Reflecting instruments are those that use
mirror
A mirror or looking glass is an object that Reflection (physics), reflects an image. Light that bounces off a mirror will show an image of whatever is in front of it, when focused through the lens of the eye or a camera. Mirrors reverse the ...
s 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
Angular distance \theta (also known as angular separation, apparent distance, or apparent separation) is the angle between the two sightlines, or between two point objects as viewed from an observer.
Angular distance appears in mathematics (in pa ...
between the objects. While reflecting instruments are used in many professions, they are primarily associated with
celestial navigation
Celestial navigation, also known as astronavigation, is the practice of position fixing using stars and other celestial bodies that enables a navigator to accurately determine their actual current physical position in space (or on the surface of ...
as the need to solve navigation problems, in particular the
problem of the longitude, was the primary motivation in their development.
Objectives of the instruments
The purpose of reflecting instruments is to allow an observer to measure the
altitude
Altitude or height (also sometimes known as depth) is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The exact definition and reference datum varies according to the context ...
of a
celestial object
An astronomical object, celestial object, stellar object or heavenly body is a naturally occurring physical object, physical entity, association, or structure that exists in the observable universe. In astronomy, the terms ''object'' and ''bod ...
or measure the angular distance between two objects. The driving force behind the developments discussed here was the solution to the problem of finding one's
longitude
Longitude (, ) is a geographic coordinate that specifies the east–west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek letter l ...
at sea. The solution to this problem was seen to require an accurate means of measuring angles and the accuracy was seen to rely on the observer's ability to measure this angle by simultaneously observing two objects at once.
The deficiency of prior instruments was well known. Requiring the observer to observe two objects with two divergent lines of sight increased the likelihood of an error. Those that considered the problem realized that the use of
specula (mirrors in modern parlance) could permit two objects to be observed in a single view. What followed is a series of inventions and improvements that refined the instrument to the point that its accuracy exceeded that which was required for determining longitude. Any further improvements required a completely new technology.
Early reflecting instruments
Some of the early reflecting instruments were proposed by scientists such as
Robert Hooke
Robert Hooke FRS (; 18 July 16353 March 1703) was an English polymath active as a scientist, natural philosopher and architect, who is credited to be one of two scientists to discover microorganisms in 1665 using a compound microscope that ...
and
Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the grea ...
. These were little used or may not have been built or tested extensively. The van Breen instrument was the exception, in that it was used by the Dutch. However, it had little influence outside of the
Netherlands
)
, anthem = ( en, "William of Nassau")
, image_map =
, map_caption =
, subdivision_type = Sovereign state
, subdivision_name = Kingdom of the Netherlands
, established_title = Before independence
, established_date = Spanish Netherl ...
.
Invented in 1660 by the Dutch Joost van Breen, the spiegelboog (mirror-bow) was a reflecting
cross staff
The term Jacob's staff is used to refer to several things, also known as cross-staff, a ballastella, a fore-staff, a ballestilla, or a balestilha. In its most basic form, a Jacob's staff is a stick or pole with length markings; most staffs ar ...
. This instrument appears to have been used for approximately 100 years, mainly in the Zeeland Chamber of the VOC (The
Dutch East India Company
The United East India Company ( nl, Verenigde Oostindische Compagnie, the VOC) was a chartered company established on the 20th March 1602 by the States General of the Netherlands amalgamating existing companies into the first joint-stock ...
).
Robert Hooke's single-reflecting instrument
![Hooke's reflecting instrument](https://upload.wikimedia.org/wikipedia/commons/9/9e/Hooke%27s_reflecting_instrument.jpg)
Hooke's instrument was a single-reflecting instrument. It used a single mirror to reflect the image of an
astronomical object
An astronomical object, celestial object, stellar object or heavenly body is a naturally occurring physical entity, association, or structure that exists in the observable universe. In astronomy, the terms ''object'' and ''body'' are often us ...
to the observer's eye.
[Charles H. Cotter ''The Mariner's Sextant and the Royal Society; Notes and Records of the Royal Society of London'', Vol. 33, No. 1 (Aug., 1978), pp. 23–36.] This instrument was first described in 1666 and a working model was presented by Hooke at a meeting of the Royal Society some time later.
