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Likewise, you can see that the pair of 51-year cycles originally identified (Table 9.3) has nothing to do with 51 calendar years, nor is it a pair of cycles. Rather, what has happened is that the period of matching has shifted to cover consecutive calendar years, so you see that both 1854/1905 and the following years 1855/1906 are not separate cycles at all. The dates are separated by another of the numbers on the list as well: the number 18,627, which is (121,461 + 1,095). In this case, 12 complete four-year cycles and three common years (3365) separate the dates. The relative positions of the leap years are different in this case and again match the remainder. |
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At this point, the mechanics of the cycles can be understood, and the matching dates can be calculated for a cycle, as well as the dates when a cycle of matching dates can start and end. |
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The calculation of all the candidate numbers raises another question, however. Are these numbers just theoretical, or do they actually predict other cycles? |
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Looking at some examples, you can see that the numbers do, in fact, correspond to cycles in the Gregorian calendar. Not all of the numbers apply to all dates or all circumstances, of course, since each number represents a certain condition that exists between the source and target sequences. |
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As an example (Table 9.6a), try the starting date of 1827 JAN 01 and the number 4,018, which represents (21,461 + 1,096) days. Here, you have discovered an 11-year (4,018-day) cycle in the Gregorian calendar, which exists under certain conditions. |
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Taking another of the numbers, you can build a similar table, as in Table 9.6b. This is yet another cycle, this time consisting of (71,461) days. In fact, this is a remnant of the old Julian calendar cycle, which is a simple 28-year cycle that applied to all years. |
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Looking at target dates after 1900, a different relative positioning of the leap years applies, creating a different set of conditions. In this case, a different set of numbers satisfy the conditions, as shown in Table 9.6c. |
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As before, the cycle ceases when the conditions that describe its functions are no longer true. When the target date passes 1900, the leap year rule creates a different set of conditions governing the relative positions of the leap year dates, and the number that describes the interval between the dates is no longer 18,267 days. |
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More importantly, however, see that on the date 1851 JAN 01, this cycle and the two previous cycles described were all operating simultaneously. That is, owing to the particular set of conditions relating these source and target date sequences, all three of the conditions existed, allowing all three of the cycles to operate. No attempt has been made to look for other cycles that may also operate for this date. |
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The point to be made here is that, on a given date, a number of cycles may operate simultaneously. The number of cycles may vary from zero to many. |
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