The sextant works based on the principle that a reflected ray of light leaves a plane surface at the same angle at which it strikes the surface, or “the angle of reflection is equal to the angle of incidence” (Bowditch, 1975) and the principle that two reflective planes or mirrors create an angle of inclination which, through logic and transposition, when doubled, equals the altitude of the celestial body: 

2BGC = BDC with line DC the observer’s line of sight 



A sextant is a doubly reflecting navigation instrument that measures the angular distance between two visible objects. The primary use of a sextant is to measure the angle between an astronomical object and the horizon for the purposes of celestial navigation. The estimation of this angle, the altitude, is known as sighting or shooting the object, or taking a sight. The angle, and the time when it was measured, can be used to calculate a position line on a nautical or aeronautical chart—for example, sighting the Sun at noon or Polaris at night (in the Northern Hemisphere) to estimate latitude. Sighting the height of a landmark can give a measure of distance off and, held horizontally, a sextant can measure angles between objects for a position on a chart.

A sextant can also be used to measure the lunar distance between the moon and another celestial object (such as a star or planet) in order to determine Greenwich Mean Time and hence longitude.





The principle of the instrument was first implemented around 1731 by John Hadley (1682–1744) and Thomas Godfrey (1704–1749), but it was also found later in the unpublished writings of Isaac Newton (1643–1727). Additional links can be found to Bartholomew Gosnold (1571–1607) indicating that the use of a sextant for nautical navigation predates Hadley's implementation. (This reference to Gosnold's use of a sextant, in a popular British travel magazine article, rather than in a nautical history journal, does not cite sources, and is very probably inaccurate.) In 1922, it was modified for aeronautical navigation by Portuguese navigator and naval officer Gago Coutinho. 

The name comes from the Latin sextus, or “one-sixth,” for the sextant’s arc spans 60°, or one-sixth of a circle. Octants, with 45° arcs, were first used to calculate latitude. Sextants were first developed with wider arcs for calculating longitude from lunar observations, and they replaced octants by the second half of the 18th century.




WHERE ARE WE - Calculating longitude and position require understanding nautical almanacs, adjusting for errors, declinations, and star charts, and that is just to identify a position, not plot a course. The sextant allowed for really precise measurements of distances and altitudes, which opened the calculations necessary to actually get a “fix” on a position. When combined with the spherical trigonometry of the navigational triangle: the spherical triangle with a side for polar distance, or the angular distance between the global position of the star; the colatitude which is the angular distance between the pole and the navigator; and the coaltitude, the distance between the navigator and the star, the sextant allowed for extremely precise calculations of latitude. The GPS system has largely replace traditional marine instruments, but one should always know how to find your position on a chart when the lights go out.




However wonderful the sextant was, there was still a piece of the puzzle of determining position missing. Without a way to measure longitude, the place on the globe east or west of the Greenwich Meridian, navigators were still limited in their knowledge, exploration and charting. It wasn’t until 1773, when John Harrison invented the chronometer, a method for keeping time, that navigation became precise. Once sailors could measure time, they could determine their speed equals distance equation, as well as determine how far east or west they were of their starting or destination point.



The H4 prize winning marine chronometer the size of a large pocket watch.


MISSING LINK - The H4 marine chronometer, as perfected by John Harrison many years before his death in 1776. It was the size of a large pocket watch. Unlike the marine chronometer that can be attributed to one man, the sextant is a development of the octant and that developed from other means, hence, the sextant is the product of many different minds. Clocks were not accurate enough before John Harrison to be considered as a true navigational instrument.



To determine position, the navigator first notes the dead reckoning (DR) position, then uses the Nautical Almanac to pinpoint where a specific celestial body is at that moment in time. Time in the almanac is Greenwich Time, or Universal Time, which is equal to Local Time plus or minus one hour for each fifteen degrees of longitude east or west of Greenwich’s longitude of zero degrees. However, longitude may be exactly what the navigator is trying to discover, so the Nautical Almanac fills in the pieces of the puzzle (Blewitt, 1995). To take a sun sight in winter, a navigator would measure the altitude of the sextant and the time. Then corrections would be made for sextant errors such as the dip, which refers to the distance the observer is from the horizon. For instance, the eye of a navigator standing on the deck of a ship may be ten feet off of the ocean. The correction to the sextant altitude would then be for twenty feet which equals 3’ using the Altitude Correction Table in the Nautical Almanac. 



Marine chronometer from HMS Beagle and Charles Darwin


SOLUTIONS - The chronometer was vital to the ability to create charts and safely navigate the world. The first chronometers were invented by a carpenter's son: John Harrison.

A Marine Chronometer is a clock that is precise and accurate enough to be used as a portable time standard; it can therefore be used to determine longitude by means of celestial navigation. When first developed in the 18th century, it was a major technical achievement, as accurate knowledge of the time over a long sea voyage is necessary for navigation, lacking electronic or communications aids. The first true chronometer was the work of one man, John Harrison, spanning 31 years of persistent experimentation and testing that revolutionized ocean navigation, so enabling the Age of Discovery to accelerate.

The Board of Longitude, charged with finding a solution to this navigation problem, failed to recognise when they had found what they were looking for. This is a frequent problem for experts who only want to recognise solutions that fit within their understanding of current knowledge - not accepting anything that does not conform. They would rather deny a solution. The marine world thought otherwise, gratefully accepting these timepieces as essential navigation aids. This included the Royal Navy's Captain James Cook (HMS Endeavour, Discovery & Resolution) and Captain Robert Fitzroy (HMS Beagle) 1763-1779.


This gimbaled Marine Chronometer seen above was one on H.M.S. Beagle during its second voyage (1831-1836) with Charles Darwin onboard. It sailed to the coast of South America, across the South Pacific towards the Galapagos Islands, New Zealand and Australia, in order to help establish a chain of reliable navigational co-ordinates around the globe.





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