Friedrich Wilhelm Bessel
Friedrich Wilhelm Bessel (* July 22, 1784 in Minden , Minden-Ravensberg ; † March 17, 1846 in Königsberg i. Pr. ) Was a trend-setting German scientist whose activities extended to the fields of astronomy , mathematics , geodesy and physics .
His interest in astronomy grew during his training as a businessman in Bremen . He acquired the mathematical basics required for understanding in self-study . With an independently developed orbit determination of Halley's comet , he won in 1804 the attention of the astronomer Wilhelm Olbers , who then him a job as an inspector at the private observatory Lilienthal by Johann Hieronymus Schroeter mediated. In 1810 Bessel was appointed professor of astronomy at the University of Königsberg and entrusted with the management of the planned observatory there, where he remained active until his death in 1846.
Bessel's main area of interest was positional astronomy , the accuracy of which he improved through pioneering work. He determined the basic constants of precession , nutation and aberration , worked out a theory for the reduction of observations, developed calculation methods and created auxiliary tables for practical implementation. Bessel included the peculiarities of the instruments in the error analysis and expanded the methods of error calculation .
In a long-term survey program, he collected position data from 75,000 stars. His best-known individual achievement is the first determination of the distance of a star in 1838.
One of the lasting fruits of his practical mathematical activity is the investigation of the Bessel functions named in his honor , which enable the mathematical description of numerous physical phenomena.
The East Prussian degree measurement planned and managed by Bessel became a model for subsequent triangulations in Germany. He succeeded in deriving values for the dimensions of the earth's ellipsoid , which until the end of the 20th century were the basis for central European land surveys ( Bessel ellipsoid ).
The gravitation as an effective force of celestial mechanics explored experimentally using a Bessel he developed pendulum apparatus . He succeeded in demonstrating the equivalence of inert and heavy mass as well as the material independence of gravity. The length of the seconds pendulum determined by him became the basis of the legal length definition of the Prussian system of measurement .
A special feature of the time was Bessel's commitment to bring the natural sciences closer to wide circles through popular lectures and essays.
Life
ancestors
Friedrich Wilhelm Bessel's ancestors can be traced back over fourteen generations using a pedigree . As lawyers, administrative officials, merchants, teachers and theologians, they belonged predominantly to the middle class. There is no evidence of a mathematician or scientist among them. His ancestors in his father's line had been administrative officials of the Principality of Minden since the 16th century , some of them in leading positions. Bessel had noble ancestors through an illegitimate daughter of a Schaumburg count in the 16th century, Johann V. von Holstein-Schaumburg (1512-1560), a son of Count Jobst I and uncle of the two Minden prince-bishops Hermann and Anton . Bessel's progenitor , the prince-bishop's chamber councilor Engelbert Bessel († 1567), was married to the Schaumburg count's daughter Johanna. Many of their descendants also carried the title of nobility . So did the prince-bishop's secret council and chancellor Johann Bessel, father of the chancellor Heinrich Bessel : In 1630 he received nobility recognition from Christian von Braunschweig-Lüneburg , administrator of the prince-bishopric of Minden, namely that of his ancestor, the imperial colonel Jobst Bessel, supposedly granted in 1494 . Bessel's uncle Christian Ludwig Bessel (1750–1813) had also received a certificate of nobility from the royal Prussian government in Minden in 1770.
family
Friedrich Wilhelm Bessel was born on July 22, 1784 as the second child of a large family with six daughters and three sons. His mother Friederike Ernestine Bessel nee Schrader (1753-1814) was the daughter of a pastor in Rehme . The father Carl Friedrich Bessel (1748–1828) was trained as a lawyer and at the time was employed as a government secretary in the Prussian civil service. Due to a sideline activity as legal counsel at the Johanniter - Kommende Wietersheim , he carried the title of legal advisor . In 1816 he came to the newly founded Higher Regional Court in Paderborn as the office director . Bessel's brothers also embarked on a legal career: the older brother Moritz Carl (1783–1874) became president of the district court in Kleve , the younger brother Theodor Ludwig (1790–1848) received the same office in Saarbrücken .
In 1810, Bessel and his sister Amalia (1786-1821) moved to Königsberg . There he married Johanna Hagen (1794–1885), a daughter of the pharmacist and polymath Karl Gottfried Hagen (1749–1829), in October 1812 . The couple had five children, four of whom reached adulthood: Wilhelm (1814–1840); Johanne Marie (1816–1902), married to Georg Adolf Erman (1806–1877); Friederike Elisabeth (Elise) (1820–1913), married to Heinrich Lorenz Behrend Lorck (1816–1877), and Johanna (1826–1856), married to Adolf Hermann Hagen (1820–1890). After the death of Bessel's son Wilhelm, King Friedrich Wilhelm IV issued an order according to which the male grandchildren and their descendants could use the name "Bessel" as an intermediate name so that it does not die out; this later gave rise to the surnames "Bessel-Lorck" and "Bessel-Hagen".
Bessel had kinship through his son Erman relations with the Berlin family of scholars Erman and through this to the local families Hitzig , Mendelssohn and Baeyer ; In 1835 he became the godfather of the future chemist Adolf Baeyer , a son of his colleague Johann Jacob Baeyer . A younger sister of Johanna Hagen was married to the Königsberg physicist Franz Ernst Neumann , with whom Bessel worked closely. Bessel's niece Louisa Aletta Fallenstein married Wilhelm Gauß , the youngest son of his colleague and friend Carl Friedrich Gauß . Bessel's cousin Justine Magdalene Helene Schrader became the wife of the later district president Daniel Heinrich Delius in 1803 .
Well-known scientists from the grandchildren were the brothers Wilhelm Erman (librarian), Adolf Erman (Egyptologist) and Heinrich Erman (lawyer) as well as the brothers Ernst Bessel Hagen (physicist) and Fritz Karl Bessel-Hagen (surgeon). The mathematician Erich Bessel-Hagen , the geographer Hermann Hagen and the lawyer Walter Erman were his great-grandchildren.
schooldays
The knowledge about Bessel's youth up to the beginning of his scientific activity comes from his fragmentary autobiography and the published correspondence with his older brother Moritz Carl Bessel .
According to his own statement, it was a strong aversion to Latin lessons that led to dropping out of school after he had attended the Minden high school up to lower secondary school . Bessel left school at the age of 14 and received private lessons in mathematics and French.
Even as a schoolboy, Bessel knew the constellations. Thanks to his extraordinary eyesight, he was able to resolve the double star Epsilon Lyrae in the constellation Lyra into two components. This star later served him to control the age-related decrease in his visual acuity.
Bessel's path to astronomy
At the beginning of 1799, Bessel began a seven-year unpaid apprenticeship to train as a businessman in the prestigious trading house Kulenkamp & Sons in Bremen . He quickly gained the trust of his superiors and from the second year he received a gratuity , which he invested in books, among other things. He worked in the field of overseas trade and was aiming for the position of a cargo attendant in order to be able to take part in an expedition overseas. Therefore, he tried to acquire the knowledge in self-study that seemed useful to him for this job: In addition to learning the foreign languages English and Spanish, he was particularly interested in nautical science .
In order to become familiar with navigation , Bessel studied a manual for geographic location determination . The mathematical fundamentals necessary for understanding, which he initially lacked, he acquired in a short time with the help of a few textbooks.
In practice, a navigator relies on instruments for measuring the elevation angles of stars , which Bessel was financially unaffordable. With the help of a carpenter and a watchmaker, he built a sextant himself and devised the - later so-called - circummeridian method with two stars at roughly the same height to determine the time . He carried out his first measurements on August 16, 1803. When he observed a star occultation at the dark edge of the moon with his small telescope , he determined the time of the occultation and compared it with information he found in the specialist journal MONTHLY Correspondence and the Berlin Astronomical Yearbook . In this way he was able to determine the longitude of Bremen himself with only a small error.
During his studies, Bessel came across previously unevaluated observational data from the English astronomer Thomas Harriot on the comet of 1607, now known as Halley's comet . This made him want to calculate the orbit of this celestial body from the data. He found the necessary knowledge in a textbook by Jérôme Lalande and in the treatise on determining the orbit of comets published by Wilhelm Olbers in 1797 .
Olbers also lived in Bremen, where he practiced as a doctor. This gave Bessel the opportunity to get in personal contact with Olbers. On July 28, 1804, he spoke to him on the street and asked if he could show him his calculations. Bessel met the interest of the open-minded Olbers and gained a mentor in him . Olbers recognized Bessel's talent and encouraged him by sending him astronomical writings. As a comet expert, Olbers immediately grasped the importance of Bessel's treatise and arranged for it to be published in the Monthly Correspondence .
Bessel as an astronomer
Lilienthal observatory
After he duly finished his apprenticeship, Bessel turned down the offer for continued employment at an annual salary of 700 thalers in the Kulenkamp company and gave up the commercial profession. In March 1806 he took the work as inspector at the private observatory of Johann Hieronymus Schroeter at nearby Lilienthal to what he annually received 100 dollars. There he succeeded Karl Ludwig Harding , who had received an appointment at the University of Göttingen .
Even before he moved to Lilienthal, in 1805 there were considerations to commit Bessel as an observator to a new public observatory in the Westphalian part of Prussia, in Münster or Paderborn . However, the project was dashed by the outcome of the war against France in 1806/1807, when Prussia lost the Westphalian territories. During his time in Lilienthal, there were considerations to get Bessel in Düsseldorf for the surveying of the Grand Duchy of Berg led by Johann Friedrich Benzenberg , or to employ him at the Seeberg observatory in Gotha ; both plans could not be realized.
In 1808, as a citizen of the Kingdom of Westphalia , Bessel was subject to military service and was acutely threatened with being called up because he belonged to the age group of 20 to 25 years; those actually to be called up were determined by lot. Bessel was lucky enough to be released from the draft, but beforehand, through the intervention of Gauß, Olbers and Schroeter, a dispensation had been obtained in the event of an unfavorable draw result.
In the course of the Prussian reforms , which also affected the education system, Wilhelm von Humboldt planned a modernization and expansion of the Königsberg Albertus University , including the establishment of an observatory. In December 1809, he first mentioned negotiations with Bessel about the appointment as professor of astronomy. He took advice from Johann Georg Tralles , physicist and member of the Berlin Academy , who suggested Johann Georg Soldner and Friedrich Wilhelm Bessel as possible candidates , for whom Humboldt decided. It was an ulterior motive of the appointment that the future astronomer should take over a considerable part of the mathematics education at the university.
On January 6, 1810, the Prussian King Friedrich Wilhelm III. Bessel became the first professor of astronomy at Albertus University and director of the observatory that was to be newly built , without attending the upper classes of a grammar school, without having passed a high school diploma , studying , doing a doctorate or habilitation . Bessel turned down a simultaneous offer to take over the already existing observatory of the University of Leipzig under significantly worse conditions.
Koenigsberg observatory
Bessel arrived in Königsberg on May 11, 1810 and took up his teaching activities in the current summer semester with lectures in astronomy and mathematics. Because of his lack of an academic degree, the professors of the Philosophical Faculty denied him the right to hold mathematical lectures. Bessel ignored the objections and continued teaching mathematics in the next semester. In order not to let the matter escalate, he finally turned to Gauß with the request to get him a diploma from the University of Göttingen - which he succeeded: with a certificate dated March 30, 1811, Bessel received the honoris causa doctorate and master’s degree . For his work he received an initial salary of 1000 thalers a year.
In scientific terms, Bessel was initially only able to continue his theoretical investigations from Lilienthal. In addition to academic lessons, the efforts to build the new observatory were the focus of his work. He selected the site and drafted a plan for the spatial structure of the building, which he knew how to enforce against other plans of the Berlin government. On November 10, 1813, he was able to move into the completed observatory. Their initial equipment consisted mainly of used devices that Friedrich von Hahn had used in his Remplin observatory and that the Prussian state had acquired from his estate in 1809.
Bessel remained loyal to Königsberg University. In the course of time he was able to expand the instrumental equipment. To carry out the observation program he planned , he needed a meridian circle , which he received in 1818; a second followed in 1841. These instruments were optical and mechanical excellence, just like the heliometer delivered in 1829 . In 1825 he refused to take over the management of the obsolete observatory of the Royal Prussian Academy of Sciences in Berlin as the successor to Johann Elert Bode .
After the observatory was up and running, Bessel increasingly called on capable students for practical observational activities, including his own son Wilhelm , who initially studied astronomy in Königsberg, but gave up his studies after two years and trained as a construction manager at the Berlin Building Academy . His death in October 1840 was a very painful loss for Bessel.
The outbreak of a cholera epidemic in Königsberg in July 1831 led to tumultuous riots in which Bessel was suspected of causing cholera by means of silver bullets that were attached to the observatory to transmit signals. When the Königsberg city administration also set up a burial place for the cholera victims in the immediate vicinity of the observatory, Bessel preferred to seal the observatory and leave the city for two months.
In 1842, Bessel, accompanied by his daughter Elise, his son-in-law Georg Adolf Erman and his mathematician friend Carl Gustav Jacob Jacobi, began his first and only trip abroad, which took him to Great Britain , where he attended the annual meeting of the British Association for the Advancement of Science in Manchester attended and met with numerous scientists such as Brewster , Sabine and Hamilton . From there he drove to Edinburgh to Henderson's and on the way back met John Herschel and Charles Babbage, among others . In Paris, where he gave a lecture as a foreign member of the Academy of Sciences, he met Jean-Baptiste Dumas and François Arago .
Bessel's health deteriorated so severely that he had to give up his observation and teaching activities from October 1844 and could hardly do any scientific work. As a token of his appreciation, Friedrich Wilhelm IV arranged for temporary treatment by his personal physician Schönlein . Bessel died on March 17, 1846 and was buried in the scholar cemetery in Königsberg. After Bessel's death, articles appeared in several major daily newspapers accusing the doctors of making a wrong diagnosis or of being completely ignorant of the nature of the disease. An autopsy, which was still rare at the time, showed that Bessel had succumbed to a tumor disease that Repsold described in his biography in 1919 as colon cancer . A new evaluation of his medical history showed that Bessel died of retroperitoneal fibrosis , which his Königsberg family doctor Raphael Jacob Kosch had correctly diagnosed as such and treated appropriately with the possibilities available at the time. According to a passport issued in 1810, Bessel was 1.68 m tall.
Bessel was quickly integrated into the Königsberg society. He was a member of the Society of Friends of Kant and is said to have been the originator of the local custom of electing an annual “ Bean King ”. Since his time in Lilienthal, Bessel made up for his work by hunting. In East Prussia he joined the Königsberg hunting company around General Oldwig von Natzmer . He was also a member of the Physico-Economic Society , where he gave a series of popular science lectures published posthumously in the 1830s.
Scientific achievements
astronomy
Comets
Friedrich Wilhelm Bessel began his scientific work in 1804 with the calculation of comet orbits. His first work on Halley's Comet provided an orbit calculation for its approach to the sun in 1607 on the basis of the observation data of Thomas Harriot and Nathaniel Torporley . The calculation of previous runs gave information about orbital disturbances by planets and made the orbit determination more reliable. What was new was his approach to assume the comet's orbit as a parabolic ellipse. For his work on the comet of 1807 he received the Lalande Prize of 1811.
The return of Halley's Comet in 1835 prompted Bessel to closely observe the change in its appearance. The resulting publication is his only one that deals with the appearance of a celestial phenomenon. Going beyond previous comet watchers, he developed a hypothesis on the origin of comet tails . He assumed that as the sun approached, the finest cometary material evaporated and that this was influenced in the direction of movement by the action of "polar forces" emanating from the sun.
