The octant, also called reflecting quadrant, is a measuring instrument

Measuring instrument

In the physical sciences, quality assurance, and engineering, measurement is the activity of obtaining and comparing physical quantities of real-world objects and events. Established standard objects and events are used as units, and the process of measurement gives a number relating the item...

 used primarily in navigation

Navigation

Navigation is the process of monitoring and controlling the movement of a craft or vehicle from one place to another. It is also the term of art used for the specialized knowledge used by navigators to perform navigation tasks...

. It is a type of reflecting instrument

Reflecting instrument

Reflecting instruments are those that use mirrors to enhance their ability to make measurements. In particular, the use of mirrors permits one to observe two objects simultaneously while measuring the angular distance between the objects...

.

Etymology

The name octant derives from the Latin octans meaning eighth part of a circle, because the instrument's arc is one eighth of a circle.

Reflecting quadrant derives from the instrument using mirrors to reflect the path of light to the observer and, in doing so, doubles the angle measured. This allows the instrument to use a one-eighth of a turn

Turn (geometry)

A turn is an angle equal to a 360° or 2 radians or \tau radians. A turn is also referred to as a revolution or complete rotation or full circle or cycle or rev or rot....

 to measure a quarter-turn

Turn (geometry)

A turn is an angle equal to a 360° or 2 radians or \tau radians. A turn is also referred to as a revolution or complete rotation or full circle or cycle or rev or rot....

 or quadrant

Circular sector

A circular sector or circle sector, is the portion of a disk enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector. In the diagram, θ is the central angle in radians, r the radius of the circle, and L is the arc length of the...

.

Newton's reflecting quadrant

Isaac Newton

Isaac Newton

Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

's reflecting quadrant was invented around 1699. A detailed description of the instrument was given to Edmond Halley

Edmond Halley

Edmond Halley FRS was an English astronomer, geophysicist, mathematician, meteorologist, and physicist who is best known for computing the orbit of the eponymous Halley's Comet. He was the second Astronomer Royal in Britain, following in the footsteps of John Flamsteed.-Biography and career:Halley...

, but the description was not published until after Halley's death in 1742. It is not known why Halley did not publish the information during his life, however this prevents Newton from getting the credit for the invention that is generally given to John Hadley

John Hadley

John Hadley was an English mathematician, inventor of the octant, a precursor to the sextant, around 1730.He was born in Bloomsbury, London, to Katherine FitzJames and George Hadley....

 and Godfrey

Thomas Godfrey (inventor)

Thomas Godfrey was an optician and inventor in the American colonies, who around 1730 invented the octant. At approximately the same time an Englishman, John Hadley, also invented the octant independently....

.

One copy of this instrument was constructed by Thomas Heath and may have been shown in Heath's shop window prior to its being published by the Royal Society in 1742.

Newton's instrument used two mirrors, but they were used in an arrangement somewhat different than the two mirrors found in modern octants and sextant

Sextant

A sextant is an instrument used to measure the angle between any two visible objects. Its primary use is to determine the angle between a celestial object and the horizon which is known as the altitude. Making this measurement is known as sighting the object, shooting the object, or taking a sight...

s. The diagram on the right shows the configuration of the instrument.

The 45° arc of the instrument (P-Q), was graduated

Graduation (instrument)

-Linear graduation:Linear graduation of a scale occurs on a straight instrument. The graduation can identify linear measures, such as inches or millimetres on a rule. They can also be non-linear such as logarithmic or other transcendental scales....

 with 90 divisions of a half-degree each. Each such division was subdivided into 60 parts and each part further divided into sixths. This results in the arc being marked in degrees, minutes and sixths of a minute (10 seconds). Thus the instrument could have readings interpolated to 5 seconds of arc. This fineness of graduation is only possible due to the large size of the instrument - the sighting telescope alone was three to four feet long.

A sighting telescope

Telescope

A telescope is an instrument that aids in the observation of remote objects by collecting electromagnetic radiation . The first known practical telescopes were invented in the Netherlands at the beginning of the 1600s , using glass lenses...

(A-B), three or four feet long, was mounted along one side of the instrument. A horizon mirror, was fixed at a 45° angle in front of the telescope's objective lens (G). This mirror was small enough to allow the observer to see the image in the mirror on one side and to see directly ahead on the other. The index arm (C-D) held an index mirror (H), also at 45° to the edge of the index arm. The reflective sides of the two mirrors nominally faced each other, so that the image seen in the first mirror is that reflected from the second.
With the two mirrors parallel, the index reads 0°. The view through the telescope sees directly ahead on one side and the view from the mirror G sees the same image reflected from mirror H (see detail drawing to the right). When the index arm is moved from zero to a large value, the index mirror reflects an image that is in a direction away from the direct line of sight. As the index arm movement increases, the line of sight for the index mirror moves toward S (to the right in the detail image). This shows a slight deficiency with this mirror arrangement. The horizon mirror will block the view of the index mirror at angles approaching 90°.

