OF ARTS AND SCIENCES. 



199 



tan B ■ 



Q = 



(.4^, ~ A'u) sin C's 



i V f S 



sin B cos B 



From the spherical triangle PSS', Fig. 4, we get 



cos i (A', — A,) 



(31) 



tan 1 (x + V) = 



tan H;f — '^) = .7 



cos i (A'^ + A,) 

 A.) 



sin i {A's + AJ 



cot J (<'s 

 cot L (f. 



ts) 



ts) 



(32) 



Referrino- ao^ain to Figf. 4, it is evident that SV is the distance, and 

 PSV the position angle of Venus from the centre of the sun. To find 

 the values of these quantities we have 



SV=S'Y' = Q ) 



K33) 



PSV = PSS'±S'SV = PSS'±SS'V = PSS'±PS'S=fPS'V') 



But PSV = w, PSS' = X, PS'S = xp, PS'V = X, and thus we get 



03 = (z ± V) T ^ (34) 



in which the upper signs are to be taken when PS'S is greater than 

 PS'V, and the lower when PS'S is less than PS'V. If it is assumed 

 that the pole which forms part of the triangle PSV is always the 

 elevated one ; and also that position angles are counted from the north 

 around by the east ; then, in the northern hemisphere, when the sun 

 is east of the meridian the position angle will be 360° — w, wliile 

 west of the meridian it will be w ; and in the southern hemisphere, 

 when the sun is east of the meridian the position angle will be 

 180° -|- w, while west of the meridian it will be 180° — m. 



Finally, if the polar distance of Venus, and the difference between 

 her right ascension and that of the sun are required, these quantities 

 may be obtained from the spherical triangle PSV by means of the 



formulae 



tan n = tan q cos (o 



tan A V cos («« ~ «^) = tan (As — n) 



sin n tan a 

 tan A ^ sin («« ~ «^) = 



(35) 



cos (A^ — ii) 



in which a, and a^ are respectively the right ascensions of the sun and 

 of Venus. 



