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{{Short description|German astronomer and mathematician (1784–1846)}}
{{Use dmy dates|date=August 2022}}
{{Use dmy dates|date=August 2022}}
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{{short description|German astronomer and mathematician}}
{{Infobox scientist
{{Infobox scientist
| name = Friedrich Bessel
| name = Friedrich Wilhelm Bessel
| image = Friedrich Wilhelm Bessel (1839 painting).jpg
| image = Friedrich Wilhelm Bessel (1839 painting).jpg
| image_size = 225px
| image_size = 225px
| caption = [[Christian Albrecht Jensen|C. A. Jensen]], ''Friedrich Wilhelm Bessel'', 1839 ([[Ny Carlsberg Glyptotek]])
| caption = [[Christian Albrecht Jensen|C. A. Jensen]], ''Friedrich Wilhelm Bessel'', 1839 ([[Ny Carlsberg Glyptotek]])
| birth_date = {{birth date|1784|7|22|df=y}}
| birth_date = {{birth date|1784|7|22|df=y}}
| birth_place = [[Minden]], [[Kingdom of Prussia]]
| birth_place = [[Minden]], [[Kingdom of Prussia]], [[Holy Roman Empire]]
| death_date = {{death date and age|df=yes|1846|3|17|1784|7|22}}
| death_date = {{death date and age|df=yes|1846|3|17|1784|7|22}}
| death_place = [[Königsberg]], [[Province of Prussia|Prussia]]
| death_place = [[Königsberg]], Kingdom of Prussia
| nationality = [[Germany|German]]
| nationality = [[Germany|German]]
| field = [[Astronomy]], [[mathematics]], [[geodesy]]
| field = [[Astronomy]], [[mathematics]], [[geodesy]]
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| doctoral_students = [[Friedrich Wilhelm Argelander]] [[Heinrich Scherk]]
| doctoral_students = [[Friedrich Wilhelm Argelander]] [[Heinrich Scherk]]
| known_for = [[Bessel function]]s<br />[[Bessel ellipsoid]]<br />[[Bessel polynomials]]<br>[[Besselian elements]]<br />[[Bessel's correction]]<br />[[Bessel's inequality]]<br>[[Kater's pendulum#Repsold–Bessel pendulum|Repsold–Bessel pendulum]]
| known_for = [[Bessel function]]s<br />[[Bessel ellipsoid]]<br />[[Bessel polynomials]]<br>[[Besselian elements]]<br />[[Bessel's correction]]<br />[[Bessel's inequality]]<br>[[Kater's pendulum#Repsold–Bessel pendulum|Repsold–Bessel pendulum]]
| prizes = [[PhD (Hon)]]<br />[[University of Göttingen]] (1811)<br />Honorary member of the [[Saint Petersburg Academy of Sciences]](1814)<br />[[Lalande Prize]] (1811), (1816)<br />[[Gold Medal of the Royal Astronomical Society]] (1829 and 1841)
| prizes = [[PhD (Hon)]]<br />[[University of Göttingen]] (1811)<br />[[Lalande Prize]] (1811), (1816)<br />[[Gold Medal of the Royal Astronomical Society]] (1829 and 1841)
| footnotes =
| footnotes =
}}
}}


'''Friedrich Wilhelm Bessel''' ({{IPA-de|ˈbɛsl̩|lang}}; 22 July 1784 – 17 March 1846) was a German [[astronomer]], [[mathematician]], [[physicist]], and [[geodesy|geodesist]]. He was the first astronomer who determined reliable values for the distance from the sun to another star by the method of [[parallax]]. Certain important mathematical functions were named [[Bessel function]]s after Bessel's death, though they had originally been discovered by [[Daniel Bernoulli]] before being generalised by Bessel.
'''Friedrich Wilhelm Bessel''' ({{IPA|de|ˈbɛsl̩|lang}}; 22 July 1784 – 17 March 1846) was a German [[astronomer]], [[mathematician]], [[physicist]], and [[geodesy|geodesist]]. He was the first astronomer who determined reliable values for the distance from the sun to another star by the method of [[parallax]]. Certain important mathematical functions were named [[Bessel function]]s after Bessel's death, though they had originally been discovered by [[Daniel Bernoulli]] before being generalised by Bessel.


== Life and family ==
== Life and family ==
⚫
Bessel was born in [[Minden]], [[Westphalia]], then capital of the Prussian administrative region [[Minden-Ravensberg]], as second son of a civil servant into a large family. At the age of 14 he left the school, because he did not like the education in Latin language, and apprenticed in the import-export concern Kulenkamp at [[Bremen]]. The business's reliance on cargo ships led him to turn his [[mathematics|mathematical]] skills to problems in [[navigation]]. This in turn led to an interest in [[astronomy]] as a way of determining [[longitude]].

⚫
Bessel was born in [[Minden]], [[Westphalia]], then capital of the Prussian administrative region [[Minden-Ravensberg]], as second son of a civil servant into a large family. At the age of 14 he left the school, because he did not like the education in latin language, and apprenticed in the import-export concern Kulenkamp at [[Bremen]]. The business's reliance on cargo ships led him to turn his [[mathematics|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 [[Heinrich Wilhelm Olbers]], a practising physician of Bremen and well-known astronomer, 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.{{sfn|Chisholm|1911}} [[Franz Xaver von Zach]] edited the results in his journal ''Monatliche Correspondenz''.
Bessel came to the attention of [[Heinrich Wilhelm Olbers]], a practising physician of Bremen and well-known astronomer, 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.{{sfn|Chisholm|1911}} [[Franz Xaver von Zach]] edited the results in his journal ''Monatliche Correspondenz''.