Shooting stars
Shooting stars are difficult to grasp as objects of observation for measuring astronomy. Johann Friedrich Benzenberg and Heinrich Wilhelm Brandes were able to determine the approximate height of the luminous phenomena above the earth's surface in 1800 and considered a terrestrial origin to be possible. Bessel refuted this view by critically appraising the accuracy of observation. He also drew up the plan for a falling star observation program that would be suitable for obtaining reliable data without carrying out it himself.
At his suggestion, in 1843 , Hauptmann Schwinck produced small-scale sky maps in stereographic projection , which were more suitable for mapping the falling stars than the maps previously used. At the time of Bessel there was only speculation about the nature of the shooting stars. He thought it possible that they “burn up completely in the higher layers of the air”.
The moon
Bessel developed a new method for determining the libration of the moon . Using the heliometer , he determined the angular distances between different points on the lunar rim from a small, circular crater in the center of the lunar disk, which is now known as Mösting A and serves as the reference point for the selenographic coordinate system. From this he received the selenographic coordinates and the first precise parameters for the libration.
Three decades after his first attempts at geographic location determination, he returned to one of the main problems of astronomical navigation, longitude determination in seafaring. By reducing the computational effort required, he improved the method of determining geographical longitude on the high seas with the help of the lunar distances .
The possible existence of a lunar atmosphere was still a topic of discussion among astronomers at the time of Bessel; Johann Hieronymus Schroeter believed that he had noticed an atmosphere of very low density. On the other hand, it was argued that shortly before and after the moon was eclipsed by the stars, no refraction-related changes in starlight were discernible. Bessel investigated the question and examined a possible deceptive interference of the moon relief on the propagation of light. By evaluating his heliometric moon observations, he was able to show that the assumption of a lunar atmosphere with the density assumed by Schroeter is not compatible with the measurement data. In doing so, he withdrew the scientific basis from the speculations still widespread at the time about the living conditions of lunar inhabitants, such as those that occupied his Munich colleague Gruithuisen .
Planets
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Bessel's first objects in practical observation included the minor planet Ceres , discovered in 1801, as well as Juno, discovered by Karl Ludwig Harding in Lilienthal in 1804 and Vesta, discovered by Heinrich Wilhelm Olbers in Bremen in 1807 .
Bessel's first publication, which did not have the observations of comets and minor planets as content, referred to the planet Saturn . In a theoretical way he showed that Wilhelm Herschel's observation that Saturn does not have its maximum diameter exactly in the equatorial plane must be based on an optical illusion.
In twelve other works on this planet, he examined the interactions between Saturn, its ring system and the satellites. Bessel used the heliometer to measure the movement of Titan , Saturn's most massive moon, and calculated the orbital data as well as an exact value for the mass of Saturn. His last work, a broad theory of the Saturn system, remained unfinished and was published posthumously as a fragment.
Bessel was able to calculate the mass of Jupiter by determining the orbit of his four satellites, which he observed heliometrically from 1832 to 1836. In it he confirmed a value already found by George Biddell Airy (1837) in a different way, which considerably improved the one published up to then and comes very close to today's.
In May 1832, Bessel observed the passage of Mercury in front of the sun. He determined the apparent diameter of Mercury, but could not detect any flattening .
The sun
To determine the size of the sun , moon and planet observations , Bessel bought a heliometer from the Munich Precision Mechanics Institute from Utzschneider and Joseph von Fraunhofer for the Königsberg observatory , for which a heliometer tower was built at the observatory. Bessel was the first astronomer to use such an instrument for a systematic series of measurements . He summarized his most important work on the heliometer and the investigations carried out with it in 1841–42 in the Astronomical Investigations .
Bessel used the Mercury transit of 1832 not only, like other astronomers, to measure the entry and exit times of the planet in front of the solar disk. Thanks to the high accuracy of the heliometer, he was able to determine the influence of the irradiation , which makes the sun appear to the observer a bit larger than it actually corresponds to. Together with Argelander , who was in Königsberg, Bessel observed the transit with two different instruments. In one of them, the disk of Mercury showed an elongated deformation shortly after or before the inner contact, which was already known from the Venus transit and is now referred to as the " drop phenomenon ". This change in shape could not be seen with the other, higher-resolution instrument, the heliometer, so that the phenomenon was recognized as being instrument- dependent.
Bessel interpreted the change in shape as an irradiation changed by the planet at the point of contact with the edge of the sun. An atmospheric cause such as the Venus transits was ruled out, since Mercury has no significant atmosphere. Recent investigations during the Mercury transits in 1999 and 2003 with the space telescope TRACE confirmed these observations.
Bessel also found that his heliometer showed the sun disk in its true diameter with practically no irradiation effect and therefore rightly bears his name. This enabled him to determine an exact value for the apparent diameter of the sun.
Eclipses
The standard tasks of astronomers traditionally include the calculation of the temporal course and the visibility area of solar eclipses . Bessel combined two previously practiced calculation methods, which go back to Johannes Kepler and Joseph-Louis Lagrange , into an extended method. The use of tabulated intermediate sizes, the Bessel elements , leads to a considerable simplification of the calculation. This method can also be used for the calculation of lunar eclipses, the coverages of stars and planets by the moon and planetary transits in front of the sun. With improvements later incorporated, it is still a standard practice today.
Stellar astronomy
Star catalogs
At the Lilienthal observatory, Bessel began working on a star catalog in 1807 at the suggestion of Wilhelm Olbers . His starting point was a list of over 3000 stars, the positions of which the English astronomer James Bradley measured with a wall quadrant between 1750 and 1761 . The raw data of the listed star locations could not yet be considered a star catalog, as they were subject to errors due to numerous influences: firstly, celestial mechanicals due to the movement of the earth in the solar system ( precession , nutation , aberration ), secondly due to atmospheric refraction and thirdly due to inaccuracies of the used Measuring devices (wall quadrant, clock). In addition, the stars change their position in relation to one another in the long term through their own movement . Bessel determined these influencing factors from Bradley's data and thus reduced his data. He published the calculated true star locations for 1755 under the title Fundamenta Astronomiae 1818. Bessel had previously published a paper on the determination of precession constants from Bradley's data, for which he received a prize from the Prussian Academy of Sciences in 1813.
Bessel developed a theory of reductions with the associated reduction terms and created tables for astronomical practice (Tabulae Regiomontanae) valid from 1750 to 1850. This work was later continued by Julius Zech and Jakob Philipp Wolfers . In the star catalogs, all data is reduced to a specific point in time. Bessel introduced a fictitious year ( Bessel year ) with the length of a tropical year , the beginning of which he set at the point in time when the mean length of the sun is exactly 280 ° ( Bessel epoch ). The time-dependent terms of his reduction formulas were later called Bessel day numbers.
The secular change in the positions of 36 fundamental stars , which Nevil Maskelyne at the Royal Greenwich Observatory had observed and cataloged, Bessel was able to give with great reliability for a period of a century (1750-1850) by using the Bradley data from the Fundamenta for these stars Astronomiae and self-measured data from 1815 and 1825 were used. In 1830, the Tabulae Regiomontanae was the first fundamental catalog of astronomy.
Zone observations
After Bessel had purchased a meridian circle from Georg von Reichenbach's workshop for the Königsberg observatory in 1818 , which was equipped with a Fraunhofer refractor , he began observing a list of stars that was supposed to exceed the existing ones in terms of abundance and accuracy. He divided the sky into zones of 2 degrees declination each , in which he systematically observed the stars up to the 9th magnitude ; that is, he measured the coordinates for right ascension and declination . Bessel initially limited the observations to declinations from −15 ° to + 15 °, the narrower area around the celestial equator . This region was already interesting because the discovery of new minor planets was most likely to be expected in it. Later Bessel extended the observation area up to + 45 ° declination. The program, in which a total of 75,000 stars were registered, took the period from 1821 to 1833 to complete; the data appeared in Volumes VII to XVII of the Königsberg Observations .
From the zone observations available up to 1825, Maximilian Weisse , head of the Krakow observatory , produced a star catalog for the almost 32,000 stars from −15 ° to + 15 ° declination, which was published in 1846. On the basis of the data, Friedrich Georg Wilhelm Struve carried out stellar statistical studies on the spatial structure of the Milky Way , which he published as a foreword to the Weisse catalog .
The Bessel zone observations were later continued in the Bonn survey by Argelander , who was Bessel's assistant in the early days of the zone observations.
Academic star maps
For astronomical work it is helpful to have the star positions available not only in lists, but also in cartographic form. In 1825, Bessel suggested to the Prussian Academy of Sciences to print the material listed in the star catalogs in star maps according to a uniform pattern, for which he presented a sample sheet from his pupil Carl August Steinheil . So that the project could be completed in a reasonable time because of its enormous scope, the Berlin Academy awarded the work orders for the individual sheets to various domestic and foreign observatories. This company thus represented an early example of successful international cooperation in the scientific field. Bessel did not take part in the implementation of the project because of his other ongoing work programs, but his former students Argelander, Steinheil and Luther worked out individual sheets, as did Karl Ludwig Harding , his Göttinger Colleague and predecessor in Lilienthal. Bessel was initially mistaken about the time required; the Berlin academic star maps were not completely available until 1859.
Further stellar astronomical work
Bessel measured the coordinates of numerous Pleiades stars and demonstrated the suitability of this star cluster for determining the precision of astronomical observation instruments.
Bessel also used the heliometer to observe double stars . In 1833 he published a small catalog with the relative distances and position angles of 38 objects. According to an appointment by Struve in Dorpat, the same stars were measured by micrometer measurements with a refractor, also created by Fraunhofer, from which conclusions were drawn about the measurement accuracy of both instruments.
Cosmic distances
Bessel's pioneering work is the first reliable determination of the distance of a fixed star by measuring its annual parallax . Even Copernicus and Kepler had realized that as part of the heliocentric system would occur a parallax effect: Nearby stars would in the light of distant stars resulting from the annual orbit around the sun, a periodic change in location show. Despite an intensive search, this effect could not be clearly proven until the beginning of the 19th century. In 1802 Johann Hieronymus Schroeter estimated the upper limit of the parallaxes for the nearest stars quite reliably at 0.75 arc seconds.
Bessel also faced this challenge, which consisted of three sub-problems: It had to
- a star as close as possible to the solar system can be found, which promised a sufficiently large parallax value,
- the measurement can be carried out with the highest precision because of the smallness of the effect and
- the parallax value can be calculated from the observation data.
When comparing the Bradley catalog with other star catalogs, Bessel found that the star 61 Cygni (constellation Swan ) has the largest proper motion of all stars measured. He also found out that it is a physical binary star , for which he determined the orbital time around the common center of gravity.
The relatively large angular distance between the two components of Cygni spoke for a great proximity to the solar system as well as its large proper movement, so that he observed this faint system with the apparent magnitude of 4.8 mag as a promising object. It was also beneficial that it could be observed as a circumpolar star almost all year round. Bessel worked according to the principle of relative parallax measurement, which had been proposed by Galileo Galilei in 1632 in his dialogue on the two main world systems : He did not measure the absolute star positions, but the changes in position of 61 Cygni relative to two apparently neighboring comparison stars, one of which is one could assume a far greater distance. The cross-shaped position of the two stars made it possible to measure them with the micrometer eyepiece exactly to the center of the double star system, for which the heliometer was ideally suited.
Because of the great self-movement of this high-speed machine in the starry sky, it was not enough to measure the positions twice every six months. Rather, what was required was a series of measurements at least one year from which the parallax was to be calculated. Bessel began the series of measurements in August 1837 and ended it in October 1838. He determined the parallax value of 0 ″, 3136 with a mean error of 0 ″, 0202. As an illustrative size comparison for the distance of 61 Cygni, Bessel calculated "the time it takes the light to travel this distance" to be 10.28 years. The so far (2015) most accurate parallax value for 61 Cygni was measured by the astrometry satellite Hipparcos with 0 ″, 286, which corresponds to a distance of 11.4 light years. Bessel's result is thus confirmed within the specified accuracy.
Struve had already started in Dorpat in 1835 to determine the parallax of the Vega (constellation " Lyra ") with his Fraunhofer refractor , and in 1837 presented provisional, still unreliable values. The royal astronomer Thomas James Henderson published in Edinburgh in 1839 a parallax value for the binary star system Alpha Centauri (constellation " Centaur "), which he had observed in Cape Town in 1832/1833 . These three researchers were friendly and did not have a priority dispute; this was only constructed decades later by science historians.
With these results the astronomers had not only expanded the conception of the cosmic orders of magnitude, but also gained second empirical evidence to support the heliocentric system after the annual aberration discovered by James Bradley in 1728 ; However, the heliocentric worldview was - due to its efficiency - no longer controversial at the time of Bessel.
"Invisible" objects
Neptune
With the more precise star catalogs and maps, the means for the precise orbit determination of rapidly moving celestial bodies (planets, comets) were now available. The Uranus, discovered by Wilhelm Herschel in 1781, turned out to be difficult because its observed orbit could not be reconciled with celestial mechanical calculations. Bessel studied this problem in detail and in 1823 drafted a hypothesis to modify the law of gravitation . Since this consideration led to a dead end, he decided not to publish it and as early as 1828 expressed the opinion: “I believe in a planet above Uranus.” From 1837 onwards, he had his student Wilhelm Flemming (1812–1840) recalculate the orbit of Uranus. His early death and Bessel's own illness prevented the project from continuing. However, when Urbain Le Verrier and John Couch Adams had calculated the probable location of this celestial body, Neptune , it was found by Johann Gottfried Galle on September 23, 1846. Galle used an already printed, but still unpublished sheet of the Berlin Academic Star Maps initiated by Bessel .
White dwarfs
When analyzing the proper movements of the cosmic high-speed runners Sirius (constellation " Big Dog ") and Prokyon (constellation " Little Dog "), Bessel discovered a long-period deviation from the straight-line movement. To interpret this initially inexplicable effect, he postulated the gravitational effect of a previously unrecognized companion star for both stars in 1844. The binary star systems known since Christian Mayer (1779) consisted of two visible components. But Bessel believed that dark, non-luminous celestial bodies could also have an effect on the star positions. This initially controversial postulate was only recognized when his Königsberg successor Christian August Friedrich Peters calculated the exact value of the deviation for Sirius in 1851 and in 1862 Alvan Graham Clark found the companion star " Sirius B ". With an apparent magnitude of 8.5 mag, but a comparatively large mass, it belongs to the white dwarfs and is the first specimen of its genus to be discovered. 1896 saw John Martin Schaeberle the white dwarf Procyon B . Because of the great luminosity of Sirius A (with −1.46 may be the brightest star in the night sky) and an unfavorable geometric constellation, Bessel could not see the companion star at the time.
Bessel immediately recognized the scope of his Sirius measurements. The method he himself worked out to perfection in the Fundamenta Astronomiae to reduce the star locations to a certain point in time had to be considered imprecise from now on, as long as the influence of these systematic rolling movements of some stars was not taken into account.
The Pole Movement
The pole height , which indicates the angular distance of the northern celestial pole to the horizon and thus the geographical latitude of the observation site, was considered to be unchangeable for a specific location until the 19th century. In 1818, Bessel discussed the theoretical question of the extent to which mass displacements in the interior of the earth or on its surface, for example through the transport of commercial products, could affect the height of the poles. He was able to rule out the latter cause, since he calculated a hundred millionth part of the earth's mass for a change in polar elevation of one arc second, but this is inconceivable as a result of human influence.
As early as the 18th century, Leonhard Euler developed a theory of the top and derived a circular motion with a phase of about 300 days for the earth as an assumed rigid body that is not completely spherically symmetrical . For the rotating earth, this postulated movement could not be verified astronomically at first.
