Acknowledgments

Acknowledgments Thanks must fi rst go to the translation experts who provided me with such a vast amount of material to work with: Telse Wokersien (German and French text), Dr. John Ramsey and Christopher Gordon (Latin text), Marcin Sawicki (Polish text), Piero Sicoli (Italian text). Additional linguistic assistance was provided by Lise Jobin and the famous author and impresario David Leddick, who generously wrote an artistic preface. Thanks to the archivists at the Paris Observatory, and the Academy of Science in Paris, who were a great help during my visit there in 2002; to Adam Perkins of Cambridge University for supplying me with the Nevil Maskelyne material; to Dr. Owen Gingerich for access to the Herschel archives on microfi lm many years ago; Raza Ansari for the Persian map of the solar system; and to Sharon Hanna, librarian at NRC, Victoria for a great deal of archival research. Thanks also to Earl Ogden for his expertise on electronic fi le issues, and Guy Ottewell for the 3D plot. Finally to Dr. Roger Ceragioli for his linguistic expertise including the proper printed way to spell Johann Schroeter, as he himself rarely, if ever, signed his name using the o with an umlaut. I began archival research for this four-volume work in 1989, at which time I met with Dr. Peter Brosche at the University of Bonn (the leading expert on Baron von Zach) and Dr. Viktor Shor of the Russian Academy of Sciences in St. Petersburg. Both have been a great assistance to me throughout the years. Regarding Dr. Shor, I can only say that the honour he conferred upon me by writing the foreword to this book is one I will always cherish. Portions of this book are based on my unpub- lished 2014 PhD thesis at the University of Southern Queensland. © Springer International Publishing Switzerland 2016 381 C. Cunningham, Early Investigations of Ceres and the Discovery of Pallas, DOI 10.1007/978-3-319-28815-4 Appendix A: Positional data on Ceres and Pallas for 1801 and 1802 Fig. A1 Positional observations of Ceres © Springer International Publishing Switzerland 2016 383 C. Cunningham, Early Investigations of Ceres and the Discovery of Pallas, DOI 10.1007/978-3-319-28815-4 384 Appendix A: Positional data on Ceres and Pallas for 1801 and 1802 Positional observations of Ceres and Pallas for 1801–1802. All the original observations have been put in standard modern notation with a Julian date and distance in AU. Tables are from Schubart ( 1976 ). Appendix A: Positional data on Ceres and Pallas for 1801 and 1802 385 Fig. A2 Positional observations of Pallas Appendix B: The Elements of Ceres by Encke By Professor Encke ( 1831 ) Since the completion of the fi rst calculations for newly determining the orbit of Ceres, one of my respected astronomical friends has given me the hope that the investigations on this subject will be more completely and more accurately per- formed by another hand. It will therefore be suffi cient in this place to explain the ground-work of my determination, in order the better to form an estimate of the confi dence to which the places derived from it are entitled. The perturbations were developed in the same manner as for the other small planets, in regard to the elements themselves, and not to the places of the planets in space. A review of the last determination of Professor Gauss (Zach’s Monthly Correspond . 1809, May) on which all places of the planet hitherto given were founded, and some trials made at the latest oppositions, seem to prove suffi ciently that the equations for the perturbations, if developed as is usual for the old planets, would require to be extended considerably beyond the fi rst power of the eccentricity, if great accordance is intended. In the same proportion, however, the calculation of a single place would have become irksome, even taking into consideration the facil- ity afforded by the excellent construction of the tables of perturbations (Zach’s Corresp . 1803, March); and therefore, even if every part had already been perfectly developed, still this method would hardly have deserved the preference on the score of brevity of computation. As an interval of time, the number of one hundred days was selected for this fi rst approximation, and only the attraction of Jupiter was taken into account. The mass of this planet was taken, according to Nicolai, at 1/1053.924. This value, which is one-eightieth part more than the old determination by Laplace, appears in the cases of Pallas, Juno , and Vesta , to agree better with the observations, and therefore seems likewise for Ceres to deserve the preference. The four oppositions necessary for deducing the elements were found to be, from the observations published, as follows (Fig. A3 ): And proceeding from the elements at the moment of the fi rst opposition, the computations of the perturbations for the following ones gave the following corrections of © Springer International