Notes on Isomagnetic Charts: VII—Mathematical Notes on Isoporic Charts and Their Singular Points

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Abstract
Summary—The nature of the isoporic lines is examined for the magnetic potential V and for the magnetic elements D, H, I, Z, and F. In general the singular points on an isomagnetic chart are not singular points on the corresponding isoporic chart, and vice versa. In particular, the singular points for V, which are dip‐poles, are usually not singular points for its rate of change . But the dip‐poles are singular points not only for D, H, and I (though not in general for Z and F) but also for , , and (though not in general for and ).If the dip‐pole is moving, it is a double focus for (which there takes all values from −∞ to +∞), and a non‐uniform ray‐pole for and the relation of the isopors to the velocity of the dip‐pole is indicated. If the dip‐pole is stationary, it is a non‐uniform ray‐pole for and a conical focus or node for (which there is zero) and for .The isopors for V, D, H, I, Z, and F for the field of a varying centered dipole are determined and illustrated. It is shown that in the region around an associated pair of local dip‐poles the isopors must be very complicated, those for D, for example, having at least eight singular points in the region. The isopors near the principal geomagnetic dip‐poles are discussed, and it is shown that in these regions certain isoporic charts appear to be inconsistent with theory.The isoporic charts for 1922 for D and H given, by the Admiralty and by H. W. Fisk are compared and discussed. For 126 points uniformly spaced at 20° intervals the average numerical difference between the indications of the two charts is 56 per cent for , and 69 per cent for H, of the average numerical value of D and H, respectively, at these points.

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