On page 40 of his book "The Calculated Confusion of Calendars", (1976), Wolfgang Alexander Shocken demontrates how he derives the value of 689,472 Hebrew years as the length of the repetition cycle of the Hebrew calendar.

He begins the demonstration by showing that the time of the molad after every 19 year lunation cycle of 235 lunar months exceeds a full week by 2 days; 16 hours; 595 parts, which is 69,715 parts = 13,943 * 5.

For the 19 year cycles to line up with the start of a week, it is necessary that a certain multiple of these cycles form an excess that is an even number of weeks. The time in parts for a full week is 7*24*1080 = 181,440 = 36,288*5.

From that information he deduces that it requires 36,288 cycles of 19 years = 689,472 years, in order to get the 19 year excesses to line up to a complete multiple of weeks.

Calendar arithmetic shows that value to be correct because the molad of Tishrei 689,473H
(4 Nov 685,720g) returns to the value of the BAHARAD, and that year is also the first year in the 19 year cycle.

First  Paged 15 Jun 1997
Next Revised 15 Jun 1997