The device consisted of three primary components, an index arm, a radial arm and a
graduated chord. The three were arranged in a triangle as in the image on the right. A telescopic sight was mounted on the index arm. At the point of rotation of the radial arm, a single mirror was mounted. This point of rotation allowed the angle between the index arm and the radial arm to be changed. The graduated chord was connected to the opposite end of the radial arm and the chord was permitted to rotate about the end. The chord was held against the distant end of the index arm and slid against it. The graduations on the chord were uniform and, by using it to measure the distance between the ends of the index arm and the radial arm, the angle between those arms could be determined. A table of
chords was used to convert a measurement of distance to a measurement of angle. The use of the mirror resulted in the measured angle being twice the angle included by the index and the radius arm.
The mirror on the radial arm was small enough that the observer could see the reflection of an object in half the telescope's view while seeing straight ahead in the other half. This allowed the observer to see both objects at once. Aligning the two objects together in the telescopes view resulted in the angular distance between them to be represented on the graduated chord.
While Hooke's instrument was novel and attracted some attention at the time, there is no evidence that it was subjected to any tests at sea.
The instrument was little used and did not have any significant effect on astronomy or navigation.
Halley's reflecting instrument
![Halley's-instrument](https://upload.wikimedia.org/wikipedia/commons/4/42/Halley%27s-instrument.png)
In 1692,
Edmond Halley
Edmond (or Edmund) Halley (; – ) was an English astronomer, mathematician and physicist. He was the second Astronomer Royal in Britain, succeeding John Flamsteed in 1720.
From an observatory he constructed on Saint Helena in 1676–77, H ...
presented the design of a reflecting instrument to the Royal Society.
This is an interesting instrument, combining the functionality of a
radio latino with a double
telescope
A telescope is a device used to observe distant objects by their emission, absorption, or reflection of electromagnetic radiation. Originally meaning only an optical instrument using lenses, curved mirrors, or a combination of both to observe ...
. The telescope (AB in the adjacent image), has an eyepiece at one end and a mirror (D) partway along its length with one
objective lens
In optical engineering, the objective is the optical element that gathers light from the object being observed and Focus (optics), focuses the ray (optics), light rays to produce a real image. Objectives can be a single Lens (optics), lens or mirr ...
at the far end (B). The mirror only obstructs half the field (either left or right) and permits the objective to be seen on the other. Reflected in the mirror is the image from the second objective lens (C). This permits the observer to see both images, one straight through and one reflected, simultaneously besides each other. It is essential that the focal lengths of the two objective lenses be the same and that the distances from the mirror to either lens be identical. If this condition is not met, the two images cannot be brought to a common
focus
Focus, or its plural form foci may refer to:
Arts
* Focus or Focus Festival, former name of the Adelaide Fringe arts festival in South Australia Film
*''Focus'', a 1962 TV film starring James Whitmore
* ''Focus'' (2001 film), a 2001 film based ...
.
The mirror is mounted on the staff (DF) of the radio latino portion of the instrument and rotates with it. The angle this side of the radio latino's
rhombus
In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. The ...
makes to the telescope can be set by adjusting the rhombus' diagonal length. In order to facilitate this and allow for fine adjustment of the angle, a
screw
A screw and a bolt (see '' Differentiation between bolt and screw'' below) are similar types of fastener typically made of metal and characterized by a helical ridge, called a ''male thread'' (external thread). Screws and bolts are used to fa ...
(EC) is mounted so as to allow the observer to change the distance between the two vertexes (E and C).
The observer sights the horizon with the direct lens' view and sights a
celestial object
An astronomical object, celestial object, stellar object or heavenly body is a naturally occurring physical object, physical entity, association, or structure that exists in the observable universe. In astronomy, the terms ''object'' and ''bod ...
in the mirror. Turning the screw to bring the two images directly adjacent sets the instrument. The angle is determined by taking the length of the screw between E and C and converting this to an angle in a table of
chords.