In the years 1842 to 1844 Bessel controlled the pole height of Königsberg with the new Meridiankreis von Repsold. In June 1844, he informed Alexander von Humboldt by letter that he had discovered a systematic change in the polar height of 0.3 arc seconds. Bessel assumed “internal changes in the earth's body” as the reason for this movement. In the 1880s, Karl Friedrich Küstner was able to verify the effect of the pole movement with extensive investigations. Seth Carlo Chandler calculated a period of approximately 430 days for the movement . Bessel's later successor in Königsberg, Erich Przybyllok , declared Bessel to be the "discoverer of the polar height fluctuations" after another data analysis. A new precise analysis of the Bessel data showed that a significant pole movement could not yet be reliably derived from them. Bessel himself had described his "suspicion of the immutability of the polar heights" as "still immature" to Humboldt and published nothing about it; his illness prevented him from further examinations.
The "personal equation"
During the intensive exchange of astronomical observation data in personal letters and in journal articles, astronomers recognized at the beginning of the 19th century that the astronomical time determinations of the same celestial objects that had been observed in different observatories gave different results. The different types of equipment used were initially made responsible for these deviations.
Since 1818, Bessel took the view that the person of the observer must also be included in the data analysis. Bessel checked the personal reliability of the data collection in 1821 through joint observations with his assistant Walbeck and found a systematic discrepancy between the two observers when registering the transit times of stars in the meridian circle. He later checked the effect with other astronomers (Argelander, Struve, Peter Andreas Hansen ) during their visits to the Königsberg observatory, where time measurements of the same stars on the same instrument revealed different differences between the values that were measured by two observers. During the long-term follow-up of this phenomenon, he also found that the time differences between two specific observers are also subject to a development over time and are not constant.
He came to the conclusion that “no observer can be sure to give absolute time moments with certainty”. It would be particularly disadvantageous in a measuring program if different observers observed the same object and the measured values obtained were mixed in the evaluation to form a series of measurements , which was quite common at the observatories at the time. Bessel is therefore considered to be the discoverer of the phenomenon that later became known as the personal equation . The term “equation”, which is used historically in astronomy, is to be understood here in the sense of “correction”. Because it is difficult to quantify, the personal equation found its way into the practice of astronomy only hesitantly; Bessel too only tried to keep their influence as low as possible.
Bessel's attempts to determine personal reaction time were only taken up and continued decades later by the emerging experimental psychology , primarily by Wilhelm Wundt .
At the time of the discovery of the personal equation, the Königsberg philosopher and educator Johann Friedrich Herbart was investigating ways of quantifying human perception. He developed the mathematical equations he formulated for this in collaboration with Bessel.
mathematics
Bessel as an "applied mathematician"
Friedrich Wilhelm Bessel stands in the tradition of those researchers whose mathematical activity was based on the processing of scientific and technical problems. Mathematics did not develop into an independent academic discipline until the beginning of the 19th century; During the reform period, the Prussian universities set up pure mathematics professorships for the first time. In the division into pure and applied mathematics that began at that time , Bessel saw himself as a representative of the latter. When August Crelle , the editor of the Journal for Pure and Applied Mathematics , asked him to collaborate on his journal, Bessel refused, saying: “But you know that my work is exclusively devoted to astronomy, that there is seldom time left, to do something mathematical, except when it is in direct connection with astronomical business. "
Bessel's services were to trace the problems back to appropriate approaches and to present the calculations in such a way that they were suitable for immediate applicability. He reformed the equations so that they allowed the most convenient calculation possible, and he supported this with numerous auxiliary tables that he enclosed in his writings.
Error calculation
Dealing with large amounts of data made a consistent error analysis inevitable. The classification into random and systematic observation errors, which is still valid today, comes from Bessel . Bessel proved that the random errors of a measurement, if they depend on numerous causes, largely obey the law of error distribution that Gauss had postulated in his error theory. He simplified the application of the least squares method .
A fundamental relationship in mathematical statistics goes back to Bessel . The variance of a sample of size n receives the term ( n - 1) in the denominator , which is known as the Bessel correction , and thus becomes an unbiased estimator for the variance of the population of this sample.
Bessel functions
While dealing with the Kepler equation for the calculation of planetary orbits and the analysis of planetary disturbances, Bessel developed the function of the radius vector in a series , for whose coefficients he formulated special auxiliary functions in integral representation. Their investigation showed him that it was a separate system of functions between which he worked out recursion and symmetry relationships and could derive statements about the distribution of the zeros . In recognition of Bessel's work, Oskar Schlömilch referred to these functions as Bessel functions in 1857 . The mathematicians Daniel Bernoulli , Euler and Lagrange had already encountered functions of this type in the 18th century , and around the same time as Bessel, Fourier and Poisson had given integral representations for them. The linear differential equations of the second order whose solutions represent the Bessel functions are named after Bessel; the associated differential operator is called the Bessel operator .
The Bessel functions are a class of cylinder functions ; they play an essential role in the mathematical description of numerous physical phenomena, such as two-dimensional vibrations , heat conduction in solid bodies or the X-ray structure analysis of helical molecules such as DNA . The diffraction of light , which can be described with Bessel functions and which limits the resolution of the telescope, is of astronomical importance .
The Bessel functions are eponymous for some technical uses. In control engineering, a type of analog filter is called a Bessel filter , which guarantees optimal transmission behavior of square-wave signals. The Bessel beam is a laser beam with a type of light propagation that is characterized by particular dimensional stability and "self-healing", whereby the shape of the beam regenerates itself after contact with an obstacle. Bessel rays are used, for example, in optical tweezers and in high-resolution microscopy .
Other achievements in mathematics
To solve his calculations, Bessel had to carry out extensive approximate calculations, in which he usually developed the functions in series . The search for suitable trigonometric series and the determination of their coefficients have repeatedly been the subject of our own investigations. He found a representation of a trigonometric polynomial of the nth degree, in which the coefficients calculated up to now can no longer be changed for a given n by adding new summands, so that the accuracy can be increased as desired with this approximation . Bessel examined the quality of the approximation through the formation of the sum using the method of the least squares and arrived at a criterion that is known today in functional analysis as Bessel's inequality .
The Bessel interpolation formula used in numerical mathematics results from his reduction calculations .
At the beginning of his time in Königsberg, when he lacked the ability to observe because of the unfinished observatory, Bessel worked on two studies on pure mathematics. The first concerned the logarithm of integral , which is an estimate of the number of prime numbers. With suitable series developments, Bessel made progress in the numerical calculation of the function values. In the second work, Bessel dealt with a theory of the mathematician Christian Kramp about the faculties , which he improved and expanded. Bessel exchanged letters about both problems with Carl Friedrich Gauss , who also dealt with them and continued the work in a generalized way.
Bessel dealt several times with problems of elementary geometry . Among other things, he provided a proof for Pascal's theorem and a solution to Pothenot's problem (reverse cut).
As early as his first decade in Königsberg, Bessel dealt with fundamental questions relating to the mathematical analysis of geodetic data. With this he laid a basis for the evaluation activities in the East Prussian degree measurement, which he directed from 1830, and in the determination of the mean earth ellipsoid .
geodesy
The East Prussian degree measurement
Up until the 19th century, it was common for astronomers to carry out large-scale land surveys - because of the partly similar measurement methods, the extensive mathematical evaluations and the incorporation of astronomical data. On his own initiative, in 1817, with the assistance of Gotthilf Hagen , Bessel undertook a small survey in the Königsberg region in order to subject the accuracy of the earlier Schroetter land survey to an examination, which revealed the imperfection of the methods used.
In 1830, Bessel took over the management of the surveying of East Prussia, the real aim of which was to connect Müffling's triangulation of the western parts of Prussia with the network that General Tenner had measured in the Baltic provinces of the Russian Empire . In the classic triangulation method, the positional relationships of distant points to one another must be determined by measuring angles using theodolite . For practical implementation, Bessel was able to fall back on the support of the Prussian army , which was responsible for surveying and cartography . The collaboration with the then captain Johann Jacob Baeyer turned out to be extremely successful ; the evaluation of their field measurements from the years 1832 to 1835 appeared in 1838.
Before the invention of today's optoelectronic devices, distance measurement was more difficult than angle measurement . The length of at least one side of the triangle had to be known, but could not be precisely measured over tens of kilometers. As a solution, a base enlargement network was created with which - starting from a short, very precisely measured "base" - the length of one main side of the triangle was determined. To measure the distance, Bessel had a basic device made according to his own ideas and used it to determine with the utmost precision a baseline from 11 to 16 August 1834 northwest of Königsberg between the towns of Mednicken and Trenk , the length of which was 1,822.330 m. In contrast to other degree measurements, in which much longer baselines were measured for the purpose of greater accuracy, Bessel chose a comparatively short distance, which he had measured three times. His basic apparatus became the standard length measurement device in geodesy over the next few decades; it remained in use in the Prussian Land Registry until 1914.
As a connection triangulation, this project formed the last link in a continuous survey chain from Spain to the northern Arctic Ocean . From the outset, Bessel designed the work as an independent degree measurement , in which the coordinates of some measuring points are determined independently of one another with the greatest possible accuracy through astronomical measurements. In the East Prussian degree measurement, these were the southern end point of the chain in Trunz near Elbing and the northern end near Memel and the Königsberg observatory. For this purpose, Bessel developed a method for compensating incomplete sets of directions, which eliminated the need to quickly observe all target points from a triangulation point almost simultaneously; the long waiting times for atmospherically favorable observation positions with a clear view were thereby considerably reduced. As a result, Bessel was able to calculate the distance of a degree of latitude in the position of East Prussia.
The accuracy of Bessel's work made the East Prussian degree measurement the model and starting point for a series of further triangulations in Prussia and other German states. His evaluation practice remained authoritative until the 1870s, when it was replaced by the simpler method of Oskar Schreiber . The project of a Central European degree measurement was later realized by Johann Jacob Baeyer.
The earth figure
As a further result of the project, Bessel succeeded in determining the dimensions of the earth figure in 1837 . From the results of the East Prussian and nine other degree measurements distributed around the world, he was able to derive the dimensions of a mean ellipsoid of revolution that comes as close as possible to all measurements. An error discovered in the French degree measurement (1792–1798) in 1841 forced Bessel to recalculate it in order to correct his values. He determined the length of the earth's meridian quadrant, the distance of the pole from the equator as 10,000.565 km, the equatorial radius as 6377.397 km and the flattening as 1 / 299.15. The length of the (German) geographic mile as the 15th part of an equatorial degree has therefore been corrected from 7428.01 meters to 7420.44 meters.
The Bessel ellipsoid was used as a reference ellipsoid for land surveying and topographic maps in Germany, Austria, Hungary and numerous other countries until the second half of the 20th century . In Germany it was used as the reference area for the German Main Triangle Network (DHDN 1990). More precise values could only be obtained through modern satellite geodesy .
Bessel was aware that the best adaptation of the geodetic measurement results for the earth is neither the shape of the sphere nor that of the ellipsoid of revolution . In contrast to the physical surface, he describes the “geometric surface” of the earth as the surface on which all parts of the force of gravity are perpendicular; for Bessel it was realized in the completely calm surface of the sea. In this way he conceptually anticipated the geoid as a level surface and an idealized earth figure.
physics
Experiments on gravitation
For two decades, Friedrich Wilhelm Bessel dealt with physical investigations that were closely related to his main activities in astronomy and geodesy. The central importance of gravity for astronomy led him to experimentally check the validity of the law of gravity. Like other physicists before him, he made use of the pendulum . The current default device reversible pendulum of Henry Kater held Bessel due to its design for not sufficiently precise, so he designed that its own pendulum apparatus according to the principle of the thread pendulum, which he by the Hamburg mechanic Johann Georg Repsold was built. What was new about these investigations was the way in which the influence of air on the measurements was taken into account. Before Bessel, only the hydrostatic effect of air resistance was considered, which reduces the amplitude of the oscillation. For the first time, Bessel dealt with the hydrodynamic phenomenon that the oscillating air increases the moment of inertia of the pendulum and thus influences the duration of the oscillation.
Since his pendulum device with the thread pendulum was difficult to transport, Bessel designed a reversion pendulum for mobile use, which was characterized by “novelty and originality”. Adolf Repsold later produced devices of this type in his company A. Repsold & Sons .
Pendulum measurements
The first major physical investigation concerned the determination of the pendulum length. According to the pendulum equation , the period of oscillation of a pendulum depends only on its length and the local value of gravity . Accordingly, between 1825 and 1827, Bessel first tried to determine the exact length of a pendulum with a half-oscillation period of one second, taking into account all unavoidable sources of error in the apparatus. For the location of the Königsberg observatory it received the value of 440.8147 Parisian lines (= 994.390 mm) as the length of the second pendulum , reduced to the sea level of 440.8179 lines (= 994.397 mm).
With his second research project, which Bessel tackled with the pendulum apparatus, he followed up on a series of experiments by Isaac Newton . The research on the Uranus problem led him to the idea of experimentally checking the validity of the law of gravitation with great accuracy, in particular whether the nature of the material of the attracting bodies exerts an influence. Bessel compared the period of oscillation of the pendulum after attaching samples made of different materials to it. In order to check whether cosmic matter behaves gravitationally exactly like terrestrial matter, he also used meteorite material. As a result, Bessel was able to ensure the material independence of the gravitational force with an accuracy several powers of ten greater than Newton. In doing so, he made an important contribution to establishing the equivalence principle of the equivalence of inert and heavy mass. Only the Eötvös experiments at the end of the 19th century were able to further increase the accuracy.
The Prussian measure of length
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A practical application of the pendulum measurements resulted from the need to determine the length dimension by law. The Prussian foot was linked to the French length measure in 1816 (1 foot = 139.13 Parisian lines). The Prussian Academy of Sciences was responsible for the production of a practically unchangeable original measure and the production of copies of it. In addition, it should be ensured that this standard could be reproduced at any time.
The project management was initially with the physicist Johann Georg Tralles , whose death prevented the completion. Finally, Bessel took over the continuation, which enforced the use of his own pendulum apparatus. In 1835 he determined the width-dependent length of the seconds pendulum for Berlin (440.739 lines) at the Berlin observatory and thus linked the length of the original dimension directly to the length of the pendulum. It was of great importance to Bessel that he had given the legal unit of measurement the option of reproducing it at any time. He had the original size (and several copies) made according to his own plans; this was considered to be the best measuring standard at the time. The Bessel scale became law in Prussia on March 10, 1839. Working with Heinrich Christian Schumacher , it was also introduced as a basic size in Denmark. Bessel was in an intensive scientific exchange with his student Carl August von Steinheil , who was commissioned as an employee of the Bavarian Academy of Sciences from 1836 to regulate the Bavarian measurement system.
Bessel was completely opposed to the metric length measure . He criticized the fact that although a natural measure, the length of the earth quadrant, had been defined as a reference variable, its size had only been determined by partial measurements and otherwise obtained by calculation. Furthermore, because of the incorrect measurements, a specific length was defined as normal by decree and thus deviated from the self-set goal of tying the meter to a natural measure.
Since the confusing variety of different measurement systems in the European countries and German territories increasingly hindered trade, traffic and technical development, numerous initiatives were taken to standardize. Within Germany, Bessel's former colleague Gotthilf Hagen represented the Prussian position before the National Assembly and in later commissions in 1849 , which was aimed at introducing the Prussian foot as a general measure of length, basing his argument against the meter as far as possible on Bessel's views. Despite its better scientific definition, the Prussian measure could not prevail against the practical advantages of the meter, which the southern German states emphasized, so that the meter was adopted by law as a legal unit in the North German Confederation in 1868 and in the German Empire on January 1, 1872 became binding.
