SECT. 2.] TO POSITION IN SPACE. 69 



In Case I. 

 = ^&amp;gt; COS /? COS (X 



1 = 9 cos /3 sin (X 

 = Q sin |3 



In Case IT. 



() COS d COS 05 



= Q cos d sin 



(&amp;gt; sin d. 



This point of the celestial sphere evidently corresponds to the zenith of the 

 place on the surface (if the earth is regarded as a sphere), wherefore, its right 

 ascension agrees with the right ascension of the mid-heaven, or with the sidereal 

 time converted into degrees, and its declination with the elevation of the pole ; 

 if it should be worth while to take account of the spheroidal figure of the earth, 

 it would be necessary to adopt for d the corrected elevation of the pole, and for 

 Q the true distance of the place from the centre of the earth, which are deduced 

 by means of known rules. The longitude and latitude X and /? will be derived 

 from a and d by known rules, also to be given below : it is evident that X coin 

 cides with the longitude of the nanagesimal, and 90 (3 with its altitude. 



60. 



If x, y, s, denote the distances of a heavenly body from three planes cutting 

 each other at right angles at the sun; X, Y, Z, the distances of the earth (either 

 of the centre or a point on the surface), it is apparent that x X,y Y, 2 Z, 

 would be the distances of the heavenly body from three planes drawn through 

 the earth parallel to the former; and these distances would have the same relation 

 to the distance of the body from the earth and its geocentric place,* (that is, the place 

 of its projection in the celestial sphere, by a right line drawn to it from the earth), 

 which x, y, z, have to its distance from the sun and the heliocentric place. Let J 

 be the distance of the celestial body from the earth ; suppose a perpendicular in 

 the celestial sphere let fall from the geocentric place on the great circle which 

 corresponds to the plane of the distances z, and let a be the distance of the 

 intersection from the positive pole of the great circle which corresponds to the 



* In the broader sense : for properly this expression refers to that case in which the right line is 

 drawn from the centre of the earth. 



