224 



DETERMINATION OF AN ORBIT FROM 



[BOOK II. 



the new values of the quantities P, Q in the new hypothesis, but these are to 

 be derived from the combination of the first three hypotheses, agreeably to the 

 method of article 120. It will then very rarely be requisite to proceed to the 

 fifth hypothesis, according to the precepts of article 121. We will now explain 

 these calculations further by an example, from which it wih 1 appear how far our 

 method extends. 



159. 



For the third example we select the following observations of Ceres, the first 

 of which has been made by OLBERS, at Bremen, the second by HARDING, at Got- 

 tingen, and the third by BESSEL, at Lilienthal. 



As the methods by which the parallax and aberration are taken account of, 

 when the distances from the earth are regarded as w r holly unknown, have already 

 been sufficiently explained in the two preceding examples, we shah 1 dispense 

 with this unnecessary increase of labor in this third example, and with that 

 object will take the approximate distances from VON ZACH S Monatlielie Corre- 

 ispondenz, Vol. XL, p. 284, in order to free the observations from the effects of 

 parallax and aberration. The following table shows these distances, together 

 with the reductions derived from them : 



J.111HJ 111 W 111U11 Lilt; llli 



o 



Eeduced time of observation . 

 Sidereal time in degrees 

 Parallax in right ascension 

 Parallax in declination 



