(0 



(2) 



(3) 



ASTRONOMY. Ixxi 



tan 8 



cos t = —-—p 

 tan 



sin 8 



cos z = ^- ~r' 

 sin <{> 



cos «^ . 

 sin a = - — s > 

 ^ cos 6 



or, if all of them are to be computed, by the formulas 



7^2 = sin (<^ + 8) sin («^ - 8), 



sin / = —■ — ; 5' sin z = -■ — ^^ cos (7 = -^ «' 



^ — sin ^ cos b sin ^ -^ cos 6 



K K cos ^ 



tan / = ■■ — :n' tan z = — — jj tan a = — rr-* 



xan I — cos <^ sm 8 sin 6 ^ K 



For special accuracy the following group will be preferred : — 



^ o , , sin ((^ - 8) 

 tan' * f = -^ — 7^ — j — s\' 



, tan K^ - g) 



tan^ (45° - i ^) = tan \{^ + 8) tan \{<^ - 8). 



h. Hour angle and azimuth of a star when in the horizon, or at the 



time of rising or setting. 



In this case the zenith distance of the star is 90°, and the required quantities 



are given by 



cos t ■=. — tan ^ tan 8, 



sin 8 



cos ^ = — - — -7 ; 



cos ^ ' 



or by 



cos (<^ — 8) 



^''^"" ^ ^ = cos (<^ + 8)' 



0, ■ ta n K90° - <i' + g) 

 tan , ^ _ ^^^ ^^^^o _ ^ _ gy 



On account of refraction, the values of t and A given by these formulas are 

 subject to the following corrections, to wit : — 



cos <;^ cos 8 sin / sin A ' 



where R is the refraction in the horizon. Thus the actual values of the hour 

 angle and azimuth at the time of rising or setting of a star are 



/ -f- A/ and A + Ay^. 



