PREDICTION or OCCULTATIONS. 



In the prediction of an occultation for a particular place, the principal objects of 

 determination are, the instant of immersion, or of the star's disappearance behind 

 the moon's limb; of emersion, or of the star's re-appearance; and the points on the 

 moon's border "where these appearances take place. 



The calculations, according to the method of the late Professor Bessel, are greatly 

 facilitated by means of the elements given in the preceding Ust. Those who may wish 

 to consult Prof Bessel's original paper on this subject, will find it in Schumacher's 

 Astronomische Nachrichten, Vol. VII., page 1 ; also in the Berliner Astronmnisclies Jahrlucli 

 for 1831, page 257. The process of computation is shown by the following equa- 

 tions : 



d = Longitude from Washington, of the place, -t- West, — East. 



<p = Geographical North Latitude of the place. 



<{)'= Geocentric North Latitude of the place. 



r = Earth's radius at the place, or the distance of the observer's position from the 

 earth's centre. 



It is unnecessary to calculate cp' and r separately, as we have 



. , (1— e^)sin<p . cos^ 



rsm(5>' = rcostp = .7= , ■ o^s 



* n/(1— e^sin^<p) N/(l-e^sm^(p) 



in which e denotes the eccentricity of the earth's meridians. 



The logarithms of ^^^^^ = log A, and of^-^^^^= log5, derived 



from e = -081697, according to the latest determination of Prof Bessel, may be taken 

 from the following table, where the geographical latitude of the place is the argument. 



