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VII. Further Remarks on the iic^lO Method of detci-iimiing the 

 Latitude of a Place, by Observations of the Pole-Star. By 

 Francis Daily, Esq. F.R.S.* 



In the last Number of the Philosopliical Magazine, I pointed 

 but the method which had been lately suggested by M. Lit- 

 trow for determining the latitude of a place by observations of 

 the zenith distance of the pole-star, at any part of its diurnal 

 revolution. Since that paper was printed I have re-considered 

 the subject more attentiveh', and find that that method is not 

 confined to the pole-star, but that it may be extended with 

 equal advantage to other stars situated at even a greater distance 

 from the pole, and whose slow motion in altitude renders them 

 peculiarly adapted to such observations. 



This will be seen from the following demonstration of the 

 general proposition: and as it does not appear to me that the 

 steps of the process have been very strictly pursued by some 

 of those mathematicians who have treated thereon (smce very 

 different results have been deduced by them), I hope I need 

 not apologize for here calling the attention of the reader once 

 more to the subject. 



Let Z be the zenith of the place of 

 observation ; P the pole ; and S the 

 place of the star, in its revolution 

 round P : from S let fall the line S Q 

 perpendicular to Z P. Then we shall 

 have Z S = z = the zenith distance of 

 the star: PS = p = the north polar 

 distance of the star : the angle Z P S 

 = t= the hour angle : Z P = vI/= the 

 co-latitude of the place : and Q P 



= u = the segment formed by the perpendicular. Now z, p, 

 and t being given, we have, by the common solutioji of the 

 case in spherical trigonometry, 



tan u = cos /. tan p 



cos u 



COS (vl/ — U] = COS Z. 



^ ' cos Jl 



Tills solution is general : and it may readily be seen that 

 by the help of seven logarithms, any particular case may be 

 determined. M.Littrow has, with a view to the more familiar 

 and easy solution of the case of the pole-star, thrown tiie 

 value of p and u into series, by the following well known ex- 

 pressions : 



* Communicated by the Author. 



F 2 tan 



