(23) |

(24) |

In the spherical limit, , this is readily integrated to give , where . is the longitude difference, corresponding the arc-length on the auxiliary sphere.

Expanding in powers of and integrating term by term, we thus
obtain:

(26) |

Vincenty[5] has again rearranged a subset of the resulting equations into nested forms more suitable for computation:

(28) |

As in Eqn. (22), the origins of , and
have been shifted from the equator to the initial point
(1). is then given by

(29) |

2002-03-21