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The following years, 1585 and 1586 tell the same story. The year 1587, however, is a Type 5 year, and so is the year 1637, which occurs exactly 50 years later. |
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There is, in fact, a pattern of year types, in which, beginning with 1583, every fourth year has the same year type as the year exactly 50 years later. Expressed another way, years 50 years apart are duplicated, but only in every fourth year, starting with 1583. |
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I'll introduce some nomenclature at this point to aid the discussion. I will call the first year of interest the source year, and the year that repeats type at some later time the target year. The year difference is the number of years that separate the source and target years. Thus, if 1583 is a source year, 1633 is the corresponding target year, and the year difference is 50 years. |
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As it turns out, this cycle is even more complex, due to the operation of the Gregorian leap year rule. Years evenly divisible by 100 are not leap years in the Gregorian calendar, and this interruption in year types disrupts the cycle described. Years evenly divisible by 100, but also evenly divisible by 400, however, are leap years by the Gregorian rule, so the years 1600 and 2000 are leap years. |
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Thus, the cycle started in 1583 was not disrupted in 1600, but it was disrupted in 1700, 1800, and 1900. It will not be disrupted in the year 2000, thanks to the operation of a rule invoked only once every four centuries. |
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The disruption to the rule by years evenly divisible by 100 has a certain characteristic form. In effect, such a year starts two separate patterns, in which every fourth year, the year type is repeated 51 years, not 50 years, later. The two patterns are themselves separated by three years. Using our nomenclature, the year difference changes from 50 years to 51 years, once the pattern carries the target year past a year evenly divisible by 100, and the pattern remains in this new mode until the source year passes the same year, at which point the pattern reverts to its original 50-year difference. |
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A concrete example will help explain. Look at the most recent example of this disruption, using a table of years. |
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