Latitude of a Place, hj Observations of the Pole-Stay. 45 



the advantage to be obtained thereby ; as I shall in tlie sequel 

 more tuUy explain. 



I have stated that different results appear to have been ob- 

 tained by different mathematicians in their solution of this 

 problem. Dr. Dirksen makes the value to be 



4>= 2 -j-^J.cos ^ — f- sin- /. cot r}/ — ^ sin^ t. cos t. cot ^ 4/ 



which differs from the formula above adduced, by having in 

 tlie third term cot ^l^ instead of cot :: ; whilst the fourth term is 

 altogether different. Mr. Horner's formula also, which is 

 much more complex than Dr. Dirksen' s, involves t^lie cot •^. 

 The tables likewise of Mr. Stevens (to which I shall presently 

 allude) as well as those of M. Schumacher, appear to be founded 

 on the same erroneous formula;. The table also recently pub- 

 lished by Capt. Lynn, in page 133 of his " Star Tables for 

 1823," and which was furnished by an eminent mathematician 

 and astronomer, seems formed on the same principle. The 

 .same may likewise be said of the rule given by the Rev. 

 Mr. Lax in Problem XIV. of his " Tables to be used with the 

 Nautical Almanac." It is not easily seen how these diflerent 

 authors can have deducetl their formulas so as to involve ex- 

 pressions depending on the co-latitude of the place of observa- 

 tion ; since it by no means enters into any of the steps of the 

 process. It is true that, in the case of the pole-star, and for 

 nautical purposes, this substitution of the co-latitude for the 

 zenith distance will not be of any consequence. But in the 

 case of stars having greater north-polar distance, and where 

 the observations are carried on in an observatory, the computa- 

 tions nmst be confined to the correct formula. In foct, since 

 the true values are in all cases more easily deduced from the 

 correct formula, there can be no good reason for, at any time, 

 liaving recourse to an erroneous one. In the example given 

 in my former paper an error of 2" woukl arise from the sub- 

 stitution of the approximate co-latitude, for the zenith distance: 

 but in the case of 2 Ursce Minoris the error would be 10 times 

 greater from a similar substitution*. These (juantities may be 

 of little or no moment at sea, but in an observatory they cannot 

 be neglected. 



• Tills star, wliicli, after tlic jjole-star, is the next resorted to for obser- 

 vations of the hititiule, as well as for the a<ljiistiiient of the transit in- 

 strument, is not one of the stars which arc inchidod in the Greeawicii 

 catalogue: therefore neither its mean ])lace at the hej^innin;,' of the year, 

 nor its apparent place at any other time is to l)e fomui in tlie Nautical Al- 

 manac. On the Continent, however, the position of this star is con- 

 sidered of so nnicli importance that (like the pole-star) its fipjxirait place, 

 both in right ascension and declination, is now calculated for cvcrj/ day \\\ 

 the year: an example svorthy of imitation in this country. 



Since 