Other achievements in physics
As part of the work on the regulation of measurement, Bessel solved the mathematical problem for the first time to determine the optimal support points of a double-bearing measuring rod, in which the changes in the rod due to gravity are as small as possible ( Bessel point ). He found the smallest deflection for a rod of the length when the points of support are at the same distance from the ends of the rod, the smallest change in length on the surface with points of support in the total length.
As a user of optical instruments, Bessel was interested in their construction. While examining the Königsberg heliometer, he developed the Bessel method for determining the focal length of lenses and lens systems, which does not require any knowledge of the position of the main optical planes .
The difference in altitude between two locations can be calculated from the measured air pressure difference using a barometric altitude formula. Bessel joined the series of researchers who started with Edmond Halley and tried to find a suitable calculation formula. He dealt with fundamental questions of barometric altitude measurement and developed a formula that took into account the different water vapor content of the air for the first time . Furthermore, he outlined a method how one could give the altitude measurements by mobile barometers greater reliability by setting up a basic barometric measuring network.
Since the atmospheric refraction, the positions of the apparent star positions changed, is influenced by the temperature, it was natural for Bessel, with the accuracy of thermometers to deal with and its own method for calibration of mercury thermometers to develop.
In 1838, Bessel gave an impressive description of an observation he had made in the Teufelsmoor in 1807 about the phenomenon of the will- o'- the- wisps , the existence of which has long been denied and the causal cause has not yet been conclusively clarified .
Although he did not do research in the field of geomagnetism himself , like the researchers Gauß, Humboldt and Erman , who were close to him, in 1842 Bessel compiled a generally understandable report on the state of research in this geophysical field, which was developing at the time .
Teaching
Friedrich Wilhelm Bessel took up his lectures shortly after his arrival in Königsberg, still during the summer semester of 1810, without ever having had a teaching position beforehand. He wrote: “My college, which I read publicly in front of a large audience, makes little or no effort for me, because I read completely freely and only briefly write down the points about which I think something to say during the lesson; ... "
Bessel's former pupil Carl Theodor Anger stated about the effect of his lectures : "His clear, lively lecture soon won him a large number of listeners [...]" and "[...] that the lessons [...] were frequent, oral and written answers Questions and tasks that were given a liveliness that, in the eyes of the audience, gave him a rare charm. ”Bessel expected his audience to have considerable mathematical knowledge, which in reality was often not available. In the opinion of Hans Victor von Unruh , who attended Bessel's lectures in 1824, "[he] lacked the standard for easy and difficult" in his academic lecture.
Until the appointment of Carl Gustav Jacob Jacobi in 1826, Bessel carried out the main part of the mathematics education at the university, because Ernst Friedrich Wrede , the professor there for mathematics and natural history , mainly devoted himself to physical and geological questions. Bessel's practice-oriented training concept at the observatory inspired Jacobi and Franz Ernst Neumann to found a "Mathematical-Physical Seminar" (1834), at which they introduced students to specialist practice. The interaction between Bessel, Jacobi and Neumann in mathematical and physical education is known as the "Königsberg School".
As an astronomer, Bessel was an honorary member of the “Royal Examination Commission for Sea Shipbuilders and Sea Shippers” from 1823 to 1839, and in this function accepted the astronavigational part of the ship master's examination.
In the course of the reform of the higher education system in Prussia initiated by Wilhelm von Humboldt , "Scientific Deputations" (from 1816: "Scientific Examination Commissions") were founded at all Prussian universities from 1810, the task of which was to reorganize the higher schools, the teaching and examining educational methods, drafting curricula, evaluating textbooks and academic writings and examining prospective high school teachers (“Examen pro facultate docendi”). Friedrich Wilhelm Bessel became an extraordinary member of the Scientific Deputation and Examination Commission in Königsberg from 1811 to 1834; as successor to Johann Friedrich Herbart , he was its director in 1820/1821. As early as 1811, Bessel submitted a proposal there about the arrangement of mathematics lessons.
Only a few statements on social issues have survived from Bessel. He was considered an unconditional supporter of the Prussian government and the royal family; Contemporaries, including Alexander von Humboldt, described his attitude as "super-royalist". The few critical statements concern, besides a remark about the inadequate status of the emancipation of Jews, above all the education system. He summarized his view of the contemporary pedagogical discussion in the words: "Many of those who argue so eagerly about pedagogical matters may speak of color like blind people without having observed children attentively and continuously."
In a detailed letter in 1828 to his friend Theodor von Schön , then President of the Province of Prussia , Bessel formulated his criticism of the conception of the grammar school with a neo-humanist character, a core element of the Prussian educational reform. In it he took the view that it was not proven and doubtful that "education of the mind" could only be obtained by studying ancient languages. Rather, it can "be obtained through any serious academic study". He uncovered internal contradictions of the new humanist concept and called for the establishment of a type of school in which mathematics and natural sciences are the "main thing". This school should be on an equal footing with the grammar schools and should also lead to university entrance qualifications. Theodor von Schön had a plan drawn up for such a school type, which, however, was initially not enforceable against the resistance that Bessel foreseen. It was not until 1859 with the 1st order secondary school - later grammar school called - a type of school in terms of the Bessel established in Prussia thoughts.
Bessel was also critical of the efficiency of the academic training. He accused a large part of the students of a lack of diligence and of a study structure that did not focus on the acquisition of the sciences, but only on the final exam, which gave them access to a secure position in the civil service. He called the university system “the most wondrous part of Germany”. The university rector Karl Rosenkranz attested to Bessel in his commemorative speech: “He found himself on a very modern, realistic point of view; that which our universities still have from the Middle Ages aroused his constant polemics. ”Furthermore, Rosenkranz emphasized that Bessel - which was not a matter of course at the time - also took over the elementary lessons for beginners and used the Latin script.
Bessel campaigned for the popularization of scientific knowledge and followed his example Olbers. Between 1832 and 1840 he gave popular science lectures on astronomical and geophysical topics in the Königsberg “Physical-Economic Society”. In the last years of his life he planned to write a "popular astronomy" as a printed work. About this he corresponded with Alexander von Humboldt, who strongly encouraged him to do so, just as Bessel in return actively supported Humboldt in his work on the cosmos by transmitting information and proofreading. Due to illness, Bessel could no longer carry out his plan.
Working method
Bessel described the tasks of astronomy with the words: “What astronomy has to achieve has always been clear: it has to give rules according to which the movements of the celestial bodies [...] can be calculated. Everything else that can be learned about the celestial bodies, for example their appearance and the nature of their surfaces, is not unworthy of attention, but it does not affect the actual astronomical interest. ”With this he distanced himself from the direction of research that he had with Johann Hieronymus Schroeter at the Lilienthal observatory , who observed the planetary surfaces with powerful reflector telescopes. Bessel did not acquire comparable instruments in Königsberg. Bessel emphasized his "lack of inclination to collect material without intending to use it ..."; he was particularly interested in the "results that can be achieved thereby."
Bessel's successes in positional astronomy were made possible by his method of recognizing, calculating or partially eliminating the inevitable errors with which the data is afflicted from the critical analysis of the observation data. Since for him instruments were not only a means of observation, but also an object of investigation, he developed a theory of instrument errors. On the one hand, he determined manufacturing-related errors, for example in the division of circles on the meridians, and on the other, errors that were caused by the measuring environment, such as changes in temperature and humidity. He also paid attention to errors that arise from long-term use of the instruments, such as deflections caused by gravity or the wear and tear of mechanical components. Bessel paid special attention to the accuracy of the clocks he used. Bessel's general view of instruments: “Every instrument is made […] twice, once in the artist's workshop from brass and steel; but for the second time from the astronomer on his paper, through the register of the necessary improvements which he has obtained through his investigation. "
Bessel always regarded astronomy as his main field of work. His occupation with mathematical and physical topics were mostly astronomically motivated.
Encke already emphasized that the lack of a traditional school education for Bessel's astronomical work hardly had a disadvantageous effect at the time, but that his commercial training was very beneficial for later work, for example the ability to manage time effectively and to be in an embarrassing manner in projects that were carried out in parallel Urge to publish the results obtained as soon as possible. The observation data obtained since November 1813 appeared from 1815 in a total of 21 volumes of the Astronomical Observations at the Royal University Observatory in Königsberg .
Exceptionally quickly for the time, he published the results of the parallax determination of 61 Cygni , which he had completed on October 2, 1838. First learned Wilhelm Olbers , as a "gift" to his 80th birthday, by a letter dated 9 October of the first-time reliable distance measurement of a fixed star. The following day Bessel sent the treatise to the Berlin Academy of Sciences , where it was read out on November 23 after a delay. On October 23, he wrote a letter in English to John Herschel , which appeared on November 9 in the Monthly Notices of the Royal Astronomical Society as the first written publication of the results. Without waiting for this, however, Bessel himself had already made his results public for the first time on November 2, 1838 in a popular science lecture to the Physico-Economic Society in Königsberg . Alexander von Humboldt presented the results to a scientific audience for the first time on November 5 , when he was reading a paper at the Academy of Sciences in Paris that Bessel had sent him in French. The detailed publication in the Astronomische Nachrichten finally appeared on December 13, 1838.
In 1811 and 1812, Bessel, together with other Königsberg professors, published the short-lived Königsberg Archive for Natural Science and Mathematics , in which he himself published several articles, including for the first time his Bradley catalog. Most of his essays appeared in the Astronomische Nachrichten , which his friend Heinrich Christian Schumacher published from 1821.
The catalog raisonné in the collected treatises edited by Rudolf Engelmann has around 400 numbers, written exclusively by Bessel as a single author. J. J. Baeyer is only mentioned as his collaborator on the work on East Prussian degree measurement, the text of which was also written entirely by Bessel .
Bessel dealt intensively with the scientific works of other researchers and has written a total of 43 reviews since 1807, mostly in the Jenaische Allgemeine Literatur-Zeitung , 39 of which were published posthumously as a collection in 1878. He built the library at the observatory as an indispensable work tool.
Bessel's scientific estate is mainly deposited in the archive of the Berlin-Brandenburg Academy of Sciences .
Caregivers
Early sponsors
Bessel received initial funding from his Minden teacher Johann Conrad Thilo , who dealt with astronomical questions himself. Thilo recognized Bessel's mathematical and scientific talent early on and campaigned for him to be allowed to leave the grammar school, which was typically dominated by Latin lessons, to begin a commercial apprenticeship. From 1802 to 1806, in the years when Bessel turned seriously to astronomy, the two exchanged letters on scientific questions.
Wilhelm Olbers was the first astronomer with whom Bessel came into personal contact when he handed over his work on Halley's Comet in 1804. Olbers recognized the extraordinary talent and encouraged Bessel by having this work published and then drawing his attention to worthwhile scientific subjects that needed to be worked on. All his life Bessel had the greatest admiration for Olbers and wrote a detailed appraisal after his death. The extensive correspondence, published almost entirely by Bessel's son-in-law Erman in 1852 , was the first closed, published correspondence between two astronomers.
Franz Xaver von Zach willingly had Bessel's first paper printed in the monthly correspondence he edited with the personal remark: "... Here a young German man is doing his pleasure, with a skill and a skill that would honor many paid and appointed astronomers, what an English professor should have done long ago out of official duties, but considered it ineffective and unnecessary to undergo such arduous work ... ”Bessel published almost all of his articles in this journal up to 1813, when it ceased publication.
At the Lilienthal observatory , which was considered to be excellently equipped for its time, Bessel was able to acquire the exercise in handling astronomical devices under the guidance of Johann Hieronymus Schroeter . Bessel's practical observations were part of Schroeter's research program on comet and planetary astronomy. However, this gave him largely a free hand for his own research, in particular the processing of Bradley's star catalog.
Carl Friedrich Gauss
At the end of 1804, Wilhelm Olbers brokered the acquaintance of Carl Friedrich Gauß , which is documented by an extensive, forty-year correspondence in which the two scientists exchanged ideas about their research programs and work results. They also met in person a few times. At his request, Gauss obtained an honorary doctorate from Göttingen University in 1811 for Bessel. Although in 1824 Bessel strongly advocated Gauss' appointment to the Academy of Sciences in Berlin, he decided to stay in Göttingen.
Later, the friendly relationship cooled significantly. In some letters, Bessel had expressed the view that Gauss devoted too much time to surveying work and criticized Gauss' reluctance to publish, which made Gauss feel patronized and offended in tone.
Johann Franz Encke
Bessel worked closely with Gauß's pupil Johann Franz Encke from 1817 when Encke took over the final editing of the Fundamenta astronomiae . In 1825, Bessel proposed Encke as the successor to Johann Elert Bode as director of the observatory at the Berlin Academy of Sciences, after he himself had refused the call he had received.
Encke has been in charge of the Academic Star Maps project initiated by Bessel since 1825 . In 1835, Bessel carried out experiments to regulate Prussian metrology at the new observatory in Berlin over several weeks.
The initially collegial relationship between the two scientists deteriorated over time. A dispute over the correct installation of a measuring instrument, which both astronomers publicly carried out in the publication organs, as well as a disagreement about a thesis advocated by Encke, which concerned the postulated influence of a "resisting medium" on the course of the comet, ultimately led to the break of the relationship . Alexander von Humboldt's intensive efforts to mediate could not bring about a rapprochement.
After Bessel's death, Encke was consulted about a proposal for Bessel's successor. In a letter to Education Minister Eichhorn , Encke criticized Bessel's promotion of young talent and took the view that Bessel had "forced his students to give up their individuality [...]." On July 1, 1846, Encke, as secretary of the Berlin Academy, gave the commemorative speech in honor of the deceased.
Alexander von Humboldt
The personal relationship with Alexander von Humboldt can be proven by an exchange of letters that lasted from 1826 to 1846. In contrast to his habit of destroying the letters addressed to him, Humboldt kept most of Bessel's letters, as Bessel was one of his main suppliers of information in the field of astronomy that he needed to write his cosmos . Bessel made numerous suggestions for improvement to the Kosmos proof sheets. Humboldt used his influence as chamberlain at the Prussian court several times to support Bessel. So he got involved in the difficult negotiations to finance the construction of the heliometer tower at the observatory. They met in person several times. Humboldt conveyed Bessel's last wish to receive a portrait of his sovereign.
Bessel's attempt to have his son-in-law, the physicist Georg Adolf Erman , elected a member of the Berlin Academy with the help of Humboldt, was less successful . Despite Humboldt's intensive efforts, the plan failed. Humboldt commented on this matter with the words: "The great men should have no relatives, where possible be without history."
Friedrich Wilhelm IV.
In his political attitude, Bessel was strictly conservative and was absolutely loyal to his monarchs. A friendly relationship developed with Friedrich Wilhelm IV. , Whom he had already met as heir to the throne; they met in person several times.
During his illness, in November 1845, Bessel expressed to Humboldt that he wanted a portrait of his sovereign. Humboldt passed the request on and Friedrich Wilhelm IV then had Franz Krüger portray him. Two weeks before his death, Bessel was able to receive the picture as an original along with a detailed cover letter written by hand as a gift from the king. In his will, Bessel bequeathed this picture to his hometown Minden, where it is now part of the Minden Museum .
The composition idea for this picture , which has attracted attention in art history as a ruler because of its design, comes from Bessel himself: “A king can only be represented in a full figure, not in a bust; the King of Prussia only in daily dress, not in festive garb, because this type of representation reminds of the solemnity, less of the king ... "
Academic students
Friedrich Wilhelm Bessel drew some gifted students to do practical work at the observatory. One of his first helpers was Gotthilf Hagen , a cousin of his wife Johanna. However, after two years, Hagen switched to surveying and hydraulic engineering.
