CELESTIAL MECHANICS: LEUSCHNER 31 



(28) BtiLLONA 



Discovered by R. Luther 1 at Bilk near Diisseldorf, March 1, 1854. 



Preliminary elements were published by Bruhns, 2 3 4 Chevallier 5 and 

 Ruemker, 5 Oudemans. 6 



From 141 observations formed into five normal places Bruhns 7 8 

 derived, originally using four longitudes and two latitudes correspond- 

 ing to the first, second, fourth and fifth normals, the first reliable 

 Elements A. As Elements A differ considerably from his previous 

 elements and those of Oudemans. He made a comparison of ephem- 

 erides which satisfied him regarding the correctness of Elements A. 

 This case is somewhat indeterminate and small errors of observation 

 would produce considerable changes in resulting elements. From 

 Elements A Bruhns 7 has published an ephemeris for 1855. 



Further ephemerides are published by Bruhns, among them for 

 1856, 9 1866, 10 (a star correction 11 November 29 by Engelmann), for 

 1867, 12 correction Aa 50 s , AS 3'.4 by Tietjen, 13 and for 1871-72. 14 



Other elements by Bruhns are published in the B. J. from 1857 to 

 1860. 



The B. J. from 1861 to 1891 contains new elements and ephemerides 

 by Bruhns originally based upon the observations of the first four 

 oppositions with perturbations by Jupiter, Saturn, and Mars. Ele- 

 ments C. 19 Whether these elements are merely brought forward by 

 perturbations or contain corrections is difficult to determine. 



From 1892 the B. J. uses von der Groeben's elements instead of 

 those by Bruhns. 



By a process of successive correction of osculating elements and 

 special perturbations by Jupiter, Saturn and Mars (perturbations by 

 the Earth and Venus were found negligible) , based on 16 normal places 

 extending over a period of thirty-two years from 1854 to 1886, von 

 der Groeben, 15 starting with a set of elements osculating for 1870, 

 September 18, derived Elements Ba, Bb, Be, Bd osculating for differ- 

 ent epochs from 1861 to 1882. These elements were brought forward 

 with special perturbations of Jupiter, Saturn and Mars to the epoch 

 1886, February 26, Elements Be, and to the epoch 1889, October 28, 

 Elements Bf. Elements Bf are adopted by the B. J. for 1892 16 and 

 1893. 17 Three observations by Ball at Luttich, October 31 to Novem- 

 ber 15, 1889, are well represented by the ephemeris. Mean Aa + s .19, 

 mean AS ".5. 



From seven observations at Washington and Tacubaya with star 

 places newly determined by Bruns and four observations by himself 

 at Diisseldorf, Luther 18 obtained a mean correction to the ephemeris 



