**Wilhelm Bessel** determined the positions and proper motions of stars. He also used a method of mathematical analysis involving what is now known as the Bessel function.

- Bessel attended the Gymnasium in Minden for four years but he did not appear to be very talented, finding Latin difficult.
- The fact that he later became proficient in Latin, teaching himself the language, probably suggests that the Gymnasium failed to inspire Bessel.
- At first Bessel received no salary from the firm but, as his accounting skills became appreciated by the firm, he received a small salary.
- Interest in the countries his firm dealt with led Bessel to spend his evenings studying geography, Spanish and English.
- In 1804 Bessel wrote a paper on Halley's comet, calculating the orbit using data from observations made by Harriot in 1607.
- He sent his results to Heinrich Olbers, the leading comet expert of his time, who recognised at once the quality of Bessel's work and Olbers gave Bessel the task of making further observations to carry his work further.
- From that time on Bessel concentrated on astronomy, celestial mechanics and mathematics.
- Olbers suggested to Bessel, who was still an apprentice to the import-export firm, that he should become a professional astronomer.
- It was only after some considerable thought that Bessel left the affluence that was guaranteed in his commercial job choosing instead the near poverty of the Observatory post.
- Bessel's brilliant work was quickly recognised and both Leipzig and Greifswald offered him posts.
- It was not possible for Bessel to receive a professorship without first being granted the title of doctor.
- A doctorate was awarded by the University of Göttingen on the recommendation of Gauss, who had met Bessel in Bremen in 1807 and recognised his talents.
- Although the Observatory at Königsberg was still under construction, Bessel took up his new post on 10 May 1810.
- Bessel's work had now become known internationally and he was honoured with the award of the Lalande Prize from the Institut de France for his tables of refraction based on Bradley's observations.
- The Königsberg Observatory was completed in 1813 and Bessel began observing there.
- It was in Königsberg that Bessel undertook his monumental task of determining the positions and proper motions of over 50000 stars which led to the discovery in 1838 of the parallax of 61 Cygni.
- From 1840 on, Bessel's health deteriorated.
- Let us examine Bessel's work in more detail.
- By eliminating all sources of error - optical, mechanical and meteorological - Bessel was able to obtain astronomical results of astonishing delicacy from which a great deal of new data could be extracted.
- Bessel's work in determining the constants of precession, nutation and aberration won him further honours, such as a prize from the Berlin Academy in 1815.
- Bessel published Bradley's stellar positions in 1818 in a work which gives the proper motion of stars.
- In 1830 Bessel published the mean and apparent positions of 38 stars over the 100 year period 1750-1850.
- From periodic variations in the proper motions of Sirius and Procyon, two of Maskelyne's 36 fundamental stars, Bessel deduced that they had companion stars in orbit which had not been observed.
- Bessel used parallax to determine the distance to 61 Cygni announcing his result in 1838.
- Bessel, using a Fraunhofer heliometer to make the measurements, announced his value of 0.314" which given the diameter of the Earth's orbit, gave a distance of about 10 light years.
- Bessel also worked out a method of mathematical analysis involving what is now known as the Bessel function.
- Bessel functions appear as coefficients in the series expansion of the indirect perturbation of a planet, that is the motion caused by the motion of the Sun caused by the perturbing body.
- In 1824 he developed Bessel functions more fully in a study of planetary perturbations and published a treatise on them in Berlin.
- It was probably Lagrange's work on elliptical orbits that first suggested to Bessel to work on the Bessel functions.
- Bessel also had a very significant impact on university teaching despite the fact that he never had a university education.

Born 22 July 1784, Minden, Westphalia (now Germany). Died 17 March 1846, Königsberg, Prussia (now Kaliningrad, Russia).

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Astronomy, Origin Germany, Physics

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive