82 



On the true Measure of a Lunar Cycle, 



I proceed to examine the true measure of a lunar cycle, and 

 how far the same is confirmed by the lunar tables in the Nautical 

 Almanack. 



From the full moon, Sept. 1801, 21 days, 19 hours, 24 min. 

 Greenwich time, to the corresponding full moon 1820, Sept. 

 21 days, 18 hours, 48 min., is precisely 6940 days, less 36 mi- 

 nutes, which is thus proved. In 6937 days is a complete num- 

 ber of weeks, to which place the day of the week in the year 

 1801, and the excess of days, will answer to the day of the week 

 in the corresponding year 1820, thus : 



Astronomical time. D. H. M. Civil time. D. H. M. 



1801 })Full m. Sept. 21 19 24 Tuesd. Sept. 22 7 24 morn. 

 1820 }) Full m. Sept. 21 18 48 Friday Sept. 22 6 48 morn. 



36 



36 



Days 6937 

 6938 

 6939 

 6940 



By the weekly cycle. 



Tuesday, Sept. 22 7 24 morn. 

 , Wednesday 



Thursday 

 Friday, Sept. 22 6 48 morn. 



6940 00 00 

 36 



36 



235 Lunations = 6939 23 24 

 19 Julian years = 6939 18 00 



Diff. 5 24 



2S5 Mean lunations, at 29 days, 12 hours, 44 min., 25 sec, 

 31 thirds, 5 1 fourths, are equal to 19 Julian years, or 6939 days, 

 IS hours, as I have already corrected the common measure of 

 one lunation by Julian time, the comparative difference is there- 

 fore the same as the former. 



D. H. M. 

 235 Lunations by Ephemeris 6939 23 24 

 Ditto by computation .. 6939 18 00 



Diff. 5 24 



This difference arises from the variation of the lunar quarters, 

 and the excess of one quarter above another, as I shajl shovr 

 presently. 



If from the New moon in September 1801 to the New moou 

 in September 1820, we would know the exact interval, and con- 

 sequently the mean of 235 lunations, we proceed as before. 



Astrono- 



