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Jamison Painter

Leap years in the calendar are a point of great dispute, due to the contradicting statements in the establishing decree[23] stating:

Each year begins at midnight, with the day on which the true autumnal equinox falls for the Paris Observatory.

and:

The four-year period, after which the addition of a day is usually necessary, is called the Franciade in memory of the revolution which, after four years of effort, led France to republican government. The fourth year of the Franciade is called Sextile.

These two specifications are incompatible, as leap years defined by the autumnal equinox in Paris do not recur on a regular four-year schedule. Thus, the years III, VII, and XI were observed as leap years, and the years XV and XX were also planned as such, even though they were five years apart. (From Wikipedia).

As we can see, in spite of the disagreement above, the FIRST method was the only one actually used.

Jamison