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For a description of the Egyptian calendar, see Budge's Egyptian Language (1971, pp. 135140). |
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The epagomenal days were intended to provide a perpetual calendar, in the sense that the same day of the year would fall on the same day of the same Decade in every year. The epagomenal days are explicitly excluded from the cycle of months and Decades. |
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The major structural problem with the FRC is its treatment of the leap year rule. The rule implemented by the Hatcher equations, and used by the SCDTL system, is essentially a Julian rule, adding a leap day every four years, beginning with the third. This rule is correct for the actual historical period of duration of the calendar, since leap years actually occurred in years 3, 7, and 11. |
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The original intention of the framers of the calendar, however, was to synchronize the calendar with the solar year by forcing the New Year day, 1 Vendemiaire, to occur at the autumnal equinox every year. The equinox, however, does not obligingly occur on the same day of the year, but varies irregularly by a day or two. The original proposal was, therefore, not practical. A proposal for a simpler and more regular leap year rule was advanced, but the calendar was abandoned before the rule could be implemented. |
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Therefore, the leap year rule for the FRC is complicated by actual historical events. By the original rule, a leap year would have occurred in year 15 and in year 20, not year 19. The simple Julian rule would have missed this year. |
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The proposed rule for leap year was similar to that for the Gregorian calendar, but pursued additional precision. The rule was, according to Reingold, Dershowitz, and Clamen (Calendrical Calculations, p. 11): |
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every fourth year is a leap year, except |
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every 100th year is not a leap year, except |
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every 400th year is a leap year, except |
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every 4,000th year is not a leap year. |
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The last correction gives the FRC an average of 365.24225 days per year, or an error of about 1 day in 20,000 years. The Gregorian calendar could be modified to use the same rule and obtain the same accuracy, although there is no reason to do so. |
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Thus, had the calendar survived, the FRC leap year rule might have been implemented along the lines of: |
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int frc_leap_year (int year)
{
if (year % 4 == 0)
{
if (year % 100 == 0)
{
if (year % 400 == 0)
{
if (y % 4000 == 0)
return (0); |
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