**Friedrich Wilhelm Bessel** (German: [ˈbɛsəl]; 22 July 1784 – 17 March 1846) was a German astronomer, mathematician, physicist and geodesist. He was the first astronomer who determined reliable values for the distance from the sun to another star by the method of parallax. A special type of mathematical functions were named Bessel functions after Bessel's death, though they had originally been discovered by Daniel Bernoulli and then generalised by Bessel.

Friedrich Wilhelm Bessel | |
---|---|

Born | 22 July 1784 |

Died | 17 March 1846 (aged 61) |

Residence | Prussia |

Nationality | Prussian (German) |

Known for | Bessel functions Stellar parallax Bessel ellipsoid (full list here) |

Awards | PhD (Hon): University of Göttingen (1811) Lalande Prize (1811) Gold Medal of the Royal Astronomical Society (1829 and 1841) |

Scientific career | |

Fields | Astronomy, mathematics, geodesy |

Institutions | University of Königsberg |

Doctoral students | Friedrich Wilhelm Argelander |

Bessel was born in Minden, Westphalia, administrative center of Minden-Ravensberg, as second son of a civil servant. He was born into a large family in Germany. At the age of 14 Bessel was apprenticed to the import-export concern Kulenkamp at Bremen. The business's reliance on cargo ships led him to turn his mathematical skills to problems in navigation. This in turn led to an interest in astronomy as a way of determining longitude.

Bessel came to the attention of a major figure of German astronomy at the time, Heinrich Wilhelm Olbers, by producing a refinement on the orbital calculations for Halley's Comet in 1804, using old observation data taken from Thomas Harriot and Nathaniel Torporley in 1607.^{[1]}

Two years later Bessel left Kulenkamp and became Johann Hieronymus Schröter's assistant at Lilienthal Observatory near Bremen. There he worked on James Bradley's stellar observations to produce precise positions for some 3,222 stars.^{[1]}

In January 1810, at the age of 25, Bessel was appointed director of the newly founded Königsberg Observatory by King Frederick William III of Prussia. On the recommendation of fellow mathematician and physicist Carl Friedrich Gauss (with whom he regularly corresponded)^{[2]} he was awarded an honorary doctor degree from the University of Göttingen in March 1811.

Around that time, the two men engaged in an epistolary correspondence.^{[3]} However, when they met in person in 1825, they quarrelled; the details are not known.^{[4]}

In 1842 Bessel took part in the annual meeting of the British Association for the Advancement of Science in Manchester, accompanied by the geophysicist Georg Adolf Erman and the mathematician Carl Gustav Jacob Jacobi.

Bessel married Johanna, the daughter of the chemist and pharmacist Karl Gottfried Hagen who was the uncle of the physician and biologist Hermann August Hagen and the hydraulic engineer Gotthilf Hagen, the latter also Bessel's student and assistant from 1816 to 1818. The physicist Franz Ernst Neumann, Bessel's close companion and colleague, was married to Johanna Hagen's sister Florentine. Neumann introduced Bessel's exacting methods of measurement and data reduction into his mathematico-physical seminar, which he co-directed with Carl Gustav Jacob Jacobi at Königsberg.^{[5]} These exacting methods had a lasting impact upon the work of Neumann's students and upon the Prussian conception of precision in measurement.

Bessel had two sons and three daughters. His eldest daughter, Marie, married Georg Adolf Erman, member of the scholar family Erman. One of their sons was the renowned Egyptologist Adolf Erman.

After several months of illness Bessel died in March 1846 at his observatory from retroperitoneal fibrosis.^{[6]}

While the observatory was still in construction Bessel elaborated the *Fundamenta Astronomiae* based on Bradley's observations. As a preliminary result he produced tables of atmospheric refraction that won him the Lalande Prize from the French Academy of Sciences in 1811. The Königsberg Observatory began operation in 1813.

Starting in 1819, Bessel determined the position of over 50,000 stars using a meridian circle from Reichenbach, assisted by some of his qualified students. The most prominent of them was Friedrich Wilhelm Argelander.

With this work done, Bessel was able to achieve the feat for which he is best remembered today: he is credited with being the first to use parallax in calculating the distance to a star. Astronomers had believed for some time that parallax would provide the first accurate measurement of interstellar distances—in fact, in the 1830s there was a fierce competition between astronomers to be the first to measure a stellar parallax accurately. In 1838 Bessel won the race, announcing that 61 Cygni had a parallax of 0.314 arcseconds; which, given the diameter of the Earth's orbit, indicated that the star is 10.3 ly away.^{[7]}^{[8]}^{[9]} Given the current measurement of 11.4 ly, Bessel's figure had an error of 9.6%. Nearly at the same time Friedrich Georg Wilhelm Struve and Thomas Henderson measured the parallaxes of Vega and Alpha Centauri.

