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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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