164 DETERMINATION OF AN ORBIT FROM [BoOK II. 



puted from the solar tables, but they are evidently to be referred to the same 

 plane, to which the observations of the heavenly body are referred. For which 

 reason the nutation will be neglected in the computation of the longitude of the 

 sun ; but afterwards this longitude, the precession being applied, will be reduced 

 to the fixed epoch, and increased by 180 degrees ; the opposite sign will be given 

 to the latitude of the sun, if; indeed, it seems worth while to take account of it : 

 thus will be obtained the heliocentric place of the earth, which, if the equator is 

 chosen for the fundamental plane, may be changed into right ascension and decli 

 nation by making use of the mean obliquity. 



117. 



The position of the earth, computed in this manner from the tables, is the 

 place of the centre of the earth, but the observed place of the heavenly body 

 is referred to a point on the surface of the earth : there are three methods of 

 remedying this discrepancy. Either the observation can be reduced to the centre 

 of the earth, that is, freed from parallax ; or the heliocentric place of the earth 

 may be reduced to the place of observation, which is done by applying the 

 parallax properly to the place of the sun computed from the tables ; or, finally, 

 both positions can be transferred to some third point, which is most conveniently 

 taken in the intersection of the visual ray with the plane of the ecliptic ; the 

 observation itself then remains unchanged, and we have explained, in article 72, 

 the reduction of the place of the earth to this point. The first method cannot be 

 applied, except the distance of the heavenly body from the earth be approxi 

 mately, at least, known : but then it is very convenient, especially when the 

 observation has been made in the meridian, in which case the declination only is 

 affected by parallax. Moreover, it will be better to apply this reduction imme 

 diately to the observed place, before the transformations of the preceding article 

 are undertaken. But if the distance from the earth is still wholly unknown, 

 recourse must be had to the second or third method, and the former will be em 

 ployed when the equator is taken for the fundamental plane, but the third will 

 have the preference when all the positions are referred to the ecliptic. 



