, as it was distributed upon the glass. We are, by this means, enabled the more easily to study the distribution in all its details. M. de Haldat thus proved that the centres, whence the radiating lines arise, are in truth the poles of the magnet, which are themselves deprived of the iron filings. The disposition of the curves formed by the iron filings is such that, divergent at their origin, they are never distinct and separate from each other throughout their extent. On the contrary, they unite again after their origin, and form species of meshes. M. de Haldat has also studied the magnetic phantoms produced by two magnets placed in relation to each other in various ways; and he estimates that this study may lead to important results on the state of magnetism in all bodies, on its power and its distribution. Long before M. de Haldat, the magnetic curves had fixed the attention of many philosophers, independently of the description given of them by Lucretius.* Thus Mushenboeck, Lambert (who had succeeded in giving the equation of their curves), Playfair, and Leslie, have also been successively occupied with them. Dr. Roget simplified the methods described by his predecessors, and pointed out some easy processes for obtaining these curves graphically. The following are the principal properties of these curves, engendered by the simultaneous and contrary or similar action of the two polarities of magnets upon parcels of soft iron, or upon infinitely small magnets. 1st. The difference of the co-sines of the angles formed with the axis of the magnetised bar by the lines which join any given point of the curve with the two poles, is a constant quantity, these angles being taken on the same side. 2nd. A tangent, drawn to any point of the curve, cuts the axis produced of the magnet producing it in such a point, that its distance from the nearest pole is to the absolute length of the magnet as the cube of the distance from the point of the tangent to the same pole is to the difference of the cubes of its distances from the two poles. * "Fit quoque, ut a lapide hoc ferri natura recedat Ac ramenta simul ferri furere intus ahenis Invenit in ferro; neque trabat quâ tranet, ut ante; Ferrea textu suo, quo pacto respuit ab se, Atque per æs agitat sine eo quod sæpe resorbet." De Rerum Naturâ, vi. 1041-54. Wakefield's edition. 3rd. The sines of the angles, formed by this tangent with the right lines which measure these distances to the two poles, are to each other as the squares of their distances. Dr. Roget described an instrument suitable for tracing these curves by a continuous movement, and founded upon the first of the principles announced above. He also acquainted us with the following process, by the aid of which they are described by points: From each pole as a centre, and with radii of an arbitrary length, two circumferences are traced. After having produced the axis until it meets them, it is divided into any number of equal parts; each of the points of the division is projected perpendicularly upon the circumference. Through the centre of each circumference, and the points that have been determined upon it, are drawn radii, indefinitely prolonged. These radii cut each other mutually in points which belong to the curves in question. If the two generating poles are heterogeneous, the curves are called convergent, and are curvilinear diagonals, in the direction of the magnetised axis, of quadrilateral intervals formed by the intersection of the radii. If the two poles are homogeneous, these curves are called divergent, and their direction is determined by that of the curvilinear diagonals perpendicular to the former, and consequently to the axis that joins the poles." He But to return to the employment of the two methods, which will give us more accurate results. With the torsion balance, Coulomb used two similar magnetised needles, one fixed, the other movable; by means of which he determined the law of the inverse of the square. He made the fixed one slide behind a thin wooden rule, which separated it from the movable one, care being taken that it remained vertical. then noted the torsion which it was necessary to give to the suspending thread, to constrain the extremity of the movable needle to remain in the plane of the magnetic meridian, and almost in contact with the fixed one, from which it was separated only by the thickness of the wooden rule. By operating in this manner, Coulomb avoided the effect upon the *For the mathematical developments, see the note D, at the end of the volume. |