340 Prof. Bessel on the Calculations rcqiiisite for predicting 



of the moon, may be most conveniently found by calculating 

 the values of 



cos S sin C«— A) , sin S cos D — cos S sin D cos fa— A) 



_;^ L and -. ^^ 



sai T sni «r 



or diiFerent times, for which purpose the latter may be thus 



, sin (g- D) cos ^ (a- AV' + sin (S+D) sin § {a - A)"- 



" * sin ir 



It will be most convenient to assume for T the full hour of 

 the place for which the Ephemeris has been calculated, nearest 

 to the middle of the occultation, and for the other times the 

 full hours next preceding and following it: by this arrange- 

 ment it will be possible to perform the interpolation from the 

 Ephemeris with coefficients, which once calculated will serve 

 for ever. In order to place together every thing requisite for 

 this calculation, I shall here communicate a table for these co- 

 efficients, which will be illustrated by the following arrange- 

 ment of the quantities to which they refer. 



Times. Places. 1 Diff. 2Diff. SDiff. 4 Diff. 



where o, a' denote the places of the moon contained in the 

 Ephemeris corresponding to the beginning t, and the end t' of 

 the 12hours in which the'times T, T+P, T + 2'', .... are con- 

 tained, and b, c, d, &c. the successive differences. If we as- 

 sume «, + a' — 2a; c, + c' = 2 c; e, + e' = 2 e; ... we have 

 the place of the moon corresponding to the time 



i (^; + r') +^X 

 by this formula 



a + X.b+ X' .c + X".d + Sic... 

 in which the coefficients have the following values : 



6. For 