The length of the sighting telescope seems remarkable, given the small size of the telescopes on modern instruments. This was likely Newton's choice of a way to reduce chromatic aberrations. Short–focal length

Focal length

The focal length of an optical system is a measure of how strongly the system converges or diverges light. For an optical system in air, it is the distance over which initially collimated rays are brought to a focus...

 telescopes, prior to the development of achromatic lenses, produced an objectionable degree of aberration, so much so that it could affect the perception of a star's position. Long focal lengths were the solution, and this telescope would likely have had both a long–focal length objective lens and a long–focal length eyepiece

Eyepiece

An eyepiece, or ocular lens, is a type of lens that is attached to a variety of optical devices such as telescopes and microscopes. It is so named because it is usually the lens that is closest to the eye when someone looks through the device. The objective lens or mirror collects light and brings...

. This would decrease aberrations without excessive magnification.

The inventors of the octant

Two men independently developed the octant around 1730: John Hadley

John Hadley

John Hadley was an English mathematician, inventor of the octant, a precursor to the sextant, around 1730.He was born in Bloomsbury, London, to Katherine FitzJames and George Hadley....

 (1682–1744), an English mathematician, and Thomas Godfrey

Thomas Godfrey (inventor)

Thomas Godfrey was an optician and inventor in the American colonies, who around 1730 invented the octant. At approximately the same time an Englishman, John Hadley, also invented the octant independently....

 (1704–1749), a glazier in Philadelphia. While both have a legitimate and equal claim to the invention, Hadley generally gets the greater share of the credit. This reflects the central role that London and the Royal Society played in the history of scientific instruments in the eighteenth century.

Two others who created octants during this period were Caleb Smith, an English insurance broker with a strong interest in astronomy (in 1734), and Jean-Paul Fouchy, a mathematics professor and astronomer in France

France

The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...

 (in 1732).

Hadley's versions

Hadley produced two versions of the reflecting quadrant. Only the second is well known and is the familiar octant.

Hadley's reflecting quadrant

Hadley's first reflecting quadrant was a simple device with a frame spanning a 45° arc. In the image at the right, from Hadley's article in the Philosophical Transactions of the Royal Society, you can see the nature of his design. A small sighting telescope was mounted on the frame along one side. One large index mirror was mounted at the point of rotation of the index arm. A second, smaller horizon mirror was mounted on the frame in the line of sight of the telescope. The horizon mirror allows the observer to see the image of the index mirror in one half of the view and to see a distant object in the other half. A shade was mounted at the vertex of the instrument to allow one to observe a bright object. The shade pivots to allow it to move out of the way for stellar observations.

Observing through the telescope, the navigator would sight one object directly ahead. The second object would be seen by reflection in the horizon mirror. The light in the horizon mirror is reflected from the index mirror. By moving the index arm, the index mirror can be made to reveal any object up to 90° from the direct line of sight. When both objects are in the same view, aligning them together allows the navigator to measure the angular distance between them.

Very few of the original reflecting quadrant designs were ever produced. One, constructed by Baradelle, is in the collection if the Musée de la Marine, Paris.

Hadley's octant

Hadley's second design had the form familiar to modern navigators. The image to the right, also taken from his Royal Society publication, shows the details.

He placed an index mirror on the index arm. Two horizon mirrors were provided. The upper mirror, in the line of the sighting telescope, was small enough to allow the telescope to see directly ahead as well as seeing the reflected view. The reflected view was that of the light from the index mirror. As in the previous instrument, the arrangement of the mirrors allowed the observer to simultaneously see an object straight ahead and to see one reflected in the index mirror to the horizon mirror and then into the telescope. Moving the index arm allowed the navigator to see any object within 90° of the direct view.

The significant difference with this design was that the mirrors allowed the instrument to be held vertically rather than horizontally and it provided more room for configuring the mirrors without suffering from mutual interference.

The second horizon mirror was an interesting innovation. The telescope was removable. It could be remounted so that the telescope viewed the second horizon mirror from the opposite side of the frame. By mounting the two horizon mirrors at right angles to each other and permitting the movement of the telescope, the navigator could measure angles from 0 to 90° with one horizon mirror and from 90° to 180° with the other. This made the instrument very versatile. For unknown reasons, this feature was not implemented on octants in general use.