Having finished his commercial education Bessel left Kulenkamp in 1806 and became assistant at [[Johann Hieronymus Schröter]]'s private observatory in [[Lilienthal, Lower Saxony|Lilienthal]] near Bremen as successor of [[Karl Ludwig Harding]]. There he worked on [[James Bradley]]'s stellar observation data to produce precise positions for some 3,222 stars.{{sfn|Chisholm|1911}}
Having finished his commercial education, Bessel left Kulenkamp in 1806 and became assistant at [[Johann Hieronymus Schröter]]'s private observatory in [[Lilienthal, Lower Saxony|Lilienthal]] near Bremen as successor of [[Karl Ludwig Harding]]. There he worked on [[James Bradley]]'s stellar observation data to produce precise positions for some 3,222 stars.{{sfn|Chisholm|1911}}


Despite lacking any higher education, especially at university, Bessel was appointed director of the newly founded [[Königsberg Observatory]] by King [[Frederick William III of Prussia]] in January 1810, at the age of 25, and remained in that position until his death. By reason of lacking any academical degree some colleagues of the Philosophical Faculty disputed Bessel's right to teach mathematics. Therefore he turned to his fellow [[Carl Friedrich Gauss]], who provided the award of an honorary doctor degree from the [[University of Göttingen]] in March 1811. Both scientists were in correspondence from 1804 to 1843. In 1837 they got in quarrel about Gauss' habit of very slow publication.<ref>{{cite journal |last1=Biermann |first1=Kurt-R. |title=Über die Beziehungen zwischen C.F. Gauß und F.W. Bessel |journal=Mitteilungen der Gauss-Gesellschaft Göttingen |volume=3 |pages=7–20 |year=1966 }}</ref>
Despite lacking any higher education, especially at university, Bessel was appointed director of the newly founded [[Königsberg Observatory]] by King [[Frederick William III of Prussia]] in January 1810, at the age of 25, and remained in that position until his death. Some elder professors of the Philosophical Faculty disputed Bessel's right to teach mathematics without any academic degree. Therefore, he turned to his fellow [[Carl Friedrich Gauss]], who provided the award of an honorary doctor degree from the [[University of Göttingen]] in March 1811. Both scientists were in correspondence from 1804 to 1843. In 1837 they got in quarrel about Gauss's habit of very slow publication.<ref>{{cite journal | last1 = Biermann | first1 = Kurt-R. | title = Über die Beziehungen zwischen C.F. Gauß und F.W. Bessel | journal = Mitteilungen der Gauss-Gesellschaft Göttingen | volume = 3 | pages = 7–20 | year = 1966 }}</ref>


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]], where he gave a report of astronomical clocks.<ref>[https://www.biodiversitylibrary.org/item/46628#page/273/mode/1up Report of the British Assiociation for the Advancement of Science.]</ref>
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]], where he gave a report on astronomical clocks.<ref>[https://www.biodiversitylibrary.org/item/46628#page/273/mode/1up Report of the British Assiociation for the Advancement of Science.]</ref>


Bessel married Johanna Hagen, 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.<ref>{{Cite book | first1=Kathryn M. | last1=Olesko|author1-link= Kathryn Olesko | title=Physics as a Calling: Discipline and Practice in the Königsberg Seminar for Physics | url=https://archive.org/details/physicsascalling00oles | url-access=registration | publisher=Cornell University Press | year=1991 | isbn=9780801422485}}</ref> These exacting methods had a lasting impact upon the work of Neumann's students and upon the Prussian conception of precision in measurement.
Bessel married Johanna Hagen, 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.<ref>{{Cite book | first1=Kathryn M. | last1=Olesko|author1-link= Kathryn Olesko | title=Physics as a Calling: Discipline and Practice in the Königsberg Seminar for Physics | url=https://archive.org/details/physicsascalling00oles | url-access=registration | publisher=Cornell University Press | year=1991 | isbn=9780801422485}}</ref> 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 elder son became an architect but died suddenly in 1840 aged 26; his younger son died shortly after birth. His eldest daughter, Marie, married the physicist [[Georg Adolf Erman]], member of the scholar family [[Erman]]. One of their sons in turn was the renowned [[Egyptologist]] [[Adolf Erman]]. His third daughter Johanna married the politician [[Adolf Hermann Hagen]]; their son was the physicist [[Ernst Bessel Hagen]] and the mathematician [[Erich Bessel-Hagen]] was a grandson of them. Bessel was [[Godparent|godfather]] of [[Adolf von Baeyer]], son of his collaborator [[Johann Jacob Baeyer]].
Bessel had two sons and three daughters. His elder son became an architect but died suddenly in 1840 aged 26; his younger son died shortly after birth. His eldest daughter, Marie, married the physicist [[Georg Adolf Erman]], member of the scholar family [[Erman]]. One of their sons in turn was the renowned [[Egyptologist]] [[Adolf Erman]]. His third daughter Johanna married the politician [[Adolf Hermann Hagen]]; one of their sons was the physicist [[Ernst Bessel Hagen]], and the mathematician [[Erich Bessel-Hagen]] was a grandson of them. Bessel was [[Godparent|godfather]] of [[Adolf von Baeyer]], son of his collaborator [[Johann Jacob Baeyer]].


After several months of illness Bessel died in March 1846 at his observatory from [[retroperitoneal fibrosis]].<ref>{{Cite journal | doi = 10.1002/asna.18460240402 | title = Bessel's Tod | language = de| trans-title = Bessel's death| journal = Astronomische Nachrichten | volume = 24 | issue = 556| pages = 49–52 | year = 1846 | url = https://books.google.com/books?id=-qAEAAAAQAAJ&pg=PA50| bibcode = 1846AN.....24...49B| last1 = Bessel | first1 = Friedrich Wilhelm }}</ref><ref>{{Cite journal| doi = 10.1007/s001310050044 | last = Neumann-Redlin von Meding | first = E. | title = Vor 150 Jahren: die Beschreibung der Retroperitonealfibrose, der "Ormond'schen Erkrankung", am Krankheitsbild F.W. Bessels (1784–1846) | journal = Der Urologe B | volume = 36| pages = 378–382| year = 1996| issue = 5 }}</ref>
After several months of illness Bessel died in March 1846 at his observatory from [[retroperitoneal fibrosis]].<ref>{{Cite journal | doi = 10.1002/asna.18460240402 | title = Bessel's Tod | language = de| trans-title = Bessel's death| journal = Astronomische Nachrichten | volume = 24 | issue = 556| pages = 49–52 | year = 1846 | url = https://books.google.com/books?id=-qAEAAAAQAAJ&pg=PA50| bibcode = 1846AN.....24...49B| last1 = Bessel | first1 = Friedrich Wilhelm }}</ref><ref>{{Cite journal| doi = 10.1007/s001310050044 | last = Neumann-Redlin von Meding | first = E. | title = Vor 150 Jahren: die Beschreibung der Retroperitonealfibrose, der "Ormond'schen Erkrankung", am Krankheitsbild F.W. Bessels (1784–1846) | journal = Der Urologe B | volume = 36| pages = 378–382| year = 1996| issue = 5 }}</ref>


== Work ==
== Work ==
[[File:Koenigsberg observatory.jpg|right|thumb|[[Königsberg Observatory]] in 1830. It was destroyed in the Second World War.]]
[[File:Koenigsberg observatory.jpg|right|thumb|[[Königsberg Observatory]] (1830)]]
[[File:Friedrich.Wilhelm.Bessel.Ausschnitt.Daguerrotypie.png|thumb|upright|Crop of a [[Daguerreotype]] (1843)]]

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.
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 [[Georg von Reichenbach|Reichenbach]], assisted by some of his qualified students. The most prominent of them was [[Friedrich Wilhelm Argelander]], his successors were [[Otto August Rosenberger]] and [[August Ludwig Busch]].
Starting in 1819, Bessel determined the position of over 50,000 stars with a [[meridian circle]] from [[Georg von Reichenbach|Reichenbach]], assisted by some of his qualified students. The most prominent of them was [[Friedrich Wilhelm Argelander]], his successors were [[Otto August Rosenberger]] and [[August Ludwig Busch]].


