J 843.] 



A perpetual Moon Table. 



105 



should be farther diminished at the rate of 89.50s. daily, which 

 amounts to 13m. 40s., giving a result of 9d. 3h. 41m. 47s. It would 

 simplify the apportionment of this difference, without giving rise to 

 sensible error on this scale to reckon it at 45m. l-16th of half a day 

 on each month. The exact position of the month marks, are in half 

 days as in the following Table : — 



t J °' [ 



January, < 2 . 



February, < 



March, . . 

 April, .... 



00 

 OO 



56-09 

 58-09 



0012 



56-21 



May, . . 



June, . 



July, . . 

 August 



552 



52-3 



51*45 



48-51 



September, 45*63 



October,.. 44*70 



November, 41*79 

 December, 40*86 



The outer card contains the years of a century in their order, from 

 left to right, at intervals, corresponding to the annual Epacts. 



A tropical year consists of 365d. 5h. 48m. 51s.* nearly, and in 12 

 lunations there are 354d. 8h. 48m. 36s., the difference between which 

 is lOd. 21h. 00m. 15s., which may be called the tropical Epact. If the 

 Calendar were kept in tropical years, this would be the constant annual 

 Epact; but in order to correspond with the Calendar years, this tropical 

 Epact should be diminished by 6h. for 3 years, and in the 4th year 

 should have a day more than in the three preceding. They would 

 then consist of lOd. 15h. 00m. 15s. and lid. 15h. 00m. 15s. respec- 

 tively. To reduce these Epacts to the scale of lunation days, they must 

 be diminished at the rate of 89s., 50 daily, or 15m. 40.93s. and 17m. 

 10.44s. or 15m. 58.33s. at an average: these become thus lOd. 14h. 

 44m. 34s. and lid. 14h. 43m. 04.5s. These would be the quantities 

 by which the years on the outer card advance to the right of those 

 preceding them, if it were true that a day is gained in every 4 years; 

 but the error on this supposition reduces the average correction as 

 above to about 4m. 50s. on each year. 



The following considerations will, however, somewhat simplify the 

 mode of writing the years in their order. In 1236 lunations, there are 

 36,499 days, 19h. 25m. 48s., in a Gregorian Century there are 36,524 

 days; being in excess of the lunations by 24d. 4h. 34m. 12s. This 

 may be called the Gregorian century Epact. If the years of the century 



* This quantity is given with some variation by different Astronomers. The above 

 is the value towards which Delambre seemed to incline. The difference of a second 

 or two is of no importance as regards the Table. 



r 



