Metonic
Table
of Leap Years
The lunar year is eleven days shorter than
the solar year, requiring the addition of an extra month
approximately every third year. To reconstruct the priestly
courses from AD 70 to the ministration of Zechariah, father of John
the Baptist, we must identify where the Jews intercalated leap
years. The best known 19 year cycle is that used by the Greeks
and Babylonians as determined by the Metonic table, named after the
Greek mathematician who discovered it. An extra month (“bet
Adar”) is added seven times in nineteen years. Leap years are
ascertained by adding the year Anno Domini to the year 747 Anno
Nepolassar (after the Babylonian monarch), then dividing by
nineteen. The remainder is the year in the cycle; a remainder
of zero is the last year in the cycle. In the table below, we
see that the years 26, 7 BC, AD 13, AD 32, and AD 70 (indicated by
yellow) were the 19th year in their respective cycles.
Leap years occupied the 3rd, 6th, 8th, 11th, 14th, 17th, and 19th
positions in each cycle (indicated by green/yellow).
The Jewish cycle of leap years was also
set in a 19 year pattern, but was offset from the Metonic table
by 8 years, so that one leap year in the 19 year cycle did not
match (year 8 in the Jewish, 16 in the Metonic, indicated by
red).
To determine leap years in the Jewish cycle, we multiply the
Jewish year from creation × 235, subtract 234, and divide by 19.
If the remainder is larger than 12, it is s leap year, if less,
it is a regular year.
For the year A.D. 32 the formula is 3792 × 235 =
891120 – 234 = 890886 ÷ 19 = 46888.73684.
46888 × 19 = 890872. 890886 – 890872 = R14.
Thus, by Jewish reckoning, A.D. 32 is a leap year, however, by this same method A.D.
30 is not, although in the Metonic cycle it is. If
we then count 42 months ( 3 1/2 years) backward from Jesus'
crucifixion Nisan 15, A.D. 33, we arrive at Heshvan 15 (Nov. 8),
A.D. 29.
Metonic Table of
Leap Years
|
Anno Nepolassar
|
Anno Domini
|
Quotient
|
Divisor
|
Numerator
|
Remainder
|
Jewish Cycle
|
|
747 +
|
70
|
= 817
|
÷ 19
|
= 43
|
R 0
|
11
|
|
747 +
|
69
|
= 816
|
÷ 19
|
= 42
|
R 18
|
10
|
|
747 +
|
68
|
= 815
|
÷ 19
|
= 42
|
R 17
|
9
|
|
747 +
|
67
|
= 814
|
÷ 19
|
= 42
|
R
16
|
8
|
|
747 +
|
66
|
= 813
|