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 the [[stellar parallax]] in [[Cosmic distance ladder|calculating the distance to a star]]. Astronomers had believed for some time that parallax would provide the first accurate measurement of interstellar distances. In 1838 Bessel announced that [[61 Cygni]] had a parallax of 0.314 [[arcsecond]]s; which, given the diameter of the [[Earth]]'s orbit, indicated that the star is 10.3 [[Light-year|ly]] away.<ref>{{Cite journal | last = Bessel | first = F. W. | author-link = Friedrich Bessel| doi = 10.1002/asna.18390160502 | title = Bestimmung der Entfernung des 61sten Sterns des Schwans | language = de| trans-title = Determination of the distance to 61 Cygni| journal = Astronomische Nachrichten | volume = 16 | issue = 365–366 | pages = 65–96 | year = 1838 | bibcode = 1838AN.....16...65B| url = https://zenodo.org/record/1424605 }}</ref><ref>{{Cite journal| doi = 10.1093/mnras/4.17.152| last = Bessel | first = F. W. | author-link = Friedrich Bessel| title = On the parallax of 61 Cygni| journal = Monthly Notices of the Royal Astronomical Society| volume = 4| issue = 17| pages = 152–161| year = 1838b| bibcode = 1838MNRAS...4..152B| doi-access = free}}</ref><ref>{{cite magazine|title=A brief history of light dates|url=http://newswatch.nationalgeographic.com/2010/11/22/a_brief_history_of_light_years/|archive-url=https://web.archive.org/web/20110415042634/http://newswatch.nationalgeographic.com/2010/11/22/a_brief_history_of_light_years/|url-status=dead|archive-date=15 April 2011|magazine=National Geographic|access-date=26 June 2020}}</ref> Given the current measurement of 11.4 ly, Bessel's figure had an error of 9.6%.
Bessel determined the first reliable value for the [[Cosmic distance ladder|distance]] between a star and the solar system with a [[heliometer]] from [[Joseph von Fraunhofer|Fraunhofer]] using the method of [[stellar parallax]]. In 1838 he published a parallax of 0.314 [[arcsecond]]s for [[61 Cygni]], which indicated that the star is 10.3 [[Light-year|ly]] away.<ref>{{Cite journal | last = Bessel | first = F. W. | doi = 10.1002/asna.18390160502 | title = Bestimmung der Entfernung des 61sten Sterns des Schwans | language = de| trans-title = Determination of the distance to 61 Cygni| journal = Astronomische Nachrichten | volume = 16 | issue = 365–366 | pages = 65–96 | year = 1838 | bibcode = 1838AN.....16...65B| url = https://zenodo.org/record/1424605 }}</ref><ref>{{Cite journal| doi = 10.1093/mnras/4.17.152| last = Bessel | first = F. W. | title = On the parallax of 61 Cygni| journal = Monthly Notices of the Royal Astronomical Society| volume = 4| issue = 17| pages = 152–161| year = 1838b| bibcode = 1838MNRAS...4..152B| doi-access = free}}</ref><ref>{{cite magazine|title=A brief history of light dates|url=http://newswatch.nationalgeographic.com/2010/11/22/a_brief_history_of_light_years/|archive-url=https://web.archive.org/web/20110415042634/http://newswatch.nationalgeographic.com/2010/11/22/a_brief_history_of_light_years/|url-status=dead|archive-date=15 April 2011|magazine=National Geographic|access-date=26 June 2020}}</ref> Compared with the current measurement of 11.4 ly, Bessel's figure had an error of 9.6%. Thanks to these results astronomers had not only enlarged the vision of the universe well beyond the cosmic magnitude, but after the discovery in 1728 by [[James Bradley]] of the [[Aberration (astronomy)|aberration of light]] a second empirical evidence of the Earth's relative movement was produced.<ref>{{Cite book |last=Hamel |first=Jürgen |title=Friedrich Wilhelm Bessel |publisher=Teubner |location=Leipzig |year=1984 |page=69 }}</ref> A short time later [[Friedrich Georg Wilhelm Struve]] and [[Thomas James Henderson|Thomas Henderson]] reported the parallaxes of [[Vega]] and [[Alpha Centauri]].
Thanks to these results astronomers had not only enlarged the vision of the universe well beyond the cosmic magnitude, but after the discovery in 1728 by [[James Bradley]] of the [[Aberration (astronomy)|aberration of light]] a second empirical evidence of the Earth's relative movement was produced.<ref>{{Cite book |last=Hamel |first=Jürgen |title=Friedrich Wilhelm Bessel |publisher=Teubner |location=Leipzig |year=1984 |page=69 }}</ref> A short time later [[Friedrich Georg Wilhelm Struve]] and [[Thomas James Henderson|Thomas Henderson]] reported 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.<ref>
Precise measurements with a new [[meridian circle]] from Adolf Repsold allowed Bessel to notice deviations in the motions of [[Sirius]] and [[Procyon]], which must be caused by the gravitational attraction of unseen companions.<ref>
{{Cite journal | last = Bessel | first = F. W. | author-link = Friedrich Bessel| title = Ueber Veränderlichkeit der eigenen Bewegungen der Fixsterne | language = de| trans-title = On Variations of the proper motions of the fixed stars| doi = 10.1002/asna.18450221002 | journal = Astronomische Nachrichten | volume = 22 | issue = 514| pages = 145–160 | year = 1844a| bibcode = 1844AN.....22..145B| url = https://zenodo.org/record/1424611 }}
{{Cite journal | last = Bessel | first = F. W. | title = Ueber Veränderlichkeit der eigenen Bewegungen der Fixsterne | language = de| trans-title = On Variations of the proper motions of the fixed stars| doi = 10.1002/asna.18450221002 | journal = Astronomische Nachrichten | volume = 22 | issue = 514, 515| pages = 145–160, 169–184 | year = 1844a| bibcode = 1844AN.....22..145B| url = https://zenodo.org/record/1424611 }}
</ref><ref>
{{Cite journal | last = Bessel | first = F. W. | author-link = Friedrich Bessel| title = Ueber Veränderlichkeit der eigenen Bewegungen der Fixsterne (Fortsetzung)| language = de| trans-title = On Variations of the proper motions of the fixed stars (continued)| doi = 10.1002/asna.18450221202 | journal = Astronomische Nachrichten | volume = 22 | issue = 515| pages = 169–184 | year = 1844b| bibcode = 1844AN.....22..169B| url = https://zenodo.org/record/1424611 }}
</ref><ref>
</ref><ref>
{{Cite journal| doi = 10.1093/mnras/6.11.136a| last = Bessel | first = F. W. | author-link = Friedrich Bessel| title = On the variations of the proper motions of Procyon and Sirius| journal = Monthly Notices of the Royal Astronomical Society| volume = 6| issue = 11| pages = 136–141| year = 1844c| bibcode = 1844MNRAS...6R.136B| doi-access = free}}
{{Cite journal| doi = 10.1093/mnras/6.11.136a| last = Bessel | first = F. W. | title = On the variations of the proper motions of Procyon and Sirius| journal = Monthly Notices of the Royal Astronomical Society| volume = 6| issue = 11| pages = 136–141| year = 1844c| bibcode = 1844MNRAS...6R.136B| doi-access = free}}
</ref>
</ref>
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]].
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]] by [[Alvan Graham Clark]] in 1862, the first discovery of a [[white dwarf]]. [[John Martin Schaeberle]] discovered Procyon B in 1896.


