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The c may be obtained for any year by the following rules: |
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1.) If the year is evenly divisible by 100, then |
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2.) If the year is not evenly divisible by 100, then apply the following rules: |
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2.1.) If the year is greater than zero, divide by 100 and add one: |
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2.2.) If the year is less than zero, divide by 100: |
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2.3.) If the year is zero, then c is zero: |
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For example, for A.D. 412, the year is greater than zero, so: |
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Likewise, for 4713 B.C., the year is 4712, which is less than zero, so: |
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In particular, note that the division operator truncates. Thus, the year 63 B.C. is 62, and |
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Note that the error term changes on the day following 28 February in those years evenly divisible by 100 and not evenly divisible by 400. |
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With these facts in hand, you may construct the following table, which may be used to convert Gregorian dates to Julian dates and vice versa. |
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The table reveals an interesting potential trap for the careless. Note that the discrepancy between the Julian and Gregorian dates is actually zero for century 2, and very small for several centuries surrounding that period. This period generally overlaps the historical period during which Mesoamerican cultures, like the Maya, were developing calendars. A proleptic Gregorian routine, then, can be mistakenly applied in the belief that it is generating Julian dates, and testing with dates in century 2 will erroneously confirm that belief. Such a misapplication is probably the source for occasional published errors in Western date equivalents of Maya dates. The proleptic Gregorian demons leave their characteristic sticky fingerprints all over these errors. |
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