46 Further Remarks on the neMo Method of determining the 



Since the latitude may at all times be so easily computed front 

 the general formula which I have deduced, it does not readily 

 appear why M. Littrow should liave considered it necessary to 

 alter the form of it, by the introduction of the series above 

 mentioned. It is true that we are enabled thereby (as far as 

 regards the pole-star) to compose tables for nautical purposes, 

 "wliich may be of great use and advantage at sea ; and save 

 much time and labour. But, this does not seem to have been 

 his object : and moreover, in an observatonj, where the greatest 

 accuracy is required, th.e approximate formula is always equally 

 laborious with, and sometimes more so than the correct one ; 

 as may be readily ascertained on trial. For, six logarithms are 

 always required; besides the proportional parts of B and C, 

 and other reductions on account of the variation in the north 

 polar distance of the star, when p and t do not correspond 

 with the value in the table. 



The observations, for determining the latitude of a place, 

 are usually formed into series of 20 or 30 each : and if we 

 could, by the help of any tables, annex to each observation its 

 correction depending on the distance of time fi-omthe mean time 

 of the whole series, and after dividing the sum by the whole 

 number ( = N) of observations, approximate towards the cor- 

 rect value by the help of any formula (similar to the plan 

 adopted by M. Delambre, in his Reduction to the meridian) a 

 great deal of time and labour might be saved in the computa- 

 tions. But M. Littrow's formula presents no such advantages. 



It is true that he has elsewhere suggested a plan of this kind, 

 but I nnich doubt whether it can be practised with conve- 

 nience or success. It is as follows : make 



sin ;). sin ^ 



sm t 



sin z 

 sin ;). sin \^ 



sm 



cos t = m. cott 



<) (' 6" 



2 sin- — 2 sin- — 2 sin- — 



2 2 2 n 



A = —-777- H —rjT -\ r—TTT- + &C. 



sm 1" sm 1" sm 1" 



where t denotes the mean time of the whole number of obser- 

 vations, and where 9, ¥, 6", &c. denote the difference between t 

 and the time of each respective observation : then by assimiing 



X = (« — ?«% cot~) --^ 



we shall have 



tnn u = tan p>- cos t 



, . . cos t£ , X 



cos (\I/ — 7i) = . cos (Z — Xj 



^ ' cos p ^ 



Now, this is precisely the same formula as that which I have 

 deduced at the commencement of this paper, with the excep- 

 tion 



