Carl Friedrich Gauss: Werke, Band VI (1874)
Original-language LaTeX transcription — source leaves 2–669.

This 919-page reader includes the historical titles and portrait; the works from De elementis ellipticis Palladis through Tafel für die Sonnen-Coordinaten and Neue Aussicht zur Erweiterung des Gebiets der Himmelskunde; the Refractionstafeln; the letters to Schumacher dated 1 April 1843 and 23 November 1847 as printed through source leaf 201; the division title Beobachtungen und Rechnungen; the Ceres reports of December 1801 and February, March, April, May, June, October and November 1802; the Pallas reports of June, July, August, October, November and December 1802; the letters to Bode of 10 September 1802 and 3 March 1803; the Mercury transit report of November 1802; and the complete Tafeln für die Störungen der Ceres, including the letter dated 26 December 1802, its four Anmerkungen, and all five tables for longitude, radius vector and latitude through source leaf 248; the Pallas reports of April/May, June and July 1803; the Ceres report of September/October 1803; Ceres und Pallas of March 1804; Neuer Comet of May 1804; and the two letters to Bode dated 30 September and 12 November 1804, including their complete observational tables and orbital elements; and Über einen neuen vom Inspector Harding in Lilienthal entdeckten höchst merkwürdigen Wandel-Stern, with its quoted letters, orbital elements, observation comparisons, stellar positions and twenty-row ephemeris; and Einige Nachrichten über den neuen Planeten, including its account of Harding’s discovery, the observations of Juno, its orbital dimensions and naming, and the historical description of its ephemeris. It also contains the Juno report of November 1804, with its comparison star, second orbital elements, discussion of the planetary orbits and seventeen observation comparisons; and Beobachtete Sternbedeckung, with both observations of 16 October 1804. The Juno report of December 1804 is also included, with its third orbital elements, thirty-one observation and comparison rows, four brightness values and complete discussion of the planet’s visibility. The Juno report of February 1805 and the Ceres report of March 1805 are included with their orbital elements, observations, comparison star, arguments and signatures. The Pallas report of April 1805 is included with its orbital elements, historical argument and signature von Zach. The Juno report of May 1805 contains the Palermo observations, their comparison with the fourth orbital elements, the fifth elements and the complete historical discussion. The two reports on the comets of 1805 contain the observations, orbital elements, quoted correspondence, coordinate formulas, distances and brightness values, with both signatures von Zach. The letter to Bode of 14 March 1806 contains the observations of Ceres, Pallas and Juno, the revised elements of the second comet of 1805, nineteen comparisons with observations, and the complete historical discussion of the comets and Gauss’s method for determining planetary orbits. The Pallas and Juno report of March 1806 contains the account of their renewed observation, the differences from the predicted positions, Gauss’s description of the observing instruments and difficulties, and the historical announcement of his work on planetary orbits. The letter to von Zach of 20 May 1806 includes the stellar identifications, parabolic and elliptical orbital elements of the second comet of 1805, both twenty-one-row comparisons with observations, the elements of the comet of 1772, and the complete discussion of orbital uncertainty and possible perturbations. The two letters to von Zach of 8 July 1806 contain the comparison of Bouvard’s observations with the parabolic and elliptical comet orbits, the discussion of parallax, aberration and methods for determining orbits, the ninth elements of Pallas with six epochs, the opposition predictions, the comparison of three observations of Juno and the historical description of the Pallas ephemeris. The letter to Bode of 30 July 1806 and the letters to von Zach of 25 August 1806 and 3 January 1807 contain the epochs and orbital elements of Pallas, Juno and Ceres, the discussion of their predicted appearances and brightness, the description of Gauss’s work on planetary orbits, and three historical notes. The letter to von Zach of 10 March 1807 contains the Pallas observations, comparison stars and discussion of the Ceres opposition. The Vesta notice preserves Olbers’s account of Gauss’s choice of the planet’s name and altar-and-flame symbol. The letter to Bode of 8 May 1807 includes the two observations, discussion of orbital uncertainty and full fifty-row comparison with observations. The letter to Bode of 23 August 1807 contains the third orbital elements of Vesta and the historical description of its ephemeris. The Vesta report of June 1807 includes the quoted correspondence, first and second orbital elements, twenty-eight observation and comparison rows, the discussion of earlier stellar catalogues, and the historical note on the Latin publication of Gauss’s work on planetary orbits. The Vesta report of July 1807 contains the discussion of the new planet’s observation and orbital calculation, the complete comparison of eighty-four observations with the second elements, and the historical comments on observational corrections and meridian observations. The Vesta report of September 1807 includes the third orbital elements, twenty-two Paris comparisons, and the historical discussion of observation, star catalogues and ephemerides. The December 1807 comet report contains the five orbital values and the quoted correspondence. The Juno notice of 23 January 1808 gives the opposition result and the discussion of the seventh elements and the next ephemeris. The two letters to Bode of 24 January and 23 July 1808 contain comet observations and orbital elements, the tenth Pallas and seventh Juno elements, observations of Juno, Vesta and Pallas, satellite entries and exits, stellar occultations, and correspondence about astronomical instruments and publications. The letter to von Lindenau of 25 January 1808 includes the Milan observations, the tenth Pallas elements, the comparison of