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Not all of the magic numbers create cycles for a given date. A given number may create a cycle for a different date, or may apply to a different date range. Two numbers may overlap in their ranges to some degree. Take the date 1827 JAN 01, for example, apply the different numbers, and see whether they represent applicable conditions, as shown in Table 9.7. |
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Thus, you can see that for the date of 1827 JAN 01, there were at least eight cycles in operation, with year periods of 11, 17, 22, 28, 39, 45, 50, and 79 years. Each cycle describes a certain set of conditions governing the relationship between leap year positions in the source and target sequences, which obtains for various periods of time, depending upon the conditions in each case. The number of iterations over which a given cycle operates is governed by the period length, which determines how quickly the cycle encounters a century boundary in either the source or target sequence and thus encounters a condition that terminates the conditions that allow it to exist. |
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| Table 9.7 Finding cycles by magic number. | | Magic Number | Target
Date JD# | Target
Date | MonthDay
Date Match | Day
Difference | | Source Date = 1827 JAN 01, JD# = 2,388,358 | | 1,827 | 2,390,185 | 1832 JAN 02 | | | | 2,191 | 2,390,549 | 1832 DEC 31 | | | | 4,018 | 2,392,376 | 1838 JAN 01 | | | | 6,209 | 2,394,567 | 1844 JAN 01 | | | | 8,036 | 2,396,394 | 1849 JAN 01 | | | | 8,400 | 2,396,758 | 1849 DEC 31 | | | | 10,227 | 2,398,585 | 1855 JAN 01 | | | | 12,054 | 2,400,412 | 1860 JAN 02 | | | | 12,418 | 2,400,776 | 1860 DEC 31 | | | | 14,245 | 2,402,603 | 1866 JAN 01 | | | | 16,436 | 2,404,794 | 1872 JAN 01 | | | | 18,263 | 2,406,621 | 1877 JAN 01 | | | | 18,627 | 2,406,985 | 1877 DEC 31 | | | | | | | | | 28,490 | 2,416,848 | 1905 JAN 02 | | | | 28,854 | 2,417,212 | 1906 JAN 01 | | |
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