Halley specified that the telescope tube be rectangular in cross section. This makes construction easy, but is not a requirement as other cross section shapes can be accommodated. The four sides of the radio latino portion (CD, DE, EF, FC) must be equal in length in order for the angle between the telescope and the objective lens side (ADC) to be precisely twice the angle between the telescope and the mirror (ADF) (or in other words – to enforce the
angle of incidence being equal to the
angle of reflection
Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The ' ...
). Otherwise, instrument
collimation
A collimated beam of light or other electromagnetic radiation has parallel rays, and therefore will spread minimally as it propagates. A perfectly collimated light beam, with no divergence, would not disperse with distance. However, diffraction pr ...
will be compromised and the resulting measurements would be in error.
The celestial object's elevation angle could have been determined by reading from graduations on the staff at the slider, however, that's not how Halley designed the instrument. This may suggest that the overall design of the instrument was coincidentally like a radio latino and that Halley may not have been familiar with that instrument.
There is no knowledge of whether this instrument was ever tested at sea.
Newton's reflecting quadrant
Newton's reflecting quadrant was similar in many respects to Hadley's first reflecting quadrant that followed it.
Newton had communicated the design to
Edmund Halley
Edmond (or Edmund) Halley (; – ) was an English astronomer, mathematician and physicist. He was the second Astronomer Royal in Britain, succeeding John Flamsteed in 1720.
From an observatory he constructed on Saint Helena in 1676–77, Ha ...
around 1699. However, Halley did not do anything with the document and it remained in his papers only to be discovered after his death.
[Daumas, Maurice, ''Scientific Instruments of the Seventeenth and Eighteenth Centuries and Their Makers'', Portman Books, London 1989 ] However, Halley did discuss Newton's design with members of the Royal Society when Hadley presented his reflecting quadrant in 1731. Halley noted that Hadley's design was quite similar to the earlier Newtonian instrument.
As a result of this inadvertent secrecy, Newton's invention played little role in the development of reflecting instruments.
The octant
What is remarkable about the octant is the number of persons who independently invented the device in a short period of time.
John Hadley
John Hadley (16 April 1682 – 14 February 1744) was an English mathematician, and laid claim to the invention of the octant, two years after Thomas Godfrey claimed the same.
Biography
He was born in Bloomsbury, London the eldest son of ...
and
Thomas Godfrey both get credit for inventing the
octant. They independently developed the same instrument around 1731. They were not the only ones, however.
In Hadley's case, two instruments were designed. The first was an instrument very similar to Newton's reflecting quadrant. The second had essentially the same form as the modern sextant. Few of the first design were constructed, while the second became the standard instrument from which the
sextant
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 celes ...
derived and, along with the sextant, displaced all prior navigation instruments used for
celestial navigation
Celestial navigation, also known as astronavigation, is the practice of position fixing using stars and other celestial bodies that enables a navigator to accurately determine their actual current physical position in space (or on the surface of ...
.
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''.
[Bedini, Silvio, ''History Corner: Benjamin King of Newport, R.I.-Part II'', Professional Surveyor Magazine, September 1997 Volume 17 Number 6](_blank)
/ref> He used a fixed prism
Prism usually refers to:
* Prism (optics), a transparent optical component with flat surfaces that refract light
* Prism (geometry), a kind of polyhedron
Prism may also refer to:
Science and mathematics
* Prism (geology), a type of sedimentary ...
in addition to an index mirror to provide reflective elements. Prisms provide advantages over mirrors in an era when polished 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 was used historically to make different kinds of mirrors from personal grooming a ...
mirrors were inferior and both the silvering
Silvering is the chemical process of coating a non-conductive substrate such as glass with a reflective substance, to produce a mirror. While the metal is often silver, the term is used for the application of any reflective metal.
Process
Mos ...
of a mirror and the production of glass with flat, parallel surfaces was difficult. However, the other design elements of Smith's instrument made it inferior to Hadley's octant and it was not used significantly.
Jean-Paul Fouchy, a mathematics professor and astronomer in France
France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of Overseas France, overseas regions and territories in the Americas and the Atlantic Ocean, Atlantic, Pacific Ocean, Pac ...