eight Juno observations and the discussion of ephemerides and numerical tables. Comet von 1807, dated 25 February 1808, contains seven observations, the comparison star and the complete discussion of the orbit and visibility. Ceres Elemente XII, dated 10 March 1808, includes the opposition results, the complete epoch and orbital-element tables, the comparison of oppositions and Schering’s historical remark. Comet von 1807, dated 2 April 1808, includes the eight Lilienthal observations, the Bremen observation, both sets of orbital elements and the complete historical discussion. The letter to von Lindenau of 27 June 1808 includes the Vesta orbital elements, the Juno and Vesta observations, the lunar occultation and Jupiter-satellite observations. Vesta. Juno. Pallas. Ceres., dated 4 July 1808, includes the complete planetary report, orbital elements, comparison positions and historical discussion. The letters to von Lindenau of 6 and 30 August 1808 and Juno Elemente VIII of 25 August 1808 contain the observations of Pallas and Juno, the opposition results, seven epochs and the eighth orbital elements of Juno, correspondence about astronomical instruments, and the complete historical remarks. Vesta. Ceres. Comet., dated 10 November 1808, contains the Berlin, Petersburg and Göttingen observations and their comparison with the orbital elements. Vesta, dated 8 April 1809, contains the Paris and Göttingen observations, the opposition result, five epochs, the fourth orbital elements, and the complete discussion of the planet’s relative brightness. The letter to von Lindenau of 20 May 1809 contains the discussion of the planetary perturbations and ephemerides, the remarks on determining the polar elevation, and the complete concluding discussion. Ceres, dated 3 June 1809, contains the observation, opposition result, nine epochs and thirteenth orbital elements, six comparisons with observed oppositions, and the complete discussion of perturbations and ephemerides. The letter to von Lindenau of 14 August 1809 contains both Pallas observations and the accounts of finding Ceres and Vesta again. Pallas. Ceres. Vesta., dated 26 August 1809, contains the complete report and historical references. The letter to von Lindenau of 23 February 1810 contains six Vesta observations, the seventeen timings of the occultation of Jupiter and its satellites, and the complete historical discussion and list of errata. Pallas, dated 24 February 1810, contains the discussion of the 1808 and 1809 oppositions, eleven Paris observations, both opposition results and the concluding historical reference. The excerpt dated 17 August 1810 contains the account of the observatory building and the Münden journey, chronometer and geographical observations. The letter to Bode of 2 September 1810 contains the discussion of the Pallas ephemeris and perturbations, the observatory and Harding’s visit to Paris, and the concluding acknowledgement. Neue Pallaselemente, dated October 1810, contains the seven orbital values and the historical description of the ephemeris. The Pallas report of December 1810 contains the account of the perturbations, the six opposition comparisons, seven orbital values, three predicted-position pairs, seven interpolation rows, the subsequent observation and comparison star, and the concluding quotation from Gauss. The Pallas report of 14 January 1811 and the letter to von Lindenau of the same date contain the perturbation argument, nine ephemeris corrections, six opposition comparisons, the December and January observations, and both sets of seven orbital elements. The Juno report of June 1811 contains the four observations, opposition result, seven orbital elements and discussion of perturbations. The letter to von Lindenau of 3 August 1811 contains the comet elements, six predicted positions, nine brightness values, the historical handwritten remark and the concluding discussion of Pallas. Pallas. Comet., dated 17 August 1811, contains the eighteen observations from Paris, Berlin and Hamburg, the seven opposition comparisons, Pallas orbital elements and opposition predictions, the comet elements, five predicted-position and brightness rows, and the complete discussion of its visibility. The Juno report of August 1811 contains the four observations, opposition result, seven orbital elements and complete discussion of perturbations and the ephemeris. Pallas, from the Astronomisches Jahrbuch for 1814, contains the letters of 10 February and 29 August 1811: the ten ephemeris rows, six Pallas observations, five Vesta observations, opposition result, historical discussion of corrections, all fifteen Ceres perturbation terms and the concluding comet notice. The Comet letter of 10 September 1811 contains the observations, orbital elements, twelve-row ephemeris, lunar-eclipse and occultation account, and the complete supplement to Articles 90 and 100 of Theoria motus corporum coelestium, including its auxiliary quantities and series. The September 1811 Comet report contains the letters of 8 and 16 September, their observations and orbital elements, the fifteen-row ephemeris, seven observation comparisons and historical footnote. The Comet report of 21 September 1811 contains the discovery and observation account, three observations, orbital elements, eleven predicted positions with distances and brightness values, and the discussion of the comet’s tail. The October 1811 Comet report contains the comparison of sixty-four observations, the letter of 14 October, the parabolic elements, three coordinate formulas and logarithmic constants, fifteen further comparisons and the discussion of Olbers’s hypothesis about the comet’s tail. The November 1811 Comet report contains the argument about the comet of 1301, an observation, the Bremer and Seeberger comparisons and the Flaugergues observations. The report of 19 December 1811 contains the examination of the orbit, parabolic elements, the discovery of the new comet, the Marseille observations, comparison-star coordinates and two observed positions. The December 1811 report contains three observations, preliminary elements, brightness values, ten comparisons and a seven-row ephemeris. The January 1812 Comet report from Monatliche Correspondenz