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.<ref>
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 transit time of stars.<ref>
{{Cite journal| doi = 10.1017/s0007087407009478| last = Hoffmann | first = Christoph | title = Constant differences: Friedrich Wilhelm Bessel, the concept of the observer in early nineteenth-century practical astronomy and the history of the personal equation| journal = British Journal for the History of Science| volume = 40| issue = 3| pages = 333–365| year = 2007| s2cid = 170080943 }}
{{Cite journal| doi = 10.1017/s0007087407009478| last = Hoffmann | first = Christoph | title = Constant differences: Friedrich Wilhelm Bessel, the concept of the observer in early nineteenth-century practical astronomy and the history of the personal equation| journal = British Journal for the History of Science| volume = 40| issue = 3| pages = 333–365| year = 2007| s2cid = 170080943 }}
</ref>
</ref>


In 1824, Bessel developed a new method for calculating 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.{{Citation needed|date=March 2020}}
In 1824, Bessel developed a new method for calculating 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.<ref>{{cite web | url = http://eclipse.gsfc.nasa.gov/SEcat5/beselm.html | title = Besselian Elements of Solar Eclipses | last = [[Fred Espenak|Espenak]] | first = Fred | author-link = | website = NASA Eclipse Website | access-date = 4 August 2023}}</ref>


On Bessel's proposal in 1825 the [[Prussian Academy of Sciences]] started the edition of the ''Berliner Akademische Sternkarten'' (''Berlin Academic Star Charts'') as an international project with [[Johann Franz Encke]] as executive editor. One unpublished new chart enabled [[Johann Gottfried Galle]] to find [[discovery of Neptune|Neptune]] near the position calculated by [[Urbain Le Verrier|Le Verrier]] in September 1846 at [[Berlin Observatory]].
On Bessel's proposal the [[Prussian Academy of Sciences]] started the edition of the ''Berliner Akademische Sternkarten'' (''Berlin Academic Star Charts'') in 1825 as an international project with [[Johann Franz Encke]] as executive editor. One unpublished new chart enabled [[Johann Gottfried Galle]] to find [[discovery of Neptune|Neptune]] near the position calculated by [[Urbain Le Verrier|Le Verrier]] in September 1846 at [[Berlin Observatory]].


In the second decade of the 19th century while studying the dynamics gravitational systems as [[n-body problem|multi-body problem]], Bessel developed what are now known as [[Bessel function]]s. Critical for the solution of certain [[differential equations]], these functions are used throughout both classical and [[quantum physics]].
In the second decade of the 19th century, while studying the dynamics gravitational systems as [[n-body problem|multi-body problem]], Bessel developed what are now known as [[Bessel function]]s. 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''&nbsp;−&nbsp;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]])''.
A [[Bessel's correction|correction]] term in the formula for the [[sample variance]] estimator is named in his honour. This is the use of the factor ''n''&nbsp;−&nbsp;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.


