AZIMUTH IN TRIGONOMETRICAL OPERATIONS. 101 



, . ^ cos PSS' 

 tan Z — 



But cos ZS 



cot SS'. sin ZS + sin PSS'. cos ZS 



cos PZ sin X 



And tang ZS — 

 /. sin ZS — 



cos PS ~ cos PS 

 cos Z cos Z 



cot PZ tan X 

 cos Z. cos I. 



Consequently tan h Z — 



cos PS 



cos PSS'. cos PS 



cot SS'. cos Z. cos X + sin PSS'. sin X 



cot PSS'. cos PS 1 



sin X cos Z 



tan SS'. tan X. sm PSS' ^ 

 cos- PS. tan i ^P 1 



sin X cos Z 



tan SS'. tan X. sin PSS' + ^ 



Where the upper sign is used, when the star is nearer the Zenith, 

 and the lower, when it is further removed from the Zenith than in the 

 position of maximum. 



If in the former of these cases, which occurs in the Western Elonga- 

 tion before, and in the Eastern after ariving at the maximum, we put 



'tanSS'. fanX.sinPSS'. \'' 



cos 



z 



— sin C 



cos'PS.taniSP ^ _ 



Then iandZ — ^- — • tauD 



sm X 



^ ^ „ COS' PS. fan }^^P. f(tn- . i r . • i 



Or a Z — ^. in seconds of a great circle 



sinX. sin i" 



2 c 



