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The Treble Bearing Problem

It may come as a surprise to many navigators that the interesting and valuable, although seemingly little-used, method in which three successive bearings of a single fixed mark are used to find course made good, has a history of not more than about half a century. When two or more suitably placed marks are in sight the course made good may readily be found from a series of fixes by cross bearings, and this technique is commonly used by coastal navigators. When, however, a single mark alone is available the reliability of running fixes depends upon the accuracy of estimations of courses and distances made good in the intervals between successive bearings. A table for finding the distance of a mark from two bearings and the distance run in the interval between observations was inserted in the first edition of Raper's Practice of Navigation in which the author informs his readers that the table was constructed at the suggestion of Sir Francis Beaufort and that it first appeared in the Nautical Magazine.