, invented an octant in 1732. His was essentially the same as Hadley's. Fouchy did not know of the developments in England at the time, since communications between the two country's instrument makers was limited and the publications of the Royal Society
The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...
, particularly the ''Philosophical Transactions
''Philosophical Transactions of the Royal Society'' is a scientific journal published by the Royal Society. In its earliest days, it was a private venture of the Royal Society's secretary. It was established in 1665, making it the first journa ...
'', were not being distributed in France.[Fauque, Danielle, ''Un instrument à réflexion pour la marine : deux propositions successives de Fouchy'', presented at Colloque Grandjean de Fouchy, March 23, 2007 at the Observatoire de Paris.] Fouchy's octant was overshadowed by Hadley's.
The sextant
:''The main article, Sextant
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 celes ...
, covers the use of the instrument in navigation. This article concentrates on the history and the development of the instrument''
The origin of the sextant is straightforward and not in dispute. Admiral John Campbell, having used Hadley's octant in sea trials of the method of lunar distances
In celestial navigation, lunar distance is the angular distance between the Moon and another celestial body. The lunar distances method uses this angle, also called a lunar, and a nautical almanac to calculate Greenwich time if so desired, or ...
, found that it was wanting. The 90° angle subtended by the arc of the instrument was insufficient to measure some of the angular distances required for the method. He suggested that the angle be increased to 120°, yielding the sextant. John Bird made the first such sextant in 1757.
With the development of the sextant, the octant became something of a second class instrument. The octant, while occasionally constructed entirely of brass, remained primarily a wooden-framed instrument. Most of the developments in advanced materials and construction techniques were reserved for the sextant.
There are examples of sextants made with wood, however most are made from brass. In order to ensure the frame was stiff, instrument makers used thicker frames. This had a drawback in making the instrument heavier, which could influence the accuracy due to hand-shaking as the navigator worked against its weight. In order to avoid this problem, the frames were modified. Edward Troughton
Edward Troughton FRS FRSE FAS (October 1753 – 12 June 1835) was a British instrument maker who was notable for making telescopes and other astronomical instruments.
Life
Troughton was born at Corney, Cumberland, the youngest of six child ...
patented the double-framed sextant in 1788.[Turner, Gerard L'E., ''Antique Scientific Instruments'', Blandford Press Ltd. 1980 ] This used two frames held in parallel with spacers. The two frames were about a centimetre apart. This significantly increased the stiffness of the frame. An earlier version had a second frame that only covered the upper part of the instrument, securing the mirrors and telescope. Later versions used two full frames. Since the spacers looked like little pillars, these were also called ''pillar sextants''.
Troughton also experimented with alternative materials. The scales were plated
Plating is a surface covering in which a metal is deposited on a conductive surface. Plating has been done for hundreds of years; it is also critical for modern technology. Plating is used to decorate objects, for corrosion inhibition, to improv ...
with silver
Silver is a chemical element with the Symbol (chemistry), symbol Ag (from the Latin ', derived from the Proto-Indo-European wikt:Reconstruction:Proto-Indo-European/h₂erǵ-, ''h₂erǵ'': "shiny" or "white") and atomic number 47. A soft, whi ...
, gold
Gold is a chemical element with the symbol Au (from la, aurum) and atomic number 79. This makes it one of the higher atomic number elements that occur naturally. It is a bright, slightly orange-yellow, dense, soft, malleable, and ductile met ...
or platinum
Platinum is a chemical element with the symbol Pt and atomic number 78. It is a dense, malleable, ductile, highly unreactive, precious, silverish-white transition metal. Its name originates from Spanish , a diminutive of "silver".
Platinu ...
