26-i On the licpeating Cinic. 



astronomers have practised this method, which on account of 

 the great liberty it gives the observer, to take his observations 

 at any time, not subjecting him to a time determined and H- 

 mited, deserves to be generally received, particularly by tra- 

 velling astronomers and mariners. 



At all times observers have contented themselves with taking 

 meridian altitudes of the pole-star at its two transits in tlie 

 four-and-twenty hours. These two points, doubtless, are the 

 most advantageous for obtaining the latitude of the place of 

 observation, independently of the declination of the star. Lat- 

 terly, it has been proposed to take the altitudes of this star at 

 the instants of its utmost digressions toward the east and west. 

 These points are much less favourable, especially when the 

 time is not determined with the greatest strictness; on the 

 contrary, it appears to me, that any other point on the ]iara]lel 

 of tins star is preferable to those two points, as I shall have 

 the honour of showing you. 



Let z be the zenith distance of the star ; p its apparent di- 

 stance from the pole of the equator; t the horary angle, 90— ^i/ 

 the latitude sought ; we shall have, by supposing the distance 

 ji small, as it is for the pole-star, 



dA) ■= —. — — '-^^ — (Zs — tans;, v sin. t. dt + cos. t. dp. 



sin -4/ COS. p ° -^ ■* 



Hence it appears that an error in the observed zenith di- 

 stance produces, every where, nearly the same error in the 

 latitude ; and this is likewise the case for the meridian transits, 

 which in this respect are not preferable to all the other jjoints 

 of the parallel of this star. As to the error in declination, it 

 is very little to be feared in the pole-star so well determined : 

 besides, the error that would result for the latitude is less in all 

 the other points of the parallel than in those of the meridian 

 transits, which under this point of view ^vould be the least ad- 

 vantageous. Again, let us consider the error of the time. It 

 is true that this error does not influence the observations made 

 in the meridian, and in this case they seem preferable to the 

 others. But when it is considered that the factor dt in the 

 preceding formula is tang. p. sin. t, it is seen that an error in 

 the time has a very small influence on the latitude, as well as 

 in every other point of the parallel. Let us suppose the error 

 in time to be one second or fifteen seconds in arc, we shall 

 have tbi' the horary angles of 6 hours. ..4 hours. ..2 hours, 

 errors in latitude of 0"-4. 0"-3 0"-2. 



All astronomical observers will agree that an error of 0"'4 

 in arc, is inappreciable, that it is mipossible to answer for it 

 with our largest circles, and our most jierfect instruments. In 

 every case, we shall still have the means of eliminating that 



crroi'. 



