Ofi the neu) Tables of Aherralion, S/c, 367 



taken if the date is before February 29 ; and the second, for 

 the remainder of the year. These lunnbers, for 1823 and 

 1824, are given at the bottom of my supplementary table. 



Tlie commencement of the year is dated from mean time at 

 Paris; and therefore another slight con-ection for the Argu- 

 ment (denoted by h) is applied when the obsei'vations are made 

 under a different meridian. In no part of England, however, 

 will this correction be of any sensible amount. 



Let f therefore denote the day of observation accordhig to 

 tlie civil mode of reckoning, and g the sidereal time of obser- 

 vation converted into the decimal part of a day ; then will the 

 argument of the Table be the quantity {f+g + fi-\-i-\-lc); 

 which is generally the given date, added to ihe fractional part 

 of a day. But, in fact, we may in most cases neglect the 

 whole of these corrections, and take out the natural numbers 

 corresponding to the logarithms in the table for the given day. 

 For, if the position of the star in declination be within 30° or 

 40° of the equator, the result in ill, will always be true to the 

 nearest tenth of a second, and frequently to the nearest hun- 

 dredth of a second in time. It is only in stars that are situated 

 near tlte pole that any error is likely to arise. The correct 

 values however may always be obtained by attending to the 

 rule given by M. IBessel; whose extreme accuracy has in- 

 duced him to retain every quantity that might, in any sensible 

 manner, affect the ultimate result. 



M. Bessel has annexed to some of the logaritlnns, the small 

 italic letter n ; which, like the + and — signs at the top of 

 .some of the columns, denotes that the natural number corre- 

 sponding thereto is to be taken with a negative sign. This 

 method had been previously adopted by M. Cinuss. Wlien 

 twoof the logarithms, witli contrary signs, are added together, 

 the result is negative: on the contrary, the addition of like 

 signs makes the result jiositive. 



In order to show the application of the tables, take the fol- 

 lowing example. Let it be required to determine the correc- 

 tion, in right ascension and declination, of |3 Leonis on Jamiary 

 20, 1822, at tlie time of its culmination. In this case we have 



Jan'. 



Argument = 20.463 

 But, in fact, the variation from d:iy lo ilay is so trifling tliat 