÷ 19
|
= 42
|
R 15
|
7
|
|
747 +
|
65
|
= 812
|
÷ 19
|
= 42
|
R 14
|
6
|
|
747 +
|
64
|
= 811
|
÷ 19
|
= 42
|
R 13
|
4
|
|
747 +
|
63
|
= 810
|
÷ 19
|
= 42
|
R 12
|
4
|
|
747 +
|
62
|
= 809
|
÷ 19
|
= 42
|
R 11
|
3
|
|
747 +
|
61
|
= 808
|
÷ 19
|
= 42
|
R 10
|
2
|
|
747 +
|
60
|
= 807
|
÷ 19
|
= 42
|
R 9
|
1
|
|
747 +
|
59
|
= 806
|
÷ 19
|
= 42
|
R 8
|
19
|
|
747 +
|
58
|
= 805
|
÷ 19
|
= 42
|
R 7
|
18
|
|
747 +
|
57
|
= 804
|
÷ 19
|
= 42
|
R 6
|
17
|
|
747 +
|
56
|
= 803
|
÷ 19
|
= 42
|
R 5
|
16
|
|
747 +
|
55
|
= 802
|
÷ 19
|
= 42
|
R 4
|
15
|
|
747 +
|
54
|
= 801
|
÷ 19
|
= 42
|
R 3
|
14
|
|
747 +
|
53
|
= 800
|
÷ 19
|
= 42
|
R 2
|
13
|
|
747 +
|
52
|
= 799
|
÷ 19
|
= 42
|
R 1
|
12
|
|
747 +
|
51
|
= 798
|
÷ 19
|
= 42
|
R 0
|
11
|
|
747 +
|
50
|
= 797
|
÷ 19
|
= 41
|
R 18
|
10
|
|
747 +
|
49
|
= 796
|
÷ 19
|
= 41
|
R 17
|
9
|
|
747 +
|
48
|
= 795
|
÷ 19
|
= 41
|
R
16
|
8
|
|
747 +
|
47
|
= 794
|
÷ 19
|
= 41
|
R 15
|
7
|
|
747 +
|
46
|
= 793
|
÷ 19
|
= 41
|
R 14
|
6
|
|
747 +
|
45
|
= 792
|
÷ 19
|
= 41
|
R 13
|
4
|
|
747 +
|
44
|
= 791
|
÷ 19
|
= 41
|
R 12
|
4
|
|
747 +
|
43
|
= 790
|
÷ 19
|
= 41
|
R 11
|
3
|
|
747 +
|
42
|
= 789
|
÷ 19
|
= 41
|
R 10
|
2
|
|
747 +
|
41
|
= 788
|
÷ 19
|
= 41
|
R 9
|
1
|
|
747 +
|
40
|
= 787
|
÷ 19
|
= 41
|
R 8
|
19
|
|
747 +
|
39
|
= 786
|
÷ 19
|
= 41
|
R 7
|
18
|
|
747 +
|
38
|
= 785
|
÷ 19
|
= 41
|
R 6
|
17
|
|
747 +
|
37
|
= 784
|
÷ 19
|
= 41
|
R 5
|
16
|
|
747 +
|
36
|
= 783
|
÷ 19
|
= 41
|
R 4
|
15
|
|
747 +
|
35
|
= 782
|
÷ 19
|
= 41
|
R 3
|
14
|
|
747 +
|
34
|
= 781
|
÷ 19
|
= 41
|
R 2
|
13
|
|
747 +
|
33
|
= 780
|
÷ 19
|
= 41
|
R 1
|
12
|
|
747 +
|
32
|
= 779
|
÷ 19
|
= 41
|
R 0
|
11
|
|
747 +
|
31
|
= 778
|
÷ 19
|
= 40
|
R 18
|
10
|
|
747 +
|
30
|
= 777
|
÷ 19
|
= 40
|
R 17
|
9
|
|
747 +
|
29
|
= 776
|
÷ 19
|
= 40
|
R
16
|
8
|
|
747 +
|
28
|
= 775
|
÷ 19
|
= 40
|
R 15
|
7
|
|
747 +
|
27
|
= 774
|
÷ 19
|
= 40
|
R 14
|
6
|
|
747 +
|
26
|
= 773
|
÷ 19
|
= 40
|
R 13
|
4
|
|
747 +
|
25
|
= 772
|
÷ 19
|
= 40
|
R 12
|
4
|
|
747 +
|
24
|
= 771
|
÷ 19
|
= 40
|
R 11
|
3
|
|
747 +
|
23
|
= 770
|
÷ 19
|
= 40
|
R 10
|
2
|
|
747 +
|
22
|
= 769
|
÷ 19
|
= 40
|
R 9
|
1
|
|
747 +
|
21
|
= 768
|
÷ 19
|
= 40
|
R 8
|
19
|
|
747 +
|
20
|
= 767
|
÷ 19
|
= 40
|
R 7
|
18
|
|
747 +
|
19
|
= 766