[[File:Igm, apparato di bessel, del 1873.jpg|thumb|Bessel's geodetic apparatus, in the museum of Istituto Geografico Militare, Florence, Italy]]
Like numerous astronomers of his time Bessel dealt on the field of [[geodesy]], too,<ref>{{cite conference
Like numerous astronomers of his time Bessel dealt on the field of [[geodesy]], too,<ref>{{cite conference
|first = T. |last = Viik
|first = T.
|last = Viik
|title = F.W. Bessel and Geodesy
|title = F.W. Bessel and Geodesy
|date = 2006
|date = 2006
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|pages = 53–63
|pages = 53–63
|url = http://www.aai.ee/~viik/PAPERS/BESSEL_GEODESY.pdf
|url = http://www.aai.ee/~viik/PAPERS/BESSEL_GEODESY.pdf
|access-date = 9 November 2013
|archive-date = 9 November 2013
|archive-url = https://web.archive.org/web/20131109130501/http://www.aai.ee/~viik/PAPERS/BESSEL_GEODESY.pdf
|url-status = dead
}}</ref>
}}</ref>
first theoretically, when he published a method for solving the main [[Geodesics on an ellipsoid|geodetic problem]].<ref>{{Cite journal | last = Bessel | first = F. W. | title = Ueber die Berechnungen der geographischen Länge und Breite aus geodätischen Vermessungen | language = de | doi = 10.1002/asna.18260041601| journal = Astronomische Nachrichten | volume = 4 | issue = 16| pages = 241–254 | year = 1825 | arxiv = 0908.1823 | bibcode = | s2cid = 118630614 | url = }}
first theoretically, when he published a method for solving the main [[Geodesics on an ellipsoid|geodetic problem]].<ref>{{Cite journal | last = Bessel | first = F. W. | title = Ueber die Berechnungen der geographischen Länge und Breite aus geodätischen Vermessungen | language = de | doi = 10.1002/asna.18260041601| journal = Astronomische Nachrichten | volume = 4 | issue = 16| pages = 241–254 | year = 1825 | arxiv = 0908.1823 | bibcode = | s2cid = 118630614 | url = }}
* {{Cite journal | last = Bessel | first = F. W. | translator-last = Ch. F. Karney | translator-first = R. E. Deakin | title = The calculation of longitude and latitude from geodesic measurements | language = en | doi = 10.1002/asna.201011352| journal = Astronomische Nachrichten | volume = 333 | issue = 8| pages = 852–861 | year = 2010 | arxiv = 0908.1824 | bibcode = 2010AN....331..852K | s2cid = 118760590 | url = }} [http://geographiclib.sourceforge.net/bessel-errata.html Errata].</ref>
* {{Cite journal | last = Bessel | first = F. W. | translator-last = Ch. F. Karney | translator-first = R. E. Deakin | title = The calculation of longitude and latitude from geodesic measurements | language = en | doi = 10.1002/asna.201011352| journal = Astronomische Nachrichten | volume = 333 | issue = 8| pages = 852–861 | year = 2010 | arxiv = 0908.1824 | bibcode = 2010AN....331..852K | s2cid = 118760590 | url = }} [http://geographiclib.sourceforge.net/bessel-errata.html Errata].</ref>
In 1830 he got the royal order for the survey of [[East Prussia]] with the purpose to connect the yet existing Prussian and Russian [[triangulation network]]s. This work was carried out in cooperation with [[Johann Jacob Baeyer]], then major of the Prussian army; the final report was published in 1838.<ref>{{cite book
In 1830 he got the royal order for the survey of [[East Prussia]] with the purpose to connect the yet existing Prussian and Russian [[triangulation network]]s. This work was carried out in cooperation with [[Johann Jacob Baeyer]], then major of the Prussian army; the final report was published in 1838.<ref>{{cite book | first1 = F. W. | last1 = Bessel| author-link1 = Friedrich Bessel | first2 = J. J. | last2 = Baeyer | title = Gradmessung in Ostpreussen und ihre Verbindung mit Preussischen und Russischen Dreiecksketten | language = de| trans-title = The East Prussian Survey and its connection with the Prussian and Russian networks | publisher = Dümmler | location = Berlin | date = 1838 | url = https://archive.org/details/bub_gb_f5AAAAAAMAAJ}}</ref>
⚫
He also obtained an estimate of increased accuracy for the [[Earth's ellipsoid]], nowadays called the [[Bessel ellipsoid]], based on several [[arc measurements]].<ref>{{Cite journal | last = Bessel | first = F. W. | doi = 10.1002/asna.18370142301 | title = Bestimmung der Axen des elliptischen Rotationssphäroids, welches den vorhandenen Messungen von Meridianbögen der Erde am meisten entspricht | language = de| trans-title = Determination of the axes of ellipsoid that fits best to the existing measurements of meridian arcs| journal = Astronomische Nachrichten | volume = 14 | issue = 333 | pages = 333–346| year = 1837 | bibcode = 1837AN.....14..333B | url = https://zenodo.org/record/1424603 }}</ref><ref>{{Cite journal | last = Bessel | first = F. W. | doi = 10.1002/asna.18420190702 | title = Ueber einen Fehler in der Berechnung der französischen Gradmessung und seinen Einfluß auf die Bestimmung der Figur der Erde | language = de| trans-title = Concerning an error in the calculation of the French survey and its influence on the determination of the figure of the Earth| journal = Astronomische Nachrichten | volume = 19 | issue = 438| pages = 97–116| year = 1841 | bibcode = 1841AN.....19...97B| url = https://zenodo.org/record/1424607 }}</ref>
|first1 = F. W. |last1 = Bessel| author-link1 = Friedrich Bessel
|first2 = J. J. |last2 = Baeyer
|title = Gradmessung in Ostpreussen und ihre Verbindung mit Preussischen und Russischen Dreiecksketten
|language = de
|trans-title=The East Prussian Survey and its connection with the Prussian and Russian networks
|publisher = Dümmler
|location = Berlin
|date = 1838
|url = https://archive.org/details/bub_gb_f5AAAAAAMAAJ
}}</ref>
⚫
He also obtained an estimate of increased accuracy for the [[Earth's ellipsoid]], nowadays called the [[Bessel ellipsoid]], based on several [[arc measurements]].<ref>{{Cite journal | last = Bessel | first = F. W. | author-link = Friedrich Bessel| doi = 10.1002/asna.18370142301 | title = Bestimmung der Axen des elliptischen Rotationssphäroids, welches den vorhandenen Messungen von Meridianbögen der Erde am meisten entspricht | language = de| trans-title = Determination of the axes of ellipsoid that fits best to the existing measurements of meridian arcs| journal = Astronomische Nachrichten | volume = 14 | issue = 333 | pages = 333–346| year = 1837 | bibcode = 1837AN.....14..333B | url = https://zenodo.org/record/1424603 }}</ref><ref>{{Cite journal | last = Bessel | first = F. W. | author-link = Friedrich Bessel| doi = 10.1002/asna.18420190702 | title = Ueber einen Fehler in der Berechnung der französischen Gradmessung und seinen Einfluß auf die Bestimmung der Figur der Erde | language = de| trans-title = Concerning an error in the calculation of the French survey and its influence on the determination of the figure of the Earth| journal = Astronomische Nachrichten | volume = 19 | issue = 438| pages = 97–116| year = 1841 | bibcode = 1841AN.....19...97B| url = https://zenodo.org/record/1424607 }}</ref>