As well as helping determine the parallax of 61 Cygni, Bessel's precise measurements using a new meridian circle from *Adolf Repsold* allowed him to notice deviations in the motions of Sirius and Procyon, which he deduced must be caused by the gravitational attraction of unseen companions.^{[10]}^{[11]}^{[12]}
His announcement of Sirius's "dark companion" in 1844 was the first correct claim of a previously unobserved companion by positional measurement, and eventually led to the discovery of Sirius B.

Bessel was the first scientist who realized the effect later called *personal equation*, that several simultaneously observing persons determine slightly different values, especially recording the transition time of stars.^{[13]}

In 1824, Bessel developed a new method for calculation the circumstances of eclipses using the so-called Besselian elements. His method simplified the calculation to such an extent, without sacrificing accuracy, that it is still in use today.

Bessel's work in 1840 contributed to the discovery of Neptune in 1846 at Berlin Observatory, several months after Bessel's death. On Bessel's proposal (1825) the Prussian Academy of Sciences started the edition of the *Berliner Akademische Sternkarten* (*Berlin Academic Star Charts*) as an international project. One unpublished new chart enabled Johann Gottfried Galle to find Neptune near the position calculated by LeVerrier in 1846.

In the second decade of the 19th century while studying the dynamics of 'many-body' gravitational systems, Bessel developed what are now known as Bessel functions. Critical for the solution of certain differential equations, these functions are used throughout both classical and quantum physics.

Bessel is responsible for the correction to the formula for the sample variance estimator named in his honour. This is the use of the factor *n* − 1 in the denominator of the formula, rather than just *n*. This occurs when the *sample mean* rather than the *population mean* is used to centre the data and since the sample mean is a linear combination of the data the residual to the sample mean overcounts the number of degrees of freedom by the number of constraint equations — in this case one. *(Also see Bessel's correction)*.

An additional field of work was geodesy.^{[14]}
Bessel published a method for solving the main
geodesic problem.^{[15]}
He was responsible for the survey of East Prussia which joined the Prussian and Russian triangulation networks^{[16]}
and he obtained an estimate of increased accuracy for the figure of the Earth,
nowadays referred to as the Bessel ellipsoid.^{[17]}^{[18]}

Despite lacking a university education, Bessel was a major figure in astronomy during his lifetime. He was elected as member of the Prussian Academy of Sciences in 1812, the French Academy of Sciences in 1816, foreign member of the Royal Swedish Academy of Sciences in 1823, and fellow of the Royal Society in 1825. In 1832, he was elected a Foreign Honorary Member of the American Academy of Arts and Sciences.^{[19]} In 1827 Bessel became member of the Royal Institute of the Netherlands, predecessor of the Royal Netherlands Academy of Arts and Sciences.^{[20]}

Bessel won the Gold Medal of the Royal Astronomical Society twice in 1829 and 1841.

The largest crater in the Moon's Mare Serenitatis and the main-belt asteroid 1552 Bessel, as well as two fjords in Greenland, Bessel Fjord, NE Greenland and Bessel Fjord, NW Greenland, were named in his honour.^{[21]}

- Latin

*Fundamenta Astronomiae pro anno MDCCLV deducta ex observationibus viri incomparabilis James Bradley in specula astronomica Grenovicensi, per annos 1750–1762 institutis*, Königsberg, 1818*Tabulae regiomontanae reductionum observationum astronomicarum ab anno 1750 usque ad annum 1850 computatæ*, Königsberg, 1830

