The table of haversines has brought to the navigator the best practical means for solving, irrespective of troublesome algebraic signs, certain required parts of the astronomical triangle. It was also noticed that this table saved a step in the time sight, as the hour angle could be picked out directly as a log haverslue. As the azimuth is but another angle of the astronomical triangle, it too should be taken directly from this haversine table. Thus far there appears to be no handy formula in any work on navigation, showing the way to accomplish this with convenience. As a large number of navigators still determine their position line by the longitude method, there is submitted here a formula which may be found helpful when used in conjunction with the time sight formula for finding hour angle, utilizing some of the same logarithms and requiring but two additional ones for determining at once both hour angle and azimuth. The formula is deduced as follows:
When the sides of a spherical triangle are known, the angles may be computed by a formula of the form.