Latitudes of Montjouy and Barcelona. 245 



quence of the method which he was obliged to employ to arrive 

 at the results. 



On examining the calculations of latitude in the second 

 volume of the * Base du Systeme Metrique,' it is soon per- 

 ceived that they had been preceded by a previous calculation, 

 the object of which was, to derive from the double passages of 

 the circumpolar stars, the declinations which are afterwards 

 employed as elements in the reduction of the observations, re- 

 garded separately as independent zenith distances. 



To us at present such a mode of proceeding may appear 

 strange, but in those times the means within the command of 

 MM. Delambre and M^chain afforded no better mode. The 

 great work of Piazzi had not then appeared ; they had only the 

 catalogues of Bradley, Meyer, Lacaille, and Lalande, in which 

 the elements of reduction employed had not the precision 

 which new and more exact observations have given. I have 

 examined the declinations of the stars they employed, such as 

 they might have been derived from the catalogues above- 

 mentioned, and I find the discordances so great, that even 

 a mean amongst them affords no sufficient guarantee. They 

 were thus obliged to have recourse to that method which 

 derives both the latitude and the declination at the same time 

 from the double passage of a circumpolar star. This method, 

 which was the most esteemed at that period, possesses decided 

 advantages when stars only are used which are very near the 

 pole, such as a. and B Ursse Minoris, in which case the latitude 

 and declination are affected only by instrumental errors ; but 

 at greater distances the errors of refraction are involved, as 

 well as others which may be peculiar to a certain star from any 

 unknown cause. 



We may now perceive, in the employment of this method, 

 the source of the anomaly which the observations with ^ Ursae 

 Majoris present at Montjouy and Barcelona. The declination 

 of the star, derived from its double passage of the meridian, 

 is influenced by the errors arising from the irregularity of 

 refraction in the passage below the pole, the possible defect of 

 verticality in the instrument in the passage above the pole, and 

 in both by the apparent though erroneous place to which the 

 star is in either case referred, in consequence of its double 

 nature. Possessing advantages now which did not (jxi^t in the 



