414? Prof. Encke on the Calculations requisite 



calculation, as here described, of the apparent place of the 

 moon. With this view it is only necessary to remark, that a 

 star in occultation can be distant from the apparent place of 

 the moon only 15', and from the mean place of the moon only 

 1° 15'. Within the limits of the moon's declination it may be 

 assumed, that stars which are so near each other have per- 

 fectly the same corrections of their places. If we therefore 

 consider the mean place of the moon as the position of a star, 

 and calculate by means of the auxiliary table in the Epbemeris 

 for every superior culmination throughout the year, the cor- 

 rection which must be applied to the mean place of a star of 

 the same right ascension and declination, in the beginning of 

 the year, in order to have the apparent place for the time of 

 the upper culmination, — we have a table giving very nearly the 

 apparent place of each star, as far as it can be occulted by the 

 moon. These are the quantities which, in the tables headed 

 "Auxiliary Tables for the Occultations of Stars," have been de- 

 noted A A and A D ; so that taking A A and A D for the 

 given moment of time from them, we have for all stars occulted 

 A' = A + AA 

 D'=D+AD. 

 In calculating these tables, as the time pressed, some of the 

 small terms have been omitted, and only these forms have 

 been assumed : 



A A =/ + h sin(H + ct) 



AD = i 4- g cos (G + a). 

 The declination of the moon will not exceed + 19° in this 

 year; and the terms multiplied by tang 8 and sin 8 will become 

 small ; likewise sec 8 and cos 8 may be put = 1. 



In order now to reduce everything to a certain form, which 

 greatly facilitates calculations which are to be frequently re- 

 peated, we may abbreviate the solution of the quadratic equa- 

 tion by introducing trigonometrical auxiliary quantities ; and 

 with this view the following expressions may be used : 



For t = h 4- I 

 ± l h + / 

 ± 2 h + /, &c. 



the following quantities may be arranged in a table with 

 single entry : log «, log b, y, r, m', ?i', the argument being * 

 for every tenth second : the quantities a', #, A r for every t, 

 will form tables with double arguments 8 and 7r. 



Thus ex.gr, that part of the general table for Berlin (latitude 



52° 31' 15", ellipticity ), which is used for the occultation 



of 82 Leonis on the 5th April 1830, is as follows: 



21 h 



