Notes on Isomagnetic Charts: III—The Isogonic and X‐, Y‐Charts for the Centered Dipole Field

Abstract

Summary—Various forms of the equations of the isogonic lines are derived, for the field of the centered magnetic dipole. The isogonic chart for this field is shown to have two singular points in addition to the four uniform ray‐poles (one at each magnetic or geographic pole); these singular points, which are situated at the intersections of the magnetic and geographic equators are rectangular nodes. The equation and form of the nodal curves are discussed. The area over which the magnetic declination exceeds the obliquity of the magnetic axis is also considered; it is shown to cover more than a third of the whole area of the sphere, however small the obliquity may be.The Y‐ and X‐isomagnetic charts are also briefly considered; the former has only two singular points, namely non‐uniform ray‐poles at the geographic poles; these are also (non‐uniform) ray‐poles of the X‐chart, which in addition has two nodes at the same points as those of the D‐chart; but in the case of X these nodes are not rectangular.