SECT. 1.] THREE COMPLETE OBSERVATIONS. 163 



highest degree of perfection that is desired. Then it will be proper to undertake 

 the final correction, in which the perturhations that the other planets cause in the 

 motion, will he taken account of: we will indicate briefly in the fourth section, 

 how these may be taken account of, so far at least, as it shall appear consistent 

 with our plan. 



116. 



Before the determination of any orbit from geocentric observations, if the 

 greatest accuracy is desired, certain reductions must be applied to the latter on 

 account of nutation, precession, parallax, and aberration : these small quantities 

 may be neglected in the rougher calculation. 



Observations of planets and comets are commonly given in apparent (that 

 is, referred to the apparent position of the equator) right ascensions and declina 

 tions. Now as this position is variable on account of nutation and precession, 

 and, therefore, different for different observations, it will be expedient, first of all, 

 to introduce some fixed plane instead of the variable plane, for which purpose, 

 .either the equator in its mean position for some epoch, or the ecliptic might be 

 selected : it is customary for the most part to use the latter plane, but the former 

 is recommended by some peculiar advantages which are not to be despised. 



When, therefore, the plane of the equator is selected, the observations are in 

 the first place to be freed from nutation, and after that, the precession being- 

 applied, they are to be reduced to some arbitrary epoch : this operation agrees 

 entirely with that by which, from the observed place of a fixed star, its mean 

 place is derived for a given epoch, and consequently does not need explanation 

 here. But if it is decided to adopt the plane of the ecliptic, there are two courses 

 Avhich may be pursued : namely, either the longitudes and latitudes, by means of 

 the mean obliquity, can be deduced from the right ascensions and declinations 

 corrected for nutation and precession, whence the longitudes referred to the mean 

 equinox will be obtained ; or, the latitudes and longitudes will be computed more 

 conveniently from the apparent right ascensions and declinations, using the appar 

 ent obliquity, and will afterwards be freed from nutation and precession. 



The places of the earth, corresponding to each of the observations, are com- 