contains the historical comparison with the Göttingen notice, three conjunction times and the complete concluding request. The Comet report of 25 January 1812 contains five observations, the orbital elements, three coordinate relations and logarithmic constants, nineteen comparisons with observations and the concluding discussion of visibility. The Comet report dated 1 March 1812 contains the observation of 2 February, twenty-one occultation observations and the discussion of observing instruments. Beobachtung of 7 March 1812 contains the account of nine stellar occultations, its twenty observation rows and both descriptions of the instruments used. The Pallas report dated 15 April 1812 contains the observation of 9 April and the complete discussion of perturbations, the coming opposition and the occultation of Alpha Tauri. The Pallas report of 25 April 1812 contains the observations and perturbation discussion, the printed cipher, Bessel’s account of double stars and their motion, and the thirteen-row comet ephemeris. The letter to Bode of 5 May 1812 contains the Pallas observations and differences, comet observations and elements, six comparison rows, twenty-five occultation observations, the Cronach geographical discussion and the concluding correspondence about the observatory and Gerling. The Pallas reports of 4 and 8 August 1812 contain the Göttingen, Bremen and Paris observations, comparisons with the orbital elements, both opposition results, the two sets of seven corrections, comparisons of eight oppositions and the predictions for the following year. Their printed differences and historical discussion of corrections are retained. The letter to Bode of 22 August 1812 and the Juno report of 9 September 1812 contain observations of Pallas and Juno, orbital corrections and elements, opposition results, and the discussion and table concerning the distances between the orbits of Ceres and Pallas. Their historical wording and differing numerical and calendar readings are retained. The Vesta report of 24 December 1812 contains the Göttingen, Seeberg and Marseille observations and comparisons, orbital elements and brightness values, and the concluding account of Nicolai’s work on the second comet of 1811. The Comet report of April 1813 contains the five Göttingen observations, Harding’s meridian observation, Enke’s and Gauss’s orbital elements, and the concluding discussion of their further refinement. Instrumente, dated 10 May 1813, contains the complete descriptions of both astronomical instruments, the seven latitude determinations, their mean and discussion of uncertainty, and the historical note describing the omitted price list. The Comet report of July 1813 contains the correspondence of 5 and 12 July, Olbers’s seven observations, Enke’s orbital elements and the direction of motion. The Pallas reports of 31 August and 4 November 1813 contain the Göttingen, Paris and Seeberg observations, the comparisons with predicted positions, the ninth observed opposition and the complete concluding discussions. The Juno correspondence of 8, 9 and 16 December 1813 and the Juno notice of 23 December contain the observations, comparison stars, both opposition results, orbital elements, the Pallas corrections and ten opposition comparisons, the historical remark signed Schering, and the complete discussion of perturbations. The Comet report of 31 January 1814 contains the observations from Neu-Tscherkask, comparison stars, reduced comet positions, differences from the elliptic elements, and Bessel’s discussion. The Juno notice of the same date contains three observations and the account of the new Königsberg observatory. The Pallas letter of 29 May 1814 contains the Juno observations and elements, both opposition results, the perturbation discussion and the description of the heliometer. The Vesta report of 13 August 1814 contains the Göttingen, Seeberg and Königsberg observations, their nineteen comparisons, the opposition result and the new orbital elements. The Pallas report of 12 December 1814 contains the prediction and observation of its tenth opposition, the Göttingen, Seeberg, Mannheim and Königsberg observations, their twenty-two comparisons, the ten-opposition comparison table and the complete discussion of the theory. The Comet reports of 20 March and 8 April 1815 contain the discovery account, observations and preliminary orbital elements. The collected Pallas correspondence dated 1 February and 24 April 1815 includes the opposition predictions and observations, brightness comparisons, winter-solstice observations and instrumental discussion, comet observations and elements, and the account of the heliometer. The Comet report of 3 July 1815 contains the two Göttingen observations and fifteen Padua observations, the parabolic and elliptical orbital elements, a seven-row ephemeris, and the complete discussion of the orbit, brightness and period. The letter to Bode of 9 August 1815 contains eleven comet observations, the parabolic and elliptical orbital elements, three Juno observations, and the complete discussion of the orbit and astronomical instruments. The Comet report of 18 September 1815 contains twelve comet observations, the orbital elements calculated by Bessel and Nicolai, their comparison with the observations, three Juno observations and their comparison, the opposition position and new Juno elements, and the complete accompanying discussion. The letter to Bode of 10 August 1816 contains the Pallas opposition prediction and brightness values, two Juno observations and the opposition results, seven Juno orbital elements, the next opposition and brightness predictions, and the complete discussion of variable stars with their positions and annual changes. The letter of 18 July 1817 contains the full discussion of the instruments, polar-height differences and the centre of the Sun; the polar-star observations and their reductions; the example of observations away from culmination with its calculations and historical footnote; and the fifteen solar observations, their reductions, the probability and refraction discussion, and the historical handwritten annotations. The collected letters to Bode of 17 March and 15 August 1817 contain the discussion