Geometrical researches concerning terrestrial magnetism

The object of this paper is to exhibit methods of conducting the mathematical inquiries which are applicable to the magnetism of the earth, by the aid of the coordinate geometry of three dimensions. When a point on the surface of the earth is given by means of its geographical coordinates, we can also refer it to any rectilinear coordinates that may be found convenient, and the transformations of the expressions can be made by known and familiar methods. Also, since at a given point the needle is deflected a measured quantity from the meridian plane, estimated on a tangent plane to the earth at the given point, and is also depressed another measured quantity below the same plane at that given point, its position is fixed by means of these measures. It will hence become capable of reference also to the same rectilinear coordinates as those into which the geographical coordinates were transformed. The equation of the line, into which the dipping-needle disposes itself, becomes, therefore, capable of expression in terms of the measured quantities above referred to ; viz., the latitude, longitude, dip, and variation. The method of obtaining the constants which enter into the equations of the needle” as referred to the equator, a given meridian, and the meridian at right angles to it, are then detailed at length by the author; and these equations are calculated for six different places : Port Bowen, Boat Island. Chamisso Island, Valparaiso, Paris, and Paramatta.