238 Proceedings of Philosophical Societies. [March^ 



which all these orbits are united. M. Lindenau has very lately 

 published a supplement to all these tables. We find in it 40 

 orbits newly determined^ 22 by Burckhardt, among which is not 

 the comet of 1095, the orbit of which he has recently calculated 

 from observations foimd in manuscript in the Observatory. The 

 same astronomer has given observations, on the motions of the 

 stars in Cassiopeia. 



Tables of the Moon. By M. Burckhardt. 



We formerly announced these tables as about to appear, and 

 we have nothing to alter in the notice which we gave, in the 

 history of the Institute for ISli. But we can at present add 

 some details respecting their composition, and their relative de- 

 gree of precision. A commission, named by the Board of 

 Longitude, was charged to examine them, it was decided that 

 they should choose a great number of observations distributed in 

 different points of the lunar, orbit, and that they should be calcu- 

 lated according to the tables of Burg and of Burckhardt, and 

 that each of the calculations should be made twice over, to prevent 

 error. To compare the difference between the calculations and 

 observations, it was resolved to employ the method of the smaller 

 squares, as that which would furnish the most probable result. 

 For the longitude the sum of the squares was 70083''' for M. 

 Burg, and only 4G02'' for M. Burckhardt. The correction of 

 the epoch for the middle of theyear 1804 was 0*2''' and O-l'^, that 

 is to say, insensible. These results were from 165 observations^ 

 made at Greenwich and at the Imperial Observatory. By 13/ 

 observations, made at the imperial Observatory, and at that of 

 the military school, the sums of the squares were 6439^' and 

 4182'^. The correction of mean longitudes for the middle of 

 1811 was 1-4'^ and O'l''. 



For the latitude the same method proved that the new tables 

 had an advantage almost equal over those of M. Burg. 



The tables of the two authors compared with the observations 

 of Delahire and Flamsteed indicated for M. Burckhardt a real 

 though smaller advantage. 



M. Burg had introduced a new equation at a long period ; but 

 between two arguments, almost equally probable, upon which 

 that equation might depend, M. Burg had decided for one. 

 After mature reflections, and by the advice of M. Laplace, who 

 had discovered this equation, M. Burckhardt decided in favour of 

 the second. These tables contain 32 equations of longitude 

 which depend only upon mean arguments, and 4 which depend 

 upon arguments successively corrected from all the preceding 

 equations. The tables of parallax are calculated solely from the 

 theo'-y of M. Lnplace. 



(To be coniinued.) 