of the Pallas ephemeris, the eight observed phases of the lunar eclipse, the account of the new observatory and its instruments, the polar-star and solar observations with their means, and the complete discussion of the differing latitude determinations and astronomical journeys. The stellar-occultation report submitted on 8 March 1818 contains all eleven recorded times, including the paired observations by Gauss and Harding. The two Comet reports of March and April 1818 contain the orbital elements, ten-row ephemeris, comparison-star observations, historical handwritten star observations, and the complete discussion of the orbit, visibility and brightness. Borda’s Kreis contains the complete account of aligning the line of sight with the circle, the definitions of the three axes and their errors, the geometric and trigonometric formulas, the observational procedures for determining and correcting the errors, the historical footnote, and the methods for horizontal and vertical adjustment. Instrumente contains the description of the new observatory and Repsold’s meridian circle, the account of its construction and adjustment, nineteen polar-star determinations with their weights and probable errors, ten observations of Uranus and their comparison with the tables, the opposition results, and the twenty-three entries in Shelton’s clock register with the full concluding discussion. The letter to Bode dated 7 September 1818 contains the comparison of the Pallas opposition calculations, the account of the improved meridian circle, both formulas for observational weights, twenty polar-star determinations, ten Uranus observations, five Saturn observations, two Pallas observations, the discussion of the observing threads, and the Uranus comparisons and opposition results. The Comet report of 18 February 1819 contains the observations of both comets discovered in November 1818, the Mannheim, Göttingen, Seeberg and Königsberg tables, the parabolic and elliptical orbital elements, ten comparisons with observations, the historical note about Seeberg time, and the complete discussion of orbital uncertainty, visibility and possible identity with the first comet of 1805. The Comet report of 24 May 1819 contains the complete discussion of the comet’s identity, orbital period and perturbations, both sets of orbital elements, the twelve-row ephemeris, two additional positions, and the concluding appeal for further observations. Instrumente, dated 18 October 1819, contains the complete description of Reichenbach’s transit telescope and its adjustment, the account of stellar visibility and the lifting apparatus, eighteen Saturn observations, twelve Vesta observations, thirteen observations of 85 Pegasi with their mean, and the discussion of that star’s proper motion. Instrumente from the Astronomisches Jahrbuch for 1822 contains the account of the 1819 comet, nine observations, parabolic orbital elements, nine local and twelve external comparisons, the full account of the transit telescope and its adjustment, six Jupiter observations, the discussion of instrumental flexure and absolute zenith distances, ten polar-star observations with their weights and mean, the historical footnote, and the concluding description of the reversing apparatus. The letter to Bode of 21 March 1820 contains eighteen Saturn observations, twelve Vesta observations, six Pallas observations, six Mars observations, and the concluding remarks on Ceres, the reduction tables and the Reichenbach meridian circle. Meridiankreis, dated 5 June 1820, contains the description of the meridian circle, its construction and adjustment, twenty-three polar-star results with their mean, the discussion of gravity, instrumental flexure and the artificial horizon, four observed culminations and two derived zenith distances, nine Mars observations and nine comparisons with the tables. The letter to Bode of 3 September 1820 contains the discussion of the Pallas ephemeris, the meridian-circle observations and their reduction, thirty-two solar declinations, twenty stellar zenith distances with collimation errors and their mean, and the concluding comparison. Instrumente, dated 20 November 1820, describes the gifts of nautical charts, a clock and a reversed pendulum, including the pendulum’s construction and sensitivity. Comet, dated 10 February 1821, contains the account of discovery and observation, the observed position and the description of its appearance. Heller Fleck im Mond, dated 22 March 1821, contains Olbers’s observations, the account of Kater’s observation, and the complete discussion of reflection, lunar libration, crystalline surfaces and the later observation. Comet, dated 17 May 1821, contains eight observations, five parabolic orbital elements, eight comparisons with the observations, twelve brightness values, and the complete discussion of visibility and weather. The letter to Bode of 26 December 1821 contains the account of the triangulation and heliotrope, the discussion of the Pallas ephemeris, eight comet observations, five orbital elements, and eighty-three comparisons from twelve observatories. The two Mondsbeobachtungen reports of February and April 1822 contain the introductions, twenty-three lunar and stellar entries with their observed differences and thread counts, the Copenhagen observations, and both Schumacher signatures. Comet, dated 15 February 1823, contains the account of Rümker’s observations of Encke’s comet in Paramatta, sixteen observations, the discussion of their reduction, the latitude, both occultation times and both longitude determinations. Nicolai’s Mondsterne of February 1823 treats the meridian difference obtained from corresponding lunar culminations, the correction from a lunar limb to the centre, hourly motion and interpolation, weighting observations made with unequal numbers of threads, and the probable error. The report includes its concluding discussion of the odd-power series and the indirect method, followed by Nicolai’s signature. Fadenintervalle of November 1823 describes the measurement of thread intervals with a second telescope and a theodolite, its optical basis, experimental conditions, fourteen measurements and three polar-star transits, the comparison of