In connecting the lunar month with the solar year, the framers of the ecclesiastical calendar adopted the period of Meton, or lunar cycle, which they supposed to be exact. A different arrangement has, however, been followed with respect to the distribution of the months. The lunations are supposed to consist of twenty-nine and thirty days alternately, or the lunar year of 354 days; and in order to make up nineteen solar years, six embolismic or intercalary months, of thirty days each, are introduced in the course of the cycle, and one of twenty-nine days is added at the end. This gives 19 × 354 + 6 × 30 + 29 = 6935 days, to be distributed among 235 lunar months. But every leap year one day must be added to the lunar month in which the 29th of February is included. Now if leap year happens on the first, second or third year of the period, there will be five leap years in the period, but only four when the first leap year falls on the fourth. In the former case the number of days in the period becomes 6940 and in the latter 6939. The mean length of the cycle is therefore 6939&FRAC34; days, agreeing exactly with nineteen Julian years.

Years of the
Century.

 X4 = 1
 X4 = 2
 X4 = 3
 X4 = 0

0

C

E

G

B, A

1 29 57 85

B

D

F

G

2 30 58 86

A

C

E

F

3 31 59 87

G

B

D

E

4 32 60 88

F, E

A, G

C, B

D, C

5 33 61 89

D

F

A

B

6 34 62 90

C

E

G

A

7 35 63 91

B

D

F

G

8 36 64 92

A, G

C, B

E, D

F, E

9 37 65 93

F

A

C

D

10 38 66 94

E

G

B

C

11 39 67 95

D

F

A

B

12 40 68 96

C, B

E, D

G, F

A, G

13 41 69 97

A

C

E

F

14 42 70 98

G

B

D

E

15 43 71 99

F

A

C

D

16 44 72

E, D

G, F

B, A

C, B

17 45 73

C

E

G

A

18 46 74

B

D

F

G

19 47 75

A

C

E

F

20 48 76

G, F

B, A

D, C

E, D

21 49 77

E

G

B

C

22 50 78

D

F

A

B

23 51 79

C

E

G

A

24 52 80

B, A

D, C

F, E

G, F

25 53 81

G

B

D

E

26 54 82

F

A

C

D

27 55 83

E

G

B

C

28 56 84

D, C

F, E

A, G

B, A