. Gold and platinum both minimized corrosion
Corrosion is a natural process that converts a refined metal into a more chemically stable oxide. It is the gradual deterioration of materials (usually a metal) by chemical or electrochemical reaction with their environment. Corrosion engine ...
problems. The platinum-plated instruments were expensive, due to the scarcity of the metal, though less expensive than gold. Troughton knew William Hyde Wollaston
William Hyde Wollaston (; 6 August 1766 – 22 December 1828) was an English chemist and physicist who is famous for discovering the chemical elements palladium and rhodium. He also developed a way to process platinum ore into malleable ingo ...
through the Royal Society and this gave him access to the precious metal.[Chaldecott, John A., ''Platinum and Palladium in Astronomy and Navigation: The Pioneer Work of Edward Troughton and William Hyde Wollaston'', Platinum Metals Review, Volume 31 Issue 2 April 1987 Pages 91–10]
Online version (pdf)
/ref> Instruments from Troughton's company that used platinum can be easily identified by the word ''Platina'' engraved on the frame. These instruments remain highly valued as collector's items and are as accurate today as when they were constructed.[Catalog 130, Spring 1987, Historical Technology Inc, Marblehead MA, USA]
As the developments in dividing engine
A dividing engine is a device employed to mark graduations on measuring instruments to allow for reading smaller measurements than can be allowed by directly engraving them. The well-known vernier scale and micrometer screw-gauge are classic e ...
s progressed, the sextant was more accurate and could be made smaller. In order to permit easy reading of the vernier, a small magnifying lens was added. In addition, to reduce glare on the frame, some had a diffuser
Diffuser may refer to:
Aerodynamics
* Diffuser (automotive), a shaped section of a car's underbody which improves the car's aerodynamic properties
* Part of a jet engine air intake, especially when operated at supersonic speeds
* The channel betw ...
surrounding the magnifier to soften the light. As accuracy increased, the circular arc vernier was replaced with a drum vernier.
Frame designs were modified over time to create a frame that would not be adversely affected by temperature changes. These frame patterns became standardized and one can see the same general shape in many instruments from many different manufacturers.
In order to control costs, modern sextants are now available in precision-made plastic. These are light, affordable and of high quality.
Types of sextants
While most people think of navigation when they hear the term ''sextant'', the instrument has been used in other professions.
;Navigator's sextant:The common type of instrument most people think of when they hear the term ''sextant''.
;Sounding sextants:These are sextants that were constructed for use horizontally rather than vertically and were developed for use in hydrographic survey
Hydrographic survey is the science of measurement and description of features which affect maritime navigation, marine construction, dredging, offshore oil exploration/offshore oil drilling and related activities. Strong emphasis is placed ...
s.
;Surveyor's sextants:These were constructed for use exclusively on land for horizontal angular measurements. Instead of a handle on the frame, they had a socket to allow the attachment of a surveyor's Jacob's staff
The term Jacob's staff is used to refer to several things, also known as cross-staff, a ballastella, a fore-staff, a ballestilla, or a balestilha. In its most basic form, a Jacob's staff is a stick or pole with length markings; most staffs ar ...
.
;Box or pocket sextants:These are small sextants entirely contained within a metal case. First developed by Edward Troughton, they are usually all brass with most of the mechanical components inside the case. The telescope extends from an opening in the side. The index and other parts are completely covered when the case cover is slipped on. Popular with surveyors for their small size (typically only in diameter and deep), their accuracy was enabled by improvements in the dividing engine
A dividing engine is a device employed to mark graduations on measuring instruments to allow for reading smaller measurements than can be allowed by directly engraving them. The well-known vernier scale and micrometer screw-gauge are classic e ...
s used to graduate the arcs. The arcs are so small that magnifiers are attached to allow them to be read.
In addition to these types, there are terms used for various sextants.
A ''pillar sextant'' can be either:
#A double-frame sextant as patented by Edward Troughton in 1788.
#A surveyor's sextant with a socket for a surveyor's staff (the pillar).
The former is the most common use of the term.
Beyond the sextant
Quintant and others
Several makers offered instruments with sizes other than one-eighth or one-sixth of a circle. One of the most common was the ''quintant'' or fifth of a circle (72° arc reading to 144°). Other sizes were also available, but the odd sizes never became common. Many instruments are found with scales reading to, for example, 135°, but they are simply referred to as sextants. Similarly, there are 100° octants, but these are not separated as unique types of instruments.
