Some aspects of positional astronomy from Bradley to Bessel

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  • Vistas in Astronomy, 1976, Vol. 20, pp. 183-186. Pergamon Press. Printed in Great Britain



    Head of the Department of History, Arehenhold-Sternwarte, Berlin G.D.R.

    In a letter from the "Committee of the Board of Longitude" addressed in 1794 to the Duke of Portland, we read that the publication of Bradley's observations would be more valuable "than all the observ- ations that had been made before at the Royal Observatory and when published, will make a new era in the science of astronomy". 1 The correctness of this assessment is partially verified by the fact that Bradley's observations were the very ones included in the Prussian Academy of Science's Gescbicbte des Fixsternbimmels.2 Bessel argued that Bradley's inexhaustible series of observations gave rise to those data "on which present and future astronomy shall be based". 3

    In another historic publication, Gebler's Pbysikaliscbes W6rterbucb (Gehler's Physical Dictionary) we find the following assessment concerning Bessel's role in applying Bradley's observations: "with what circumspection particularly... (Bradley) embraced the entire field of observational astronomy and what reliable results his observations offer, has been completely demonstrated by Bessel". 4 This refers, above all, to Bessel's Fundamenta Astronomia (1818). Bradley and Bessel are in fact the corner-stones of possibly the most splendid epoch in the development of positional astronomy. It can be stated without exaggeration that the positional astronomy of the 18th and 19th century essentially represented the history of the effects of Bradley's outstanding work and that from among the direct successors of Bradley, it was Bessel who achieved the greatest advance.

    The rapid development of positional astronomy based upon Bradley's observations has several roots:

    (a) Bradley's discovery of aberration and nutation made possible radical improvements in the re- duction of observations;

    (b) Bradley recognized the role played by observational instruments in the attainment of accuracy and equipped the Greenwich Observatory with instruments of unprecedented precision which, at the same time, reflected the high standard of craftsmanship in England;

    (c) while observing, Bradley paid attention to possible errors in his observations. He selected for example stars which culminate close to the zenith at Greenwich. By means of an appropriate instrument with a short arc he avoided a number of instrumental errors. Moreover Bradley made notes of atmospheric temperature and pressure during the time of observation and there- by established values for subsequent corrections.

    Bessel's outstanding role as a processor of Bradley's materials is, in essence, based upon three facts: (1) Bessel was a past-master in eliminating instrumental errors. He is reputed to have said: "that the quality of observations depends more on an exact familiarity with the instruments than on the instruments themselves", s Every instrument is, according to a well-known statement by Bessel, made twice: .."once in the workshop of an artisan working with brass and steel and, for the second time, on his paper, through the record of the necessary improvements".6(2) Bessel had at his disposal more precise values of the elements of reduction. (3) Bessel was able to rely upon comprehensive works such as Maskelyne's Greenwich observations and Piazzi's star catalogue.

    Nevertheless, there was no steep path to success from Bradley to Bessel; on the contrary, Bessel himself indicated the existence of a discontinuity in the development of positional astronomy after Bradley when he wrote: "The end of the [18th] century did not justify the expectations aroused at its middle". 7 By that he meant to say that after Bradley's death a transitional period of stagnation set in in Greenwich and that in the other European countries, too, despite some deliberate efforts to


  • 184 D.B. HERRMANN

    improve the situation, no outstanding successes were achieved. Only after the turn of the century did new impulses bring about a rapid advance in positional astronomy. Bessel even argued that this was a general rule in the development of science: "each of the periods ... shows ... an unmistakable conformity of its course: it is opened with splendour, but the intention of its founder vanishes with him, only to be understood by a future scientist ... This is the nature of the history of the sciences in general". 8

    To construct a quantitative analysis of Bessel's first thesis we have studied the temporal develop- ment of some parameters which seem suitable for gaining a deeper insight into that historic process; namely, the accuracy of star positions (expressed by the reciprocal value of the accuracy of angular measurements to the nearest second of arc), the number of star catalogues as well as the number of stellar observations, and the number of existing observatories. The sources of our data were relevant summaries by Mineur 9 (accuracies), Knobel x (catalogues and positions), and Stroobant 11 (observ- atories).

    Figure 27.1 demonstrates the chronological development of the accuracy and of the number of positions, observatories and catalogues in a standardized presentation: it reveals that Bradley made



    ' ' I ' ' ' ' I ' i l IDt years

    1750 1800

    Fig. 27.1. Development of characteristic indices: 1 - accuracies (curve is constructed from three points only, corresponding to Flamsteed's, Piazzi's and Bessel's values); 2 - positions; 3 - observatories; 4 - catalogues. The absolute values for 1720 are: accuracy lOt'; number of positions - 26570; number of observatories - 8; number of catalogues - 63.

    his observations in a period which was already marked by a slow growth in all these indices of positional astronomy (viz. 1750-62). Not until decades after Bradley's death did the observing characteristics experience a steep increase. An analysis of the three growth curves shows that from about the year 1800, developments in the catalogues as well as the increase in the number of observ- atories and in the accuracy of measurement can be well represented by the exponential function Nt = No. eCC t. In this formula, N t denotes the number of observed objects at the end of 1970 and the current year minus 1720. The following mean exponents including standard deviations apply to the individual indices:

  • Some aspects of positional astronomy from Bradley to Bessell 185

    accuracies a = 0.024 (1800-1850) catalogues tv = 0.0113 + 0.0002 (1820-1850) observatories a = 0.0181 -+ 0.0006 (1780-1850)

    By comparing our previously-published growth curve for observatories established during the nineteenth century, ~2 with the relative increase in the number of catalogues - the latter being a typical "product" of the observatories - we clearly perceive the strong positive correlation; there being, however, a less marked rise in the publication of catalogues than in the number of new observatories. In addition, we are not entitled to ignore the tendency of a growth of the mean number of objects per catalogue (Fig. 27.2). This likewise becomes clearly recognizable only after the year





    . , n i i . , o I I I

    1750 1800


    Fig. 27.2. The development of the mean number of positions (p) per catalogue (c), expressed in thousands.

