Bowditch on the elements of the orhit of a comet. 



m 



bt of their accuracy expressed or even insinuated ; fo 

 i hope it will not be considered as trc 



passing 



too much on 



the Academy to devote a little time to the cxpl 



od. thou 



o 



now much used. I 



r 



briefly the principles of the compulation usx?d by N 

 form of the proposed equations, and the cause of il 



the 



of 



ing the elements of the orbit of a comet, I have thought it would 

 not be amiss to add, in another seclion, some reflections upon the 

 method that La Place has given for that purpose in the first vol- 

 ume of his '< Mecanique Celeste ;" together with some reductions 

 in the calculations. 



SECTION FIRST. 



Having three geocentric longitudes of ^ 



tervals with tbe corresponding longitudes of the earth 



d 



distances from the sun, knowing 



tions^ neailv the longitude of th 



T)re\i<»us calrula- 



ding 



comet's 



K, and its inclination to the ecliptic I, we may 



P 



the 



■ 



truel >ngitudeof the nodeK + wP, and the true inclination 1+ w Qj 

 (P and Q being any assumi-.d small quantities from 20' to -iO') by 

 the foUouins; process, by means of three operations similar to Ihose 



double vosiiion or rule ofjahe 



tic. 



In ihcfrst operation the longitude of the node is put=K, the inclination 



second operation 

 third operation 





I; 



1 + Q. 



In the first operation we have the elements K, T, which deter- 

 mine the assumed plane of the comefs orbit ; and then the geocen- 



tric longitudes and latitudes of the comet beins; 



3 



known, together 



with the longitudes of the earth and its distances fiom the sun, w« 