There was interest in much larger instruments for special purposes. In particular a number of full circle instruments were made, categorized as reflecting circles and repeating circle
Developed from the reflecting circle, the repeating circle is an instrument for geodetic surveying, invented by Etienne Lenoir in 1784, while an assistant of Jean-Charles de Borda, who later improved the instrument. It was notable as being the ...
s.
Reflecting circles
The reflecting circle was invented by the German
German(s) may refer to:
* Germany (of or related to)
**Germania (historical use)
* Germans, citizens of Germany, people of German ancestry, or native speakers of the German language
** For citizens of Germany, see also German nationality law
**Ger ...
geometer
A geometer is a mathematician whose area of study is geometry.
Some notable geometers and their main fields of work, chronologically listed, are:
1000 BCE to 1 BCE
* Baudhayana (fl. c. 800 BC) – Euclidean geometry, geometric algebra
* ...
and astronomer
An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, natural satellite, moons, comets and galaxy, g ...
Tobias Mayer
Tobias Mayer (17 February 172320 February 1762) was a German astronomer famous for his studies of the Moon.
He was born at Marbach, in Württemberg, and brought up at Esslingen in poor circumstances. A self-taught mathematician, he earned a l ...
in 1752, with details published in 1767. His development preceded the sextant and was motivated by the need to create a superior surveying instrument.
The reflecting circle is a complete circular instrument graduated to 720° (to measure distances between heavenly bodies, there is no need to read an angle greater than 180°, since the minimum distance will always be less than 180°). Mayer presented a detailed description of this instrument to the Board of Longitude
The Commissioners for the Discovery of the Longitude at Sea, or more popularly Board of Longitude, was a British government body formed in 1714 to administer a scheme of prizes intended to encourage innovators to solve the problem of finding lon ...
and John Bird used the information to construct one sixteen inches in diameter for evaluation by the Royal Navy.[May, William Edward, ''A History of Marine Navigation'', G. T. Foulis & Co. Ltd., Henley-on-Thames, Oxfordshire, 1973, ] This instrument was one of those used by Admiral John Campbell during his evaluation of the lunar distance method
Lunar most commonly means "of or relating to the Moon".
Lunar may also refer to:
Arts and entertainment
* ''Lunar'' (series), a series of video games
* "Lunar" (song), by David Guetta
* "Lunar", a song by Priestess from the 2009 album ''Prior t ...
. It differed in that it was graduated to 360° and was so heavy that it was fitted with a support that attached to a belt. It was not considered better than the Hadley octant and was less convenient to use. As a result, Campbell recommended the construction of the sextant.
Jean-Charles de Borda
Jean-Charles, chevalier de Borda (4 May 1733 – 19 February 1799) was a French mathematician, physicist, and Navy officer.
Biography
Borda was born in the city of Dax to Jean‐Antoine de Borda and Jeanne‐Marie Thérèse de Lacroix.
In 175 ...
further developed the reflecting circle. He modified the position of the telescopic sight in such a way that the mirror could be used to receive an image from either side relative to the telescope. This eliminated the need to ascertain that the mirrors were precisely parallel when reading zero. This simplified the use of the instrument. Further refinements were performed with the help of Etienne Lenoir. The two of them refined the instrument to its definitive form in 1777. This instrument was so distinctive it was given the name ''Borda circle'' or ''repeating circle
Developed from the reflecting circle, the repeating circle is an instrument for geodetic surveying, invented by Etienne Lenoir in 1784, while an assistant of Jean-Charles de Borda, who later improved the instrument. It was notable as being the ...
''.
Borda and Lenoir developed the instrument for geodetic surveying
Geodesy ( ) is the Earth science of accurately measuring and understanding Earth's figure ( geometric shape and size), orientation in space, and gravity. The field also incorporates studies of how these properties change over time and equiva ...
