70 RELATIONS PERTAINING SIMPLY [BOOK 1. 



plane of the distances x; and, finally, let I be the length of this perpendicular, or 

 the distance of the geocentric place from the great circle corresponding to the 

 distances z. Then I will be the geocentric latitude or declination, according as the 

 plane of the distances e is the ecliptic or the equator ; on the other hand, a -(- N 

 will be the geocentric longitude or right ascension, if N denotes, in the former 

 case, the longitude, in the latter, the right ascension, of the pole of the plane of 

 the distances x. Wherefore, we shall have 



x X = /J cos b cos a 

 y Y= z/ cos b sin a 

 z Z = A sin b . 



The two first equations will give a and A cos b ; the latter quantity (which must 

 be positive) combined with the third equation, will give I and d. 



61. 



We have given, in the preceding articles, the easiest method of determining 

 the geocentric place of a heavenly body with respect to the ecliptic or equator, 

 either free from parallax or affected by it, and in the same manner, either free 

 from, or affected by, nutation. In what pertains to the nutation, all the difference 

 will depend upon this, whether we adopt the mean or true position of the equator; 

 as in the former case, we should count the longitudes from the mean equinox, 

 in the latter, from the true, just as, in the one, the mean obliquity of the ecliptic 

 is to be used, in the other, the true obliquity. It appears at once, that the greater 

 the number of abbreviations introduced into the computation of the coordinates, 

 the more the preliminary operations which are required ; on which account, the 

 superiority of the method above explained, of d-eriving the coordinates immedi 

 ately from the eccentric anomaly, will show itself especially when it is necessary 

 to determine many geocentric places. But when one place only is to be com 

 puted, or very few, it would not be worth while to undertake the labor of calcu 

 lating so many auxiliary quantities. It will be preferable in such a case not to 

 depart from the common method, according to which the true anomaly and radius 

 vector are deduced from the eccentric anomaly; hence, the heliocentric place 