|
÷ 19
|
= 40
|
R 6
|
17
|
|
747 +
|
18
|
= 765
|
÷ 19
|
= 40
|
R 5
|
16
|
|
747 +
|
17
|
= 764
|
÷ 19
|
= 40
|
R 4
|
15
|
|
747 +
|
16
|
= 763
|
÷ 19
|
= 40
|
R 3
|
14
|
|
747 +
|
15
|
= 762
|
÷ 19
|
= 40
|
R 2
|
13
|
|
747 +
|
14
|
= 761
|
÷ 19
|
= 40
|
R 1
|
12
|
|
747 +
|
13
|
= 760
|
÷ 19
|
= 40
|
R 0
|
11
|
|
747 +
|
12
|
= 759
|
÷ 19
|
= 39
|
R 18
|
10
|
|
747 +
|
11
|
= 758
|
÷ 19
|
= 39
|
R 17
|
9
|
|
747 +
|
10
|
= 757
|
÷ 19
|
= 39
|
R
16
|
8
|
|
747 +
|
9
|
= 756
|
÷ 19
|
= 39
|
R 15
|
7
|
|
747 +
|
8
|
= 755
|
÷ 19
|
= 39
|
R 14
|
6
|
|
747 +
|
7
|
= 754
|
÷ 19
|
= 39
|
R 13
|
4
|
|
747 +
|
6
|
= 753
|
÷ 19
|
= 39
|
R 12
|
4
|
|
747 +
|
5
|
= 752
|
÷ 19
|
= 39
|
R 11
|
3
|
|
747 +
|
4
|
= 751
|
÷ 19
|
= 39
|
R 10
|
2
|
|
747 +
|
3
|
= 750
|
÷ 19
|
= 39
|
R 9
|
1
|
|
747 +
|
2
|
= 749
|
÷ 19
|
= 39
|
R 8
|
19
|
|
747 +
|
1
|
= 748
|
÷ 19
|
= 39
|
R 7
|
18
|
|
747 +
|
1 BC
|
= 747
|
÷ 19
|
= 39
|
R 6
|
17
|
|
747 +
|
2 BC
|
= 746
|
÷ 19
|
= 39
|
R 5
|
16
|
|
747 +
|
3 BC
|
= 745
|
÷ 19
|
= 39
|
R 4
|
15
|
|
747 +
|
4 BC
|
= 744
|
÷ 19
|
= 39
|
R 3
|
14
|
|
747 +
|
5 BC
|
= 743
|
÷ 19
|
= 39
|
R 2
|
13
|
|
747 +
|
6 BC
|
= 742
|
÷ 19
|
= 39
|
R 1
|
12
|
|
747 +
|
7 BC
|
= 741
|
÷ 19
|
= 39
|
R 0
|
11
|
|
747 +
|
8 BC
|
= 740
|
÷ 19
|
= 38
|
R 18
|
10
|
|
747 +
|
9 BC
|
= 739
|
÷ 19
|
= 38
|
R 17
|
9
|
|
747 +
|
10 BC
|
= 738
|
÷ 19
|
= 38
|
R
16
|
8
|
|
747 +
|
11 BC
|
= 737
|
÷ 19
|
= 38
|
R 15
|
7
|
|
747 +
|
12 BC
|
= 736
|
÷ 19
|
= 38
|
R 14
|
6
|
|
747 +
|
13 BC
|
= 735
|
÷ 19
|
= 38
|
R 13
|
4
|
|
747 +
|
14BC
|
= 734
|
÷ 19
|
= 38
|
R 12
|
4
|
|
747 +
|
15 BC
|
=733
|
÷ 19
|
= 38
|
R 11
|
3
|
|
747 +
|
16 BC
|
= 732
|
÷ 19
|
= 38
|
R 10
|
2
|
|
747 +
|
17 BC
|
= 731
|
÷ 19
|
= 38
|
R 9
|
1
|
|
747 +
|
18 BC
|
= 730
|
÷ 19
|
= 38
|
R 8
|
19
|
|
747 +
|
19 BC
|
= 729
|
÷ 19
|
= 38
|
R 7
|
18
|
|
747 +
|
20 BC
|
= 728
|
÷ 19
|
= 38
|
R 6
|
17
|
|
747 +
|
21 BC
|
= 727
|
÷ 19
|
= 38
|
R 5
|
16
|
|
747 +
|
22 BC
|
= 726
|
÷ 19
|
= 38
|
R 4
|
15
|
|
747 +
|
23 BC
|
= 725
|
÷ 19
|
= 38
|
R 3
|
14
|
|
747 +
|
24 BC
|
= 724
|
÷ 19
|
= 38
|
R 2
|
13
|
|
747 +
|
25BC
|
= 723
|
÷ 19
|
= 38
|
R 1
|
12
|
|
747 +
|
26 BC
|
= 722
|
÷ 19
|
= 38
|
R 0
|
11
|
|
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