Astronomical Society. S63 



Adding to the above elements the perturbations given by M. de 

 Pontecoulant, the elements for 1835 are as follow : 



Semiaxis major 17-98355 



Excentricity -967348 



Perihelion passage, 1 835, Oct. 31 4 h 47 m Mean time from Paris midnight. 



Inclination 17 42' 50" 



Longitude of ascending node ... 55 359 

 Longitude of perihelion 304 23 39 



Mr. Lubbock then briefly explains the mode by which these ele- 

 ments were computed. 



In the second note, Mr. Lubbock analyses a very valuable paper 

 upon the same subject, by M. Ilosenberger, contained in the Astron. 

 Nach. Nos. 180 and 181. 



M. Rosenberger first obtained approximate elements from five of 

 Messier's observations, adopting the semiaxis major of Damoiscau. 

 He then calculated the effect produced upon the elements by the 

 perturbations of the seven large planets, for every ten days, from 

 the 1st of -January to the end of May 1759. With the corrected 

 elements belonging to each day, he computed an ephemeris of the 

 comet, employing, for this purpose, the Solar Tables of Carlini, as 

 corrected by Bessel, having regard both to precession and nuta- 

 tion. These computed places were carefully compared with the 

 observed places. The positions of the stars with which the comet 

 was compared were taken, when possible, from the Fundamenta 

 Astronomice, or Piazzi's Catalogue. When these were wanting, the 

 Histoire Celeste and Bessel's Zones were resorted to, and many 

 stars were determined by Professor Bessel for this purpose. In 

 reducing the observations, parallax and the differences of refraction 

 were taken into account. Finally, all the observations which could 

 be depended upon, those of Messier, Maraldi, Cassini, Bradley, Hell, 

 and Darquier, were combined and made use of by the method of 

 least squares. The elements resulting from this comparison are 

 compared with Messier's observations, and the differences do not 

 exceed half a minute in space. Mr. Lubbock finds the differences 

 between his elements and those of M. Rosenberger more consider- 

 able than he had expected, especially the excentricity: they are, 

 however, of the order of the uncertainty which must exist in the 

 calculation of the perturbations of the elements, between 1759 and 

 1835, and therefore practically of little importance. 



It is to be regretted that M. Rosenberger has not used the semi- 

 axis major of M. de Pontecoulant. He has, however, computed the 

 variation of the elements produced by a small change in the semi- 

 axis major, whence, adopting the value given by M. de Pontecou- 

 lant, the elements of the orbit are 



Semiaxis major 18-0763 



Excentricity -96766333 



Perihelion passage 1759, March 13-0763 Mean time from Paris midnight. 

 Longitude of ascending node .... 53 47' 47"' 19 

 Distance of perihelion from node 110 3727-90 

 Inclination of orbit 17 21 44 



Mr. Lubbock is, however, inclined to doubt whether this method 



3 A 2 is 