== Honors and prizes ==
== Honors and prizes ==
Line 105: Line 97:
* Fellow of the [[Royal Society]] in 1825<ref>{{cite web | title = Fellows | url = https://catalogues.royalsociety.org/CalmView/Overview.aspx?src=CalmView.Persons&r=(((Surname=%27Bessel%27))) | publisher = The Royal Society | access-date = 23 April 2023}}</ref>
* Fellow of the [[Royal Society]] in 1825<ref>{{cite web | title = Fellows | url = https://catalogues.royalsociety.org/CalmView/Overview.aspx?src=CalmView.Persons&r=(((Surname=%27Bessel%27))) | publisher = The Royal Society | access-date = 23 April 2023}}</ref>
* Foreign Honorary Member of the [[American Academy of Arts and Sciences]] in 1832<ref name="AAAS">{{cite web|title=Book of Members, 1780–2010: Chapter B|url=http://www.amacad.org/publications/BookofMembers/ChapterB.pdf |archive-url=https://web.archive.org/web/20060618085806/http://amacad.org/publications/BookofMembers/ChapterB.pdf |archive-date=2006-06-18 |url-status=live|publisher=American Academy of Arts and Sciences|access-date=24 June 2011}}</ref>
* Foreign Honorary Member of the [[American Academy of Arts and Sciences]] in 1832<ref name="AAAS">{{cite web|title=Book of Members, 1780–2010: Chapter B|url=http://www.amacad.org/publications/BookofMembers/ChapterB.pdf |archive-url=https://web.archive.org/web/20060618085806/http://amacad.org/publications/BookofMembers/ChapterB.pdf |archive-date=2006-06-18 |url-status=live|publisher=American Academy of Arts and Sciences|access-date=24 June 2011}}</ref>
* Member of the Royal Institute of the Netherlands, predecessor of the [[Royal Netherlands Academy of Arts and Sciences]] in 1827<ref>{{cite web|url=http://www.dwc.knaw.nl/biografie/pmknaw/?pagetype=authorDetail&aId=PE00002153 |title=Friedrich Wilhelm Bessel (1784 - 1846) |publisher=Royal Netherlands Academy of Arts and Sciences |access-date=22 May 2016}}</ref>
* Member of the Royal Institute of the Netherlands, predecessor of the [[Royal Netherlands Academy of Arts and Sciences]] in 1827<ref>{{cite web|url=http://www.dwc.knaw.nl/biografie/pmknaw/?pagetype=authorDetail&aId=PE00002153 |title=Friedrich Wilhelm Bessel (1784–1846) |publisher=Royal Netherlands Academy of Arts and Sciences |access-date=22 May 2016}}</ref>
* Member of the [[American Philosophical Society]] in 1840<ref>{{Cite web|title=APS Member History|url=https://search.amphilsoc.org/memhist/search?year=1840;year-max=1840;smode=advanced;startDoc=21|access-date=9 April 2021|website=search.amphilsoc.org}}</ref>
* Member of the [[American Philosophical Society]] in 1840<ref>{{Cite web|title=APS Member History|url=https://search.amphilsoc.org/memhist/search?year=1840;year-max=1840;smode=advanced;startDoc=21|access-date=9 April 2021|website=search.amphilsoc.org}}</ref>
* Member of the [[Accademia nazionale delle scienze|National Academy of Science]] in Verona (1842),<ref>{{cite web | title = Elenco Cronologico soci stranieri | url = https://www.accademiaxl.it/accademia/elenco-cronologico-soci-stranieri/ | publisher = Accademia nazionale delle scienze | access-date = 12 April 2024}}</ref>
* Bessel won the [[Gold Medal of the Royal Astronomical Society]] twice, in 1829 and 1841<ref>{{Cite web | title = The Gold Medal | url = https://ras.ac.uk/sites/default/files/2021-03/Gold%20Medal%202021.pdf | access-date = 23 April 2023 | website = Royal Astronomical Society}}</ref>
* Bessel won the [[Gold Medal of the Royal Astronomical Society]] twice, in 1829 and 1841<ref>{{Cite web | title = The Gold Medal | url = https://ras.ac.uk/sites/default/files/2021-03/Gold%20Medal%202021.pdf | access-date = 23 April 2023 | website = Royal Astronomical Society}}</ref>


Line 114: Line 107:


Geographical commemorations are two fjords in Greenland, [[Bessel Fjord|Bessel Fjord, NE Greenland]] and [[Bessel Fjord, NW Greenland]].
Geographical commemorations are two fjords in Greenland, [[Bessel Fjord|Bessel Fjord, NE Greenland]] and [[Bessel Fjord, NW Greenland]].

''Xyletinus besseli''<ref>{{Cite journal | title = Xyletinus besseli Alekseev & Bukejs 2019, sp.nov | journal = Zenodo | date = 2019 | url = https://zenodo.org/records/5945261 | language=en | doi = 10.5281/zenodo.5945261 | last1 = Alekseev | first1 = Vitalii I. | last2 = Bukejs | first2 = Andris }}</ref> a fossil [[beetle]] from the [[Eocene]] belonging to the family [[Ptinidae]], found in the [[Baltic amber]] in [[Sambia Peninsula|Sambia]], was named in his honour.<ref name="Alekseev Bukejs 2019 p. ">{{cite journal | last1=Alekseev | first1=Vitalii I. | last2=Bukejs | first2=Andris | title=Two new species of Xyletinus Latreille (Ptinidae: Xyletininae) in Eocene Baltic amber | journal=Zootaxa | volume=4668 | issue=4 | date=2019-09-12 | pages=zootaxa.4668.4.5 | issn=1175-5334 | doi=10.11646/zootaxa.4668.4.5 | pmid=31716608 | s2cid=203411805 }}</ref>

BeSSel, the [https://www3.mpifr-bonn.mpg.de/staff/abrunthaler/BeSSeL/index.shtml ''Bar and Spiral Structure Legacy Survey''], is named after him.


== Publications ==
== Publications ==
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** Vol. 3: ''VI. Geodäsie. VII. Physik. VIII. Verschiedenes – Literatur''. Leipzig 1876.
** Vol. 3: ''VI. Geodäsie. VII. Physik. VIII. Verschiedenes – Literatur''. Leipzig 1876.
* {{Citation
* {{Citation
| year =1878
| year = 1878
| title =Recensionen von Friedrich Wilhelm Bessel
| title = Recensionen von Friedrich Wilhelm Bessel
| location =Leipzig
| location = Leipzig
| editor =Rudolf Engelmann
| editor = Rudolf Engelmann
| publisher = Kessinger Publishing
}}
}}
{{refend}}
{{refend}}
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[[Category:19th-century German mathematicians]]
[[Category:19th-century German mathematicians]]
[[Category:Fellows of the American Academy of Arts and Sciences]]
[[Category:Fellows of the American Academy of Arts and Sciences]]
[[Category:Foreign Members of the Royal Society]]
[[Category:Foreign members of the Royal Society]]
[[Category:19th-century German astronomers]]
[[Category:19th-century German astronomers]]
[[Category:Astronomers from the Kingdom of Prussia]]
[[Category:German geodesists]]
[[Category:German geodesists]]
[[Category:Honorary members of the Saint Petersburg Academy of Sciences]]
[[Category:Honorary members of the Saint Petersburg Academy of Sciences]]
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[[Category:People from Minden]]
[[Category:People from Minden]]
[[Category:People from East Prussia]]
[[Category:People from East Prussia]]
[[Category:People from the Kingdom of Prussia]]
[[Category:Mathematicians from the Kingdom of Prussia]]
[[Category:Recipients of the Gold Medal of the Royal Astronomical Society]]
[[Category:Recipients of the Gold Medal of the Royal Astronomical Society]]
[[Category:Recipients of the Lalande Prize]]
[[Category:Recipients of the Lalande Prize]]

