A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: John Brown
Date: 2014 Jun 11, 10:33 -0700
Yes, but what Bowditch has to say about haversines applies equally to versines. Did the fact that versine values are between 0 and 2 and those of the haversine are between 0 and 1 make a difference to the compilers or users of nautical tables?
Burton's 4 Figure Navigation Tables use versines and his notes simply say that "all navigational formulae in which the haversine occurs remain true when the versine is substituted".
Incidentally, from the same notes, when calculating zenith distance using the haversine/versine formula, Burton recommends adding the true altitude to the calculated zenith distance to arrive at the intercept, then:-
Excess (over 90 deg) = Towards
Defect (from 90 deg) = Away
Which saves the step of subtracting either of the altitude or the zenith distance from 90 deg.