±10 Prof. Encke^on the Calculations requisite 



g . sin t . cos <p 



OL — 



-* — -sin (0— a) 



, / o .sin tr. cos® \ 8 . _ ,. x 



-K- -) sm2 («— )■ 



COS $ (a— a) 



tang y = tang p 



cos {tf— a— §(«'— «)} 



8 , = 5 _ ( ^^ )sin(y _ 8) 

 _ i(1 ^_j^y sin2(y _ 8) _ .. .. 



j / p . sin ?r . sin <p \ , ~ x 



?=r + r ( sin, f )cOB(y-») + .... 



From the calculations for two or more moments will be found 

 the true parallactic motion of the moon in right ascension and 

 declination A a' and A 8'. The quantities A' and D' being 

 likewise derived from A and D, we have, for the time of the 

 beginning and end of the occultation, t± At ; At being found 

 by this quadratic equation 



(A'-*'- A*. Aa'f cosS' 3 + (IV-V-At AS') 9 = ^' 9 

 in which for H the value corresponding to t ± A t must already 

 be adopted. 



In the calculations for predicting occultations there is no 

 preliminary knowledge of the times when they will happen. 

 Numerous useless trials would therefore be necessarily made, if 

 it were required to insure that no star had been passed over. 



The distance of the two moments of time from which A a' 

 and A 8' are to be calculated, may safely amount to an hour. 

 The hour angle of the moon being 0— a, positive if west of 

 the meridian, the calculations for parallax may be facilitated, 

 if the motion of the moon is referred not to mean time, but to 

 true lunar time. For if t denote any hour angles (the western 

 ones being positive), each differing 1 5° from the other during 

 the greatest diurnal arc of the moon, consequently within about 

 15 h to 9 h , one may calculate for every t a table with double 

 entries 8 and tt, from which a!— a, 8' — 8, r'— r may be immedi- 

 ately taken. 



This would require altogether nineteen tables, which indeed 

 would be only for one place, but of permanent use. We have 

 here supposed that the quantities t, a, 8, r, m may be easily found 

 for the different values of t. 



For this purpose are given the three columns on pages IV 

 and VI, headed " Moon on the Meridian." They give the time 

 and the place of the moon during her upper and lower culmi- 

 nations at Berlin ; or if the sign h denote true hours of the 

 moon, the time and place of the moon being referred to the 



centre 