Latest revision as of 21:48, 18 November 2024

Friedrich Wilhelm Bessel
C. A. Jensen, Friedrich Wilhelm Bessel, 1839 (Ny Carlsberg Glyptotek)
Born(1784-07-22)22 July 1784
Minden, Kingdom of Prussia, Holy Roman Empire
Died17 March 1846(1846-03-17) (aged 61)
Königsberg, Kingdom of Prussia
NationalityGerman
Known forBessel functions
Bessel ellipsoid
Bessel polynomials
Besselian elements
Bessel's correction
Bessel's inequality
Repsold–Bessel pendulum
AwardsPhD (Hon)
University of Göttingen (1811)
Lalande Prize (1811), (1816)
Gold Medal of the Royal Astronomical Society (1829 and 1841)
Scientific career
FieldsAstronomy, mathematics, geodesy
InstitutionsUniversity of Königsberg
Doctoral studentsFriedrich Wilhelm Argelander Heinrich Scherk

Friedrich Wilhelm Bessel (German: [ˈbɛsl̩]; 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. Certain important mathematical functions were named Bessel functions after Bessel's death, though they had originally been discovered by Daniel Bernoulli before being generalised by Bessel.

Life and family

[edit]

Bessel was born in Minden, Westphalia, then capital of the Prussian administrative region Minden-Ravensberg, as second son of a civil servant into a large family. At the age of 14 he left the school, because he did not like the education in Latin language, and apprenticed in 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 Heinrich Wilhelm Olbers, a practising physician of Bremen and well-known astronomer, 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] Franz Xaver von Zach edited the results in his journal Monatliche Correspondenz.

Having finished his commercial education, Bessel left Kulenkamp in 1806 and became assistant at Johann Hieronymus Schröter's private observatory in Lilienthal near Bremen as successor of Karl Ludwig Harding. There he worked on James Bradley's stellar observation data to produce precise positions for some 3,222 stars.[1]

Despite lacking any higher education, especially at university, Bessel was appointed director of the newly founded Königsberg Observatory by King Frederick William III of Prussia in January 1810, at the age of 25, and remained in that position until his death. Some elder professors of the Philosophical Faculty disputed Bessel's right to teach mathematics without any academic degree. Therefore, he turned to his fellow Carl Friedrich Gauss, who provided the award of an honorary doctor degree from the University of Göttingen in March 1811. Both scientists were in correspondence from 1804 to 1843. In 1837 they got in quarrel about Gauss's habit of very slow publication.[2]

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, where he gave a report on astronomical clocks.[3]

Bessel married Johanna Hagen, 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.[4] 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 elder son became an architect but died suddenly in 1840 aged 26; his younger son died shortly after birth. His eldest daughter, Marie, married the physicist Georg Adolf Erman, member of the scholar family Erman. One of their sons in turn was the renowned Egyptologist Adolf Erman. His third daughter Johanna married the politician Adolf Hermann Hagen; one of their sons was the physicist Ernst Bessel Hagen, and the mathematician Erich Bessel-Hagen was a grandson of them. Bessel was godfather of Adolf von Baeyer, son of his collaborator Johann Jacob Baeyer.

After several months of illness Bessel died in March 1846 at his observatory from retroperitoneal fibrosis.[5][6]

Work

[edit]
Königsberg Observatory (1830)
Crop of a Daguerreotype (1843)

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 with a meridian circle from Reichenbach, assisted by some of his qualified students. The most prominent of them was Friedrich Wilhelm Argelander, his successors were Otto August Rosenberger and August Ludwig Busch.

Bessel determined the first reliable value for the distance between a star and the solar system with a heliometer from Fraunhofer using the method of stellar parallax. In 1838 he published a parallax of 0.314 arcseconds for 61 Cygni, which indicated that the star is 10.3 ly away.[7][8][9] Compared with the current measurement of 11.4 ly, Bessel's figure had an error of 9.6%. Thanks to these results astronomers had not only enlarged the vision of the universe well beyond the cosmic magnitude, but after the discovery in 1728 by James Bradley of the aberration of light a second empirical evidence of the Earth's relative movement was produced.[10] A short time later Friedrich Georg Wilhelm Struve and Thomas Henderson reported the parallaxes of Vega and Alpha Centauri.

Precise measurements with a new meridian circle from Adolf Repsold allowed Bessel to notice deviations in the motions of Sirius and Procyon, which must be caused by the gravitational attraction of unseen companions.[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 by Alvan Graham Clark in 1862, the first discovery of a white dwarf. John Martin Schaeberle discovered Procyon B in 1896.

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 transit time of stars.[13]

In 1824, Bessel developed a new method for calculating 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.[14]

On Bessel's proposal the Prussian Academy of Sciences started the edition of the Berliner Akademische Sternkarten (Berlin Academic Star Charts) in 1825 as an international project with Johann Franz Encke as executive editor. One unpublished new chart enabled Johann Gottfried Galle to find Neptune near the position calculated by Le Verrier in September 1846 at Berlin Observatory.

In the second decade of the 19th century, while studying the dynamics gravitational systems as multi-body problem, 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.

A correction term in the formula for the sample variance estimator is 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.

Bessel's geodetic apparatus, in the museum of Istituto Geografico Militare, Florence, Italy

Like numerous astronomers of his time Bessel dealt on the field of geodesy, too,[15] first theoretically, when he published a method for solving the main geodetic problem.[16] In 1830 he got the royal order for the survey of East Prussia with the purpose to connect the yet existing Prussian and Russian triangulation networks. This work was carried out in cooperation with Johann Jacob Baeyer, then major of the Prussian army; the final report was published in 1838.[17] He also obtained an estimate of increased accuracy for the Earth's ellipsoid, nowadays called the Bessel ellipsoid, based on several arc measurements.[18][19]

Honors and prizes

[edit]

Bessel was one of the first members of the Order Pour le Merite (Civil class) when it was established in 1842.[29]

The first cosmic object named after Bessel is the largest crater in the Moon's Mare Serenitatis.[30] The main-belt asteroid 1552 Bessel was named at the centenary of the parallaxe determination in 1938.[31]

Geographical commemorations are two fjords in Greenland, Bessel Fjord, NE Greenland and Bessel Fjord, NW Greenland.