- German

*Untersuchungen über die scheinbare und wahre Bahn des im Jahre 1807 erschienenen grossen Kometen.*[*Investigations on the apparent and the real orbit of the great comet of 1807*], Königsberg, 1810*Untersuchung der Größe und des Einflusses des Vorrückens der Nachtgleichen.*[*Investigations on precession*], Berlin, 1815*Untersuchungen über die Länge des einfachen Secundenpendels.*[*Investigations on the length of the seconds pendulum*], Berlin, 1828*Versuche über die Kraft mit welcher die Erde Körper von verschiedener Beschaffenheit anzieht.*[*Experiments on the force with which the earth attracts things of different matter*], Berlin, 1832*Gradmessung in Ostpreußen und ihre Verbindung mit Preußischen und Russischen Dreiecksketten.*[*The East Prussian Survey and its connection with the Prussian and Russian networks*], Berlin, 1838*Darstellung der Untersuchungen und Maaßregeln, welche, in 1835 bis 1838, durch die Einheit des Preußischen Längenmaaßes veranlaßt worden sind.*[*Description of the investigations and rules arranged in 1835 to 1838 for the standardization of the prussian unit of length*], Berlin, 1839*Astronomische Beobachtungen auf der Königlichen Universitäts-Sternwarte zu Königsberg.*[*Astronomical Investigations (XXI Volumes)*], Königsberg, 1815–1844*Astronomische Untersuchungen.*[*Astronomical Investigations. (2 Volumes)*], Königsberg, 1841–1842- Heinrich Christian Schumacher, ed. (1848),
*Populäre Vorlesungen über wissenschaftliche Gegenstände von F.W.Bessel.*[*Popular lectures on scientific subjects*], Hamburg - Rudolf Engelmann (ed.),
*Abhandlungen von Friedrich Wilhelm Bessel.*[*Treatises of Friedrich Wilhelm Bessel*]- Vol. 1:
*I. Bewegungen der Körper im Sonnensystem. II. Sphärische Astronomie*. Leipzig 1875 - Vol. 2:
*III. Theorie der Instrumente. IV. Stellarastronomie. V. Mathematik*. Leipzig 1876 - Vol. 3:
*VI. Geodäsie. VII. Physik. VIII. Verschiedenes – Literatur*. Leipzig 1876.

- Vol. 1:
- Rudolf Engelmann, ed. (1878),
*Recensionen von Friedrich Wilhelm Bessel*, Leipzig

- ^
^{a}^{b}Chisholm 1911. **^**Clifford J. Cunningham,*Bode's Law and the Discovery of Juno: Historical Studies in Asteroid Research*, Springer, 2017, pp. 121ff..**^**Helmut Koch,*Introduction to Classical Mathematics I: From the Quadratic Reciprocity Law to the Uniformization Theorem*, Springer, p. 90.**^**Oscar Sheynin,*History of Statistics*, Berlin: NG Verlag Berlin, 2012, p. 88.**^**Olesko, Kathryn M. (1991).*Physics as a Calling: Discipline and Practice in the Königsberg Seminar for Physics*. Cornell University Press.**^**Bessel, Friedrich Wilhelm (1846). "Bessel's Tod" [Bessel's death].*Astronomische Nachrichten*(in German).**24**(556): 49–52. Bibcode:1846AN.....24...49B. doi:10.1002/asna.18460240402.**^**Bessel, F. W. (1838). "Bestimmung der Entfernung des 61sten Sterns des Schwans" [Determination of the distance to 61 Cygni].*Astronomische Nachrichten*(in German).**16**(365–366): 65–96. Bibcode:1838AN.....16...65B. doi:10.1002/asna.18390160502.**^**Bessel, F. W. (1838b). "On the parallax of 61 Cygni".*Monthly Notices of the Royal Astronomical Society*.**4**(17): 152–161. Bibcode:1838MNRAS...4..152B. doi:10.1093/mnras/4.17.152.**^**"A brief history of light dates". National Geographic. Retrieved 14 August 2013.**^**Bessel, F. W. (1844a). "Ueber Veränderlichkeit der eigenen Bewegungen der Fixsterne" [On Variations of the proper motions of the fixed stars].*Astronomische Nachrichten*(in German).**22**(514): 145–160. Bibcode:1844AN.....22..145B. doi:10.1002/asna.18450221002.**^**Bessel, F. W. (1844b). "Ueber Veränderlichkeit der eigenen Bewegungen der Fixsterne (Fortsetzung)" [On Variations of the proper motions of the fixed stars (continued)].*Astronomische Nachrichten*(in German).**22**(515): 169–184. Bibcode:1844AN.....22..169B. doi:10.1002/asna.18450221202.**^**Bessel, F. W. (1844c). "On the variations of the proper motions of Procyon and Sirius".*Monthly Notices of the Royal Astronomical Society*.**6**(11): 136–141. Bibcode:1844MNRAS...6R.136B. doi:10.1093/mnras/6.11.136a.**^**Hoffmann, Christoph (2007). "Constant differences: Friedrich Wilhelm Bessel, the concept of the observer in early nineteenth-century practical astronomy and the history of the personal equation".*British Journal for the History of Science*.**40**(3): 333–365. doi:10.1017/s0007087407009478.**^**Viik, T. (2006).*F.W. Bessel and Geodesy*(PDF). Struve Geodetic Arc 2006 International Conference: The Struve Arc and Extensions in Space and Time. August 13–15, 2006. Haparanda and Pajala, Sweden: Lantmäteriet, Gävle, Sweden, 2006. pp. 53–63.**^**Bessel, F. W. (2010) [1825]. . Translated by C. F. F. Karney & R. E. Deakin. "The calculation of longitude and latitude from geodesic measurements".*Astronomische Nachrichten*.**331**(8): 852–861. arXiv:0908.1824. Bibcode:2010AN....331..852K. doi:10.1002/asna.201011352. English translation of*Astron. Nachr.***4**, 241–254 (1825). Errata.**^**Bessel, F. W.; Baeyer, J. J. (1838).*Gradmessung in Ostpreussen und ihre Verbindung mit Preussischen und Russischen Dreiecksketten*[*The East Prussian Survey and its connection with the Prussian and Russian networks*] (in German). Berlin: Dümmler.**^**Bessel, F. W. (1837). "Bestimmung der Axen des elliptischen Rotationssphäroids, welches den vorhandenen Messungen von Meridianbögen der Erde am meisten entspricht" [Determination of the axes of ellipsoid that fits best to the existing measurements of meridian arcs].*Astronomische Nachrichten*(in German).**14**(333): 333–346. Bibcode:1837AN.....14..333B. doi:10.1002/asna.18370142301.**^**Bessel, F. W. (1841). "Ueber einen Fehler in der Berechnung der französischen Gradmessung und seinen Einfluß auf die Bestimmung der Figur der Erde" [Concerning an error in the calculation of the French survey and its influence on the determination of the figure of the Earth].*Astronomische Nachrichten*(in German).**19**(438): 97–116. Bibcode:1841AN.....19...97B. doi:10.1002/asna.18420190702.**^**"Book of Members, 1780–2010: Chapter B" (PDF). American Academy of Arts and Sciences. Retrieved 24 June 2011.**^**"Friedrich Wilhelm Bessel (1784 - 1846)". Royal Netherlands Academy of Arts and Sciences. Retrieved 22 May 2016.**^**Schmadel, Lutz D. (2007). "(1552) Bessel".*Dictionary of Minor Planet Names – (1552) Bessel*. Springer Berlin Heidelberg. p. 123. doi:10.1007/978-3-540-29925-7_1553. ISBN 978-3-540-00238-3.