In 1820 the observatory was granted its own assistant position. The first regular assistant from 1820 to 1823 was Friedrich Wilhelm August Argelander (1799–1875), who later took over the management of the observatories in Åbo , Helsingfors and Bonn . He was followed by Otto August Rosenberger (1800–1890) from 1823 to 1826, who then went to Halle as professor of astronomy and director of the observatory . His successor Carl Theodor Anger (1803-1858) left the Königsberg observatory after five years to take over the management of a newly founded one in Danzig .
August Ludwig Busch (1804–1855) moved from Danzig to Königsberg in 1824 together with Joseph von Eichendorff , who employed him as a private teacher for his children, and studied astronomy and mathematics at Bessel. In 1831 he became Anger's successor as an assistant and in 1835 received the newly created position of observer. After Bessel's death, he was initially appointed interim, from 1849 officially director of the Königsberg observatory .
The activities of Heinrich Schlueter (1815–1844), assistant from 1841 to 1844, ended with his premature death. Moritz Ludwig Georg Wichmann (1821–1859) succeeded him as assistant, in 1850 as an observer and, after Busch's death, Bessel's second successor as director of the observatory.
Eduard Luther (1816–1887) had been professor of astronomy at the Albertus University since 1855 and, after Wichmann's death, also took over the management of the observatory, which enabled him to reunite Bessel's full official authority.
Bessel's student Heinrich Ferdinand Scherk (1798–1885) became professor in Halle and head of the observatory in Kiel , while Emile Plantamour (1815–1882) took over the management of the Geneva observatory .
Carl August von Steinheil (1801-1893) became a professor at the University of Munich ; he devoted himself particularly to the regulation of measurement in Bavaria. His main interest was in instrument making, for which he founded the company C. A. Steinheil & Sons .
As mathematicians, Siegfried Heinrich Aronhold , Karl Wilhelm Borchardt , Otto Hesse , Ferdinand Joachimsthal , Friedrich Julius Richelot and Philipp Ludwig von Seidel studied with Bessel .
Memberships and honors
The first scientific association that Friedrich Wilhelm Bessel made a member was the Society of Sciences, Agriculture and Art in Strasbourg (1812). In 1814 he was appointed to the Russian Academy of Sciences in St. Petersburg; it was followed by the Academy of Sciences in Paris (1816), the Royal Danish Academy of Sciences in Copenhagen (1821), the Royal Society of Edinburgh (1823), the Royal Swedish Academy of Sciences in Stockholm (1823), the Royal Society in London (1825), the Royal Dutch Institute of Sciences in Amsterdam (1827), the Academy of Sciences and Literature in Palermo (1827), the Dutch Academy of Sciences in Haarlem (1830) and the American Academy of Arts and Sciences in Cambridge (Massachusetts ) (1832).
In Germany he was elected as a member of the Royal Prussian Academy of Sciences in Berlin (1812), the Academy of Sciences in Göttingen (1826) and finally in the Royal Bavarian Academy of Sciences in Munich (1842).
He was also accepted into the East Prussian Physical and Economic Society (1814) and the Royal German Society (1817) in Königsberg, the Society for the Advancement of All Science in Marburg (1817), the Natural Research Society in Danzig (1829), the Royal Astronomical Society in London (1832), the Royal Society of Sciences in Uppsala (1836), the American Philosophical Society in Philadelphia (1840), the Italian Society of Sciences in Modena (1842), the Philosophical and Literary Society in Manchester (1843) and the Imperial-Royal Italian Athenaeum in Florence (1844).
Bessel received the Lalande Prize of the French Academy in 1811 for a work on atmospheric refraction , and in 1812 he was awarded by the Prussian Academy for his “investigation of the size and influence of the advancement of the equinoxes”. In 1829 he received the Royal Astronomical Society gold medal for his zone observations and in 1841 for parallax determination.
Bessel was an honorary doctor of the University of Göttingen and an honorary member of the University of Kazan .
When the Pour le Mérite Peace Class for Science and the Arts was founded in 1842, Bessel was one of the first members appointed by Friedrich Wilhelm IV at the suggestion of Alexander von Humboldt.
Bessel has received the Prussian Order of the Red Eagle three times since 1824 , most recently (1844) with the star for 2nd class, and from abroad the Danish Order of Dannebrog (1821), the Russian Order of Saint Stanislaus (1837) and the Swedish North Star Order (1841).
Friedrich Wilhelm III. appointed Bessel in 1832 to the "secret councilor".
Bessel as the scientific namesake
Culture of remembrance
In numerous German towns there are streets, paths or squares that bear the name of Friedrich Wilhelm Bessels. The first such name was given during Bessel's lifetime in 1844 at the instigation of Friedrich Wilhelm IV in Berlin's Friedrichstadt , today the Kreuzberg district . The new Berlin observatory was built near this street in 1835 ; today the area bears the name Besselpark .
In Königsberg , Besselstrasse led to the observatory since 1856 , and a place at the foot of the observatory hill was called Besselplatz . The Bessel bust of Johann Friedrich Reusch , which has been missing since the Second World War , has stood in the garden of the observatory since 1882 . At the base of the equestrian statue of Friedrich Wilhelm III. by August Kiß , which was set up on Paradeplatz in 1851 , Friedrich Wilhelm Bessel appeared on a bronze relief as a representative of the scholarly class. A portrait medallion with Bessel's head by the sculptor Rudolf Siemering was attached to the new building of the Albertus University in Königsberg in 1862 . The Königsberg memorials were destroyed as a result of the Second World War. A secondary school, the building of which was retained, was named Bessel from 1921 to 1945. In what is now Kaliningrad , a memorial stone has been commemorating Friedrich Wilhelm Bessel at the site of the destroyed observatory since 1975. In 1989 a street was named after him again and a memorial plaque was attached to house number 2 there.
Jürgen Goertz created the “ Besselei ” memorial for Bremen , which was erected on the Hanseatenhof near Bessel's former place of residence and work. Also in Bremen, in the Ostliche Vorstadt district, is the Besselstrasse residential group , which was built in 1869 .
The Besselgymnasium in Minden bears his name. A memorial plaque is attached to the house at Kampstrasse 28, where he was born. A bust of the astronomer by Doris Richtzenhain has been standing on the Minden market square (Martinitreppe) since 1996.
The first cosmic object to be given Bessel's name is the Bessel moon crater in the Mare Serenitatis . This name, made by Wilhelm Beer and Johann Heinrich Mädler in 1837, was confirmed by the International Astronomical Union in 1935. A century after the first parallax determination, the asteroid (1552) Bessel received its name in 1938. A structural element in the Cassini division of Saturn's rings has been called the Bessel division (Bessel Gap) since 2009 .
In 1845, while Bessel was still alive, the Bark Bessel was put into service as the largest ship in the Bremen fleet and was primarily used for emigrants to North America. In 1981 the sea hydrographic service of the GDR put the Bessel surveying vessel into operation.
On the occasion of Bessel's 200th birthday, the Astronomical Society held its annual meeting in 1984 in his native Minden. On the same occasion, the Deutsche Bundespost issued an 80-pfennig special stamp with a circulation of 31,450,000 copies, and a commemorative medal was minted in the “Mindener Geschichtstaler” series.
The Alexander von Humboldt Foundation annually awards a Friedrich Wilhelm Bessel Research Prize endowed with 45,000 euros.
Portraits
Numerous portraits were made of Bessel, the first being a plaster plaque by Leonhard Posch (1810). Well-known portraits were created by Heinrich Joachim Herterich (1825), Johann Eduard Wolff (1834, 1844) and Christian Albrecht Jensen (1839). The pictures by Wolff and Jensen provided the basis for further portraits by other artists. A copper engraving by Eduard Mandel (1851) based on the portrait of Wolff is considered a "canonical" representation because of its widespread use and also served as a template for the graphic design of the special postage stamp of the German Federal Post Office (1984).
Furthermore, Bessel had several daguerreotypes made of himself and his family , including by the Königsberg physicist Ludwig Moser , who, like Bessel's student Carl August von Steinheil, was one of the pioneers of this technique.
Bessel in literature
Two years after Bessel's death, Edgar Allan Poe mentioned Heureka Friedrich Wilhelm Bessel and the results of his parallax measurement in his cosmogonic essay .
Arno Schmidt lets Bessel appear as a minor character in his “Historical Revue” Massenbach in a scene that takes place in Wilhelm Olbers' observatory. Schmidt also incorporated Bessel in other plants.
In Daniel Kehlmann's novel Die Vermessung der Welt , Bessel appears as a conversation partner of Carl Friedrich Gauß.
Fonts
- Investigations into the apparent and true orbit of the great comet that appeared in 1807 . Koenigsberg 1810.
- Investigation of the size and influence of the advancement of the equals . Berlin 1815.
- Fundamenta Astronomiae per anno MDCCLV deducta ex observationibus viri incomparabilis James Bradley in specula astronomica Grenovicensi, per annos 1750–1762 institutis . Koenigsberg 1818.
- Investigations into the length of the simple second pendulum . Berlin 1828.
- Tabulae regiomontanae reductionum observationum astronomicarum from anno 1750 usque ad annum 1850 computatæ . Koenigsberg 1830.
- Experiment with the force with which the earth attracts bodies of various types . Berlin 1832.
- Degree measurement in East Prussia and its connection with Prussian and Russian triangular chains. Executed by FWBessel, director of the Königsberg observatory, Baeyer, major in the general staff . Berlin 1838 (text by FWBessel).
- Presentation of the investigations and rules of measurement which, in 1835 to 1838, were initiated by the unit of the Prussian length measure . Berlin 1839.
- Astronomical observations at the Royal University Observatory in Königsberg. I. (1815) to XXI. (1844) (observations from the years 1813 to 1835).
-
Astronomical studies,
- 1st volume. Koenigsberg 1841
- 2nd volume. Koenigsberg 1842.
- Heinrich Christian Schumacher (Ed.): Popular lectures on scientific subjects by FWBessel. Hamburg 1848.
-
Rudolf Engelmann (Ed.): Treatises by Friedrich Wilhelm Bessel. 3 volumes,
- 1. Volume: I. Movements of the Bodies in the Solar System. II. Spherical Astronomy . Leipzig 1875
- 2nd volume: III. Theory of Instruments. IV. Stellar Astronomy. V. Mathematics . Leipzig 1876
- Volume 3: VI. Geodesy. VII. Physics. VIII. Miscellaneous - Literature . Leipzig 1876.
- Rudolf Engelmann (Ed.): Reviews of Friedrich Wilhelm Bessel . Leipzig 1878.
Correspondence
- Adolph Erman (Ed.): Correspondence between W.Olbers and FWBessel. Leipzig 1852 (2 volumes).
- Royal Prussian Academy of Sciences (ed.): Correspondence between Gauss and Bessel. Leipzig 1880, ISBN 3-487-05551-1 .
- Royal Academies of Sciences in Berlin and Munich (ed.): Correspondence between Bessel and Steinheil. Leipzig / Berlin 1913.
- Hans-Joachim Felber (Ed.): Correspondence between Alexander von Humboldt and Friedrich Wilhelm Bessel (= contributions to Alexander von Humboldt research. Volume 10). Akademie Verlag, Berlin 1994, ISBN 3-05-001915-8 , ISSN 0232-1556
- Jürgen W. Koch: The correspondence between Friedrich Wilhelm Bessel and Johann Georg Repsold . Koch, Holm 2000, ISBN 3-89811-533-X .
literature
decreasing chronologically
- Eberhard Neumann-Redlin von Meding : FW Bessel among the Königsberg scientists. His collaboration with K. G. Hagen, C. G. Jacobi and F. Neumann. In: Klemens Adam, Gerd Huneke, Heinrich Rademacher (Red.): Friedrich Wilhelm Bessel. 1784-1846. Articles about the life and work of the famous astronomer . Besselgymnasium der Stadt Minden, Minden 1996, pp. 67–80.
- Kasimir Lawrynowicz : Friedrich Wilhelm Bessel, 1784–1846 (= Vita Mathematica, Volume 9). Translated from Russian by Katja Hansen-Matyssek and Heinz Matyssek. Birkhäuser Verlag, Basel / Boston / Berlin 1995, ISBN 3-7643-5113-6 (Original: Nauka, Moscow 1989, ISBN 5-02-005884-X ). Critical review by Wolfgang R. Dick in Die Sterne 72 (1996), pp. 242–243 ( preprint ; with indication of some translation-related errors).
- Jürgen Hamel : Friedrich Wilhelm Bessel (= biographies of outstanding natural scientists, technicians and physicians , volume 67). BG Teubner, Leipzig 1984.
- Friedrich Wilhelm Bessel: I love you, but heaven is closer to me. An autobiography in letters. Published by Edith Schlieper. City of Minden, Minden 1984.
- Erich Schoenberg : Bessel: Friedrich Wilhelm. In: New German Biography (NDB). Volume 2, Duncker & Humblot, Berlin 1955, ISBN 3-428-00183-4 , pp. 179-181 ( digitized version ).
- Johann Adolf Repsold : Friedrich Wilhelm Bessel. In: Astronomische Nachrichten 210 (1919), No. 5028, Col. 161-214.
- Karl Christian Bruhns : Bessel: Friedrich Wilhelm . In: Allgemeine Deutsche Biographie (ADB). Volume 2, Duncker & Humblot, Leipzig 1875, pp. 558-567.
- Gustav Adolph Jahn : Friedrich Wilhelm Bessel, died March 17, 1846 in Königsberg. Obituary in: Oswald Marbach (ed.): Literature and Art Report , 1846, No. 5, pp. 17-18 ( digitized version ).
Web links
- Literature by and about Friedrich Wilhelm Bessel in the catalog of the German National Library
- Works by and about Friedrich Wilhelm Bessel in the German Digital Library
- Publications by Friedrich Wilhelm Bessel in the Astrophysics Data System ADS
- John J. O'Connor, Edmund F. Robertson : Friedrich Wilhelm Bessel. In: MacTutor History of Mathematics archive .
- JS Worse: The double star 61 Cygni. accessed on September 12, 2015
- Legacy pieces on Friedrich Wilhelm Bessel in the State and University Library Bremen
Individual evidence
- ^ Leopold von Bessel: Pedigree of the astronomer Friedrich Wilhelm Bessel (= pedigrees of famous Germans. Fourth episode, delivery 7). Leipzig 1937.
- ↑ Erich Schoenberg: Bessel, Friedrich Wilhelm. In: Neue Deutsche Biographie 2 (1955), pp. 179–180 ( online version ).
- ^ Gothaisches Genealogisches Taschenbuch der Briefadeligen houses. 1915. Ninth year, Justus Perthes, Gotha 1914, p. 68.
- ^ Historical paperback of the nobility in the Kingdom of Hanover , Hanover 1840, p. 82 ; Ernst Heinrich Kneschke : New General German Adels Lexicon , Volume 1, Leipzig 1859, p. 382 ; GHdA , Adelslexikon Volume I, Volume 53 of the complete series, Limburg an der Lahn 1972, p. 366.
- ^ Gothaisches Genealogisches Taschenbuch der Briefadeligen houses. 1915. Ninth year, Justus Perthes, Gotha 1914, p. 71.
- ↑ Bessel's Bible from a private source. In: Neue Westfälische, October 19, 2018.
- ↑ Kinship Bessel – Hagen
- ^ Leopold von Bessel: pedigree of the astronomer Friedrich Wilhelm Bessel. Leipzig 1937, p. 6.
- ↑ Kinship Bessel – Erman
- ↑ Relatives Bessel – Mendelssohn
- ↑ Kinship Bessel – Baeyer
- ↑ Jürgen Hamel, Ernst Buschmann: Friedrich Wilhelm Bessels and Johann Jacob Baeyer's cooperation in the "Degree measurement in East Prussia" 1830–1838 (= communication no. 189 of the Institute for Applied Geodesy ). Frankfurt am Main 1996, p. 9.
