88 0?i the true Measure of a Lunar Cycle, &c. 



lunar year, and consequently of a mean lunation, which is this: 

 The |)recise number of lunar years in 912 Julian years being 

 known, and the number of days in four Julian years, here are 

 three numbers given to find the fourth ; viz. 912 : 940 :: 1461 : 



D. H. M. S. T. 



H17. -*4; = 4 lunar years. 4)14.17 11 32 25 32 



1 Lunar year 354 8 53 6 23 



1 Lunation 29 12 44 25 27 



This measure of a mean lunation corresponds with Julian time 

 exactly, and differs not a minute in the lunar cycles and periods 

 above named : so that if a table was constructed on this plan, 

 eight calendar years would coitain 99 synodical months, and 

 the sun and moon's place very nearly correspond : this was a 

 period of the ancient astronomers, wliich added to eleven more 

 years, constituted the cycle of 19 years, called the Enncadecae- 

 ierida, as 1 have noted in a former number. 



Jt is a curious part of historical astronomy to see how philo- 

 sophers have exercised themselves in these investigations in dif- 

 ferent ages; and notwithstanding their differences between them- 

 selves in former and latter times, it is admirable to see how nearly 

 the ancient astronomers agree with the moderns in the general 

 estimate of the lunar motions. 

 Eudoxus, who flourished in the 100th Olym- D- H. M. S. T. 



piad, reckoned the mean lunation at 29 12 43 38 11 



Meton, the author of the lunar cycle. An. 



ante Chr. 422 29 12 4126 48 



Calippus. An. ante Chr. 330 .. 29 12 44 12 45 



Hipparchus theBvthinian. An.anteChr. 136 29 12 44 3 15 

 Ptolomy. A.D. 140 .. .. 29 12 44 3 20 



Prutenic Tables 29 12 44 3 10 



Alphonsine Tables 29 12 44 3 3 



Tycho Brahe 29 12 44 3 9 



Dr. Keil 29 12 44 2 



Mr. Whiston 29 12 44 



LaCaills 29 12 44 3 



Ferguson's Tables 29 12 44 3 2" 



Mayer 29 12 44 1 53 



The principal causes of the disparity of these quantities are. 

 the different quantities assigned to the solar year, and the dif- 

 ferent denomination of years, solar, Julian, or sidereal time. One 

 second of difference in a cycle of 19 years produces 3 minute;-, 

 55 seconds, and in a period of 912 years amounts to 3 hour;, 

 55 minutes; and one minute in a lunation produces 3 hours, 

 55 minutes in a cycle of 19 years, and in 912 such years amounts 

 to 7 days, 20 hours j and if in any quantity the measure of 235 



lunations 



