## Fundamenta astronomiae pro anno MDCCLV deducta ex observationibus viri incomparabilis James Bradley in specula astronomica Grenovicensi per annos 1750-1762 institutis.

Königsberg: Friedrich Nicolovius, 1818.

First edition, rare in such fine condition, of this work which “constitutes a milestone in the history of astronomical observations, for until then positions of stars could not be given with comparable accuracy: through Bessel’s work, Bradley’s observations were made to mark the beginning of modern astrometry” (Walter Fricke in DSB). Bessel used Bradley's data to give a reference system for the positions of stars and planets and also to determine the positions of stars. To reduce the star positions to one fixed date he had to deduce errors in Bradley’s instruments and errors caused by refraction, eliminate the effects of the Earth's motion and its precession, and other effects. “The star catalogue containing the results of Bradley’s observations was completed by Bessel in 1818 after ten years work. The title is *Fundamenta astronomiae *… As a rule, Bradley had made five observations per star in RA [right ascension] and four observations in DEC [declination] … The information which Bessel has included in the *Fundamenta *consists of the name of the stars, the magnitude, RA and DEC to 1/10 of a second or arc for 1755, and the values of Bessel’s annual precession for 1755 and 1800. The clock stars which served for the determination of the equinox and equator by means of observations of the Sun were observed about 50 times. Although Bessel was certainly the only astronomer of his time able to reduce Bradley’s observations, the work must have been extremely exhausting for him. He wrote that an astronomer should never carry out more observations than he can reduce himself. In the case of Bradley’s observations, however, Bessel had recognized their usefulness for providing the best possible coordinate system for the epoch 1755. Second, he recognized the need of accurate first-epoch observations for the determination of proper motions of stars and for the establishment of a reference system for a large interval of epochs. In fact, in the *Fundamenta* he has already given the proper motion for each of the stars for which second-epoch observations were made around 1800 by Piazzi in Palermo, Italy. For the determination of precession from such proper motions, Bessel was awarded a prize by the Berlin Academy of Sciences” (Fricke, pp. 12-13).

James Bradley (1693-1762) succeeded Halley to the post of Astronomer Royal in 1742, a position he held until his death. “The bulk of Bradley’s observations were published after his death in an atmosphere of acrimony. Dispute between his heirs and the British Admiralty over the ownership of his work delayed publication until 1798–1805. The German mathematician Friedrich Bessel analyzed and organized his data, correcting for the small errors in Bradley’s instruments, and then computing star positions” (DSB, under Bradley).

“In 1807 Olbers encouraged [Bessel] to do a reduction of Bradley’s observations of the positions of 3,222 stars, which had been made from 1750 to 1762 at the Royal Greenwich Observatory. This task led to one of his greatest achievements ...

“Bessel recognized that Bradley’s observations gave a system of very accurate star positions for the epoch 1755 and that this could be utilized in two ways. First, a reference system for the measurement of positions of stars and planets was required. Second, the study of star motions necessitated the determination of accurate positions for the earliest possible epoch. Tobias Mayer had determined fundamental star positions from his own observations around the middle of the eighteenth century, but Bradley was never able to reduce his own numerous observations.

“The observations of star positions had to be freed of instrumental errors, insofar as these could be determined from the measurements themselves, and of errors caused by the earth’s atmosphere (refraction). The apparent star positions at the time of a particular observation (observation epoch) had to be reduced to a common point in time (mean epoch) so that they would be freed of the effects of the motion of the earth and of the site of observation. For this a knowledge of the precession the nutation, and the aberration was necessary. Bessel determined the latitude of Greenwich for the mean epoch 1755 and the obliquity of the ecliptic, as well as the constants of precession, nutation, and aberration. To determine precession from proper motions, Bessel used both Bradley’s and Piazzi’s observations ...

“The positions of Bradley’s stars valid for 1755 were published by Bessel as ‘Fundamenta astronomiae pro anno 1755’ (1818). This work also gives the proper motions of the stars, as derived from these observations of Bradley, of Piazzi, and of Bessel himself. It constitutes a milestone in the history of astronomical observations, for until then positions of stars could not be given with comparable accuracy: through Bessel’s work, Bradley’s observations were made to mark the beginning of modern astrometry. During this investigation Bessel became an admirer of the art of observation as practiced by Bradley; and because Bradley could not evaluate his own observations, Bessel followed and also taught the principle that immediately after an observation, the reduction had to be done by the observer himself. Further, he realized that the accurate determination of the motions of the planets and the stars required continuous observations of their positions until such motions could be used to predict ‘the positions of the stars … for all times with sufficient accuracy’” (DSB).

Bessel (1784-1846) left school at age 14 to become an import-export apprentice in Bremen where his accounting skills were quickly appreciated. Interest in the countries his firm dealt with led Bessel to spend his evenings studying geography, Spanish and English. His interests turned towards navigation and he considered the problem of finding the position of a ship at sea. This in turn led him to study astronomy and mathematics and he began to make observations to determine longitude. In 1804, Bessel published a paper on Halley's comet. From that time on, he concentrated on astronomy, celestial mechanics and mathematics. In 1806, he accepted the post of assistant at a private observatory near Bremen. Bessel’s brilliant work was quickly recognized. He was appointed director and professor of astronomy at a new observatory in Königsberg. It was not possible for Bessel to receive a professorship without first being granted the title of doctor, so a doctorate was awarded by the University of Göttingen on the recommendation of Gauss, who had met Bessel in 1807 and recognized his talents. Bessel’s work had now become known internationally, and he was honored with the award of the Lalande Prize from the Institut de France for his tables of refraction based on Bradley’s observations. In 1812, he was elected to the Berlin Academy, and won a prize from the Berlin Academy in 1815. In 1825 he was elected a Fellow of the Royal Society. Bessel remained in Königsberg for the rest of his life, pursuing his research and teaching without interruption. He undertook his monumental task of determining the positions and proper motions of over 50,000 stars. From periodic variations in the proper motions of Sirius and Procyon, Bessel deduced that they had companion stars in orbit which had not been observed. He announced that Sirius had a companion in 1841, thus being the first to predict the existence of ‘dark stars’. Bessel used parallax to determine the distance to 61 Cygni, announcing his result in 1838 – this was the first determination of the distance to one of the fixed stars. The Royal Astronomical Society awarded him their gold medal to mark this achievement. In 1817, Bessel also worked out a method of mathematical analysis involving what is now known as the Bessel functions. The interest in these functions arose in the treatment of the problem of the perturbation in the planetary system. This special class of functions that have become an indispensable tool in applied mathematics, physics and engineering. He also made contributions beyond astronomy and mathematics. His contributions to geodesy include a correction in 1826 to the seconds pendulum, the length of which is precisely calculated so that it requires exactly one second for a swing. In 1841 he deduced a value of 1/299 for the ellipticity of the Earth, the amount of elliptical distortion by which the Earth's shape departs from a perfect sphere.

Norman 226; Honeyman 311; Houzeau & Lancaster 10117. Fricke, ‘Friedrich Wilhelm Bessel (1784-1846). In Honor of the 200th Anniversary of Bessel's Birth,’ Astrometric Binaries, Proceedings of the Conference in Bamberg, Germany, 13-15 June 1984 (Kopal & Rahe, eds.), *Astrophysics and Space Science* 110, pp. 11-19.

Folio (330 x190 mm), pp. [xii], [1], 3-325, [1, errata]. Contemporary red moiré boards with gilt-lettered spine.

Item #2660

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Price:
$2,400.00
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