for predicting Occultations of Stars by the Moon, 413 



double entry, 8 from —30° to +30° for every fifth degree, and 

 7T from 53' to 62' for every third minute : 



, , / p . sin<r.cos<0 \ 9 . _ «./«*.»-- 



a'= — hi 1 5 — -) sin2r .343/ '75 



- \ cos d / 



V = _ h ( *■**£** )* si.. 2 (y-8) . 3437-75 



(p . sin«r . sin <p \ , _. 



siny ) • cos (r-») 



The values are expressed in hundredth parts of minutes of a 

 degree. By this means we find 



a! — a = a sec 8 -f- a' 



8' - 8 = a. sin (y- 8) + # 

 r* — r = Ar 

 almost as accurately as it is required for the most exact cal- 

 culation, as the error will very rarely amount to 1". 



Besides these values, the parallactic velocity of the moon, as 

 it may be called, or the quantities A ex! and A V are required. 

 The first differences of a and 8 give her velocity in right 

 ascension m, and in declination w, with reference to the centre 

 of the earth ; and as differences higher than the second are neg- 

 lected, we may assume that for t = 6 h and r = 18 h the first 

 differences are 12 ?n and 12 n. The unity of time is here the 

 true lunar time, whose ratio to mean time is determined by the 

 first differences of the times calculated. 



In the values for a'— a, 8' — 8, the three variable quantities are 

 7T, 8, and t. The variation of the terms of the second order 

 will never be of consequence ; and in those of the first, % may 

 without hesitation, and even 8 may, be considered as constant. 

 The influence of the latter assumption would only become 

 sensible if the time of the beginning or end of the occultation 

 should be far distant from the lunar hour assumed for r ; in 

 which case, however, the first differential quotients only would 

 likewise not be sufficient. If therefore we calculate for every 

 t, neglecting smaller quantities, 



m' = — q . sin 7r . cos <p . cos t . 900 

 w r = — § . sin 7T . cos <p . sin t . 900 

 and arrange their logarithms to four places of decimals for 

 every 7r, we shall have very nearly 



A ai = m -f w sec 8 

 A 8' = n + n' sin 8. 

 It now remains only to facilitate the calculation of A' and D' 

 from A and D ; as the errors arising from neglecting this cal- 

 culation, especially towards the end of the year, would far ex- 

 ceed the errors arising in the most unfavourable cases from the 



calculation, 



