4 PREFACE. 



Bessel's formuLe (Astron. Nachr., No. 145, and Astron. Jahrbucli for 1831 j 

 are preserved unaltered. The several columns of the general list now 

 contain, 1, the date; 2, the star's name; 3, the star's magnitude; 4, the 

 limiting parallels of visibility; 5, "Washington mean time of the moon's true 

 conjunction with the star in right ascension ; 6, Washington hour angle, in 

 time, of the star at the time of true conjunction ; 7, co-ordinate q at the time 

 of true conjunction; 8, hourly variation p' of co-ordinate j9 ; 9, hourly varia- 

 tion ^ of co-ordinate q\ 10, logarithmic sine of the star's declination; 

 11, logarithmic cosine of the star's declination. 



At the time of true conjunction ^> = 0; for any other time cr+ {t),p = {t)p', 

 and q = y + {t) q'. 



H being for true conjunction, h = H+ sidereal equivalent of (;'), and, for 

 the same reason, 2' = cT + (;!). The notation is made to correspond to these 

 changes. 



The sign + will hereafter be given to west longitudes, and the sign — to 

 east longitudes. The value of the constant k has been changed by re- 

 taining Mr. Airy's correction of the lunar parallax, and rejecting the cor- 

 rection of asj part of semi-diameter, which Avas before applied. The small 



1 — e- 

 table containing the values of log. A = ,-t\ 1 ■ i \ and of log. B = 



'^ x/ (1 - e^ sm^ 1-) ° 



is retained. 



■v/ (1 — e' sin^ $) 



The object in increasing the general list is, to provide the means of fre- 

 quent determinations of the longitude throughout the earth; to make it 

 especially useful to geographers in general, to the boundary and other sur- 

 veyors of the Government in the interior, to the coast survey of the United 

 States on both oceans, and to the explorers of unknown parts of the 

 continent. 



At the close of the general list will be found Bessel's formulfp, and an 

 example of their use, together with some suggestions as to the manner in 

 which the lists may be rendered more convenient to those who resort to 

 them habitually. 



CHARLES HENRY DAVIS, Superintendent. 