their errors, and the determination of telescope magnification. Sternbedeckung of February 1824 gives four observations of the Pleiades occultation of 29 August 1820. The letter to Bode of 21 April 1824 contains nine comet observations, five orbital elements, thirty-two comparisons, and a remark on an observation from Altona. The Comet report of June 1824 contains nine meridian observations and an account of their observing conditions and reductions. The letter to Bode of 5 August 1825 contains fourteen Pallas and seven Ceres observations with a discussion of the planets’ positions and the Pallas ephemeris. The Comet report of 10 April 1826 presents five sets of orbital elements and discusses the possible identity of the comets observed in 1772, 1805 and 1826, together with the limits of the available observations. The report on Hardy’s pendulum clock of 26 June 1826 describes its mercury compensation and gives twenty-one clock readings with twenty daily rates. The letter to Bode of 10 July 1826 contains eight observations each of Pallas and Ceres, with the accompanying accounts of their observing conditions. The article on chronometric longitude determination of November 1826 presents its method of least squares, relative weights and accuracy estimates, nineteen comparison observations for five chronometers, and calculations for Greenwich, Helgoland, Altona and Bremen. The Comet report of September 1827 contains three observations, five orbital elements and an account of their agreement with the middle observation. The Pallas report of October 1827 gives four observations and their observing conditions. The notice on the greatest solar altitude explains a choice of hour-angle origin for reducing observations near meridian passage. Its referenced table is absent from the collected source passage. The letter to Schumacher of 11 October 1827 gives eight solar observations with their corrections and five Ceres observations. The Ceres report of 1829 gives eight observations and describes the weather that prevented observation of opposition. The letter of 20 July 1830 contains nine Ceres observations, seven Pallas observations, and an observation of the occultation of Aldebaran. The letter of 12 May 1832 reports the transit and culmination of Mercury. The Pallas report of 1834 contains three observations, and the report of 1838 gives two timings for the occultation of chi Leonis. The eclipse notice of 1839 gives the observed beginning on 15 March 1838, and the occultation notice of 1841 gives the timings of Gauss and Goldschmidt. Two bracketed historical notices concern comet observations and elliptic elements. The letter of 17 January 1844 contains comet observations, discussion of their uncertainty, and a chronometer argument; the report of 17 February 1844 contains two further observations and a star comparison. The observation and element lists referred to by the two notices, the ephemeris mentioned in the letter, and the later comparison mentioned at the end of the report are absent from these collected passages. The report of the lunar eclipse of 31 May 1844 contains 34 entry rows and 39 exit rows, with the observations of Gauss and Goldschmidt, followed by an account of the colours seen during totality and the signature of Gauss. The comet report published on 1 August 1844 contains the two observations of 23 July and their comparison counts. The notice of 17 August records Goldschmidt’s calculation of elements without reproducing them. The letters of 8 and 10 August contain four observations, their comparisons with the parabolic elements, and accounts of the weather and comparison stars. The letter of 18 August 1844 contains four comet observations and the discussion of comparison stars, thread intervals and clock reductions. The letters of 1, 3, 6 and 8 September contain comet observations, six catalogue comparisons, and the discussion of stellar motion, refraction and observing conditions. The letters of 15 October and 11 November 1844 contain three comet observations, two comparison-star positions, six orbital elements and three comparisons with signed residuals. The ephemeris mentioned at their close is absent from the collected passage. The comet report published on 25 January 1845 contains five comet observations and five comparison-star positions, with the observing account and the remark on Harding’s chart. The elements and improvement attributed to Rümker and Sievers are mentioned without a reproduced list. The report on Colla’s comet contains the Göttingen observation of 12 June 1845. The first observations of Le Verrier’s planet include three meridian positions, followed by the letter of 22 October 1846 with a fourth observation and its concluding statement on a circular orbit. The letter of 31 October 1846 describes determination of the nadir point, illumination of the observing threads, and the removal of an ocular lens. Its optical diagram includes the two lenses, mirror, threads and lamp. The Neptune report of 15 August 1847 contains three meridian observations. The Iris report dated 7 September 1847 contains the account of discovery and identification, five observations, seven orbital elements, and the discussion of the orbit and expected brightness. The reports published on 16 September and 14 October 1847 contain six Iris observations and one Neptune observation, with the accounts of clouds, faint light and comparison stars. The Gould elements mentioned in the latter report are not reproduced in the collected passage. The letters to Schumacher of 11 and 21 October 1847, with the intervening report, contain nine Iris positions, the solar-eclipse and spot-entry timings, and the discussion of nadir corrections, comparison stars and observing conditions. The Flora report and letters of January 1848 contain five observations, four signed comparisons with the calculated positions, and the accounts of brightness, illumination and observing conditions. The letters of 22 May and 4 June 1848 concerning the planet discovered by Graham contain three observations, seven orbital elements, and the accounts of observing conditions, comparison and the removal of the instrument. The separate comparison sheet mentioned in the latter letter is not reproduced