- ↑ Families Hagen – Bessel – Neumann
- ^ Armin Wolf : The pedagogue and philosopher Johann Conrad Fallenstein (1731-1813) - Genealogical relationships between Max Weber , Gauß and Bessel. In: Genealogy. Volume 7 (1964), pp. 266–269.
- ↑ Kinship Bessel – Delius
- ↑ Marriage Germany, 1558–1929. Database, FamilySearch ( https://familysearch.org/ark:/61903/1:1:JH8R-CN1 : 11 February 2018), Daniel Heinrich Delius and Helene Schrader, 28 Nov 1803; citing Sankt Martini Evangelical, Minden City, Westphalia, Prussia; FHL microfilm 442,175.
-
↑ FW Bessel: Brief memories of moments in my life. Königsberg 1846. printed in:
- Adolph Erman: Correspondence between W.Olbers and FWBessel. Leipzig 1852, pp. IX – XXX ( dig )
Rudolf Engelmann: Treatises by Friedrich Wilhelm Bessel. Volume I. Leipzig 1875, pp. XI – XXIV ( dig )
JA Repsold: Friedrich Wilhelm Bessel. In: Astronomical News. Vol. 210 (1919), col. 161-214, here: col. 161-177 ( dig ).
- Adolph Erman: Correspondence between W.Olbers and FWBessel. Leipzig 1852, pp. IX – XXX ( dig )
- ↑ FW Bessel: I love you, but heaven is closer to me. An autobiography in letters. Minden 1984.
- ^ Jürgen Hamel: Friedrich Wilhelm Bessel . Leipzig 1984, p. 12f.
- ^ Johann Adolf Repsold: Friedrich Wilhelm Bessel. In: Astronomical News. Volume 210 (1919), No. 5028, Col. 161-214, here Col. 163f. ( dig ).
- ^ Jürgen Hamel: Friedrich Wilhelm Bessel . Leipzig 1984, p. 14.
- ↑ Johann Gottlieb Bohnenberger : Instructions for determining geographical location, especially by means of the mirror sextant. Vandenhoeck and Ruprecht, Göttingen 1795 ( dig ).
- ^ JF Encke: memorial speech on Bessel. Treatises of the Berlin Academy of Sciences for 1846, p. XXV.
- ^ Jürgen Hamel: Friedrich Wilhelm Bessel . Leipzig 1984, p. 15.
- ↑ JJ de la Lande: Astronomical manual or the star art in a short teaching term. Leipzig 1775.
- ^ Wilhelm Olbers: Treatise on the easiest and most convenient method to calculate the orbit of a comet from a few observations . Industrie-Comptoir, Weimar 1797 ( dig ).
- ^ Jürgen Hamel: Friedrich Wilhelm Bessel . Leipzig 1984, p. 18f.
- ↑ Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846 . Basel 1995, p. 29.
- ↑ Ludwig Franzisket : Plans to build an observatory in Münster around 1800. In: Treatises from the State Museum for Natural History in Münster in Westphalia. Volume 43 (1981), supplement pp. 35-54, here p. 51.
- ↑ a b Jürgen Hamel: Friedrich Wilhelm Bessel . Leipzig 1984, p. 24.
- ↑ Monika Lahrkamp: The French time. In: Wilhelm Kohl (Hrsg.): Westphalian history. Volume 2: The 19th and 20th Centuries. Pp. 2–43, here p. 37.
- ↑ Sigmund Gundelfinger : Three letters from CF Gauss to Joh. Von Müller . In: Journal for pure and applied mathematics Volume 131 (1906), pp. 1-7 ( dig ).
- ^ Adolph Erman (Ed.): Correspondence between W. Olbers and FW Bessel. Leipzig 1852, Volume 1, pp. 183-185 (letters from Olber to Bessel from August 1 and 21, 1808; dig ).
- ↑ Royal Prussian Academy of Sciences (ed.): Correspondence between Gauss and Bessel. Leipzig 1880, pp. 84–85 (letter from Bessel to Gauß of July 24, 1808; dig ).
- ^ Report of the Section of Cult and Teaching to the King, December 1809. In: Andreas Flitner and Klaus Giel (eds.): Wilhelm von Humboldt - works in five volumes. Volume IV: Writings on politics and education. 3. Edition. Darmstadt 1982, pp. 210-238, here p. 232.
- ↑ Dietmar Fürst: The establishment of the Königsberg observatory in the light of the files of the Prussian state. Part 1: Up to Bessel's arrival in Königsberg. In: Contributions to the history of astronomy. Volume 1. Harri Deutsch, Thun / Frankfurt am Main 1998, ISBN 3-8171-1568-7 , pp. 79-106, here pp. 87-101.
- ↑ C. Schilling (Ed.): Wilhelm Olbers - His life and his works. Second volume. Correspondence between Olbers and Gauss. First division. Berlin 1900 (Olbers' letter to Gauß of January 17, 1810).
- ↑ Dietmar Fürst: The establishment of the Königsberg observatory in the light of the files of the Prussian state. Part 2: From Bessel's arrival in Königsberg to the start of construction on the observatory. In: Contributions to the history of astronomy. Volume 2. Harri Deutsch, Thun / Frankfurt am Main 1999, ISBN 3-8171-1590-3 , pp. 145–188, here pp. 145–154.
- ↑ Dietmar Fürst: The establishment of the Königsberg observatory in the light of the files of the Prussian state. Part 3: The history of the building of the observatory. In: Contributions to the history of astronomy. Volume 3. Harri Deutsch, Thun / Frankfurt am Main 2000, ISBN 3-8171-1635-7 , pp. 22-67.
- ↑ Dietmar Fürst, Jürgen Hamel: Friedrich Wilhelm Bessel and the instruments of the Remplin observatory (Mecklenburg) (= Archenhold observatory Berlin-Treptow, special edition no. 23). Berlin 1986.
- ^ Klaus-Dieter Herbst: The development of the meridian circle 1700–1850. GNT-Verlag, Bassum / Stuttgart 1996, ISBN 3-928186-21-3 , pp. 170-177.
- ↑ Dietmar Fürst: The history of the heliometer of the Königsberg observatory. In: Contributions to the history of astronomy. Volume 6. Harri Deutsch, Thun / Frankfurt am Main 2003, ISBN 3-8171-1717-5 , pp. 90-136.
- ↑ JC Poggendorff : Biographical-literary concise dictionary for the history of the exact sciences . First volume. Leipzig 1863, p. 178 ( dig ).
- ^ Dietmar Fürst: Bessel and the cholera epidemic 1831 in Königsberg. An episode from Bessel's life. In: Contributions to the history of astronomy. Volume 8. Harri Deutsch, Thun / Frankfurt am Main 2006, ISBN 978-3-8171-1771-0 , pp. 112-149.
- ^ Report of the British Association for the Advancement of Science. Retrieved June 16, 2014 .
- ↑ Sur la refraction astronomique. In: Comptes Rendus hebdomadaires des séances de l'Académie des Sciences, 1842, Volume 2, pp. 181-185.
- ↑ Friedrich Wilhelm Bessel's diary entries about his trip to England in the summer of 1842. In: Volker Rodekamp (Ed.): Friedrich Wilhelm Bessel 1784–1846 - His path to the stars . Minden 1984, pp. 34-38.
- ↑ E. Neumann-Redlin von Meding: The scholars on the "old Neurossgärter cemetery", the scholarly cemetery in Königsberg. In: Königsberger Bürgerbrief 2012, No. 80, pp. 54–56.
- ^ HNZ: Königsberg, October 7th. In: Frankfurter Oberpostamts-Zeitung . Appendix to No. 289. Frankfurt October 20, 1846, p. 2861 ( limited preview in Google Book Search [accessed July 22, 2020]).
- ↑ Review by Raphael Kosch : Bessel's last illness, described and explained by Dr. Kosch, Königsberg 1846, in: Neue Prussische Provinzialblätter, Volume 2, Tag & Koch, Königsberg 1846, pp. 391–392 ( limited preview in the Google book search [accessed on July 22, 2020]).
- ↑ Diedrich Wattenberg : After Bessel's death. A collection of documents (= publications of the Archenhold observatory . No. 7). Berlin-Treptow 1976, p. 12.
- ^ E. Neumann-Redlin von Meding: 150 years ago: the description of retroperitoneal fibrosis, the "Ormond's disease", based on the clinical picture of FW Bessels (1784–1846). In: Der Urologe (B), Volume 36 (1996), pp. 378-382 (with further references; doi: 10.1007 / s001310050044 ).
- ↑ RJ Kosch: Bessel's last illness, described and explained by Dr. Kosch. Koenigsberg 1846.
- ^ Jürgen Hamel: Friedrich Wilhelm Bessel . Leipzig 1984, p. 84.
- ^ Gesellschaft der Freunde Kants eV (No longer available online.) Archived from the original on September 24, 2015 ; Retrieved November 8, 2015 . Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.
- ^ Leopold von Bessel: The Königsberg hunting picture. In: Archives for kin research . Volume 15 (1938), pp. 4-8, 37-40, 87-90, 151-154; here p. 4, 39.
- ^ Heinrich Christian Schumacher (Ed.): Popular lectures on scientific subjects by F. W. Bessel. Hamburg 1848 ( ETH Zurich , dig ).
- ^ FW Bessel: Calculation of Harriot's and Torporley's observations of the Comet from 1607. In: Monthly Correspondenz . Volume X (1804), p. 425.
- ^ FW Bessel: About the calculation of the true anomaly in an orbit not very different from the parabola. In: Monthly Correspondence. Volume XII (1805), p. 197.
- ↑ Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846 . Basel 1995, p. 24.
- ↑ a b Jürgen Hamel: Friedrich Wilhelm Bessel . Leipzig 1984, p. 33.
- ↑ FW Bessel: Observations on the physical condition of Halley's comet and remarks caused by it. In: Astronomical News. Volume XIII (1836), No. 302, col. 185-232 ( dig ).
- ^ Jürgen Hamel: Friedrich Wilhelm Bessel . Leipzig 1984, pp. 72-74.
- ^ FW Bessel: About shooting stars. In: Astronomical News. Volume XVI (1839), No. 380, 381, col. 321-350 ( dig ).
- ^ Jürgen Hamel: Friedrich Wilhelm Bessel . Leipzig 1984, pp. 75-76.
- ^ FW Bessel: About the determinations of the libration of the moon, through observations. In: Astronomical News. Volume XVI (1839), No. 376, col. 257-272; No. 377, col. 273-280 ( dig ).
- ^ A b Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846 . Basel 1995, p. 232.
- ↑ FW Bessel: New type of calculation for the nautical method of moon distances. In: Astronomical News. Volume X (1832), No. 218, col. 17-32; No. 219, col. 33-48; No. 220, col. 49-62 ( dig ).
- ^ FW Bessel: Remarks about an assumed atmosphere of the moon. In: Astronomical News. Volume XI (1834), No. 263, col. 411-420 ( dig ).
- ↑ FW Bessel: About the figure of Saturn, with regard to the attraction of his rings. In: Monthly Correspondenz , Volume XV (1807), pp. 239-260.
- ^ FW Bessel: Determination of the orbit of the Hugenic Saturn satellite. In: Astronomical News. Volume IX (1831), No. 193-195, col. 1-52 ( dig ).
- ↑ a b Jürgen Hamel: Friedrich Wilhelm Bessel . Leipzig 1984, p. 65.
- ^ FW Bessel: Theory of the Saturn System. In: Astronomical News. Volume XXVIII, No. 649, col. 1-16; No. 652, col. 49-60; No. 669, col. 321-338; No. 670, col. 337-350; No. 672, col. 371-392 ( dig ).
- ↑ a b F. W. Bessel: passage of mercury through the sun. In: Astronomical News. Volume X (1832), No. 228, col. 185-196 ( dig ).
- ↑ Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846 . Basel 1995, p. 233.
- ↑ Lutz Brandt: The heliometer - an almost unknown instrument. In: The Stars. Volume 69 (1993), pp. 94-110. here: p. 101.
- ^ FW Bessel: passage of mercury through the sun. In: Astronomical News. Volume X (1832), No. 228, col. 185-196, here: col. 187-188 ( dig ).
- ↑ G. Schneider, JM Pasachoff, L. Golub: Space Studies of the Black Drop Effect at a Mercury transit . 2003 (PrePrint; dig ).
- ^ FW Bessel: Analysis of the eclipses . In: Astronomical Investigations. Volume 2. pp. 95-240 ( dig ).
- ↑ Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846 . Basel 1995, pp. 230-232.
- ^ Jürgen Hamel: Friedrich Wilhelm Bessel . Leipzig 1984, pp. 30-37.
- ^ FW Bessel: Investigation of the size and influence of the advancement of the night equals. Berlin 1815 ( dig ).
- ^ FW Bessel: Tabulae Regiomontanae. Königsberg 1830, p. XXIV ( dig ).
- ↑ Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846 . Basel 1995, p. 154.
- ↑ Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846 . Basel 1995, pp. 175-176.
- ^ Jürgen Hamel: Friedrich Wilhelm Bessel . Leipzig 1984, p. 43f.
- ^ M. Weisse: Positiones mediae stellarum fixarum in Zonis Regiomontanis a Besselio inter −15 et + 15 ° declinationis observatorum, ad annum 1825 deductae et in catalogum ordinarae. St. Petersburg 1846.
- ↑ Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846 . Basel 1995, pp. 118-120.
- ^ Jürgen Hamel: Bessel's project of the Berlin academic star maps. In: The Stars . Vol. 65 (1989), pp. 11-19.
- ^ Derek Jones: Academic Star Maps, Berlin 1830–59. In: Highlights of Astronomy, Vol. 12, 2002, pp. 367-370 ( dig ).
- ^ FW Bessel: Astronomical investigations. 1st volume . Königsberg 1841, pp. 280-295 ( dig ).
- ↑ Hans Strassl : The first determination of a fixed star distance . In: The natural sciences . Volume 33 (1946), Issue 3, pp. 65-71, here p. 71.
- ^ Jürgen Hamel: Friedrich Wilhelm Bessel . Leipzig 1984, pp. 57-61.
- ↑ Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846 . Basel 1995, p. 202.
- ↑ Dieter B. Herrmann : Cosmic widths. Leipzig 1981, p. 23.
- ↑ a b F. W. Bessel: Determination of the distance of the 61st star of the swan. In: Astronomical News. Volume XVI (1838), No. 365, 366, col. 65-96 ( dig ).
- ↑ Dieter B. Herrmann: Cosmic widths. Leipzig 1981, p. 37.
- ^ Hipparcos catalog: 61 Cygni. (No longer available online.) Archived from the original on April 19, 2013 ; Retrieved November 8, 2015 . Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.
- ↑ Dieter B. Herrmann: Cosmic widths. Leipzig 1981, pp. 38-40.
- ↑ Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846 . Basel 1995, p. 209.
- ^ Jürgen Hamel: Friedrich Wilhelm Bessel . Leipzig 1984, p. 69.
- ↑ Jürgen Hamel: Bessel's hypothesis of specific gravity and the problem of the Uranus movement. In: The Stars. Vol. 60 (1984), pp. 278-283.
- ↑ Hans-Joachim Felber (Ed.): Correspondence between Alexander von Humboldt and Friedrich Wilhelm Bessel. Berlin 1994, p. 44 (letter from Bessel to Humboldt of July 2, 1828).
- ^ A b c Jürgen Hamel: Friedrich Wilhelm Bessel . Leipzig 1984, p. 77.
- ↑ Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846 . Basel 1995, p. 224.
- ↑ FW Bessel: About the influence of changes in the earth's body on the pole height. In: Journal of Astronomy and Allied Sciences. Volume 5, Tübingen 1818.
- ↑ JG Hagen : Bessel's "Suspicion against the immutability of the pole height". In: Astronomical News. Volume 136 (1894), No. 3253, col. 207-208 ( dig ).
