288 



Astronomical and Nautical Collections. 



preceding, and the three following the given time, and take their 

 first, second, third, and fourth differences, also the mean of the 

 two second differences standing on each side of the given time, 

 and the mean of the two fourth differences. Then to the propor- 

 tional part of the middle first difference, corrected by the equation 

 of mean second difference, apply the correction found in the first 

 Table annexed answering to the middle third difference, and the 

 correction in the second Table answering to the mean fourth dif- 

 ference, and the result will be the moon's place correct. 



Examples, 



1. Given the following right ascensions of the moon from the 

 Nautical Almanac, required her right ascension on 6th July, 1823, 

 at 3 hours. 



A. R. 



Istdiif. 



2d diff. 



4th diff. 



It 



- 38 

 -h 1 



Mean 

 + 38 



Mean 

 - I'si 



Moon's A. R. July 6, Noon 

 Proportional part of first diff. 

 Equation of mean second diff. 

 Equation of third diff. 

 Equation of fourth diff. 



Moon's A. R. July 6, at 3 hours 



76 



57 33 

 2 6 8 



- 17-6 



- 2-5 



- 0-3 



79 3 20-6 



2. Required the moon's right ascension on 4th July, 1823, at 

 18 hours. 



A. R. 



+ 



1st diff. 



7 18 2 

 7 36 20 



7 53 26 



8 7 58 

 8 18 40 



3d diff. 



- 1 ]'2 



2 24 



3 50 



4th diff. 



- 1 



1 



Mean 



- 1 19 



