Equinoxes

The Decree of the National Convention On the era, the beginning and the organization of the year And on the names of the days and months

 From the 4th day of Frimaire, the second year of the French Republic, one and indivisible. (November 24, 1793)

The National Convention, after hearing its Committee of Public Instruction, decrees the following:

First Article. The era of the French counts from the founding of the Republic, which took place on September 22, 1792, of the vulgar era, the day when the sun arrived at the true autumn equinox, by entering the sign of Libra at nine hours eighteen minutes thirty seconds in the morning, for the Paris observatory...

Article III. Each year begins at midnight, with the day the true autumn equinox falls for the Paris observatory...

Article X. The ordinary year receives one more day, depending on whether the position of the equinox includes it, in order to maintain the coincidence of the calendar year with the celestial movements. This day, called the Day of the Revolution, is placed at the end of the year and forms the sixth of the Sansculotides.

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

Notice the contradiction between articles 3 and 10. It was presumed that a leap year would occur every four years, skipping one automatically every 128 years or so. Unfortunately, Delambre was away at the time, probably measuring how many meters there were between the equator and the North Pole. When he returned, he explained that Article 3 would cause a gap of five years between leap years about three times a century, and would be uneven and difficult to predict. 

Delambre wrote a report. First, he calculated the start of the first 400 years, and the leap years. Then, made a proposal to fix the calendar. See the page on the Reformed calendar. 

Below is the first day of the year, 1 Vendémiaire, as calculated by Delambre, with decimal times, for 400 years. "S" indicates sextile (leap) year; extra day added to end of year. Times are of equinoxes in Paris true solar time, about 17 minutes ahead of GMT/UTC. Times are only approximate and do not account for planetary perturbations, but the dates are correct. The Republican year begins at the preceding midnight.

ER	CE	Date & decimal	Time

Exact times of equinoxes during the Republic

ER   CE   Date    GMT     Paris   H.M. S.
 1  1792 Sep 22 09:00:30 09:18:30 3 87 85
 2  1793 Sep 22 14:55:19 15:11:38 6 33 08
 3S 1794 Sep 22 20:46:23 21:01:31 8 76 05
 4  1795 Sep 23 02:27:55 02:44:49 1 14 45
 5  1796 Sep 22 08:23:55 08:41:48 3 62 36
 6  1797 Sep 22 14:10:39 14:27:12 6 02 22
 7S 1798 Sep 22 19:50:07 20:05:43 8 37 30
 8  1799 Sep 23 01:40:47 01:58:15 0 82 12
 9  1800 Sep 23 07:25:31 07:40:41 3 19 92
10  1801 Sep 23 13:13:08 13:26:00 5 59 72
11S 1802 Sep 23 19:02:13 19:17:29 8 03 80
12  1803 Sep 24 00:43:31 00:59:02 0 40 99
13  1804 Sep 23 06:39:47 06:58:08 2 90 37
14  1805 Sep 23 12:29:00 12:46:57 5 32 60