also determined as part of the solution of the great circle problem are the arc lengths, formula_76 and formula_77, measured from the equator crossing to formula_7 and formula_10. the distance formula_15 is found by computing the length of a portion of perimeter of the ellipse using the formula giving the meridian arc in terms the parametric latitude. in applying this formula, use the semi-axes for the great ellipse (instead of for the meridian) and substitute formula_76 and formula_77 for formula_20.