SECT. 2.] TO POSITION IN SPACE. 75 



4 J 



d ^/ / sin (X T] d \ -\- cos (X 



, , / cos b sin 5 sin (i /) , , r cos 2 6 , - . cos 2 b 



in which the terms which contain d/ d A are to be multiplied by 206265, or the 

 rest are to be divided by 206265, if the variations of the angles are expressed in 

 seconds. 



V. The inverse problem, that is, the determination of the heliocentric from 

 the geocentric place, is entirely analogous to the problem solved above, on which 

 account it would be superfluous to pursue it further. For all the formulas of 

 article 62 answer also for that problem, if, only, all the quantities which relate to 

 the heliocentric place of the body being changed for analogous ones referring to 

 the geocentric place, L -\- 180 and B are substituted respectively for L and B, 

 or, which is the same thing, if the geocentric place of the sun is taken instead of 

 the heliocentric place of the earth. 



65. 



Although in that case where only a very few geocentric places are to be 

 determined from given elements, it is hardly worth while to employ all the 

 devices above given, by means of which we can pass directly from the eccentric 

 anomaly to the geocentric longitude and latitude, and so also to the right ascen 

 sion and declination, because the saving of labor therefrom would be lost in 

 the preliminary computation of the multitude of auxiliary quantities ; still, the 

 combination of the reduction to the ecliptic with the computation of the geocen 

 tric longitude and latitude will afford an advantage not to be despised. For if the 

 ecliptic itself is assumed for the plane of the coordinates s, and the poles of 

 the planes of the coordinates x,y, are placed in 8, 90 -f- 8, the coordinates are 

 very easily determined without any necessity for auxiliary quantities. We have, 



x = r cos u 



y = r cos/ sin M 



zrsmismti Z=R i&nB 



