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Studies in the History of Statistics and Probability Studies in the History of Statistics and Probability Vol. 6. Collected Translations F. W. Bessel, C. F. Gauss and about them Compiled and translated by Oscar Sheynin Berlin 2016 Contents Introduction by Compiler I. Kurt-R. Biermann, C. F. Gauss as a historian of mathematics and astronomy, 1983 II. C. F. Gauss, Determination of the latitudinal difference between the observatories in Göttingen and Altona by observations with a Ramsden zenith sector, 1828 III. Kurt-R. Biermann, On the relations between C. F. Gauss and F. W. Bessel, 1966 IV. Kurt-R. Biermann, The changed of our concept of Gauss, 1991 V. Kurt-R. Biermann, An inborn player in the scientific work of C. F. Gauss, 1991 VI. F. W. Bessel, Brief recollections of my life, 1852 VII. R. Engelmann, [Supplement to Bessel’s Recollections], 1876 VIII. Joh. A. Repsold, Friedrich Wilhelm Bessel, 1920, with Supplements IX. F. W. Bessel, About Olbers, 1844 X. Oscar Sheynin, The other Bessel, unpublished Introduction by the Compiler The works of Gauss are mentioned throughout, and I list them here. Werke, Bde 1 – 12. Göttingen, 1863 – 1930. Reprint: Hildesheim, 1973 – 1981. Werke, Ergänzungsreihe, Bde 1 – 5. Hildesheim, 1973 – 1981. These volumes are reprints of the previously published correspondence of Gauss with Bessel (Bd. 1); Bolyai (Bd. 2); Gerling (Bd. 3); Olbers (Bd. 4, No. 1 – 2); and Schumacher (Bd. 5, No. 1 – 3). Notation: W-i = Werke, Bd. i. W/Erg-i = Werke, Ergänzungsreihe, Bd. i. Bessel’s Abhandlungen, Bde 1 – 3. Leipzig, 1875 – 1876 are his selected works (editor, R. Engelmann). A list of Bessel’s works is in his Abhandlungen, Bd. 3, pp. 490 – 504. These contributions are there numbered; two numbers are provided for those that are included in the Abhandlungen. Notation: [No. i] = Bessel’s contribution i included in the list, but not in the Abhandlungen [No. i/j] = Bessel’s contribution i included both in the list and in the Abhandlungen and accompanied there by number j Many letters exchanged by Bessel. Gauss, Olbers and Schumacher are quoted. Notation: B – S = letter from Bessel to Schumacher; G – O = letter from Gauss to Olbers; etc Special notation: S, G, i means see Document i on my website www.sheynin.de or on its copy at Google, Oscar Sheynin, Home. The document is in my translation from Russian or German or in its original English if barely available. I mention three representatives of the Repsold family, all of them manufacturers of optical instruments; the last-mentioned was also the author of [viii]: Johann Georg, 1770 – 1830; Adolf, 1806 – 1871; Johann Adolf, 1838 – 1919 Finally, I was unable to understand the description of some astronomical instruments, especially since the appropriate German terms are too difficult to find in English translations. General Comments to Some Items [i] This tiny contribution does not include any discoveries. On the contrary, it contains serious errors (see Notes 3 and 9) and, in general, Gauss had not thought it out properly (Notes 5 and 14). His own later statement, which Biermann quoted at the very beginning, is valid here also: Gauss has neither time nor inclination for [prior] literary studies. The title of Biermann’s paper is thus too generous for Gauss. Biermann, for his part, vainly tried to enhance the significance of Gauss’ efforts and his own comments are not at all sufficient. There are two other instances in which Gauss made wrong statements about his predecessors, both in his Theory of Motion (1809). First, in § 177 he stated that Laplace (actually, Euler) first calculated the integral of the exponential function of a negative square. However, he later noted his mistake (Sheynin 2013, § 10A1.4). Second, in § 186 Gauss attributed to Laplace one of the two conditions of the Boscovich method of adjusting observations. [ii] This writing is certainly little known. It clearly shows Gauss’ attitude to investigation of instruments and to observations proper, and it proves once again (see [i, Note 16]) that not only Bessel, but he and Gauss had originated the attitude just mentioned. Thus, Gauss was apparently the first to investigate the errors of graduation (§ 3.8). He also attempted to consider the effect of gravity on the bending of telescopes (§ 3.14). Bessel studied the same effect much later (1844; 1846). Another interesting noveltiy was Gauss’ reasoning belonging, to the later physical geodesy (Note 27). The value of this writing is, however, lowered due to some unexplained conclusions and, worse, strange statements, see for example Notes 7, 16, 18, 22. Strange is also the inclusion of 16 unnamed stars in the provided tables, for example, in § 1. And, after studying the determination of a certain coefficient θ (§§ 3.9 – 3.10) it turned out that in another context θ was not needed at all (§ 4). An explanation would have been quite proper. [vi] Bessel′s talent as well as his diligence are clearly seen in these Recollections. He could have, but happily did not become a prominent businessman. In the beginning of § 4 he tells us that he feared of losing his job, but the following events refuted his opinion, and his yearly bonuses gradually became rather impressive. In his childhood Bessel detested the rudiments of Latin (§ 1), but in 1818 he published an important contribution (Fundamenta Astronomiae) in that language (and even earlier had reviewed a few works in Latin), so when did he learn the language? The included text of Olbers’ letter to Bessel of 1804 (§ 9) deserves special attention. [viii] It will be difficult or even impossible to find elsewhere much of the unearthed information. The description is not, however, always coherent and many statements (some of them formulated by Repsold himself) are not sufficiently explained. Especially disturbing is the obviously wrong remark at the end of § 28 that Bessel, apparently in 1840 or earlier, had already visited Oxford. His journey to England occurred in 1842 (§ 30). At the end of his paper the author makes known that Bessel and his wife were buried near his observatory. It is desirable to find out whether their graves and/or the ruins of his observatory are still in existence in present Kaliningrad. [ix] This brief essay provides a general impression about the life and work of Olbers and it is the more valuable since the author (Bessel) had been intimately connected with his hero. [x] I point out an unexpected aspect of Bessel’s work, and I note here that there exists a general tendency for concealing the negative sides of the work of our betters. I Kurt-R. Biermann C. F. Gauss as a historian of mathematics and astronomy K.-R. Biermann, C. F. Gauss als Mathematik- und Astronomiehistoriker. Hist. Math., vol. 10, 1983, pp. 422 – 434 Dedicated to Prof. Dr. Kurt Vogel on the occasion of his 95th birthday Abstract (in Author’s Translation) In 1810, Gauss published two essays on the history of mathematics and astronomy in Germany between 1700 and 1800. Today, these papers are unnoticed. Here these papers are reproduced and discussed. Preliminary Remark It can be presumed that experts in the works of Gauss will shake their heads since they know about the Princeps mathematicorum’s dislike of historical and literary research and popular expositions. Thus (G – S, 6 July 1840), Gauss wrote to his intimate friend: I reluctantly express myself in detail about the achievements attained by others working in the same field as I did, if only not being entirely convinced in that I really may mention them approvingly. And, again, Nevertheless, I recognize […] that I did not at all study critically [the history of the theory of magnetism]. As a rule, I am unable to decide just like that who should be favourably mentioned and thus to unconditionally reinforce myself. And, when desiring to provide authoritative connections, it would have been necessary to conduct prior literary studies for which I have neither time nor inclination. Indeed, such investigations are not exactly to my taste. And when Gauss was about to propose prize mathematical problems to [his] Göttingen students, he (G – S, 25 Jan. 1842) stated: I do not like to propose historical problems and prefer to occupy myself with my own work. The practised dislike of searching for, and quoting his predecessors earned him C. G. J. Jacobi’s reproach: For Gauss, it is not de mortuis nil nisi bene [nothing but good should be spoken of the dead] but de mortuis et de vivis nil [nothing about either the dead or the living], see his letter to Bessel of 3 April 1835 (Biermann 1963, p. 222), see also [ ]. However, Gauss felt himself prepared to compile a popular paper (1836) for Schumacher’s Astron. Jahrbücher (Tübingen, 1836 – 1844), and thus to please his intimate friend. It occurred, however, that Humboldt misunderstood some of it, and Gauss disappointedly reported to his friend (G – S, 15 April 1836): After all, it is apparently my own fault. In spite of my efforts, I have not properly achieved necessary clarity. On 10 May 1853, he wrote to Humboldt (Biermann 1977, p. 112): For a long time now, I am not setting high store on attaining a taste of haute culture or the so-called high position by reading popular literature or attending popular lectures. I rather believe that in science a tried and tested insight can only be attained by our own efforts and by treating of that, which was proposed by others. In 1977, an unnoticed exception (1813) to the Gauss rule of refusing to compile popular historical surveys came to light, and I am reprinting it below. I was unable to find it in any bibliographies of Gauss’ works1.
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