100 Astronomical and Nautical Collections. 



or sin. OP . = cos. rP ^ Z) - sin. P X sin. Z x sin.= JZSP X ■ ^ 



Therefore by substituting in this latter equation, the former value 

 of sin.' I ZSP, we get, 

 sin. OP = COS. (P- Z) _ sin.P Xsin.Zx sin.KS+p) X sin.^ (S -p)X 2 



' ' sin. P X sin. I x R 



or sin. Lat. = cos. (P-^Z) — cosec. I x cos. A x sin. ^(S+p) 

 X sin. \ (S— p) X , which is the same as the rule. 



Example I. 

 January 30, 1825, in N. latitude, let the altitudes of Capella and 

 Castor when on the same vertical be respectively 48° and 17° 45'. 

 Required the latitude. 



1. cosec. I = 0.297764 P = 44 I'l 17 



1. cosin. A = 9.825511 I = 30 15 



1. sin.|.S+i3= 9.961028 

 1.3in.i.S^= 9.162025 

 const.log. = 0.30103O 

 N = 352663 9.547358 



n. cos. P3:Z= 999271 i.S+p=66 5 17 



-N = 3.>2663 ^.S-p= 8 21 



Lat. 40° 17' 11" ~646608 = n. s. 