Publishing Switzerland 2016 387 C. Cunningham, Early Investigations of Ceres and the Discovery of Pallas, DOI 10.1007/978-3-319-28815-4 388 Appendix B: The Elements of Ceres by Encke Fig. A3 The four required oppositions Fig. A4 Corrections of the elements the elements, in which however the precession is still to be added to all the longi- tudes (Fig. A4 ). These determinations require, perhaps, a repetition, being calculated with elements which give for the single oppositions places erroneous by fi fteen minutes. For this very reason I did not deem it necessary to produce a perfect accordance of the elements with the oppositions, but was satisfi ed with such as gave errors in longitude less than 3″. The elements thus deduced, and true for the moment of the epoch, the longitude being referred, for the sake of agreement with the other small planets, to the mean equinox of 1810, are as follows: Elements of Ceres. Mass of Jupiter 1/1053.294 Epoch 1822. Jan. 22. 0h mean time at Goettingen. L = 127° 36′ 51″.6 π = 147 o 36 57′ 6 S Mean equinox 1810. Ω = 80 41 55.0 i = 10 38 7.7 φ = 4 31 18.0 μ = 770.72468 (sidereal). A rigorous comparison with the geocentric observations at the times of the above four oppositions, has presented the following differences (Fig. A5 ). Appendix B: The Elements of Ceres by Encke 389 Fig. A5 Differences in the observations Fig. A6 Observations of Ceres by Gauss in 1827 The two subsequent oppositions of 1827 and 1829 served as a test of the accuracy of the elements. For the former one Prof. Gauss had the kindness to communicate to me the following observations (Fig. A6 ). Hence the oppositions of Ceres will be deduced as follows (Fig. A9 ): For the opposition of 1829, I received the following excellent observations from Professors Schwerdt at Speyer [in Bavaria] and [Friedrich] Argelander at Abo [in Finland], which are the more creditable as at the time of that opposition it was diffi cult to fi nd this planet (Fig. A7 ): The computations of the perturbations, taken in the same sense as above, gave the following corrections of the elements (Fig. A8 ). Opposition Ceres 1827. Sept. 26. 9h 30′ 45″. Mean time at Goettingen. Heliocentric longitude… 2° 58′ 19″.5 Geocentric latitude −15 41 56 .4 Opposition Ceres 1829. Jan. 1. 4h 8′ 47″. Mean time at Goettingen. Heliocentric longitude… 101° 3′ 13″.5 Geocentric latitude +5 56 5.5 The mean geocentric errors in all six oppositions are consequently (Fig. A10 ): 390 Appendix B: The Elements of Ceres by Encke Fig. A7 Observations from the opposition of 1829 Fig. A8 Corrections of the elements Fig. A9 Data from 1827, 1828 and 1829 where the last somewhat more considerable difference answers to heliocentric errors of 13″ in longitude, and 7″ in latitude; so that it is to be hoped, even if these errors are chargeable to the elements only, and not, perhaps, also partly to the per- turbation caused by Saturn and Mars , which have been neglected, that these errors will not render the fi nding of Ceres diffi cult for the approaching years, until the orbit shall have been more accurately determined. Appendix B: The Elements of Ceres by Encke 391 Fig. A10 The mean geocentric errors The early development of the perturbations of Ceres , which was almost contem- porary with the determination of the orbit itself, and the certainty, thereby obtained, of always being, for the future, sure of its position within ten or fi fteen minutes of a degree, would appear to have been the cause that this planet, the fi rst-discovered of the small ones, has been least observed in recent years; – at any rate I have not suc- ceeded in obtaining accurate observations of Ceres at the times of its opposition, even since the period that the oppositions of the other small planets have been regu- larly observed by meridian instruments in German observatories. It is possible that some oppositions have really been entirely neglected. It is the more desirable that the future oppositions should not pass by unnoticed, as Ceres might likewise afford additional means of determining the mass of Jupiter , or might assist in answering the question which has lately been agitated, Whether for all planets, the attraction is rigorously proportional to their mass? [This is the end of the paper by Encke.] Further to Encke’s work on the asteroids at this time, we have two contributions from British periodicals, both of which involve White’s Ephemeris , disparagingly described at the time as “the especial favourite of all small amateurs of astronomy, who may possess a small equatorial, a small ‘achromatic Dollond,’ a pocket chro- nometer by the ‘elder Arnold,’ and a small pair of Carey’s old globes, in a small attic observatory; whither they love to retire, when all their neighbours are going to bed; with serenity in their hearts, and White in their hand.” ( The Magazine of Popular Science 1836, vol.

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