Appendix II Power series solutions suitable for the tropics.

In this appendix are the derivation of those expansions unsuitable for use at South African latitudes. Where the magnitude of the latitude in radians is a lot smaller than 1, these may in fact be faster and better than the Newton-Raphson approaches given above.

• Power series of in terms of t
• The inverse of as a power series.
• Expanding L, the distance along the central meridian from the equator.
• Expanding R as a Taylor series of an analytic function.
  • Matching terms in the power series.
• Inverting the transform.