On the true Measure of a Lunar Cycle. 87 



In 400 solar years are 146097 days, less two hours, 40 mi- 

 nutes, containing 2871 weeks; and in 21 days, 10 hours, 32 

 minutes, are three entire weeks ; therefore, from Thursday, 

 June 1415, to Thursday, July 1815, add 146097 days, and the 

 additional days will show the day of the month and week of the 

 corresponding New moon, and the exact number of solar days 



elapsed. 



H. M. 



1415 June 15 Thursday .... 7 15 morn. 



1815 June 15 Thursday 146097 



22 Thursday 146104 



29 Thursday 146111 



July 6 Thursday 146118 11 47 night 



146118 16 32 

 DiflFerence of meridians 52 



15 40 

 Excess of solar time .. 2 40 



146118 13 00 

 146118 10 32 



2 28 

 The mean of these differences brings the elapsed period to 

 146118 solar days, 12 hours; then 



Days. 

 4948 Lunations .. 146118 

 1237 Lunations .. 36529 



235 Lunations . . 6939 



12 Lunations . . 354 



I Lunation . . 29 



This computation so nearly approximates with Julian time, 

 that whatever equations may be requisite in conforming it with 

 solar tropical time, there is a stability given to the lunar reckon- 

 ing which cannot fail to recommend it as a basis in all, and espe- 

 cially large calculations, as I shall now explain. 



In 912 Julian years are 48 lunar cycles, and 940 hmar years, 

 consisting of 11280 complete lunar months, in which time the 

 moon anticipates the sun eight hours, three minutes, 24 seconds. 



Days. H. M. S. 



912 Julian years .. 333108 

 940 Lunar years .. 333107 15 56 36 



8 3 24 

 There is another method of con)puting tht- measure of the 



lunnr 