. Since it was not used for the celestial measures, it did not use double reflection and substituted two telescope sights. As such, it was not a reflecting instrument. It was notable as being the equal of the great theodolite
The Ramsden surveying instruments are those constructed by
Jesse Ramsden and used in high precision geodetic surveys carried out in the period 1784 to 1853. This includes the five great theodolites—great in name, great in size and great in accura ...
created by the renowned instrument maker, Jesse Ramsden
Jesse Ramsden FRS FRSE (6 October 1735 – 5 November 1800) was a British mathematician, astronomical and scientific instrument maker. His reputation was built on the engraving and design of dividing engines which allowed high accuracy measureme ...
.
Josef de Mendoza y Ríos
Josef (also José or Joseph) de Mendoza y Ríos (1761–1816) was a Spanish astronomer and mathematician of the 18th century, famous for his work on navigation.
The first work of Mendoza y Ríos was published in 1787: his treatise about the scien ...
redesigned Borda's reflecting circle (London, 1801). The goal was to use it together with his Lunar Tables published by the Royal Society
The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...
(London, 1805). He made a design with two concentric circles and a vernier scale
A vernier scale, named after Pierre Vernier, is a visual aid to take an accurate measurement reading between two graduation markings on a linear scale by using mechanical interpolation, thereby increasing resolution and reducing measurement unc ...
and recommended averaging three sequential readings to reduce the error. Borda's system was not based on a circle of 360° but 400 grads
The Grid Analysis and Display System (GrADS) is an interactive desktop tool that is used for easy access, manipulation, and visualization of earth science data. The format of the data may be either binary, GRIB, NetCDF, or HDF-SDS (Scientific Da ...
(Borda spent years calculating his tables with a circle divided in 400°). Mendoza's lunar tables have been used through almost the entire nineteenth century (see Lunar distance (navigation)
In celestial navigation, lunar distance is the angular distance between the Moon and another celestial body. The lunar distances method uses this angle, also called a lunar, and a nautical almanac to calculate Greenwich time if so desired, or b ...
).
Edward Troughton also modified the reflecting circle. He created a design with three index arms and verniers. This permitted three simultaneous readings to average out the error.
As a navigation instrument, the reflecting circle was more popular with the French navy than with the British.
Bris sextant
The Bris sextant is not a true sextant, but it is a true reflecting instrument based on the principle of double reflection and subject to the same rules and errors as common octants and sextants. Unlike common octants and sextants, the Bris sextant is a fixed angle instrument capable of accurately measuring a few specific angles unlike other reflecting instruments which can measure any angle within the range of the instrument. It is particularly suited to determining the altitude of the sun
The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
or moon
The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
.
Surveying sector
Francis Ronalds
Sir Francis Ronalds FRS (21 February 17888 August 1873) was an English scientist and inventor, and arguably the first electrical engineer. He was knighted for creating the first working electric telegraph over a substantial distance. In 1816 ...
invented an instrument for recording angles in 1829 by modifying the octant. A disadvantage of reflecting instruments in surveying
Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial two-dimensional or three-dimensional positions of points and the distances and angles between them. A land surveying professional is ca ...
applications is that optics
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviole ...
dictate that the mirror and index arm rotate through half the angular separation of the two objects. The angle thus needs to be read, noted and a protractor
A protractor is a measuring instrument, typically made of transparent plastic or glass, for measuring angles.
Some protractors are simple half-discs or full circles. More advanced protractors, such as the bevel protractor, have one or two sw ...
employed to draw the angle on a plan. Ronalds’ idea was to configure the index arm to rotate through twice the angle of the mirror, so that the arm could then be used to draw a line at the correct angle directly onto the drawing. He used a sector
Sector may refer to:
Places
* Sector, West Virginia, U.S.
Geometry
* Circular sector, the portion of a disc enclosed by two radii and a circular arc
* Hyperbolic sector, a region enclosed by two radii and a hyperbolic arc
* Spherical sector, a po ...
as the basis of his instrument and placed the horizon glass at one tip and the index mirror near the hinge connecting the two rulers. The two revolving elements were linked mechanically and the barrel supporting the mirror was twice the diameter of the hinge to give the required angular ratio.
References
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External links
National Maritime Museum
Portrait of a merchant navy captain holding a Caleb Smith Octant.
Astronomical instruments
Celestial navigation
Angle measuring instruments
Navigational equipment