- John Frederick William Herschel,
*A brief notice of the life, researches, and discoveries of Friedrich Wilhelm Bessel*, London: Barclay, 1847 (on-line) - Karl Christian Bruhns (1875), "Bessel, Friedrich Wilhelm",
*Allgemeine Deutsche Biographie (ADB)*(in German),**2**, Leipzig: Duncker & Humblot, pp. 558–567 - Jürgen Hamel: Friedrich Wilhelm Bessel. Leipzig 1984 ISSN 0232-3516.
- Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846. Basel, Boston, Berlin 1995, ISBN 3-7643-5113-6.
- Chisholm, Hugh, ed. (1911).
*Encyclopædia Britannica*.**3**(11th ed.). Cambridge University Press.
. - Gilman, D. C.; Peck, H. T.; Colby, F. M., eds. (1905). .
*New International Encyclopedia*(1st ed.). New York: Dodd, Mead. -
*The Nuttall Encyclopædia*. 1907.
. - Publications of Friedrich Wilhelm Bessel Astrophysics Data System ADS

- Fricke, Walter (1970–80). "Bessel, Friedrich Wilhelm".
*Dictionary of Scientific Biography*.**2**. New York: Charles Scribner's Sons. pp. 97–102. ISBN 978-0-684-10114-9.

- O'Connor, John J.; Robertson, Edmund F., "Friedrich Bessel",
*MacTutor History of Mathematics archive*, University of St Andrews. - Friedrich Bessel at the Mathematics Genealogy Project

13P/Olbers is a periodic comet with an orbital period of 69 years. It fits the classical definition of a Halley-type comet with (20 years < period < 200 years).Heinrich Wilhelm Matthias Olbers (Bremen) discovered the comet on March 6, 1815. Its orbit was first computed by Carl Friedrich Gauss on March 31, Friedrich Bessel calculated an orbital period as 73 years, later as 73.9 years, calculations by other astronomers during that era resulted anywhere between 72 and 77 years.The comet was last detected in 1956. It will next come to perihelion on June 30, 2024. the comet will be closest to the Earth on January 10, 2094 when it passes at a distance of 0.756 AU.There is some speculation that 13P/Olbers has an associated meteor shower on Mars coming from the direction of Beta Canis Major.

1552 Bessel1552 Bessel, provisional designation 1938 DE1, is a stony Eoan asteroid from the outer regions of the asteroid belt, approximately 18 kilometers in diameter.

It was discovered on 24 February 1938, by Finnish astronomer Yrjö Väisälä at Turku Observatory in Southwest Finland, and named after German astronomer Friedrich Bessel.

1844 in scienceThe year 1844 in science and technology involved some significant events, listed below.

Alvan Graham ClarkAlvan Graham Clark (July 10, 1832 – June 9, 1897) was an American astronomer and telescope-maker.

