Distance Off by Vertical Sextant Angle

Extract

Distance off by measuring the elevation of a mountain top above the horizon has been a popular means of finding position at sea ever since Captain Lecky published his famous tables. This popularity persists into the radar age because distance off can often be found from a vertical sextant angle long before a ship is within effective radar range of the coast. In view of this it is surprising that the standard textbooks on navigation give scant attention to this method and any seaman finding himself without Lecky's tables would find little guidance elsewhere.

Wing Commander E. W. Anderson in The Principles of Navigation indicates that the whole angle subtended by a mountain at a ship can be found by adding half the estimated distance off in miles to the visible angle in minutes, having first corrected this angle for dip and refraction. This can be proved by simple geometry by showing that the angle subtended by the part of a mountain hidden to an observer at sea-level is equal to half the distance off.