[ 32 ] 

 V. On the Elements of Halley's Comet at its last Appearance. 



M. O. A. RoSENBERGER*. 



A S this celebrated comet will return again in a few years, 

 ■^^ the following investigation of its path when last visible 

 may not be without interest ; especially as a complete treatise 

 on this body, such as Laplace desired in his Mecan.Cel. torn. iv. 

 p. 214', is still a desideratum, and must be established on a 

 more perfect knowledge than we have hitherto possessed of 

 its elements at the time of its two last appearances. 



I have taken all the observations susceptible of a new 

 reduction as the foundation of my work, and am moreover 

 indebted to Professor Bessel, for the communication of a 

 series of unpublished observations by Bradley, through the 

 kindness of Dr. S. P. Rigaud, at Oxford. Although these ob- 

 servations do not offer so many details as are necessary for 

 a new reduction, I consider this defect sufficiently compen- 

 sated by the known accuracy of the observer, and have con- 

 sequently brought them into my calculation. The great dis- 

 turbances which this comet suffered, during the time of its 

 appearance, by the joint action of the planets, have been 

 taken into consideration ; the semi-axis major of its orbit 

 for the beginning of the year 1759 has been supposed = 

 18*083275, as stated by Damoiseau in his prize essay {Me- 

 morie dclla Reale Academia delle Scienze di Torino, torn. xxiv. 

 p. 36). This value properly refers to the moment of the pe- 

 rihelion ; but I have allowed it to remain unaltered for the 

 commencement of the year, which may be the more readily 

 conceded, since Damoiseau only considers its disturbances 

 by Jupiter, Saturn, and Uranus ; and, moreover, because I 

 have stated in my essay the changes which each element suf- 

 fers in consequence of a change in the value of the semi- 

 axis major, in order to satisfy the observations as nearly as 

 possible. 



Five mean places of the comet, for the 25th of January, 2nd 

 of February, 7th of April, 5th and ISth of May, deduced from 

 the numerous observations of Messier at those periods, gave 

 me the following very approximate elements, referred to the 

 mean equinox of January 0, 1 759. 

 Semi-axis major of the orbit a = 18*083275 



Excentricity e= *96768269 



Perihelion passage ( — T) = Jan. "71*56261 ....or March 



Long, of the ascending node « = 53° 47' 56"*84. 12*56261 

 Dist. of perih. from the node co = 110 37 8 '23 m. time 

 Inclination of the orbit i = 162 21 51 "35 at Paris. 



• From the Astronomiiche Nachrichten, No. 180. 



With 