- ↑ Erich Przybyllok : FW Bessel as the discoverer of the polar height fluctuations. In: Astronomical News. Volume 242 (1931), No. 5804, col. 365-368 ( dig ).
- ↑ Peter Brosche, Helmut Lenhardt: The pole movement from the observations of FW Bessel 1842-1844. In: Journal of Geodesy, Geoinformation and Land Management. Volume 136 (2011), pp. 329-337.
- ^ Letters between Gauss and Bessel. Leipzig 1880. pp. 272-277 (letter from Bessel to Gauß of June 15, 1818; dig ).
- ↑ Christoph Hoffmann: Under observation - nature research in the time of the sensory apparatus. Wallstein Verlag, Göttingen 2006, pp. 147, 166 (detailed processing of Bessel's investigations on the personal equation).
- ↑ Christoph Hoffmann: Under observation - nature research in the time of the sensory apparatus. Wallstein Verlag, Göttingen 2006, pp. 172–179.
- ↑ Christoph Hoffmann: Under observation - nature research in the time of the sensory apparatus. Wallstein Verlag, Göttingen 2006, p. 188.
- ^ Johann Friedrich Herbart: De attentionis mensura causisque primariis. Königsberg 1822, pp. 60-64 ( dig ).
- ^ A b Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846 . Basel 1995, p. 155.
- ^ Gert Schubring: The German mathematical community. In: John Fauvel et al. (Ed.): Möbius and his volume - The rise of mathematics and astronomy in Germany in the 19th century. Basel / Boston / Berlin 1994, pp. 31-46.
- ^ Facsimile of a manuscript by Bessel. In: Journal for pure and applied mathematics. Volume 35 (1847), p. 369 (letter from Bessel to Crelle of January 6, 1828; dig ).
- ↑ Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846 . Basel 1995, p. 137.
- ^ FW Bessel: Investigation of the probability of observation errors. In: Astronomical News. Volume XV (1838), No. 358, 359, col. 369-404 ( dig ).
- ↑ Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846 . Basel 1995, p. 156.
- ↑ FW Bessel: A tool to facilitate the application of the method of least squares. In: Astronomical News. Volume XVII (1840), No. 399, col. 225-230 ( dig ).
- ^ Oskar Schlömilch: About the Bessel function. In: Journal of Mathematics and Physics. Volume 2 (1857), pp. 137-165.
- ↑ Christian Strutz: Bessel functions for the X-ray structural analysis of the α-helix and the double helix. Retrieved November 8, 2015 .
- ↑ Dirk Eidemüller: Lattice light disk microscope. In: Spektrum.de, October 23, 2014. Retrieved November 8, 2015 .
- ^ The 2014 Nobel prize for Chemistry: Super-resolution microscopy. (No longer available online.) Formerly in the original ; Retrieved November 8, 2015 . ( Page no longer available , search in web archives ) Info: The link was automatically marked as defective. Please check the link according to the instructions and then remove this notice.
- ^ Klaus Biener: On the 150th anniversary of the death of Friedrich Wilhelm Bessel. In: RZ-Mitteilungen. No. 12 (1996), pp. 56-58.
- ↑ Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846 . Basel 1995, pp. 156–157.
- ↑ a b J. Sommer : Bessel as a mathematician. In: Journal of Surveying . Volume 40 (1911), pp. 333-341.
- ↑ Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846 . Basel 1995, pp. 157-159.
- ^ FW Bessel: About a sentence from the theory of the conic sections. In: Rudolf Engelmann (Ed.): Treatises by Friedrich Wilhelm Bessel. 2nd volume. Leipzig 1876, pp. 358-360 ( dig ).
- ↑ FW Bessel: About a task of practical geometry. In: Monthly Correspondence. Volume XXVII (1813), pp. 222f. ( dig ).
- ↑ Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846 . Basel 1995, p. 237.
- ^ FW Bessel: Trigonometric determination of some points in Königsberg and examination of some angles of Textor's measurement of Prussia. In: Journal of Astronomy. IV (1817), pp. 286-296.
- ↑ Hans-Joachim Felber (Ed.): Correspondence between Alexander von Humboldt and Friedrich Wilhelm Bessel. Berlin 1994, p. 72 (letter from Bessel to Humboldt of June 2, 1830).
- ↑ Jürgen Hamel, Ernst Buschmann: Friedrich Wilhelm Bessels and Johann Jacob Baeyers cooperation in the "Degree measurement in East Prussia" 1830–1838 (= Communication No. 189 from the Institute for Applied Geodesy ). Frankfurt am Main 1996.
- ↑ Degree measurement in East Prussia and its connection with Prussian and Russian triangular chains. Executed by FWBessel, director of the Königsberg observatory, Baeyer, major in the general staff . Berlin 1838.
- ↑ a b Wolfgang Torge : History of geodesy in Germany. 2nd Edition. Berlin / New York 2009, pp. 160–163.
- ^ Jürgen Hamel: Friedrich Wilhelm Bessel . Leipzig 1984, p. 54.
- ↑ Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846 . Basel 1995, pp. 240-244.
- ^ Wolfgang Torge: The long way to the Prussian land surveying: on the 100th anniversary of the death of Oscar Schreiber (1829-1905). In: Zeitschrift für Vermessungswesen , 130th year (2005), pp. 359–371.
- ↑ a b Jürgen Hamel: Friedrich Wilhelm Bessel . Leipzig 1984, p. 55.
- ↑ FW Bessel: Determination of the axes of the elliptical spheroid of rotation, which corresponds most to the existing measurements of meridional arcs of the earth. In: Astronomical News. Volume XIV (1837), No. 333, col. 333-346 ( dig ).
- ↑ Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846 . Basel 1995, p. 250.
- ↑ FW Bessel: About an error in the calculation of the French degree measurement and its influence on the determination of the figure of the earth. In: Astronomical News. Volume XIX (1841), No. 438, col. 97-116 ( dig ).
- ↑ Meyers Konversationslexikon. 4th edition. 1885–1892, Volume 5, keyword: Earth. Publishing house of the Bibliographisches Institut, Leipzig and Vienna.
- ↑ FW Bessel: About the influence of the irregularities of the figure of the earth, on geodetic work and their comparison with astronomical determinations. In: Astronomical News. Volume XIV (1837), No. 329-331, col. 269-312 ( dig ).
- ↑ Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846 . Basel 1995, pp. 238-239.
- ^ Jürgen W. Koch: The correspondence between Friedrich Wilhelm Bessel and Johann Georg Repsold . Koch, Holm 2000, p. 19 (letter from Bessels to J. G. Repsold of March 3, 1823).
- ^ Jürgen Hamel: Friedrich Wilhelm Bessel . Leipzig 1984, p. 46.
- ↑ FW Bessel: About the influence of a resisting means on the movement of a pendulum. In: Astronomical News. Volume IX (1831), No. 204, col. 221-236 ( dig ).
- ↑ Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846 . Basel 1995, p. 255.
- ^ FW Bessel: Construction of a symmetrically shaped pendulum with reciprocal axes. In: Astronomical News. Volume XXX (1849), No. 697, col. 1-6 ( dig ).
- ↑ Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846 . Basel 1995, p. 259.
- ↑ a b Jürgen Hamel: Friedrich Wilhelm Bessel . Leipzig 1984, p. 48.
- ↑ Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846 . Basel 1995, pp. 256-258.
- ↑ Roland Eötvös: About the attraction of the earth to various substances. In: Mathematical and scientific reports from Hungary. Eighth volume, 1889–1890. Berlin / Budapest 1891, pp. 65–68.
- ↑ Measure and Weight System for the Prussian States. May 16, 1816. In. Collection of Laws for the Royal Prussian States 1816 . No. 10, pp. 142-148, Law No. 356 ( dig ).
- ^ Jürgen Hamel: Friedrich Wilhelm Bessel . Leipzig 1984, p. 49.
- ↑ Georg Strasser: The Toise, the Yard and the Meter. In: General surveying news . Volume 81 (1974), pp. 2–20.
- ↑ Law on the original size of the Prussian state in the pursuit of the law of May 16, 1816. In: Collection of laws for the Royal Prussian States 1839 . No 7, p. 94, Law No. 1986 ( dig ).
- ↑ Cornelia Meyer-Stoll: The measure and weight reforms in Germany in the 19th century with special consideration of the role of Carl August Steinheil and the Bavarian Academy of Sciences (= Bavarian Academy of Sciences, Philological-Historical Class, Treatises, New Series, Issue 136 ). Munich 2010, pp. 49-77.
- ↑ FW Bessel: About what astronomy teaches us about the shape and interior of the earth. In: Popular lectures on scientific subjects by F. W. Bessel. Hamburg 1848, pp. 34-67, here pp. 52-54 ( dig ).
- ^ Jürgen Hamel: Friedrich Wilhelm Bessel . Leipzig 1984, p. 51.
- ↑ Cornelia Meyer-Stoll: The measure and weight reforms in Germany in the 19th century… Munich 2010, pp. 96–100, 151–154.
- ^ Jürgen Hamel: Friedrich Wilhelm Bessel . Leipzig 1984, p. 50.
- ↑ Presentation of the investigations and rules of measure which, in 1835 to 1838, were initiated by the unification of the Prussian length measure. Appendix I. Influence of gravity on the figure of a staff resting on two points of the same height. Berlin 1839, pp. 132, 135 ( dig ).
- ↑ Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846 . Basel 1995, p. 243.
- ↑ FW Bessel: About a means for determining the focal length of the objective glass of a telescope. In: Astronomical News. Volume XVII (1840), No. 403, col. 289-294 ( dig ).
- ↑ Richard Rühlmann : The barometric height measurements and their significance for the physics of the atmosphere. Leipzig 1870, pp. 10-12, 21-24 ( dig ).
- ^ FW Bessel: About height determinations by the barometer. In: Astronomical News. Volume XII (1835), No. 279, col. 241-254 ( dig ).
- ^ FW Bessel: Comments on barometric altitude measurement. In: Astronomical News. Volume XV (1838), No. 279,356, col. 329-360 ( dig ).
- ^ FW Bessel: Method of correcting the thermometer. In: Annalen der Physik und Chemie Volume VI (1826), pp. 287–308 ( dig ).
- ↑ FW Bessel: Are there will-o'-the-wisps? In: Annals of Physics and Chemistry. Volume XXXXIV (1838), p. 366 ( dig ).
- ↑ FW Bessel: About the magnetism of the earth. In: Schumacher's yearbook for 1843, pp. 1-56.
- ^ Jürgen Hamel: Friedrich Wilhelm Bessel , Leipzig 1984, p. 29.
- ↑ Memory of Bessel's life and work. From Dr. Anger. Danzig 1846, p. 12.
- ↑ Heinrich von Poschinger (Ed.): Memories from the life of Hans Viktor von Unruh. Stuttgart / Leipzig / Berlin / Vienna 1895, p. 29 ( dig ).
- ^ Herbert Pieper: Carl Gustav Jacob Jacobi (1804-1851). In: Dietrich Rauschning , Donata v. Nerée: The Albertus University of Königsberg and its professors. (= Yearbook of the Albertus University of Königsberg / Pr. Volume XXIX) Berlin 1995, pp. 473–488, here: p. 479.
- ^ Karl-Heinz Schlote : The Königsberg School. In: Dietrich Rauschning , Donata v. Nerée: The Albertus University of Königsberg and its professors (= yearbook of the Albertus University of Königsberg / Pr. Volume XXIX). Berlin 1995, pp. 499-508.
- ↑ Kathryn M. Olesko: Physics as a calling - Discipline ans practice in the Königsberg Seminar for Physics. Cornell University Press Ithaca, London 1991, pp. 42-43, 99-127.
- ↑ K. Walter: Bessel as an examiner for seafarers. In: News of the Olbers Society Bremen. No. 130 (1984), pp. 12-16.
- ^ Wilhelm von Humboldt: Ideas for an instruction for the scientific deputation in the section of public education. In: Andreas Flitner and Klaus Giel (eds.): Wilhelm von Humboldt - works in five volumes. Volume IV: Writings on politics and education. 3. Edition. Darmstadt 1982, pp. 201-209 ( dig ).
- ↑ Handbook on the Royal Prussian Court and State for the year 1834 , p. 212.
- ↑ Handbook on the Royal Prussian Court and State for the year 1821 , p. 177.
- ↑ Walter Asmus: Johann Friedrich Herbart - An educational biography. Volume II. Heidelberg 1970, p. 67.
- ^ Jürgen Hamel: Friedrich Wilhelm Bessel . Leipzig 1984, p. 86.
- ↑ FW Bessel: overpopulation. (Article in the Königsberger Hartungschen Zeitung No. 40 of February 17, 1845. In the collected papers, the "Hartungsche Zeitung" was erroneously referred to by the publisher R. Engelmann as the " Königsberger Allgemeine Zeitung ", but it was not founded until 1875. In the foreword to 3rd volume of the treatises, p. VI, the correct name is found. Dig ).
- ↑ Dietmar Fürst: Friedrich Wilhelm Bessel on the importance of astronomical observations and the Prussian education system. In: Contributions to the history of astronomy. Volume 10. Harri Deutsch, Thun / Frankfurt am Main 2010, ISBN 978-3-8171-1863-2 , pp. 218-235.
- ↑ Edith Schlieper: Friedrich Wilhelm Bessel, man and his family. In: FW Bessel: I love you but heaven is closer to me. An autobiography in letters. Minden 1984, p. 124 (letter from Bessel to father Carl Friedrich Bessel of November 26, 1821).
- ↑ From the papers of the minister and burgrave of Marienburg Theodor von Schön. Volume 4: Appendices to Part 2. Berlin 1876, pp. 468-473 ( dig ).
- ↑ From the papers of the minister and burgrave of Marienburg Theodor von Schön. Volume 4: Appendices to Part 2. Berlin 1876, pp. 476-526 ( dig ).
- ↑ Friedrich Paulsen : History of the learned teaching. 3rd ed. Berlin, Leipzig 1921, pp. 551-552, 558-560, 570 ( dig ).
- ↑ Dietmar Fürst: Friedrich Wilhelm Bessel on the importance of astronomical observations and the Prussian education system. In: Contributions to the history of astronomy. Volume 10. Harri Deutsch, Thun / Frankfurt am Main 2010, ISBN 978-3-8171-1863-2 , pp. 218–235, here pp. 232–233 (letters to Heinrich Christian Schumacher from February 1, 1837, 22. April 1837, January 15, 1840).
- ^ Rudolf Borchardt: German Speeches. Munich 1925, pp. 207–226, here p. 225.
- ^ Rudolf Borchardt: German Speeches. Munich 1925, pp. 207–226, here pp. 222, 214.
- ↑ Kurt-R. Biermann: FW Bessel's project of a popular astronomy in his correspondence with Alexander von Humboldt. In: Publications of the Archenhold Observatory. No. 6 (1974), pp. 35-43.
- ^ Jürgen Hamel: Friedrich Wilhelm Bessel . Leipzig 1984, p. 87.
- ^ FW Bessel: About the current standpoint of astronomy. In: Popular lectures on scientific subjects by FW Bessel. Hamburg 1848, p. 5f.
- ^ FW Bessel: Astronomical investigations . 1st volume. Königsberg 1841, p. III ( dig ).
- ^ Jürgen Hamel: Friedrich Wilhelm Bessel . Leipzig 1984, p. 39f.
- ^ FW Bessel: About the current standpoint of astronomy. In: Popular lectures on scientific subjects by F. W. Bessel. Hamburg 1848, p. 432 ( dig ).
- ^ Jürgen Hamel: Friedrich Wilhelm Bessel . Leipzig 1984, p. 88.