Comparing this instrument to the photo of a typical octant at the top of the article, one can see that the only significant differences in the more modern design are:

• The location of the horizon mirror and telescope or sighting pinnula is lower.
• The internal bracing of the frame is more central and robust.
• The position of the shades for the index mirror is in the path between the index and horizon mirrors rather than at the top of the instrument.
• Multiple shades are used to allow for different levels of shading.
• Separate shades are provided on the horizon mirror for sighting a low sun position with a very bright horizon.
• The second horizon mirror and accompanying alidade is not provided.

Smith's Astroscope

Caleb Smith, an English insurance broker with a strong interest in astronomy, had created an octant in 1734. He called it an Astroscope or Sea-Quadrant. His used a fixed prism

Prism (optics)

In optics, a prism is a transparent optical element with flat, polished surfaces that refract light. The exact angles between the surfaces depend on the application. The traditional geometrical shape is that of a triangular prism with a triangular base and rectangular sides, and in colloquial use...

 in addition to an index mirror to provide reflective elements. Prisms provide advantages over mirrors in an era when polished speculum metal

Speculum metal

Speculum metal is a mixture of around two-thirds copper and one-third tin making a white brittle alloy that can be polished to make a highly reflective surface. It is used primarily to make different kinds of mirrors including early reflecting telescope optical mirrors...

 mirrors were inferior and both the silvering

Silvering

Silvering is the chemical process of coating glass with a reflective substance. When glass mirrors first gained widespread usage in Europe during the 16th century, most were made of an amalgam of tin and mercury, but by the 19th century mirrors were commonly made through a process by which silver...

 of a mirror and the production of glass with flat, parallel surfaces was difficult.

In the drawing to the right, the horizon element (B) could be a mirror or a prism. On the index arm, the index mirror (A) rotated with the arm. A sighting telescope

Telescope

A telescope is an instrument that aids in the observation of remote objects by collecting electromagnetic radiation . The first known practical telescopes were invented in the Netherlands at the beginning of the 1600s , using glass lenses...

 was mounted on the frame (C). The index did not use a vernier or other device at the scale (D). Smith called the instrument's index arm a label, in the manner of Elton for his mariner's quadrant

Elton's quadrant

An Elton's quadrant is a derivative of the Davis quadrant. It adds an index arm and artificial horizon to the instrument. It was invented by John Elton a sea captain who patented...

.

Various design elements of Smith's instrument made it inferior to Hadley's octant and it was not used significantly. For example, one problem with the Astroscope was that angle of the observer's line of sight. By looking down, he had greater difficulty in observing than an orientation with his head in a normal orientation.

Advantages of the octant

The octant provided a number of advantages over previous instruments.

The sight was easy to align because the horizon and the star seem to move together as the ship pitched and rolled. This also created a situation where the error in observation was less dependent on the observer, as he could directly see both objects at once.

With the use of the manufacturing techniques available in the 18th century, the instruments were capable of reading very accurately. The size of the instruments was reduced with no loss of accuracy. An octant could be half the size of a Davis quadrant with no increase in error.

Using shades over the light paths, one could observe the sun directly, while moving the shades out of the light path allowed the navigator to observe faint stars. This made the instrument usable both night and day.

By 1780, the octant and sextant had almost completely eliminated all previous instruments.

Production of the octant

Early octants were constructed primarily in wood, with later versions incorporating ivory and brass components. The earliest mirrors were polished metal, since the technology to produce silvered

Silvering

Silvering is the chemical process of coating glass with a reflective substance. When glass mirrors first gained widespread usage in Europe during the 16th century, most were made of an amalgam of tin and mercury, but by the 19th century mirrors were commonly made through a process by which silver...

 glass mirrors with flat, parallel surfaces was limited. As glass polishing techniques improved, glass mirrors began to be provided. These used coatings of mercury-containing tin amalgam; coatings of silver or aluminum were not available until the 19th century. The poor optical quality of the early polished speculum metal

Speculum metal

Speculum metal is a mixture of around two-thirds copper and one-third tin making a white brittle alloy that can be polished to make a highly reflective surface. It is used primarily to make different kinds of mirrors including early reflecting telescope optical mirrors...

 mirrors meant that telescopic sights were not practical. For that reason, most early octants employed a simple naked-eye sighting pinnula instead.
Early octants retained some of the features common to backstaves

Backstaff

The backstaff or back-quadrant is a navigational instrument that was used to measure the altitude of a celestial body, in particular the sun or moon...

, such as transversals

Transversal (instrument making)

Transversals are a geometric construction on a scientific instrument to allow a graduation to be read to a finer degree of accuracy. Transversals have been replaced in modern times by vernier scales.-History:...

 on the scale. However, as engraved, they showed the instrument to have an apparent accuracy of only two minutes of arc while the backstaff appeared to be accurate to one minute. The use of the vernier scale allowed the scale to be read to one minute, so improved the marketability of the instrument. This and the ease in making verniers compared to transversals, lead to adoption of the vernier on octants produced later in the 18th century.

