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LXI. On finding the Latitude by the Altitudes of two Stars. 

 By M. Smith, Esq. 



To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, 

 f SEND you the following very simple and accurate method 

 *• of determining the latitude of any place in the northern 

 hemispheres, by the altitudes of the two stars Aliath (or s Ursa 

 Majoris) and y Cassiopeia, taken at the same instant, without 

 the hour of the night or any other data being required. The rule 

 supposes the two stars to differ exactly twelve hours in right 

 ascension ; it will therefore be rigorously correct in the year 

 1831, and will not produce an error of a mile in the latitude 

 for at least ten years before and after that period. The alti- 

 tudes used must of course be the true altitudes of the stars, or 

 those corrected for refraction and the dip of the horizon, and 

 five places of decimals in the logarithms will be sufficiently ac- 

 curate. I need not trouble you with the demonstration of the 

 rule, as it is precisely analogous to that of reducing the lunar 

 distance, and will therefore be understood by every astronomer. 



The altitudes of the Stars Aliath and y Cassiopeia? given, to 

 find the latitude of the place of observation: — 



Rule. — Add together the two zenith distances and the con- 

 stant arc 63° 20'; take half the sum, from which subtract the 

 zenith distance of Aliath and the constant arc 63° 20', noting 

 the remainders. 



Add together the sines of the two remainders, and the 

 logarithm in the following table; take half the sum of these 

 three logarithms, from which subtract the sine of half the dif- 

 ference between the declination and altitude of Aliath; the 

 remainder is the tangent of an arc; the sine of this arc sub- 

 tracted from the said half sum of the logarithms, leaves the 

 sine of half the required co-latitude. 

 Table. ' 



Example. 