in the collected passage. The letter of 19 August 1848 gives an observed and a mean position of the star associated with Hind; the collected comparison ends with three omission dashes. The Parthenope report contains two observations and an account of observing conditions; the elements named in its heading are not reproduced in the passage. The Victoria letter gives three observations and describes the limits of their accuracy. The solar-eclipse report of 28 July 1851 records six timings by Gauss, Westphal and Klinkerfues. The Psyche article discusses determination from four positions and gives eight orbital elements; its historical notice states that the accompanying comparison is not printed. A closing note by Schering lists five later letters from 1853–1854 without reproducing their observations. The section Beurtheilungen und Anzeigen nicht eigner Schriften opens with the complete 1805 review of Rohde’s method for determining planetary masses, including its three objections and the numerical example concerning Mars. The collected excerpt dated 18 May 1806 contains Gauss’s clarification concerning Rohde’s formula. The letters from Lindenau of 17 February 1806 and from Zach of 6 April 1807 discuss the review and its publication. The complete review dated 10 March 1807 discusses Güssmann’s criticism of Olbers’s method for determining cometary orbits, including the geometrical construction, projection formulas, observational uncertainty, and a historical bibliographical note. The complete review of Zach’s Tabulae speciales, dated 2 January 1808, discusses precession, aberration, nutation, stellar catalogues, and the numerical comparisons between the two volumes. The complete review of Connoissance des tems for 1808 and 1809, dated 7 April 1808, discusses astronomical observations, instruments, planetary discoveries, geographical determinations, and the purposes of astronomical research. The complete review of Cagnoli’s catalogue of 501 stars, dated 14 May 1808, discusses its observational basis, instruments, stellar positions, and aberration and nutation tables. The complete review of Pasquich’s proposals for the observatory at Ofen, dated 28 May 1808, describes its instruments, their manufacture and delivery, and plans for a new observatory. The complete report on the Seeberg observatory, dated 2 July 1808, contains six solar and seven lunar observations, their mean differences from the tables, planetary results, and discussions of parallax, refraction, and restoration of the observatory. The review of the third edition of Laplace’s Exposition du système du monde, dated 23 July 1808, discusses all five books and contains five tables of planetary elements. The review of Bode’s Astronomisches Jahrbuch for 1810, dated 26 September 1808, discusses the ephemeris and its collected articles. The review dated 13 October 1808 discusses Picot’s account of comets and the new planets and Sigorgne’s argument about the formation of the Earth. The review dated 5 November 1808 discusses Bouvard’s tables of Jupiter and Saturn, their observational comparisons, and two correction formulas. The notice dated 3 December 1808 describes Humboldt’s geographical observations and Oltmans’s calculations. The review dated 17 April 1809 describes Harding’s celestial atlas, its stellar observations and catalogues, its format and coordinate grid, and the contents of its first four sheets. The review dated 10 June 1809 discusses Humboldt and Bonpland’s Voyage, its geographical observations, instruments, observing conditions and atmospheric refraction. The review dated 17 June 1809 discusses Connoissance des tems for 1810, its astronomical observations and articles, meridian measurements and tables. The report dated 17 July 1809 discusses Lindenau’s investigations of the solar diameter, with annual and monthly solar-radius tables, the ellipsoidal model and the comparison of horizontal and vertical measurements. Its concluding notice discusses Wisniewski’s lunar-occultation observations. The review of Dentrecasteaux’s Voyage, edited by Rossel, discusses nautical instruments, latitude and longitude observations, lunar parallax and magnetic measurements at six locations. The review of Regner’s Supplementum discusses solar parallax, absolute and relative lunar motion, and the interpretation of experiments with falling bodies, pendulums and levers. The report dated 16 June 1810 discusses Lindenau’s measurements of the solar diameter, with monthly and annual tables, comparisons between observing periods, and an account of irradiation and observing methods. The review dated 24 September 1810 discusses Connaissance des tems for 1811, including Paris observations, the obliquity of the ecliptic, Saturn’s ring, methods of determining latitude and time, and astronomical and meteorological notices. The review dated 10 November 1810 examines Knitlmayer’s proposed relations between planetary and satellite distances, masses and densities, including two formulas and a critical discussion of their use. The review dated 16 February 1811 discusses Bessel’s study of the comet of 1807, including the observing account, field-diameter formulas, elliptical elements, planetary perturbations, and uncertainty of the orbital period. The review dated 23 February 1811 considers Schulze’s astronomy textbook and the teaching of astronomy. The two reviews dated 18 May 1811 discuss Seyffer’s determination of Munich’s longitude from eclipse observations and Nouet’s astronomical observations in Egypt, including geographical positions and magnetic measurements. The review dated 9 September 1811 discusses Pasquich’s theoretical and practical astronomy textbook and its appendix of auxiliary tables, including the distinction between durations and instants of time and the use of astronomical tables and observations. The review dated 2 December 1811 discusses Klüber’s description of the Mannheim observatory, its building and instruments, the succession of astronomers, its wartime history and subsequent restoration, and its geographical position. The review dated 14 December 1811 discusses the Connoissance des tems for 1812, geographical and astronomical observations, lunar and clock calculations, capillarity, and Delambre’s