  A concise derivation of the "Joel equations", which allow for the
determination of the axis angle 2V from measurements of extinction directions
on a spindle stage, is provided starting from the wave-equation. Only analytic
methods and no geometric arguments referring to stereographic projections are
invoked. For error free data, the resulting equations allow for a closed form
solution. If angle data with measurement error are to be used, a maximum
likelihood estimation methodology is proposed, which may be solved using e.g.
iterative reweighting. The method is tested with and compared to published
data.
