104 Reduction of Stellar I'hotoijrajyhs. 



Jf^ Xsec ^5+ N, Y, for Xsec rf, 



dfy Xsecf5+iV^,, r, for F, 



where ilf , ilf , i\^^, -A^,, are computed by the following formuljB : 

 sin n sin X=cosffl cos (O — a) 

 sin ri cos iV ^ sin f 



G = cot ( rf + iV^) 



H = tan C^ — a) sin iV cosec ( rS + A'') 



Mx=ft {i^H^— G tan f5) sin i" 



N^ ==3.1^ /? ( G! jH" sec (5 — if tan rf sec rf) sin 1" 



iify = 15 /3 ( (^ B" cos <^ + H sin f5) sin 1" 



iV,, =/3 ( i+(?2) sin i" 



111 these formulae (^^ — a) is the hour-angle, and /9 the constant 

 of refraction. The coefficients are so arranged that the correc- 

 tion for X sec 8 will come out in seconds of time, and that for Y 

 in seconds of arc, if A'seccJand Fare themselves expressed in 

 seconds of time and arc respectively. 



When the hour-angle does not exceed about one hour, the 

 above formulae may advantageously be replaced by the following, 

 especially if it is intended to tabulate the coefficients 31^, etc., for 

 a given declination, with the hour-angle as argument. If we put : 



t =& — a 



and suppose t to be expressed in minutes of time, and compute : 



tan I = V tan (p 



[6.4531 — 10] Wi--= P cos </> sec {<p — c5) sec ^ sin i" 



[1.1308 — -lo] u"2 = 4 /3sin 2 ^sec^ (<^— ^) sec (5 cos (Z+f^) cosec Z sin^i^sin i" 



[2.9169 — 10] W3 = iV/^ sin {<p- — a (5) cos ^ sec^ S sec'^ ((f> — S) sin i^sin 1" 



[4.9681 — 10] if4=. V /^ sin 2 sec^ {<p — (?) sin i™sin i" 



[6.4532 — 10] w^ = P sec^ ((/> — 6) sin i" 



[6.4637—10] iVg = yV ^<^4 tan (0 — S) sin 1'" 



where the constant logarithmic coefficients at the left-hand side 

 are computed from the Besselian refraction table, using a con- 

 stant value of log /5; which may be done safely, when the zenith 

 distance does not exceed 45°. They include the effect of the dif- 

 ference between. the photographic and visual refraction constants, 

 and will therefore only need to be increased b}^ the usual loga- 

 rithm depending on the. meteorological instruments. We then 

 have : 