treatment of Gauss’s astronomical methods. The reviews dated 27 June and 3 October 1812 discuss d’Aguila’s proposed world system and the third and fourth instalments of Harding’s star atlas. Gerling’s orthographic-projection review dated 28 November 1812 treats eclipse calculations and the annular solar eclipse of 7 September 1820. Carlini’s solar-table review dated 3 December 1812 discusses the method of calculation, aberration, lunar and planetary perturbations, and a four-row numerical comparison. Zach’s table review dated 7 December 1812 discusses aberration and nutation, with a comparison for Alpha Tauri and the use of stellar and time tables. The review dated 6 February 1813 discusses Bode’s Astronomisches Jahrbuch for 1814 and 1815, including all sixty-five articles and notices, astronomical observations, methods of determining orbits, parallax, instruments and atmospheric hypotheses. The review dated 8 March 1813 discusses Burckhardt’s lunar tables, their comparison with Bürg’s tables, the arrangement of the lunar equations, long-period inequalities and horizontal parallax. The review dated 3 June 1813 discusses Connaissance des tems for 1813 and 1814, including geographical positions, least squares, lunar inequalities, Lagrange’s account of comet origins and Gauss’s objections, time conversion and meteorological observations. The Milan ephemerides review dated 14 June 1813 discusses the calendars for 1812 and 1813, planetary positions, instruments, lunar theory, pendulums and observatory buildings. The report dated 5 July 1813 describes Lindenau’s work on Mercury, its observational basis and eleven rows of orbital elements. The report dated 31 January 1814 concerns Bessel’s determination of precession from 4585 stellar observations, with four numerical formulas and a discussion of unequal precession. The review dated 14 February 1814 discusses the Philosophical Transactions for 1813, including Pond’s solar observations and stellar catalogues, Wollaston’s fine metal wires and micrometer, and Kater’s comparison of reflecting telescopes. The review dated 10 March 1814 discusses Bode’s astronomical yearbook for 1816, its ephemerides, observations, refraction, comet theories, celestial projections and instruments. The review dated 24 March 1814 discusses the Milan ephemerides for 1814, comet and planetary observations, stellar catalogues, astronomical clocks and meteorological observations. The review dated 2 May 1814 considers Mollweide’s interpretation of Virgil’s astronomical imagery, with two Latin quotations and an account of stellar rising and setting. Its closing reference directs readers to Volume IV for the other portions of the review. The review dated 31 December 1814 examines Zach’s study of mountain attraction, astronomical and geodetic measurements near Marseille, the interpretation of observational errors and the positions of stars. It includes the printed latitude and longitude comparisons. The review dated 19 January 1815 discusses the Milan ephemerides for 1815, circumpolar observations at Brera, atmospheric refraction and annual parallax, planetary observations and tables, and meteorological observations. It includes four two-row comparisons. The review dated 18 February 1815 discusses the astronomical yearbook for 1817, observations and instruments, variable stars and stellar positions, and Kramp’s method of determining a cometary orbit. It includes four comparisons of the polar star’s annual motion and the equations discussed in the assessment. The review dated 11 March 1815 discusses the Connaissance des tems for 1816, the origins and motions of comets, probability, astronomical and geodetic comparisons, and the use of observing instruments. It includes the printed probability expressions and seven comparisons of stellar positions. The review dated 23 March 1815 discusses Soldner and Stefenelli on the reduction of observed azimuths, averaging and Taylor expansions, instrumental observations, and spherical-triangle formulas. The review dated 10 June 1815 discusses Piazzi’s catalogue of 7646 stars, proper motions, precession, catalogue arrangement and comparisons with earlier observations. It includes two precession formulas. The review dated 3 February 1816 discusses Müller’s manual for calculating solar eclipses, its two computational approaches and its use by beginners. The review dated 23 March 1816 discusses Carlini’s Milan ephemerides for 1816, stellar refraction, the periodic movement of buildings, Vesta’s orbital quantities, occultations, the obliquity of the ecliptic and Milan rainfall. The review dated 9 January 1817 discusses Harding’s celestial atlas, its coverage of the sky, its use for comet observations, the projection of the northern sheets and their constellations. The review dated 5 April 1817 discusses the Connaissance des tems for 1818, its ephemerides, aberration and parallax tables, cometary and planetary calculations, tides, probability and observational accuracy, twilight and Saturn tables. The review dated 12 May 1817 discusses Schumacher’s determination of the latitude of the Mannheim observatory, its instruments, corrections to zenith distances, stellar and solar observations and their accuracy. It includes three correction formulas and nine comparisons of stellar observations. The review dated 7 July 1817 discusses the Roman tables of parallax in altitude, longitude and latitude, their numerical organization and auxiliary tables, the formulas used with them and their application by repeated approximation. It concludes with an assessment of the tables and their dedication. The review dated 8 September 1817 considers the Milan ephemerides for 1817, a comparison of stellar observations and instruments, and an analytical method for determining celestial orbits. It discusses the use of three and four observations, the effects of observational errors and a related construction. The review dated 19 March 1818 considers Delambre’s tables of the eclipses of Jupiter’s satellites, their observational and theoretical foundations, and the determination of the equation of light and the constant of aberration. The review dated 2 May 1818 discusses Prosperin’s study of the orbits that satellites would follow if their primary