Xyletinus besseli[32] a fossil beetle from the Eocene belonging to the family Ptinidae, found in the Baltic amber in Sambia, was named in his honour.[33]

BeSSel, the Bar and Spiral Structure Legacy Survey, is named after him.

Publications

[edit]
Tabulae Regiomontanae reductionum observationum astronomicarum ab anno 1750 usque ad annum 1850 computatae, 1830
Latin
  • Fundamenta Astronomiae pro anno MDCCLV deducta ex observationibus viri incomparabilis James Bradley in specula astronomica Grenovicensi, per annos 1750–1762 institutis. Königsberg: Friedr. Nicolovius. 1818.
  • Tabulae Regiomontanae reductionum observationum astronomicarum ab anno 1750 usque ad annum 1850 computatae. Saint Petersburg: Brüder Borntraeger. 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
  • Bessel, Friedrich Wilhelm; Baeyer, Johann Jacob (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], Berlin, Bibcode:1838goiv.book.....B
  • 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 Observations (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.
  • Rudolf Engelmann, ed. (1878), Recensionen von Friedrich Wilhelm Bessel, Leipzig: Kessinger Publishing
Correspondence

See also

[edit]

References

[edit]
  1. ^ a b Chisholm 1911.
  2. ^ Biermann, Kurt-R. (1966). "Über die Beziehungen zwischen C.F. Gauß und F.W. Bessel". Mitteilungen der Gauss-Gesellschaft Göttingen. 3: 7–20.
  3. ^ Report of the British Assiociation for the Advancement of Science.
  4. ^ Olesko, Kathryn M. (1991). Physics as a Calling: Discipline and Practice in the Königsberg Seminar for Physics. Cornell University Press. ISBN 9780801422485.
  5. ^ 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.
  6. ^ Neumann-Redlin von Meding, E. (1996). "Vor 150 Jahren: die Beschreibung der Retroperitonealfibrose, der "Ormond'schen Erkrankung", am Krankheitsbild F.W. Bessels (1784–1846)". Der Urologe B. 36 (5): 378–382. doi:10.1007/s001310050044.
  7. ^ 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.
  8. ^ 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.
  9. ^ "A brief history of light dates". National Geographic. Archived from the original on 15 April 2011. Retrieved 26 June 2020.
  10. ^ Hamel, Jürgen (1984). Friedrich Wilhelm Bessel. Leipzig: Teubner. p. 69.
  11. ^ 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, 515): 145–160, 169–184. Bibcode:1844AN.....22..145B. doi:10.1002/asna.18450221002.
  12. ^ 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.
  13. ^ 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. S2CID 170080943.
  14. ^ Espenak, Fred. "Besselian Elements of Solar Eclipses". NASA Eclipse Website. Retrieved 4 August 2023.
  15. ^ Viik, T. (2006). F.W. Bessel and Geodesy (PDF). Struve Geodetic Arc 2006 International Conference: The Struve Arc and Extensions in Space and Time. 13–15 August 2006. Haparanda and Pajala, Sweden: Lantmäteriet, Gävle, Sweden, 2006. pp. 53–63. Archived from the original (PDF) on 9 November 2013. Retrieved 9 November 2013.
  16. ^ Bessel, F. W. (1825). "Ueber die Berechnungen der geographischen Länge und Breite aus geodätischen Vermessungen". Astronomische Nachrichten (in German). 4 (16): 241–254. arXiv:0908.1823. doi:10.1002/asna.18260041601. S2CID 118630614.
  17. ^ 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.
  18. ^ 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.
  19. ^ 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.
  20. ^ M. E. Maidron : Le Prix d#Astronomie fondé par Lalande, p. 460, 461
  21. ^ "Friedrich Wilhelm Bessel". Berlin-Brandenburgische Akademie der Wissenschaften. Retrieved 23 April 2023.
  22. ^ "Les membres du passé". Académie des Sciences – Institut de France. Retrieved 23 April 2023.
  23. ^ "Fellows". The Royal Society. Retrieved 23 April 2023.
  24. ^ "Book of Members, 1780–2010: Chapter B" (PDF). American Academy of Arts and Sciences. Archived (PDF) from the original on 18 June 2006. Retrieved 24 June 2011.
  25. ^ "Friedrich Wilhelm Bessel (1784–1846)". Royal Netherlands Academy of Arts and Sciences. Retrieved 22 May 2016.
  26. ^ "APS Member History". search.amphilsoc.org. Retrieved 9 April 2021.
  27. ^ "Elenco Cronologico soci stranieri". Accademia nazionale delle scienze. Retrieved 12 April 2024.
  28. ^ "The Gold Medal" (PDF). Royal Astronomical Society. Retrieved 23 April 2023.
  29. ^ "Friedrich Wilhelm Bessel". Orden pour le Mérite für Wissenschaften und Künste. Retrieved 23 April 2023.
  30. ^ Wilhelm Beer, Johann Heinrich Mädler: Der Mond nach seinen kosmischen und individuellen Verhältnissen oder allgemeine vergleichende Selenographie. Berlin 1837, S. 231–232
  31. ^ Schmadel, Lutz D. (2007). "(1552) Bessel". Dictionary of Minor Planet Names. Springer Berlin Heidelberg. p. 123. doi:10.1007/978-3-540-29925-7_1553. ISBN 978-3-540-00238-3.
  32. ^ Alekseev, Vitalii I.; Bukejs, Andris (2019). "Xyletinus besseli Alekseev & Bukejs 2019, sp.nov". Zenodo. doi:10.5281/zenodo.5945261.
  33. ^ Alekseev, Vitalii I.; Bukejs, Andris (12 September 2019). "Two new species of Xyletinus Latreille (Ptinidae: Xyletininae) in Eocene Baltic amber". Zootaxa. 4668 (4): zootaxa.4668.4.5. doi:10.11646/zootaxa.4668.4.5. ISSN 1175-5334. PMID 31716608. S2CID 203411805.

Further reading

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