CELESTIAL MECHANICS: LEUSCHNER 35 



(93) MINERVA 



Discovered by J. Watson 1 1867, August 24, at Ann Arbor, and ob- 

 served on three successive days. Estimated to be of llth magnitude. 



P. Lehmann 2 in Berlin computed his first orbit from the observa- 

 tions to October 2, covering an heliocentric arc from 60 to 75 after 

 perihelion. An ephemeris for 1867, November and December, 

 deviated +0 8 .33 in a, 2".0 in 8 from the observations. These ele- 

 ments were repeated in B. J. 1870. Elements A. 



Lehmann changed his Elements A to the Elements B given in B. 

 J. 1871 without statement of the observations used, the perturbations 

 applied or the representation of the observations. The most prom- 

 inent changes are the improvement of the longitude of perihelion by 

 1, and also the increase of the eccentricity, besides diminution of the 

 mean motion by 1" a day, to a value as much below the mean mean 

 motion as the osculating value was above. This error in the mean 

 .motion made a new computation necessary which Lehmann published 

 in B. J. 1872 without explanation. Elements C. A further improve- 

 ment was obtained by the next set of Elements D by Lehmann in 

 B. J. 1873. These elements were (perhaps) brought up with per- 

 turbations to the new osculation in 1872 as published in B. J. 1874 

 and 1875. Elements E. To the. elements M, \L and < corrections were 

 applied. The resulting Elements F are given in B. J. for 1876-1880. 

 Then Lehmann undertook to make a final determination of the orbit 

 from the first 7 oppositions with special perturbations by Jupiter and 

 Saturn, (as stated in Bauschinger, Tabellen, etc.) These Elements G 

 were probably published in B. J. with change of osculation until the 

 issue 1913. 



Berberich corrected the Elements G empirically by the observations 

 in the oppositions 1899, 1902, 1907, 1908, 1911, and derived the. Ele- 

 ments H, which were published in B. J. 1914. B. J. 1915 gives the 

 elements by Leuschner. 6 



The general perturbations by Jupiter were developed by W. S. 

 Eichelberger. 3 The basic elements were obtained "from a special 

 discussion, by the author, of the observations from 1867 to 1879, in- 

 clusive." Elements I. The method is that of Hansen for absolute 

 perturbations of the first order retaining the eccentric anomaly in 

 the argument. The constants of integration were determined. With 

 these perturbations and the preliminary Elements I the observations 

 from 1867 to 1884 were compared. A least squares solution was made 

 and the final Elements J obtained. The comparison with the observa- 

 tions is not given. 



