The octant, also called the ‘Hadley quadrant’, was invented by John Hadley in 1730. They have a 45° arc but can measure 90°. They operate similarly to the back-staff, but use a mirror to reflect the sun through colored filters to line up the horizon. Like the reflecting circle and later sextant light reflected from an object is displaced by twice that angle, so even though octants were fitted with an arc of only one-eighth of a circle, they gave an effective reading of twice that or 45°, same as an quadrant. So the ancient quadrant lived on. Octants were made of wood, often mahogany and ebony in the late 1700s with brass and ivory fittings and silvered scales. As testimony to their enduring value less elegant models were still being certified for marine navigation as late as 1925. The sextant was conceptualised in the late 1750s based on the contemporary invention of the reflecting circle even though it resembles an octant. The earlier ones were large, heavy and cumbersome. They employ a relatively small 60-degree arc and refined methods of marking degrees on the scale lead to hand-held versions that became rapidly popular by the end of the century. The sextant with its superior accuracy allowed crude estimates of longitude based on the ‘lunar distance’ method (distance of certain stars from the moon) that was discovered in 1767. The American military adapted sextants to aircraft in 1922. They were designed for reference to the broad and steep angle between the aircraft and horizon. Some were attached to gyroscopes and called gyro-sextants. In 1933 an electrically driven gyro-octant was tested. Sextants are still made and sold as backup navigation devises, and seamen are still instructed in their use.

Standards were established for clocks and compasses by the mid-1700s and chronometers, clocks that keep time at some reference position, usually homeport, were carried aboard most ships by the end of the eighteenth century. If time at a reference longitude were known, navigators could take ‘lunar distance’ measurements from key stars and use look up tables to determine longitude.

The station pointer is a triple-armed circular protractor (instruments vary from about 5 to 12 inches in diameter) originally made of brass that is placed over a map or chart to determine a ship’s position (or on land, the user’s location) relative to three distant points that are on the map. Other instruments of navigation include ocean depth gauges or depth sounders which were replaced by echo-sounding and sonar in the 1920s, ships logs, navigational charts, traverse boards or helmsman’s boards which record a ship’s course when it was tracking into the wind and was used with a compass and ship’s log. Traverse boards were in use at least by the sixteenth century. Ancient techniques that were used to estimate a ships speed employed ropes with a log or board tied to the end, hence the origin of ‘log’ or ‘logging’, log-lines or ropes with knots tied at 6-foot intervals (fathoms), were used. Recent ship speedometers from the early 1900s use small foot-long torpedoes with spiral fins attached to a rope with a speed gauge.