Note on the geometry of the Earth magnetic field useful to Faraday effect experiments

The geometric factor (M) involving the earth's magnetic field in the Faraday effect equation is studied. A total of 48 coefficients is used to compute this factor. Some representative curves are shown. It is found that in general this factor is not a constant for a given ray. However, when a ray passes near the saddle point of the ‘M-surface’ M can be assumed to be constant along the ray with reasonable accuracy. In other regions of the sky an empirical average value of M must be used for a given ray and its value depends on the direction of the ray and the a priori ionization density profile. The results are compared with values computed by using dipole earth field.