106 



A perpetual Moon Table. 



[No. 134. 



be written out on the card at intervals of lOd. 15h. and lid. 15h. a Gre- 

 gorian Century will consist of 1236 lunations, 24 days and 12 hours. In 

 order to compare these results, the 24d. 12h. must be increased at the rate 

 of 89593s. daily, or the 24d. 4h. 34 m. 12s. must be decreased at the rate 

 of 89.500 daily, to have them in common or lunation days respectively. 

 The latter will be the more convenient, as the adjustment is to be 

 made on the card which has lunation days ; the correction to be sub- 

 tracted from 24d. 4h. 34m. 12s. is 36m. 05s. which leaves 24d. 3h. 

 58m. 07s. as the Gregorian Century Epact on days of 29^ to a lunation, 

 the difference between which and the 24d. 12h. given by the card or 

 8h. 01m. 53s. is the error generated in a Gregorian Century by using 

 the Epacts lOd. 15h. and lid. 15h. Now this quantity is as nearly 

 as may be § or 67 p. c. of half a day, and being distributed over the 

 whole century, becomes § p. c. of half a day for each year. The odd 

 15h. of the Epact is half a day, and \ or 25 p. c. of half a day. Hence 

 counting by the 59 half days, and beginning at 00 the year, 01 will 

 stand at 21.25=|=21.24 to the right of zero: the year 02 at 2 (21.25-1) 

 =42.49 and the year 03 at 3 (21.25|)=63.73=4.73 after rejecting 59 

 or a whole circumference. In this manner the following Table was 

 made : — 



TABLE I. 



oo { 



01 

 02 



57.00 

 00.00 

 21.24 

 42.49 21 



20 



4.73 



27.97 

 49.21 

 11.46 

 32.70 



55.95 

 18.19 

 39.43 



24.92 



46.16 



8.41 



29.65 



52.89 

 15.14 

 36.38 



57.62 



21.87 

 43.11 

 35.35 

 26.60 



49.84 

 12.08 

 33.33 

 54.57 



18.81 



40.06 



2 30 



23.54 



46.79 



9.03 



30.27 



51.52 



15.76 

 37.00 



»{ 



o3U 



58.25 

 20.49 



43.73 



5.98 



27.22 



12.71 

 33.95 

 55.19 

 17.44 



40-68 



24.17 

 45.41 



9.65 

 30.90 

 52.14 

 14.38 

 35.63 



37.63 76 



58.87 

 21.11 

 42.36 



6.60 

 27. 

 49.09 

 11.33182 

 83 

 34.57 

 55.81 

 18.C 

 39.30 



3.55 

 24.79 

 46.03 



8.28 



31.52 

 52.76 

 15.01 

 36.25 

 57.49 





0.49 

 21.74 

 42.98 



5.22 



28.47 

 49.73 

 11.93 

 33.20 



56.44 



18.68 



39.93 



2.17 



25.41 



46.66 



8.90 



30.14 



53.39 

 15.63 

 36.87 

 58.11 



£ 



20.36 

 22.36 

 43 

 5.85 

 27, 



'48.33 

 50 



The years being writ- 

 ten in their places shew 

 very plainly the Meto- 

 nic Cycle of 19 and the 

 Calippian of 76 years. 

 That of Meton is well 

 known as the Golden 

 Number. 



Cycles of 11, 8, and 

 3 years may also be 

 observed, and the order 

 of their succession is 

 worthy of being kept in 

 mind as helping to find 

 readily the place of any 

 required year on the 

 card. 



A little practice will 

 Ishew the value of this 

 remark, and besides it, 

 no other seems neces- 

 sary. 



