86 Mr. _Ba.ily's proj)Osed Tables for the 



11. There is, however, another correction necessary in the 

 application of these tables, to which I have not yet alluded. 

 It is well known to all practical astronomers that every star 

 will once in every year culminate tidcc in a mean solar day, 

 when the sun has the same right ascension as the star: and 

 the fictitious day will then have gained a day on the civil 

 mode of x'eckoning astronomical time. This correction is 

 common to all the stars : and when the annual values are 

 computed it is usual to annex an asterisk to the interval which 

 includes the day above alluded to; and the intervals, so 

 marked, will comprehend eleven culminations of the star. For 

 those stars also whose right ascension is between O*" and 

 IS*" 4'4"' we must make a. further addition of unity to the given 

 date from the commencement of the year to the day on which 

 it is in conjunction with the sun. These corrections M. Bessel 

 denotes by the letter / : so that the Argument for entering the 

 tables will be 



T = T + 2 — i' — /, 



where T denotes the given day, according to the civil mode of 

 reckoning astronomical time, from noon to noon : x the same 

 nominal date in the tables ; / a number which must be taken 

 equal to 0, 1 or 2, according to the circumstances of the case * ; 

 and X and I the same as in my Introduction to the New Tables 

 of Precession, Aberratioti, &c. already alluded to. 



12. These three corrections, — viz. 1° for the commence- 

 ment of the year ; 2° for the day of culmination with the sun ; 

 and' 3° fo)- the longitude, — are all that are required in the 

 use of these tables. The argument being once found for the 

 given year, the requisite differences for the computation of 

 the a7iniial tables are easily deduced, in most cases by in- 

 spection, and always very readily by the assistance of a small 

 auxiliary table of proportional parts. 



13. The lunar-nutation may be computed for intervals of 

 100 days only: for, the motion of the moon's node is so slow 

 that it will be unnecessary to compute for any smaller inter- 

 vals. The mean longitude of the moon's node on January 1, 

 1800, when the mean longitude of the sun Avas 281°, was, by 

 the recent tables of M.Damoiseau, equal to 33°*2107 : and the 



* If the right ascension of the star is greater than IS*" 44'", i is equal to 

 0, from January 1 to the clay on which the sun's right ascension is the 

 same as that of the star; and, after that period, it is equal to 1, to the 

 end of the year. If the right ascension of the star is less than IS"" 44™, 

 2 is equal to 1 from January 1 to the day on which the sun's true right 

 ascension is the same as that of the star; and, after that period, it is equal 

 to 2, to the end of the year. Thus, for a. Aquilcc, April 10th, according 

 to the civil mode of reckoning astronomical time, will be equal to the ta- 

 Indar April 1 1th, because in this case i is equal to 1. 



mean 



