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LI 11. On the Calculations requisite for predict iiig Occultations 

 of Stars by the Moon. By Professor Bessel*. 



1. — TJ^VERY observer of occultations must be aware how 

 -^-^ desirable or even necessary it is to know approxi- 

 mately the times of disappearance and reappearance of a star, 

 as also the place on the moon's disk where the latter takes place; 

 in order that the attention may not be weakened by being too 

 long on the stretch, or diverted by the uncertainty of the place. 

 To me, at least, it has always been necessary to calculate be- 

 forehand the occultation which I intended to observe, for my 

 place of observation. I do not find anywhere an explanation of 

 the most convenient method of conducting this calculation ; 

 although Lagrange's paper in the Berlin Ephemeris for 1 782 

 contains its essential points, which have since been adopted 

 in various works. 



The columns of M.. and Decl. of the moon for every twelve 

 hours of apparent time, which are to be found in the Conn, des 

 Terns, as well as in the Nautical Almanac, greatly facilitate 

 this calculation ; but it is still more simplified by the same data, 

 for every mean noon and midnight, which are given in the ex- 

 cellent Ephemeris of Encke, with the accuracy of the tables 

 themselves. 



I shall first solve the problem with strict exactness, and next 

 point out such an appi'oximation as will be sufficient for the 

 purpose of making the observation ; and, lastly, I shall show 

 what data the Ephemeris ought to contain, in order that the 

 same quantities for other places may be deduced from the re- 

 sults of the calculations thus instituted for one place. 



2. The symbols which I shall employ are as follow: 



A apparent.^. \ of the occulted star. 



L) Decl. J 



a. true M. 



5 Decl 



^ equatorial parallax 



p horizontal semidiameter }» of the moon. 



«' apparent M. 



g' Decl 



p' apparent semidiameter 



P- f'^l^*"'^?^ t^'"^ 1 of the place 



<?> latitude ... If observa- 



jp' corrected latitude f ■ 



r distance from tlie centre of the earth J 



If we now draw a great circle through the star and the cen- 



* From Schumacher's Astr. Xachr, vol. vii. p. 1 ; also in Enckc's Ephe- 

 meris iot 1831, p. 257. 



tre 