Born in Fall River, Massachusetts, he was the son of Alvan Clark, founder of Alvan Clark & Sons.

On January 31, 1862, while testing a new 18.5-inch (470 mm) aperture great refractor telescope in Cambridgeport, Massachusetts, Clark made the first ever observation of a white dwarf star. This discovery of Sirius B, or affectionately "the Pup", proved an earlier hypotheses (Friedrich Bessel in 1844) that Sirius, the brightest star in the night sky with an apparent magnitude of −1.46, had an unseen companion disturbing its motion. Clark used the largest refracting telescope lens in existence at the time, and the largest telescope in the United States, to observe the magnitude 8 companion.

Clark's 18.5 inch refracting telescope was then delivered to his customer, the landmark Dearborn Observatory of Northwestern University in Evanston, Illinois, where it is still being used today.

Bessel's correctionIn statistics, **Bessel's correction** is the use of *n* − 1 instead of *n* in the formula for the sample variance and sample standard deviation, where *n* is the number of observations in a sample. This method corrects the bias in the estimation of the population variance. It also partially corrects the bias in the estimation of the population standard deviation. However, the correction often increases the mean squared error in these estimations. This technique is named after Friedrich Bessel.

In estimating the population variance from a sample when the population mean is unknown, the uncorrected sample variance is the *mean* of the squares of deviations of sample values from the sample mean (i.e. using a multiplicative factor 1/*n*). In this case, the sample variance is a biased estimator of the population variance.

Multiplying the uncorrected sample variance by the factor

gives an *unbiased* estimator of the population variance. In some literature, the above factor is called **Bessel's correction**.

One can understand Bessel's correction as the degrees of freedom in the residuals vector (residuals, not errors, because the population mean is unknown):

where is the sample mean. While there are *n* independent observations in the sample, there are only *n* − 1 independent residuals, as they sum to 0. For a more intuitive explanation of the need for Bessel's correction, see § Source of bias.

Generally Bessel's correction is an approach to reduce the bias due to finite sample size. Such finite-sample bias correction is also needed for other estimates like skew and kurtosis, but in these the inaccuracies are often significantly larger. To fully remove such bias it is necessary to do a more complex multi-parameter estimation. For instance a correct correction for the standard deviation depends on the kurtosis (normalized central 4th moment), but this again has a finite sample bias and it depends on the standard deviation, i.e. both estimations have to be merged.

Bessel filterIn electronics and signal processing, a Bessel filter is a type of analog linear filter with a maximally flat group/phase delay (maximally linear phase response), which preserves the wave shape of filtered signals in the passband. Bessel filters are often used in audio crossover systems.

The filter's name is a reference to German mathematician Friedrich Bessel (1784–1846), who developed the mathematical theory on which the filter is based. The filters are also called Bessel–Thomson filters in recognition of W. E. Thomson, who worked out how to apply Bessel functions to filter design in 1949. (In fact, a paper by Kiyasu of Japan predates this by several years.)

The Bessel filter is very similar to the Gaussian filter, and tends towards the same shape as filter order increases. While the time-domain step response of the Gaussian filter has zero overshoot, the Bessel filter has a small amount of overshoot, but still much less than common frequency domain filters.

Compared to finite-order approximations of the Gaussian filter, the Bessel filter has better shaping factor, flatter phase delay, and flatter group delay than a Gaussian of the same order, though the Gaussian has lower time delay and zero overshoot.

Bessel processIn mathematics, a Bessel process, named after Friedrich Bessel, is a type of stochastic process.

Bessel–Clifford functionIn mathematical analysis, the **Bessel–Clifford function**, named after Friedrich Bessel and William Kingdon Clifford, is an entire function of two complex variables that can be used to provide an alternative development of the theory of Bessel functions. If

is the entire function defined by means of the reciprocal Gamma function, then the Bessel–Clifford function is defined by the series

The ratio of successive terms is *z*/*k*(*n* + *k*), which for all values of *z* and *n* tends to zero with increasing *k*. By the ratio test, this series converges absolutely for all *z* and *n*, and uniformly for all regions with bounded |*z*|, and hence the Bessel–Clifford function is an entire function of the two complex variables *n* and *z*.

Carl Theodor Anger (Danzig, 31 July 1803 – Danzig, 25 March 1858) was a German mathematician and astronomer. He was a student of and assistant to Friedrich Bessel at the Königsberg Observatory from 1827 until 1831. Thereafter, he was appointed as astronomer by the Naturforschende Gesellschaft in Danzig.Besides his scientific work, especially that related to Bessel functions, he is also known for his first-hand biographical notes on the life of Bessel.

