for 'predicting Occultations of Stars by the Moon. 417 



tween which it lies, and to take out of the two values, always 

 the one which is nearer to a lunar hour, if one would not be- 

 sides apply for this case a simple interpolation. 



As an example, I add the complete calculation of the oc- 

 cultation of 82 Leonis, where every one will easily perceive 

 the signification of the numbers from the auxiliary and paral- 

 lax tables. 



82 Leonis. 



T= 21 1 



7 h 20'-9 



1-3685 



0-0014 



-f- 23-44 



+ 0-16 



+ 23-60 



69 11-40 

 4-2-71 

 0-4319 

 1-1565 



10 40-6 

 9-9924 

 1-1641 

 1-1723 



168° 47'-8 

 1-6877, 

 9-9225 



— 40-75 



— 0-31 



— 41-06 



4- 3 59-74 

 4- 14-34 

 1-3646 

 0-9469„ 

 110 550 

 9-9704 

 1-3942 

 0-3968 



1830, April 5. 



169° 13'-70 



4-0-41 



169 14-11 



4- 4o 40'-8 



61 27-7 



56 46-9 



14-76 



4- 0-11 



4-4° 14'-29 



-0-21 



+4 14-08 



it as 54' 1 1 



f 29'-31 

 0-7865„ 

 00014 

 -6-10 



+ 14-87 



4- 23-21 

 log. 61'-8... 

 log. cosS'... 

 259° 45'-6 



9-9930" 

 9-9918 

 9-4146 

 1-5691 



Disappearance 

 Reappearance 



9-2499" 

 1-5609 

 — 6-5 

 7 14-4 

 ± 9-6 

 7 4-8 

 7-24-0 



u 



- 9'-35 

 0-7865 

 8-9116 

 4- 0-5 



- 8-85~ 

 1-7910 

 9-9989 



4- 12-1 



4- 14-8 



1-0828 



1-1703 



11723 



35° 



5 



The rigorous calculation has given 



Disappearance 7 h 4' 21" 

 Reappearance 7 24 16 

 The calculations for the Ephemeris may be facilitated by some 

 auxiliary tables. 



With this view I have calculated by interpolation the posi- 

 tion of the moon for every third lunar hour. This table, while 

 it increases the safety, reduces besides the calculation of the 

 rising and setting of the moon, every one of which would 

 otherwise have required a separate calculation, to a mere 

 copying of figures. For if we write the table from which we 

 take for any given declination the semidiurnal arc of the moon, 

 in such a manner that the lunar hours of the form 3n are al- 

 ways taken separately, and the excess of the semidiurnal arc 

 above these lunar hours is converted by the mean motion of 

 the moon into mean time, we have without any further cor- 

 rection the times of rising and setting, more accurately than 

 they are ever required for any purpose. A second auxiliary 



New Series. Vol. 4. No. 24. Dec. 1828. 3 H table 



