Finally, we have all the background knowledge required to understand how we might calculate the French Republican Calendar. This is a calendar that was created and saw widespread use during the French Revolution for around 12 years from 1793 to 1805, when Napoleon abolished it in favour of the Gregorian calendar. These days, it is mainly of interest historically, as we might see in names of events like the Coup of 18 Brumaire.
The idea of the calendar is simple: every year is divided into 12 months of 30 days each, named Vendémiaire, Brumaire, Frimaire, Nivôse, Pluviôse, Ventôse, Germinal, Floréal, Prairial, Messidor, Thermidor, Fructidor. Since a solar year is around 365¼ days, it adds 5 complementary days, and one more in leap years: la Fête de la Vertu, la Fête du Génie, la Fête du Travail, la Fête de l’Opinion, la Fête des Récompenses, and la Fête de la Révolution (leap years only). The first year started on September 22, 1792, the founding of the French Republic, which also happens to be the autumnal equinox.
The part about the calendar that I found intriguing was the way it handled leap years — every year started on the date of the autumnal equinox at the Paris Observatory, no matter what. As such, a year is a leap year if the next autumnal equinox happens 366 days later instead of the normal 365, and the calendar will never drift against the seasons — at least if we followed the calendar as originally specified. Unfortunately, perhaps due to laziness, all the versions of the calendar I could find online used alternative leap year schemes that reduced the calendar into a mere variant of the Gregorian calendar, complete with its ability to drift out of sync with the seasons.
The most popular scheme for leap years these days is the so-called Romme method, which follows the same leap year rules as the Gregorian calendar, except applied to the years of the French Republic. I find it distasteful, mostly because it made years 4, 8, and 12 leap years when historically, years 3, 7, and 11 were leap years instead, thus altering history on top of eliminating one of the intriguing features of the calendar.
For this reason, I constructed my own version based completely on equinoxes, and I will be explaining exactly how to calculate the dates so that no one has to keep making Romme versions out of ignorance.
Last time, we introduced an equinox as “the point [in the sky] where the celestial equator intersects with the ecliptic.” This is perhaps an unfamiliar definition, as an equinox is more commonly defined as the time when the centre of the sun is directly above the equator. So, what does our point definition really mean?
To understand this, we must start by understanding how the various coordinate systems for points in the sky work in astronomy. Eventually, this will help us calculate the exact time of the equinox, from which we will finally be able to calculate the French Republican Calendar.
In this post, we shall cover the following concepts:
Last time, we started our quest to understand the art of time-keeping by first trying to understand what years and dates are. Today, we shall take a look at time itself, and understand how we might divide up a day.
For most of us, the basic unit of time is the second, ticking constantly. However, the reality is far more complicated than that. The question “what is a second?” has more than one correct answer, and it all depends on which time standard (i.e. clock) you are using.
In this post, we shall cover the most common time standards:
- Uniform Time.
- Solar Time.
- Universal Time.
- Reconciling the difference between uniform time and solar time.
On the way, we shall also examine what a day actually is.
I recently created an interactive version of the French Republican Calendar, using the original equinox-based system of leap years. This was not my first encounter with calendars and time-keeping — back in 2021, I had created a programming contest about calendars for World Emoji Day (July 17th, the date most often shown on the calendar emoji 📅), and most of what I learned then was applied to my French Republican Calendar app.
While creating these, I was forced to confront the inherent difficulties of time-keeping. At first glance, it seems deceptively simple — one simply has to count the number of seconds, and once enough seconds have passed, we say that a day has passed, and when enough days have passed, we say that it is a new year. This seems simple enough. At this point, you might remember that there isn’t an integer number of days in a year, which is why leap years are needed.
This is, however, a simplified explanation of something far more complicated. As we shall see, the rotation of the Earth itself is not consistent. This is the reason behind the dreaded leap seconds, but I am getting ahead of myself. Other factors at play include time dilation caused by relativity. I thought I’d share some of the knowledge, so that we may all gain a greater appreciation of the work needed to make clocks tick correctly.
This subject is beyond what a single blog post can cover, so instead, I shall turn this into a series. First, we shall cover the background knowledge needed to understand the rest of the series, starting with years and dates: