ASTRONOMY. Ixix 



For logarithmic application of (4) we may write 



m- = cos ^ cos 8, n^ = sin'-' 2 (<J^ ~ ^)> 



tan JV= "' sin ^ t, (5) 



n 



, n in . , 



sin i s = -irr= ^ — TrSm \ t. 



cos yv sin iV -^ 



c. Declination and hour angle in terms of altitude and azimuth. 



The fundamental relations for this case are 



sin 8 = sin (^ sin h — cos ^ cos h cos A, 

 cos S cos / = cos (/) sin h -j- sin <^ cos h cos .<4, (i) 



cos 8 sin / = cos // sin A. 



For logarithmic computation by means of an auxiliary angle J/ one may write 



VI sin M:= cos h cos ^, tan J/= cot // cos A, 



m cos 7J/= sin //, 



. 5j ■ ^ L A4-\ . , ta-n A sin J/ ,-. 



sin 8 = w sin (c^ — M), tan / = — -— , (2) 



cos {(ji — M) 



cos 8 cos / = f/i cos (cfi — M), 



cos 8 sin / ^ cos // sin A, tan 8 = tan (</> — J/) cos /. 



d. Hour angle and azimuth in terms of zenith distance. 



, cos z — sin (h sin 8 



cos / = —^ . 



cos </) cos 8 



tan= ^ ^ ^ sin_Or^-^)_co^(a^-^) ^ ^ w^ , g _|_ ^). 

 ^ cos o- cos (o- — 2) ' - VV' I I / 



. sin cf> cos ^r — sin 8 



cos .r4 = ^ : . 



cos cf) sin 2 



tan^ i ^ = sin (g- - <^) cos (cr - 2) ^ ^ ^ ^^ _|_ g _^ ^), 

 cos o- sin (o- — 8) - V I 



e. Formulas for parallactic angle. 



cos z = sin 8 sin ^ -\- cos 8 cos <^ cos /, 

 sin z cos ^ = cos 8 sin — sin 8 cos (ft cos /, 

 sin 2 sin (/ = cos ^ sin /, 



sin 8 = cos z sin <^ -j- sin " cos <f> cos /, 

 cos 8 cos ^ ^ sin s sin cf) -(- cos s cos ^ cos ^, 

 cos 8 sin <7 = cos <f> sin .^. 



(0 