Octants were produced in large numbers. In wood and ivory, their relatively low price compared to an all-brass sextant made them a popular instrument. The design was standardized with many manufacturers using the identical frame style and components. Different shops could make different components, with woodworkers specializing in frames and others in the brass components. For example, Spencer, Browning and Rust, a manufacturer of scientific instruments in England from 1787 to 1840 (operating as Spencer, Browning and Co. after 1840) used a Ramsden

Jesse Ramsden

Jesse Ramsden FRSE was an English astronomical and scientific instrument maker.Ramsden was born at Salterhebble, Halifax, West Riding of Yorkshire, England. After serving his apprenticeship with a cloth-worker in Halifax, he went in 1755 to London, where in 1758 he was apprenticed to a...

 dividing engine

Dividing engine

A dividing engine is a device specifically employed to mark graduations on measuring instruments.-History:There has always been a need for accurate measuring instruments...

 to produce graduated

Graduation (instrument)

-Linear graduation:Linear graduation of a scale occurs on a straight instrument. The graduation can identify linear measures, such as inches or millimetres on a rule. They can also be non-linear such as logarithmic or other transcendental scales....

 scales in ivory. These were widely used by others and the SBR initials could be found on octants from many other manufacturers.

Examples of these very similar octants are in the photos in this article. The image at the top is essentially the same instrument as the one in the detail photos. However, they are from two different instrument makers - the upper is labelled Crichton - London, Sold by J Berry Aberdeen while the detail images are of an instrument from Spencer, Browning & Co. London. The only obvious difference is the presence of horizon shades on the Crichton octant that are not on the other.
These octants were available with many options. A basic octant with graduations directly on the wood frame were least expensive. These dispensed with a telescopic sight, using a single- or double-holed sighting pinnula instead. Ivory scales would increase the price, as would the use of a brass index arm or a vernier.

Demise of the octant

In 1767 the first edition of the Nautical Almanac

The Nautical Almanac

The Nautical Almanac has been the familiar name for a series of official British almanacs published under various titles since the first issue of The Nautical Almanac and Astronomical Ephemeris, for 1767: this was the first nautical almanac ever to contain data dedicated to the convenient...

 tabulated lunar distances, enabling navigators to find the current time from the angle between the sun and the moon. This angle is sometimes larger than 90°, and thus not possible to measure with an octant. For that reason, Admiral John Campbell

John Campbell (governor)

John Campbell was born in or before 1720, parish of Kirkbean, near Dumfries, Kirkcudbrightshire, Scotland and died 16 December 1790, at his house at Charles Street, Berkeley Square, London, England. Campbell was a British naval officer, navigational expert and colonial governor.Campbell joined the...

, who conducted shipboard experiments with the lunar distance method, suggested a larger instrument and the sextant

Sextant

A sextant is an instrument used to measure the angle between any two visible objects. Its primary use is to determine the angle between a celestial object and the horizon which is known as the altitude. Making this measurement is known as sighting the object, shooting the object, or taking a sight...

 was developed.

From that time onward, the sextant was the instrument that experienced significant development and improvements and was the instrument of choice for naval navigators. The octant continued to be produced well into the 19th century, though it was generally a less accurate and less expensive instrument. The lower price of the octant, including versions without telescope, made it a practical instrument for ships in the merchant and fishing fleets.

One common practice among navigators up to the late nineteenth century was to use both a sextant and an octant. The sextant was used with great care and only for lunars, while the octant was used for routine meridional altitude measurements of the sun every day. This protected the very accurate and pricier sextant, while using the more affordable octant where it performs well.

From the early 1930s through the end of the 1950s, several types of civilian and military bubble octant instruments were produced for use aboard aircraft. All were fitted with an artificial horizon in the form of a bubble, which was centered to align the horizon for a navigator flying thousands of feet above the earth; some had recording features.

Use and adjustment

Use and adjustment of the octant is essentially identical to the navigator's sextant, which see for information on these topics.

Other reflecting instruments

Hadley's was not the first reflecting quadrant. Robert Hooke

Robert Hooke

Robert Hooke FRS was an English natural philosopher, architect and polymath.His adult life comprised three distinct periods: as a scientific inquirer lacking money; achieving great wealth and standing through his reputation for hard work and scrupulous honesty following the great fire of 1666, but...

 invented a reflecting quadrant in 1684 and had written about the concept as early as 1666. Hooke's was a single-reflecting instrument. Other octants were developed by Jean-Paul Fouchy and Caleb Smith in the early 1730s, however, these did not become significant in the history of navigation instruments.