68 RELATIONS PERTAINING SBITLY [BOOK I. 



I. The plane of Z is the ecliptic itself, and the longitudes of the poles of the 

 remaining planes, the distances from which are -X&quot;, Y, are respectively N, and 

 J\ r -U90; then 



X=Rcos(L N), Y = Swci(L JV), Z=Q. 



II. If the plane of Z is parallel to the equator, and the right ascensions of the 

 poles of the remaining planes, from which the distances are X, Y, are respectively 

 and 90, we shall have, denoting by the obliquity of the ecliptic, 



X=RcosL, Y=RcoszsinL, Z=RsinssinL. 



The editors of the most recent solar tables, the illustrious VON ZACH and DE 

 LAWBRE, first began to take account of the latitude of the sun, which, produced 

 by the perturbations of the other planets and of the moon, can scarcely amount 

 to one second. Denoting by B the heliocentric latitude of the earth, which will 

 always be equal to the latitude of the sun but affected with the opposite sign, we 

 shall have, 



In Case I. 



X = R cos B cos (L N) 



Z=RsinB 



In Case 



X = R cos B cos L 



Y= R cos B cos s sin L R sin B sin e 



Z R cos B sin g sin L -\- R sin B cos f. 



It will always be safe to substitute 1 for cos B, and the angle expressed in parts 

 of the radius for sin B. 



The coordinates thus found are referred to the centre of the earth. If , 77, , 

 are the distances of any point whatever on the surface of the earth from three 

 planes drawn through the centre of the earth, parallel to those which were drawn 

 through the sun, the distances of this point from the planes passing through the 

 sun, will evidently be X -{- , Y-\- 77, Z -\- L : the values of the coordinates , 17, C, 

 are easily determined in both cases by the following method. Let (&amp;gt; be the radius 

 of the terrestrial globe, (or the sine of the mean horizontal parallax of the sun,) 

 X the longitude of the point at which the right line drawn from the centre of the 

 earth to the point on the surface meets the celestial sphere, /? the latitude of the 

 same point, a the right ascension, d the declination, and we shall have, 



