1843.] A perpetual Moon Table. 107 



The middle card has on its inner circle the days of the Moon's age, 

 and the known characters for New and Full Moon, and for First and 

 Last Quarters ; on the outer circles are the full centuries of Old and New 

 style. The manner of writing the days of the Moon's age is obvious 

 enough, and requires no explanation. That of writing the full centu- 

 ries is now to be shewn. 



The Gregorian Century Epact being 24d. 4h. 34m. 12s., the Julian 

 Epact is 25d. 4h. 34m. 12s., and by intervals corresponding to these 

 times will these centuries follow each other towards the right. But as 

 these quantities are much greater than half a lunation, they may be 

 subtracted from 29d. 12h. 44m. 03s., and the remainders 5d. 8h. 09m. 

 51s. and 4d. 8h. 09.51s. will be the intervals of the successive centu- 

 ries towards the left. These being in common time are to be reduced 

 to that of the card at the rate at 89.50s. daily, as formerly shewn, 

 when they become 5d. 8h. 01m. 53s. and 4d. 8h. 03m. 22.5s. respec- 

 tively. If these be taken at 5d. 8h. and 4d. 8h. by neglecting the 

 small excess the error in 400 years will be 9m. 01-7s. and in 4000 

 years only lh. 30m. 27s. For the last 4000 years this error would be 

 rather convenient than otherwise, as tending to neutralize that arising 

 from neglecting the acceleration, which for the same period, as already 

 stated, would be about 2h. 44m. 54s. the difference between which 

 and the quantity now omitted being lh. 14m. 27s.* 



New style centuries may be carried forward at the same rates of 

 5d. 8h. and 4d. 8h. as far as we please, (though in point of fact they 

 are not required before the full century 15) ; as in the following Table, 

 to which if thought necessary may be applied corrections for the error 

 0031 here admitted, as also for the acceleration. 



* It is hardly necessary to remark, that we have no recorded observations so fat- 

 back as 4000 years, and that many of the earliest recorded are uncertain to half an 

 hour or more. The Table may therefore be depended on farther back than is likely 

 ever to be required. 



