IXX ASTROXO.MY. 



The first three of these are adapted to logarithmic computation as follows : — 



n sin iV= cos </> cos /, 

 n cos A'= sin <^, 



cos z = ?i sin (S -f- i\^), 

 sin z cos q =^ ti cos (8 -|- 7V), 

 sin sin q =^ cos ^ sin /; 

 whence 



tan iV= cot (^ cos /, 



tan / sin JV . s 



'^" ^ "" ^ = sin (8 + ^y ^^> 



tan s cos ^ = cot (8 -}- A^). 



A similar adaptation results for the last three of equations (i) by interchanging 

 8 and z. The equations (2) give both z and q in terms of <f}, S, and /, without 

 ambiguity, since tan z is positive for stars above the horizon. 



If A, s, and q are all required from ^, 8, and /, they are best given by the 

 Gaussian relations 



sin ^ z sin ^(A -\- q) = s'm \ t cos ^(<^ -j~ ^)> 



sin ^ 2 cos J(^ -|- ^) :^ cos h t sin ^(<^ — ^), / \ 



cos ^ 2 sin \{A — q) =:. sin ^ t sin ^(<^ -f" S), 



cos ^ 2 cos ^(^ — q)z= cos ^ / cos i(^ — S). 



f. Hour angle, azimuth, and zenith distance of a star at elongation. 



In this case the parallactic angle is 90° and the required quantities are given by 



the formulas 



tan <^ 



cos / = 7 oT' 



tan 



sin A=^ 7» (i) 



cos ^ ^ ^ 



sin ^ 



cos z = —■ — j* 

 sin 6 



When all of the quantities /", A, and z are to be computed the following formulas 

 are more advantageous : — 



A^ = sin (8 + <^) sin (8 - <^), 



sin / = 7 — -■ — 5' cos A = ——-7' sin z = -^—^■> (2) 



cos cj) sin 6 cos ^ sin ^ ' 



^ , cos 8 A" 



tan/=^ — ; 5' tan ^ = — tt-^ tan 2 = 



sin cj) cos 8 ' A' sin ^ 



g. Hour angle, zenith distance, and parallactic angle for transit of a 



star across prime vertical. 



In this case the azimuth angle is 90° and the required quantities are given by 

 the formulas 