    1800, following a gradual increase. It is interesting to note that the positional accuracy experienced a far steeper increase than either the number of observatories or catalogues. This is obviously the most sensitive index of an intensification based on the ideas, discoveries, and solutions of individuals such as Bradley, Piazzi and Bessel.

    Notice that the steep increase in those characteristic developments did not start until after Bradley's death, which confirms Bessel's thesis. Positional astronomy owes its material basis to the needs of society in general and of navigational science in particular. The interest of society, however, remains unabated only until the relevant problems are solved. On the other hand, a large number of new problems capable of accelerating the rate of development arise when a question is to be solved in a scientific way, even although the initial impetus for the establishment of a new branch of science no longer operates. An important part of the public demand for more reliable positional astronomy -

  • 186 D.B. HERRMANN

    as was expressed in the prize offered in 1714 by the British Parliament - was already fulfilled when Bradley started his observations in Greenwich. 13 The long time which then elapsed before Bradley's observations were published, and the subsequent odyssey regarding the printing of Bessel's Fundamenta Astronomiae 14 prove, or so I believe, the declining public interest in basic research on positional astronomy. There existed however, powerful internal impulses resulting from a number of discoveries and events which, though without any major social relevance, are among the most scientific successes of the positional astronomy in this period: the discovery of binary stars, of Uranus, of the minor planets, of stellar parallaxes, and of the precise analytical description of the Sun's movement, all con- siderably stimulated observation activities. To this we may add new successes in the field of mechanics which further increased the already high demands on the accuracy of observations. These activities were externally reflected in the foundation of the first astronomical periodicals containing a high proportion of papers on mathematical geography which were, on the one hand, results; and, on the other hand, the basis for a continuing rapid advance in the field of astronomy, is It would be well worth analysing the respective roles of the various internal factors in the development of positional astronomy, with a view to obtaining thereby an exact causal explanation of the relatively sudden acceleration of the developments which we have been considering.

    Acknowledgements : My thanks are due to E. Rothenberg (Berlin), H. Loos, and A. D6rnbrack, members of Treptow's working group for History of Astronomy for their help in collecting data.


    1. See E.G. Forbes, "Dr. Bradley's Astronomical Observations", Quarterly Journal o f the Royal Astronomical Society, 6 (1965), 327. See also E.G. Forbes, Greenwicb Observatory, Vol. 1, Origins and Early History (1675--1835) (London 1975).

    2. See Gescbicbte des Fixsternbimmels, Abt. I, Bd. 1, Karlsruhe 1922, Ed. by the Preussische Akademie der Wissenschaften p. VI.

    3. F.W. Bessel, Popula're Vorlesungen iiber wissenscbaftlicbe Gegenstande, Nacb dem Tode des Verfassers bgg. yon H.C. Scbumacber (Hamburg, 1848), p. 538.

    4. Jobann Samuel Traugott Gebler's Pbysikaliscbes Worterbucb, neu bearbeitet yon Brandes, Gmelin, Homer, Muncke, Pfaffi Bd. 1 (Leipzig, 1825), p. 416.

    5. See Bessel, F.W., Letter to J.G. Tralles, CentraI-Archiv of the Academy of Sciences of the GDR, Bessel's unpublished papers. See also H.-G. Korber, "Bessels Methode zur Prufung eines Instrumententeilkreises", Scbriftenreibe fur Gescbicbte der Naturwissenscbaften, Tecbnik und Medizin 4 (1967), 10, 45-52.

    6. Bessel, F.W. op. cit., p. 432. 7. Op. cit., p. 16. 8. Op. cit., p. 435. 9. H. Mineur: Histoire de l'Astronomie stellaire jusqu'a l'Epoque contemporaine = Actualites scientifiques et

    industrielles 115 (Paris, 1934). 10. E.B. Knobel: "The Chronology of Star Catalogues", Mem. Royal Astr. Soc. 43 (1877), 1--76. 11. P. Stroobant et al., Les Observatoires astronomiques et les Astronomes (Tournai - Paris, 1931). 12. D.B. Herrmann,"An exponential law for the establishment of Observatories in the nineteenth century",

    Journal for the History of Astronomy 4 (1973), 57-58. See also, Die Sterne 49 (1973), 48-52. 13. See E.G. Forbes: Tobias Mayer's Opera lnedita (London, 1971), p. 7. 14. D.B. Herrmann, "Bernhard August yon Lindenau und die Fundamenta Astronomiae yon F.W. Bessel",

    Vortrage und ScbHften der Arcbenbold-Sternwarte Nr. 20 (Berlin-Treptow, 1968). 15. D.B. Herrmann, "Die Entstehung der astronomischen Fachzeitschriften in Deutschland (1798-1821)",

    Veroffentlicbungen der Arcbenbold-Sternwarte Nr. 5 (Berlin-Treptow, 1972).