Christian August Friedrich PetersChristian August Friedrich Peters (September 7, 1806 – May 8, 1880) was a German astronomer. He was the father of astronomer Carl Friedrich Wilhelm Peters. He was born in Hamburg and died in Kiel.

Peters was the son of a merchant and, although he did not attend secondary school regularly, he obtained a good knowledge of mathematics and astronomy. In 1826 he became assistant to Heinrich Christian Schumacher at Altona Observatory. Schumacher encouraged him to study astronomy and Peters did a PhD under Friedrich Bessel at the University of Königsberg. In 1834 he became an assistant at Hamburg Observatory and in 1839 joined the staff of Pulkovo Observatory. In 1849 he became professor of astronomy at Königsberg and soon after succeeded Bessel as director of the observatory there. In 1854 he became director of the Altona Observatory and editor of the Astronomische Nachrichten. Peters edited the journal for the rest of his life, being responsible for 58 volumes of the journal. In 1872 the observatory moved to Kiel and he moved there and continued in his post. In 1866, he was elected a foreign member of the Royal Swedish Academy of Sciences.

Peters became a name in the literature on the theory of errors for his 1856 note on the estimation of precision using absolute deviations from the mean.

Peters won the Gold Medal of the Royal Astronomical Society in 1852.

Floating collimatorFloating collimator was an early collimator widely used in astronomical observations. It was invented by an English physicist and astronomer Captain Henry Kater about 1825.His collimator was meant to replace a level, or plumb-line, in astronomical observations, and to furnish a ready and perfectly exact method of determining the position of the horizontal or zenith point on the limb of a circle or zenith sector. Its principle is the invariability, with respect to the horizon, of the position assumed by any body of invariable figure and weight floating on a fluid.

Floating collimator consists of a rectangular box containing mercury, on which is floated a mass of cast-iron about twelve inches long, four broad, and half an inch thick, having two short uprights or Y's of equal height, cast in one piece with the rest. On these is firmly attached a small telescope, furnished with cross wires, or, what is better, crossed portions of the fine balance-spring of a watch, set flat-ways, and adjusted very exactly in the sidereal focus of object glass.

The float is browned with nitric acid to prevent the adhesion of the mercury, and is prevented from moving laterally by two smoothly polished iron pins, projecting from its sides in the middle of its length, which play freely in vertical grooves of polished iron in the sides of the box.

When this instrument is used, it is placed at a short distance from the circle whose horizontal point is to be ascertained, on either side, suppose the north, of its centre, and the telescopes of the circle and of the collimator are so adjusted as to look mutually at each other's cross wires, in the manner practised by astronomers Gauss and Friedrich Bessel, first of all coarsely, by trial, applying the eye to the eyeglasses of the two instruments alternately; and, finally, by illuminating the cross wires of the collimator by a lantern and oiled paper, taking care to exclude false light by a black screen, having an aperture equal to that of the collimator, and making the coincidence in the manner of an astronomical observation, by the fine motion of the circle.

The microscopes on the limb are then read off, and thus the apparent zenith distance of the collimating point, intersection of the wires, is found. The collimator is then transferred to the other (south) side of the circle, and a corresponding observation made without reversing the circle, but merely by the motion of the telescope on the limb. The difference of the two zenith distances so read off is double the error of the zenith or horizontal point of the graduation, and their semi-sum is the true zenith distance of the collimating point, or the co-inclination of the axis of the collimating telescope to the horizon.

By the experiments detailed in captain Kater's paper, read before the Royal Society in 1825, it appears that the error to be feared in the determination of the horizontal point by this instrument, can rarely amount to half a second, if a mean of four or five observations be taken. In 151 single trials, two only gave an error of two seconds, and one of these was made with a wooden float.

Georg Adolf ErmanGeorg Adolf Erman (12 May 1806 – 12 July 1877) was a German physicist.

Erman was born in Berlin as the son of Paul Erman. He studied natural science at the universities of Berlin and Königsberg, spent from 1828 to 1830 in a journey round the world, an account of which he published in Reise um die Erde durch Nordasien und die beiden Ozeane (1833-1848). The magnetic observations he made during his travels were utilized by Carl Friedrich Gauss in his theory of terrestrial magnetism. He was appointed professor of physics at Berlin in 1839, and died there in 1877. From 1841 to 1865 he edited the Archiv für wissenschaftliche Kunde von Russland, and in 1874 he published, with H. J. R. Petersen, Die Grundlagen der Gauss'schen Theorie und die Erscheinungen des Erdmagnetismus im Jahre 1829.

Erman married, Marie Bessel, daughter of Friedrich Bessel, and they were the parents of Johann Peter Adolf Erman.