planets ceased to act upon them, the conditions on those orbits, and the relation of that hypothetical construction to natural motion. The review dated 21 May 1818 examines Bode’s astronomical yearbook for 1820, observations and instruments, methods of calculation, planetary masses, least squares, eclipses, stellar constants, terrestrial flattening, comet orbits and secular changes of the Earth’s orbit. The review dated 11 March 1819 examines the Connaissance des tems for 1820, its calendar and geographic tables, pendulum experiments and regulation, geodesy, comet orbits, refraction, historical observations of Uranus, planetary perturbations and the application of probability to triangulation. The review dated 20 May 1819 examines the Astronomisches Jahrbuch for 1821, including stellar positions and observational weights, refraction and instrument errors, comet observations, astronomical alignments, the latitude of Krakau and the accuracy of astronomical instruments. The review dated 29 November 1819 examines the Connaissance des tems for 1821, including lunar libration, orbit determination, terrestrial rotation and density, stellar catalogues, geodetic measurements, Uranus observations and atmospheric refraction. The review dated 6 January 1820 discusses Piazzi’s Lezioni elementari di astronomia, its intended audiences and seven books, astronomical instruments, stellar precession, planetary motion and comet-orbit methods. The review dated 29 January 1820 discusses Hallaschka’s Elementa eclipsium, its treatment of solar-eclipse calculation and mapping, and its astronomical tables and reference meridian. The review dated 7 February 1820 examines Bode’s astronomical yearbook for 1822, stellar names and observations, eclipse predictions, comet orbits, astronomical instruments and methods of calculation. The report dated 26 June 1820 presents Gerling’s calculations for the solar eclipse of 7 September 1820, with solar and lunar positions, eclipse times and contacts for twenty cities, formulas for nearby places, the boundaries of the annular zone and observing instructions. The review dated 8 January 1821 examines Bode’s astronomical yearbook for 1823, the physical nature and motions of comets, observations of the Sun and Venus, stellar and planetary positions, astronomical instruments, geographical positions and eclipse calculations. The review dated 21 April 1823 discusses Brambilla’s Milan ephemerides for 1823, Oriani’s mountain measurements and Carlini’s determination of geographical positions by powder signals, together with astronomical and meteorological observations. The review of Bode’s yearbook for 1826 discusses geodetic observations, terrestrial refraction, Olbers’s account of the brightness of the sky, comets, optical observations and instruments. Ehrenrettung presents Gauss’s defence of Pasquich’s comet observations, with the printed reductions, comparison tables and historical notes. The review of the Connaissance des tems for 1826 discusses observations, pendulum experiments, lunar atmospheric effects and azimuth measurements. The review of Damoiseau’s lunar tables compares theoretical and empirical methods and gives three pairs of mean errors. The review of Paris astronomical observations discusses the instruments, meridian marks, calibration and timing of observations from 1810 to 1819. The review of Herschel and South’s double-star observations discusses apparent alignments, stellar systems and changes in relative positions. The review of Tobias Mayer’s observations discusses their publication, instruments, reduction and use in astronomy. The review of the Connaissance des tems for 1829 treats astronomical calculations, geodetic measurements, time determination and the attraction of spheroids. The review of G. Moll’s Mercurius in Sole visus describes Dutch observations of Mercury transits and the occultation of Saturn on 8 May 1832. The report on Steinheil’s prism photometer discusses competing instruments, a table of stellar brightness ratios, artificial-star experiments and the Göttingen Society’s prize decision. The reviews of Beer and Mädler’s planetary studies and Beima’s monograph discuss the Moon, planetary observations and Saturn’s ring. Schering’s concluding remarks, all ten leaves of the historical contents and the printer’s imprint are included. This reader follows the printed sequence through page 664. Modern digital metadata, the copy-specific library stamp and blank versos are outside the reading text.

The collected edition contains historical brackets describing ephemerides that it does not reproduce. Those descriptions are retained; the absent periodical tables, maps, star lists and instrument price list are not supplied. The November 1847 letter also refers to an Iris calculation that does not appear in the supplied printing. This reader does not include the complete original periodical contributions where the collected edition omits material.

Prose, formulas, numerical tables, headings, thirty-seven historical notes, fourteen printed altar-and-flame symbols, seven printed comet symbols, eight partly unidentified marks, and the optical diagram are editable LaTeX. The sole image is the historical portrait. Historical spellings, punctuation, blank cells and printed numerical irregularities are retained. Contemporary fonts represent historical glyphs; this is not a typographic facsimile. Ambiguous and damaged marks require qualified readings. An inherited CMEX10 font lacks a PDF ToUnicode map, so not every mathematical glyph has a complete Unicode extraction mapping.

AI transcription and source checking: GPT-6 Astra. No human or independent-model review is claimed.

Build requirements: XeLaTeX, the packages named in common.tex and source.tex, Latin Modern OpenType fonts, Times New Roman and Segoe UI Symbol. Run build.ps1 with xelatex on PATH, or run xelatex twice on source.tex. The PowerShell helper uses the shared TeX mutex and exits immediately if another build holds it.


This is an AI-transcribed original-language edition with AI-produced typesetting. Historical authorship and inherited editorial contributions retain their printed credits. Authorship, source identity and rights notices appear in RIGHTS_AND_CREDITS.md.
