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Art. X. ASTRONOMICAL AND NAUTICAL 

 COLLECTIONS. 



No. XIX. 



i. A Method of finding the Latitude at Sea, by the Altitudes qf 

 two fixed Stars when on the same Vertical. By C. Blackburn, 

 Esq., of the Royal Naval College, Porismouth. 



Let the corrected altitude, polar and zenith distances of that hea- 

 venly body which has the greater altitude, be denoted by A, P, Z ; 

 and the corresponding quantities belonging to that heavenly body 

 which has the less altitude be denoted by a, p, z. Let A — a be 

 called I ; and P + I be called S ; then 



Rule. 

 Add together the five following logarithms, viz., the I . cosec. I ; 



the Z. cosin. A ; the Z. sin. |S+p; the Z . sin. ^ S—p, and the con- 

 stant logarithm 0.301030 ; and reject 30 from the index. 



Subtract the natural number* belonging to this logarithm from 

 the nat. cosin. P — Z ; the remainder will be the nat. sine of the 

 true latitude. 



Demoxstration. 



Let the figure represent a projection of the hemisphere upon the 

 plane of the meridian ; Z the zenith, P the pole ; HO the horizon ; 

 S, s, two places of the same, or dilferent heavenly bodies on the 

 same vertical Zx; PS and Ps meridians ; then by the principles of 

 spherical trigonometry, 



cos.^ 1 PSs =i R'Xsin4(PS + Ss + Ps )xsin .|(PS+Ss-P^) 



sin. PS X sin. Ss 

 or sin.= ^ ZSP = R° X sin.|(S + p) X sin .^ (S-p) 

 sin. P X sin. I 



Again, cos. ZP = cos. (PS ^ZS) — sin. PS x sin. ZS X sin.'' \ 

 ZSP X -^ 



• If the index of the lop:arilhin be 9, find the natural number to as many 

 places as tlie Tables are calculated to : if the index be 6, to one less, and so on. 



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