HeliometerA heliometer (from Greek ἥλιος hḗlios "sun" and measure) is an instrument originally designed for measuring the variation of the sun's diameter at different seasons of the year, but applied now to the modern form of the instrument which is capable of much wider use.The basic concept is to introduce a split element into a telescope's optical path so as to produce a double image. If one element is moved using a screw micrometer, precise angle measurements can be made. The simplest arrangement is to split the object lens in half, with one half fixed and the other attached to the micrometer screw and slid along the cut diameter. To measure the diameter of the sun, for example, the micrometer is first adjusted so that the two images of the solar disk coincide (the "zero" position where the split elements form essentially a single element). The micrometer is then adjusted so that diametrically opposite sides of the two images of the solar disk just touch each other. The difference in the two micrometer readings so obtained is the (angular) diameter of the sun. Similarly, a precise measurement of the apparent separation between two nearby stars, A and B, is made by first superimposing the two images of the stars and then adjusting the double image so that star A in one image coincides with star B in the other. The difference in the two micrometer readings so obtained is the apparent separation or angular distance between the two stars.

The first application of the divided object-glass and the employment of double images in astronomical measures is due to Servington Savary from Exeter in 1743. Pierre Bouguer, in 1748, originated the true conception of measurement by double image without the auxiliary aid of a filar micrometer, that is by changing the distance between two object-glasses of equal focus. John Dollond, in 1754, combined Savary's idea of the divided object-glass with Bouguer's method of measurement, resulting in the construction of the first really practical heliometers. As far as we can ascertain, Joseph von Fraunhofer, some time not long before 1820, constructed the first heliometer with an achromatic divided object-glass, i.e. the first heliometer of the modern type.The first successful measurements of stellar parallax (to determine the distance to a star) were made by Friedrich Bessel in 1838 for the star 61 Cygni using a Fraunhofer heliometer. This was the 6.2-inch (157.5 mm) aperture Fraunhofer heliometer at Königsberg Observatory built by Joseph von Fraunhofer's firm, though he did not live to see it delivered to Bessel. Although the heliometer was difficult to use, it had certain advantages for Bessel including a wider field of view compared to other great refractors of the period, and overcame atmospheric turbulence in measurements compared to a filar micrometer.

Karl Gottfried HagenKarl Gottfried Hagen (24 December 1749 – 2 March 1829) was a German chemist.

Hagen was born and died in Königsberg, Prussia.

He founded the first German chemical laboratory at the University of Königsberg, thus establishing the scientific discipline of pharmaceutical chemistry in Germany. He worked as a Professor in the field of physics, chemistry and mineralogy.

His daughter, Johanna, married the astronomer Friedrich Bessel.

Another daughter, Louise Florentine, married the physicist Franz Ernst Neumann.

Lalande PrizeThe Lalande Prize (French: Prix Lalande) was an award for scientific advances in astronomy, given from 1802 until 1970 by the French Academy of Sciences.

The prize was endowed by astronomer Jérôme Lalande in 1801, a few years before his death in 1807, to enable the Academy of Sciences to make an annual award "to the person who makes the most unusual observation or writes the most useful paper to further the progress of Astronomy, in France or elsewhere."

It was combined with the Valz Prize (Prix Valz) in 1970 to create the Lalande-Valz Prize and then with a further 122 foundation prizes in 1997, resulting in the establishment of the Grande Médaille. The Grande Medaille is not limited to the field of astronomy.

Moritz Ludwig George WichmannMoritz Ludwig George Wichmann (1821 – 1859) was a German astronomer. He was an ardent observer of minor planets. A student of Friedrich Bessel, he observed with the famous Königsberg heliometer. In 1853 he published a determination of the parallax of Groombridge 1830.The asteroid 7103 Wichmann and the Wichmann crater on the Moon were named in his honour.

Stellar parallax

**Stellar parallax** is the apparent shift of position of any nearby star (or other object) against the background of distant objects. Created by the different orbital positions of Earth, the extremely small observed shift is largest at time intervals of about six months, when Earth arrives at exactly opposite sides of the Sun in its orbit, giving a baseline distance of about two astronomical units between observations. The parallax itself is considered to be half of this maximum, about equivalent to the observational shift that would occur due to the different positions of Earth and the Sun, a baseline of one astronomical unit (AU).

Stellar parallax is so difficult to detect that its existence was the subject of much debate in astronomy for hundreds of years. It was first observed in 1806 by Giuseppe Calandrelli who reported parallax in α-Lyrae in his work "*Osservazione e riflessione sulla parallasse annua dall’alfa della Lira*". Then in 1838 Friedrich Bessel made the first successful parallax measurement, for the star 61 Cygni, using a Fraunhofer heliometer at Königsberg Observatory.

