292 APPENDIX. 



If these values are substituted in the general expression for coordinates, 



a k cos (f cos jfTsin E -j- a k sin l(cos E e] 

 and if we put 



a cos (f = b 



n , . Tl I 21 -COS (a - 2 2)1 



a cos 2 i i cos TI 1 4- tan 2 i a - = ^ 



L cos a J 



b cos 2 * sin * [l + tan 2 4 1 8in (-28)1 = # 



sin n \ 



2 1 2 i -sin ( 2Q)1 j/ 



a cos 2 4 z sin nil tan- i z - = A 



L sin a J 



, n . . o , .COS( - 28)1 i-., 



b cos 2 i a cos n 1 bur J - == - 



L cos n J 



a sin sin (n & ) = J.&quot; 

 i sin e cos (it & ) = B&quot; 



the- coordinates will be 



x = A (cosE e)-\-B sinE = ^l (1 esecE)+JB sin E 

 y = A (cosE e)-\- smE = A f (1 esecE) -(-^ sinE 

 z = A&quot; (cos E e) 4- B&quot; sin E = A&quot; (l e sec E) + B&quot; sin E. 



If the equator is adopted as the fundamental plane instead of the ecliptic, 

 the same formulas may be used, if Q,,n, and i are referred to the equator by 

 the method of article 55. Thus, if Q e denote the right ascension of the node 

 on the equator, for Q, n, and i, we must use 8 E , Q e -{-(n 8) .4, and i 

 respectively. 



This form has been given to the computation of coordinates by Prof. PEIRCE, 

 and is designed to be used with ZECH S Tables of Addition and Subtraction Logarithms. 



Example. The data of the example of articles 56 and 58, furnish 

 Q ==15830 50&quot;.43, TT = = 122 12 23&quot;.55, t=ll 43 52&quot;.89 when the equator 

 is adopted as the fundamental plane ; and also log b 0.4288533. 



Whence we find 



log cos (n 2 Q, ) 9.9853041 n log sin (n 2 Q) 9.4079143 



log sec n 0.2732948 n logcosecTt 0.0725618 



log tan 2 H 8.0234332 log tan 2 U 8.0234332 



logo 8.2820321 logs 7.5039093 



