Equations are derived to deduce the height and geographical position of auroral arcs from observations of the azimuths at several zenith angles such as are obtained by surveying the sky photometrically in almucantars or by all-sky camera photographs. The arc must lie along a small circle of the spherical earth and its height must remain constant along the path of the observations. Imperfect geometry of real arcs and the limited accuracy of observations necessitate a graphical solution to the problem. The method is found to be particularly useful for middle-latitude subvisual red arcs. Observational data on nine such arcs suggest a relationship between their height and geomagnetic latitude.
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M. H. Rees (1963) studied this question.