- ^ JF Encke: memorial speech on Bessel. Treatises of the Berlin Academy of Sciences for 1846, pp. XXiii – XXIV.
- ↑ General directory of Bessel's writings. In: Rudolf Engelmann (Ed.): Treatises by Friedrich Wilhelm Bessel. 3rd volume. Leipzig 1876, pp. 490–504, here p. 501 ( dig ).
- ^ Adolph Erman (Ed.): Correspondence between W. Olbers and FW Bessel. Leipzig 1852, Volume 2, pp. 429-433 (letter from Bessel to Olbers of October 9, 1838; dig ).
- ↑ On the Parallax of 61 Cygni. (A letter from Prof. Bessel to Sir J. Herschel). In: Monthly Notices of the Royal Astronomical Society IV (17), pp. 152-161 ( dig ).
- ^ FW Bessel: Measurement of the distance of the 61st star in the constellation of the swan. In: Heinrich Christian Schumacher (Ed.): Popular lectures on scientific subjects by FWBessel. Hamburg 1848, pp. 208-268 ( dig ).
- ^ Observations pour déterminer la parallaxe annuelle de la 61e étoile du Cygne. (Extrait d'une Lettre de M. Bessel à M. de Humboldt.) In: Comptes Rendus hebdomadaires des séances de l'Académie des Sciences, 1838, pp. 785-793 ( dig ).
- ^ Rudolf Engelmann (Ed.): Treatises by Friedrich Wilhelm Bessel. 3rd volume. Leipzig 1876. pp. 490–504 ( catalog raisonné ).
- ^ Rudolf Engelmann (Ed.): Reviews by Friedrich Wilhelm Bessel . Leipzig 1878 ( dig ).
- ^ Friedhelm Schwemin: Unknown reviews from Bessel. In: Contributions to the history of astronomy. Volume 12. Akademische Verlagsanstalt, Leipzig 2014, ISBN 978-3-944913-44-5 , pp. 220-22.
- ↑ Dieter B. Herrmann: Bessel's library at the Königsberg observatory. In: The Stars. Volume 61 (1985), pp. 96-103 (with a photo of the observatory ruins from the post-war period).
- ↑ BBAW: Bessel estate overview. Retrieved November 8, 2015 .
- ^ Klaus Klauss: The estate of Friedrich Wilhelm Bessel (1784–1846) in the central archive of the Academy of Sciences of the GDR. In: The Stars. Vol. 62 (1986), pp. 35-39.
- ↑ Marianne Nordsiek: Johann Conrad Thilo, Minden teacher Friedrich Wilhelm Bessel. In: Messages from the Minden History Society . Volume 56 (1984), pp. 132-140.
- ^ M. Wichmann: Contributions to the biography of FW Bessel. In: Journal for popular communications in the field of astronomy. Volume 1 (1860), pp. 133-193.
- ↑ Klemens Adam: Olbers, Thilo, Bessel and the Saturn - message about a previously unknown manuscript. In: News of the Olbers Society Bremen. No. 172 (1996), pp. 16-17.
- ^ FW Bessel: About Olbers. In: Astronomical News. Volume XXII (1844), No. 421, col. 265-270 ( dig ).
- ^ Diedrich Wattenberg: Wilhelm Olbers in correspondence with astronomers of his time (= sources of the history of science. Volume 2). GNT-Verlag, Stuttgart 1994, ISBN 3-928186-19-1 , p. 9.
- ↑ Peter Brosche (Ed.): Astronomy of the Goethe time (= Ostwald's classic of exact sciences , volume 280). Harri Deutsch publishing house, Thun / Frankfurt am Main 1995, p. 22.
- ^ DB Herrmann: Bessel's departure from Lilienthal and his relationship with Schroeter in later times. In: News of the Olbers Society Bremen. No. 67 (1966), pp. 9-12.
- ^ Letters between Gauss and Bessel (= Carl Friedrich Gauss: Works, Supplementary Series Volume 1). Leipzig 1880 (Reprint: Olms, Hildesheim 1975, ISBN 3-487-05551-1 ; dig ).
- ↑ Kurt-R. Biermann: About the relationship between CF Gauß and FW Bessel. In: Communications from the Gauß Society in Göttingen. No. 3 (1966), pp. 7-20.
- ↑ Fundamenta astronomiae (preface). Retrieved June 23, 2016 .
- ^ Johann Adolf Repsold: Friedrich Wilhelm Bessel. In: Astronomical News. Volume 210 (1919), No. 5028, Col. 161-214, here Col. 201-205 ( dig ).
- ↑ Dietmar Fürst: The changing relationship between Friedrich Wilhelm Bessel and Johann Franz Encke - An attempt to explain. In: Wolfgang R. Dick, Dietmar Fürst (ed.): Life courses and heavenly paths (= Acta Historica Astronomiae. Volume 52). Akademische Verlagsanstalt, Leipzig 2014, ISBN 978-3-944913-42-1 , pp. 159–204.
- ↑ Kurt-R. Biermann (Ed.): Correspondence between Alexander von Humboldt and Heinrich Christian Schumacher. Berlin 1979, pp. 79-80 (letter from Humboldt to Schumacher of December 26, 1837).
- ↑ Diedrich Wattenberg: After Bessel's death. A collection of documents. Berlin-Treptow 1976, p. 32 (letter to Eichhorn dated April 11, 1846).
- ^ JF Encke: memorial speech on Bessel. Treatises of the Berlin Academy of Sciences for 1846.
- ^ Hans-Joachim Felber (Ed.): Correspondence between Alexander von Humboldt and Friedrich Wilhelm Bessel (= contributions to Alexander von Humboldt research. Volume 10). Berlin 1994.
- ↑ Kurt-R. Biermann: Alexander von Humboldt (= biographies of outstanding natural scientists, technicians and physicians. Volume 47). 3. Edition. Leipzig 1983, p. 118.
- ↑ Hans-Joachim Felber (Ed.): Correspondence between Alexander von Humboldt and Friedrich Wilhelm Bessel. Berlin 1994, pp. 160-180.
- ↑ Hans-Joachim Felber (Ed.): Correspondence between Alexander von Humboldt and Friedrich Wilhelm Bessel. Berlin 1994, p. 46 (letter from Humboldt to Bessel of November 13, 1828).
- ↑ Alexander von Humboldt Chronology
- ↑ Kurt-R. Biermann (Ed.): Correspondence between Alexander von Humboldt and Heinrich Christian Schumacher. Berlin 1979, pp. 114–115 (letter from Humboldt to Schumacher of July 3, 1844).
- ↑ a b Hans-Joachim Felber (Ed.): Correspondence between Alexander von Humboldt and Friedrich Wilhelm Bessel. Berlin 1994, p. 205 (letter from Bessel to Humboldt of November 1, 1845).
- ^ Ilse Foerst-Crato: The picture of Friedrich Wilhelm IV. In the Mindener Heimatmuseum. In: Mindener Heimatblätter. Volume 36 (1964), pp. 228–232.
- ^ Académie des Sciences: Members
- ^ Royal Society of Edinburgh: Biographies (p. 81)
- ^ Royal Society: Members
- ^ KNAW: Members
- ↑ AAAS: Members (p. 48)
- ^ BBAW: Members
- ↑ BAdW: Members
- ↑ APHS: Members
- ↑ a b Volker Rodekamp (ed.): Friedrich Wilhelm Bessel 1784–1846 - His path to the stars (= texts and materials from the Mindener Museum , issue 2). Minden 1984, p. 49.
- ^ RAS: Gold Medals
- ^ Besselstrasse in Germany. Retrieved May 25, 2016 .
- ↑ Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846 . Basel 1995, pp. 101-102.
- ↑ Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846 . Basel 1995, pp. 268–269 (with photo).
- ^ Memorial stone for Friedrich Wilhelm Bessel in Kaliningrad. (No longer available online.) Archived from the original on September 14, 2017 ; Retrieved November 8, 2015 . Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.
- ↑ Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846 . Basel 1995, p. 274 (with photo).
- ↑ Arno Langkavel: Astronomers rediscovered while traveling. Thoben, Quakenbrück 1995, p. 22.
- ^ Besselei . Retrieved November 8, 2015 .
- ↑ memorial plaque. Retrieved November 8, 2015 .
- ↑ Bessel bust in Minden. Retrieved November 8, 2015 .
- ↑ artou.de. Retrieved November 8, 2015 .
- ^ Wilhelm Beer, Johann Heinrich Mädler: The moon according to its cosmic and individual circumstances or general comparative selenography. Berlin 1837, pp. 231-232 ( dig ).
- ↑ Name of the ring elements of Saturn. Retrieved November 8, 2015 .
- ↑ Edith Schlieper: Friedrich Wilhelm Bessel, man and his family. In: FW Bessel: I love you but heaven is closer to me. An autobiography in letters. Minden 1984, pp. 22-23.
- ↑ Communications of the Astronomical Society No. 62. Hamburg 1984.
- ^ Münzfreunde Minden und Umgebung eV (Ed.): Medals on Minden City History (= series of publications by Münzfreunde Minden, no. 32). Minden 2014, pp. 86-89.
- ^ Friedrich Wilhelm Bessel Mindener Geschichtstaler. Retrieved February 27, 2018 .
- ^ Leopold von Bessel: The portraits of the astronomer Friedrich Wilhelm Bessel. In: Communications of the Association for the History of East and West Prussia. Volume 13 (1939), number 4, pp. 45–52, 56–61; Volume 14 (1939), number 1, pp. 1–12, 30–38.
- ↑ Horst Michling: On the Bessel portrait of Herterich. In: Communications of the Gauss Society. No. 3 (1966), pp. 21-23.
- ^ HW Duerbeck, EH Geyer: The Bessel portrait by Jensen. In: Communications from the Astronomical Society. No. 62. Hamburg 1984, p. 191. (There are still three of Jensen's four versions of the picture: in the Bonn observatory , the Pulkowa observatory and the Ny Carlsberg Glyptotek .)
- ↑ Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846 . Basel 1995, p. 94.
- ↑ Kasimir Ławrynowicz: Friedrich Wilhelm Bessel, 1784–1846 . Basel 1995, pp. 95-96.
- ^ Bessel family (daguerreotype). Retrieved November 8, 2015 .
- ^ EA Poe: Eureka. in: EA Poe - The collected work in ten volumes. Volume 5. Olten / Freiburg 1966, p. 896.
- ^ Arno Schmidt: Massenbach - A historical review. In: Belphegor. Munich, Karlsruhe 1961, here: pp. 364–374.
- ↑ Josef Huerkamp: “An unbelievable case” or Arno Schmidt on Schroeter's trail. In: Jörg Drews , Heinrich Schwier (Ed.): "Lilienthal or the astronomers". Historical materials for a project by Arno Schmidt. edition text + kritik, Munich 1984, pp. 320–338.
- ↑ Daniel Kehlmann: The measurement of the world. Rowohlt, Hamburg 2005, pp. 156-160.
Remarks
- ↑ Bessel's ancestors included the mayor of Bremen Johann Esich and the theologian Johannes Lonicer (Leopold von Bessel: Ahnentafel ... , pp. 5, 14).
- ↑ The archivist Karl Friedrich Leonhardt subjected the family tradition “the Bessel family is a noble one”, which Bessel reproduced in his autobiography and which was adopted by some later biographers, to an examination. He described the alleged ancestral line as "adventurous filiation" and "deliberate forgery". (K. F. Leonhardt: On the genealogy of Hanoverian city families . In: Hannoversche Geschichtsblätter . New series, Volume 4 (1936/37), pp. 184-206; therein: IV. Die Bessel and von Bessel, pp. 194-199.)
- ^ "Franz Willhelm Friderich" is entered as the first name in the baptismal register. Bessel never used the first name “Franz”, but instead used the first name “Friedrich Wilhelm” in all publications. In private he was called "Fritz". (Source: F. W. Bessel: I love you but heaven is closer to me. Minden 1984, foreword).
- ↑ The date of birth is June 21st in the baptismal register. (Source: St.-Marien-Gemeinde Minden: Baptism, marriage and death registers 1766–1800. Baptism register 1784, No. 14) According to Leopold von Bessel: Ahnentafel… , p. 7, the church book is in this case through detailed investigations to be regarded as unreliable. Bessel's father entered July 21, 1784 as the date of birth in his family Bible. Bessel himself always gave July 22nd as his date of birth.
- ↑ At that time the " government " in Prussia was mainly a judicial authority (source: Hans Nordsiek: Das Prussische Fürstentum Minden at the time of Frederick the Great. Minden 1986, pp. 36–38).
- ↑ Bessel described the professors opposing him as "old stick fish" who "harassed" him. (Friedrich Wilhelm Bessel: I love you but heaven is closer to me. An autobiography in letters. Ed. By the city of Minden and Edith Schlieper. Minden 1984, p. 109: letter to Carl Bessel dated July 2, 1810.)
- ↑ This misdiagnosis has since been found widely in the Bessel biographies, including Hamel (1984, p. 83). The autopsy expressly ruled out cancer as the cause of death. The royal personal physician Schönlein had also made a wrong diagnosis. Lawrynowicz (1995, p. 97) gives "malignant gastric ulcers".
- ↑ for comparison: ratio mass of Saturn / mass of the sun according to Bessel (1831, p. 48): 1 / 3497.24; current (2014): 1 / 3498.7.
- ↑ for comparison: ratio of the mass of Jupiter / mass of the sun according to Bouvard (1815): 1 / 1070.5; Airy (1837): 1/1046.77; Bessel (1842): 1 / 1047.879; current (2014): 1 / 1047,394. Bessel and Airy measured about the same time, but Bessel published later.
- ↑ As a basic scientific work, it was published in Latin , as was customary at the time, and the translation was provided by the Königsberg classical philologist Karl Ludwig Struve , director of the Old Town High School . (Adolph Erman (Ed.): Correspondence between Bessel and Gauss. Volume 2, Leipzig 1852, p. 33: Letter from Bessel to Olbers of November 13, 1816; dig .)
- ↑ It was the first scientific project of the Academy of Sciences: Berlin-Brandenburg Academy of Sciences: Friedrich Wilhelm Bessel (short biography). Retrieved June 16, 2014 .
- ↑ Otto Ule first used the "light year" as the unit of distance in 1851. ( What we read in the stars. In: Deutsches Museum: Journal for Literature, Art and Public Life 1. P. 721–738, here P. 728–729.)
- ↑ With the current value of the speed of light, Bessel's parallax value leads to 10.44 light years.
- ↑ Teichmann contradicts this topos of the Bessel reception that the proof of parallax can be taken as proof of the heliocentric system: Even within the geocentric system , parallax and aberration can be explained by additional hypotheses. ( Jürgen Teichmann : Change of the world view (= cultural history of natural sciences and technology, edited by the Deutsches Museum Munich ). 2nd edition. Scientific book society , Darmstadt 1983, p. 115.)
- ↑ John Pond was the first to coined the term personal equation in 1832 . (Christoph Hoffmann: Under observation - natural research in the time of the sensory apparatus. Wallstein Verlag, Göttingen 2006, p. 208.)
- ↑ The term geoid itself was first used by Johann Benedikt Listing in 1872 .
- ↑ A replica is in the German Historical Museum in Berlin.
- ↑ After the appointment as a knight of the Dannebrog order, Bessel's contributions in the Astronomical News from the editor H. Chr. Schumacher were marked with the stereotype "From Professor and Knight Bessel" since 1821.
| personal data | |
|---|---|
| SURNAME | Bessel, Friedrich Wilhelm |
| BRIEF DESCRIPTION | German astronomer, mathematician and geodesist |
| DATE OF BIRTH | July 22, 1784 |
| PLACE OF BIRTH | Minden |
| DATE OF DEATH | March 17, 1846 |
| Place of death | Königsberg (Prussia) |