Sextant (navigation instrument)

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 start 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implemented around 1731 by John Hadley (1682-1744) and Thomas Gofrey (1704-1749), but it was also found later in the unpublished writings of Isaac Newton (1643-1727). In 1922, it was modified for aeronautical navigation by Portuguese navigator and Naval Officer Gago Coutinho.

Navigational sextants

Navigators' sextants were primarily used for ocean navigation.

Advantages

Like the Davis quadrant, the sextant allows celestial objects to be measured relative to the horizon, rather than relative to the instrument. This allows excellent precision. However, unlike the backstaff, the sextant allows direct observations of stars. This permits the use of the sextant at night when a backstaff is difficult to use. For solar observations, filters allow observation of the sun.

Since the measurement is relative to the horizon, the measuring pointer is a beam of light that reaches to the horizon. The measurement is thus limited by the angular accuracy of the instrument and not the sine error of the length of an alidade, as it is in a mariner's astrolabe or similar older instrument. 

A sextant does not require a completely steady aim, because it measures a relative angle. For example, when a sextant is used on a moving ship, the image of both horizon and celestial object will move around in the field of view. However, the relative position of the two images will remain steady, and as long as the user can determine when the celestial object touches the horizon the accuracy of the measurement will remain high compared to the magnitude of the movement. 

The sextant is not dependent upon electricity (unlike many forms of modern navigation) or anything human-controlled (like GPS satellites). For these reasons, it is considered an eminently practical back-up navigation tool for ships. 

Taking a sight

A sight (or measure) of the angle between the sun, a star, or a planet, and the horizon is done with the 'star telescope' fitted to the sextant using a visible horizon. One a vessel at sea even on misty days a sight may be done from a low height above the water to give a more definite, better horizon. Navigators hole the sextant by its handle in the right hand, avoiding touching the arc with the fingers. 

For a sun sight, a filter is used to overcome the glare such as "shades" covering both index mirror and the horizon mirror designed to prevent eye damage. By setting the index bar to zero, the sun can be viewed through the telescope. Releasing the index bar (either by releasing a clamping screw, or on modern instruments, using the quick-release button), the image of the sun cam be brought down to about the level of the horizon. It is necessary to flip back the horizon mirror shade to be able to see the horizon, and then the fine adjustment screw on the end of the index bar is turned until the bottom curve (the lower limb) of the sun just touches the horizon. 'Swinging' the sextant about the axis of the telescope ensures that the reading is being taken with the instrument held vertically. The angle of the sight is then read from the scale on the arc, making use of the micrometer or vernier scale provided. The exact time of the sight must also be noted simultaneously, and the height of the eye above sea-level recorded. 

An alternative method is to estimate the current altitude (angle) of the sun from navigation tables, then set the index bar to that angle on the arc, apply suitable shades only to the index mirror, and point the instrument directly at the horizon, sweeping it from side to side until a flash of the sun's rays are seen in the telescope. Fine adjustments are then made as above. This method is less likely to be successful for sighting stars and planets. 

Star and planet sights are normally taken during nautical twilight at dawn or dusk, while both the heavenly bodies and the sea horizon are visible. There is no need to use shades or to distinguish the lower limb as the body appears as a mere point in the telescope. The moon can be sighted, but it appears to move very fast, appears to have different sizes at different times, and sometimes only the lower or upper limb can be distinguished due to its phase. 

After a sight is taken, it is reduced to a position by looking at several mathematical procedures. The simplest sight reduction is to draw the equal-altitude circle of the sighted celestial object on a globe. The intersection of that circle with a dead-reckoning track, or another sighting, gives a more precise location. 

Sextants can be used very accurately to measure other visible angles, for example between one heavenly body and another and between landmarks ashore. Used horizontally, a sextant can measure the apparent angle between two landmarks such as a lighthouse and a church spire, which can then be used to find the distance off or out to sea (provided the distance between the two landmarks is known). Used vertically, a measurement of the angle between the lantern of a lighthouse of known height and the sea level at its base can also be used for distance off. 

Adjustment 

Due to the sensitivity of the instrument it is easy to knock the mirrors out of adjustment. For this reason a sextant should be checked frequently for errors and adjusted accordingly. 

There are four errors that can be adjusted by the navigator and they should be removed in the following order. 

Perpendicularity error 

This is when the index mirror is not perpendicular to the frame of the sextant. To test for this, place the index arm at about 60° on the arc and hold the sextant horizontally with the arc away from you at arms length and look into the index mirror. The arc of the sextant should appear to continue unbroken into the mirror. If there is an error then the two views will appear to be broken. Adjust the mirror until the reflection and direct view of the arc appear to be continuous. 

Side error

This occurs when the horizon glass/mirror is not perpendicular to the plane of the instrument. To test for this, first zero the index arm then observe a star through the sextant. Then rotate the tangent screw back and forth so that the reflected image passes alternately above and below the direct view. If in changing from one position to another the reflected image passes directly over the unreflected image, no side error exists. If it passes to one side, side error exists. The user can hold the sextant on its side and observe the horizon to check the sextant during the day. If there are two horizons there is side error; adjust the horizon glass/mirror until the star merge into one image or the horizons are merged into one. Side error is generally inconsequential for observations and can be ignored or reduced to a level that is merely inconvenient. 

Collimation error

This is when the telescope or monocular is not parallel to the plane of the sextant. To check for this you need to observe two stars 90° or more apart. Bring the two stars into coincidence either to the left or the right of the field of view. Move the sextant slightly so that the stars move to the other side of the field of view. If they separate there is collimation error. As modern sextants rarely use adjustable telescopes, they do not need to be corrected for collimation error. 

Index error

This occurs when the index and horizon mirrors are not parallel to each other when the index arm is set to zero. To test for index error, zero the index arm and observe the horizon. If the reflected and direct image of the horizon are in line there is no index error. If one is above the other adjust the index mirror until the two horizons merge. This can be done at night with a star or with the moon .