Once a star's parallax is known, its distance from Earth can be computed trigonometrically. But the more distant an object is, the smaller its parallax. Even with 21st-century techniques in astrometry, the limits of accurate measurement make distances farther away than about 100 parsecs (or roughly 300 light years) too approximate to be useful when obtained by this technique. This limits the applicability of parallax as a measurement of distance to objects that are relatively close on a galactic scale. Other techniques, such as spectral red-shift, are required to measure the distance of more remote objects.

Stellar parallax measures are given in the tiny units of arcseconds, or even in thousandths of arcseconds (milliarcseconds). The distance unit parsec is defined as the length of the leg of a right triangle adjacent to the angle of one arcsecond at one vertex, where the other leg is 1 AU long. Because stellar parallaxes and distances all involve such skinny right triangles, a convenient trigonometric approximation can be used to convert parallaxes (in arcseconds) to distance (in parsecs). The approximate distance is simply the reciprocal of the parallax: For example, Proxima Centauri (the nearest star to Earth other than the Sun), whose parallax is 0.7687, is 1 / 0.7687 parsecs = 1.3009 parsecs (4.243 ly) distant.

Timeline of stellar astronomyTimeline of stellar astronomy

2300 BC — First great period of star naming in China.

134 BC — Hipparchus creates the magnitude scale of stellar apparent luminosities

185 AD — Chinese astronomers become the first to observe a supernova, the SN 185

964 — Abd al-Rahman al-Sufi (Azophi) writes the Book of Fixed Stars, in which he makes the first recorded observations of the Andromeda Galaxy and the Large Magellanic Cloud, and lists numerous stars with their positions, magnitudes, brightness, and colour, and gives drawings for each constellation

1000s (decade) — The Persian astronomer, Abū Rayhān al-Bīrūnī, describes the Milky Way galaxy as a collection of numerous nebulous stars

1006 — Ali ibn Ridwan and Chinese astronomers observe the SN 1006, the brightest stellar event ever recorded

1054 — Chinese and Arab astronomers observe the SN 1054, responsible for the creation of the Crab Nebula, the only nebula whose creation was observed

1181 — Chinese astronomers observe the SN 1181 supernova

1580 — Taqi al-Din measures the right ascension of the stars at the Constantinople Observatory of Taqi ad-Din using an "observational clock" he invented and which he described as "a mechanical clock with three dials which show the hours, the minutes, and the seconds"

1596 — David Fabricius notices that Mira's brightness varies

1672 — Geminiano Montanari notices that Algol's brightness varies

1686 — Gottfried Kirch notices that Chi Cygni's brightness varies

1718 — Edmund Halley discovers stellar proper motions by comparing his astrometric measurements with those of the Greeks

1782 — John Goodricke notices that the brightness variations of Algol are periodic and proposes that it is partially eclipsed by a body moving around it

1784 — Edward Pigott discovers the first Cepheid variable star

1838 — Thomas Henderson, Friedrich Struve, and Friedrich Bessel measure stellar parallaxes

1844 — Friedrich Bessel explains the wobbling motions of Sirius and Procyon by suggesting that these stars have dark companions

1906 — Arthur Eddington begins his statistical study of stellar motions

1908 — Henrietta Leavitt discovers the Cepheid period-luminosity relation

1910 — Ejnar Hertzsprung and Henry Norris Russell study the relation between magnitudes and spectral types of stars

1924 — Arthur Eddington develops the main sequence mass-luminosity relationship

1929 — George Gamow proposes hydrogen fusion as the energy source for stars

1938 — Hans Bethe and Carl von Weizsäcker detail the proton-proton chain and CNO cycle in stars

1939 — Rupert Wildt realizes the importance of the negative hydrogen ion for stellar opacity

1952 — Walter Baade distinguishes between Cepheid I and Cepheid II variable stars

1953 — Fred Hoyle predicts a carbon-12 resonance to allow stellar triple alpha reactions at reasonable stellar interior temperatures

1961 — Chūshirō Hayashi publishes his work on the Hayashi track of fully convective stars

1963 — Fred Hoyle and William A. Fowler conceive the idea of supermassive stars

1964 — Subrahmanyan Chandrasekhar and Richard Feynman develop a general relativistic theory of stellar pulsations and show that supermassive stars are subject to a general relativistic instability

1967 — Eric Becklin and Gerry Neugebauer discover the Becklin-Neugebauer Object at 10 micrometres

1977 — (May 25) The Star Wars film is released and became a worldwide phenomenon, boosting interests in stellar systems.

2012 — (May 2) First visual proof of existence of black-holes. Suvi Gezari's team in Johns Hopkins University, using the Hawaiian telescope Pan-STARRS 1, publish images of a supermassive black hole 2.7 million light-years away swallowing a red giant.

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