500 Trench National Institute* 



to the observation of the distances from a star to a terrestrial 

 object for the determination of the azimuths. M. Burck- 

 hardt has contrived a new one, which he discovered by twice 

 differencing the formulae of the altitudes. The correction of 

 the second differences is proportional to the square of the 

 variation of the horary angle multiplied by a constant. This 

 square may be taken in the table which M. Delambre has 

 given ; and immediately we easily determine the correction, 

 having precise results for the hour, notwithstanding the 

 inequalities of motion in the altitude. 



In the observations of a star before and after its passage 

 to the meridian, in order to have the meridian height, we 

 may suppose the declination constant when a star or even 

 the sun is observed about the time of the solstices ; but to- 

 wards the equinoxes in particular, we must take an account 

 of the variation in declinations j and M. Delambre has also 

 given on this head a formula of a convenient application 

 to all the planets, and even to the moon. M. Burckhardt 

 now gives another, still simpler, since it merely consists in 

 adding to the mean altitude the motion in declination be- 

 tween the mean instant and the passage to the meridian ; 

 but this seems to require more rigorously an equal number 

 of observations before and after the passage, as well as equa- 

 lity among the corresponding horary angles. 



The parallax of right ascension requires a second correc- 

 tion when the moon is under observation ; M. Burckhardt 

 reduces it into tables of an equally convenient construction 

 and application; he is the first who examined this problem, 

 by means of which Borda's circle will give the meridian al- 

 titudes of the moon with the same precision as that of the 

 stars, the declination of which has no sensible motion. 



When a star is very distinct, like the sun and moon, it 

 is easy to bring it into the object glass for each successive 

 observation; but when it is a star, we experience greater 

 difficulties : the use of the azimuth circle, intended for 

 these inquiries, is tedious and inconvenient ; we may see in 

 the meridian the various methods resorted to by M. Delam- 

 bre. M. Burckhardt proposes a moveable arc of a circle, 

 which he attaches to the azimuth circle with a screw, and 



which 



