o/'Halley's Comet at its last Appearance. 35 



tions. In the solution of the equations of condition which 

 resulted from the right ascensions or declinations of each 

 observer, I considered the longitude of the ascending node 

 and of the perihelion (which elements are obtained with com- 

 paratively the least certainty) as unchangeable; I then de- 

 termined the least sum of the squares of the remaining errors 

 arising from the change of the three other elements, e, T, i; 

 I divided this sum by the number of the observations em- 

 ployed diminished by three units, and considered the quo- 

 tient as the square of the mean error of the series of ob- 

 servations so treated. Having thus found, as well as cir- 

 cumstances would allow, the proportional accuracy of the 

 right ascensions and declinations of every observer, all the 

 observations of each astronomer were brought together, and 

 the mean errors of the right ascensions of every observer 

 again more rigorously determined in the same manner, by 

 a new calculation founded both on right ascensions and 

 declinations; and the proportional precision of the different 

 observations was assumed accordingly. The exactness of 

 the right ascensions of the same observer was also made 

 proportional to the cosine of the declination, as it could be 

 done without rendering the calculation more difficult. If 

 there were several observations in one day by the same astro- 

 nomer, I gave to each of them the value -"7" -■, where n 



is the number of the observations ; but of different state- 

 ments of the place of the comet, founded on a comparison 

 of different stars with one and the same observation of it, I 

 took the arithmetical mean, and considered it as the result of 

 one observation. 



As the communication of the calculated ephemeris for the 

 apparent position of the comet, as well as for the differential 

 quotients of the right ascension and dechnation of the same, 

 with regard to the elements of its path, and the detail of the 

 reduction of the observations, can scarcely have any interest, 

 I only subjoin here the observed places of the comet, cor- 

 rected for j)arallax, and the errors of the ephemeris from 

 these places, so taken ; these errors must be added to the ob- 

 served positions of the comel, in order to obtain these given 

 in the ephemeris. 



[The author here gives the Obsei-vations of: 1. Messier.- 

 2. Maraldi : 3. Cassini de Tliury ; 4. Bradley; 5. Hell ; 

 6. Darquier, La Caille, Lulofs, Le Sear and Jacquier, for 

 ■which the reader is referred to the Astronomische Nachrichten.] 



1. Messier's Observations are found in the Mem. de I' Acad. 

 V '2 des 



