Stop looking for noon at 2 pm — just find it!
Note for non-French speakers: there is an expression in French about : “Looking for noon at 2 pm”. If you are looking for noon at 2 pm, it means you are complicating things unecessarily : looking for things that do not exist, or not seeing the obvious. Typically people will tell you not to look for noon at 2 pm (“Ne cherche pas midi à quatorze heures”), keep it simple!
Hence the linguistic interest of this post.
We saw in a previous article (here) that in some places in France, there can be days when the difference between solar time and standard time is exactly one hour.
In France, it will therefore be 1:00 PM on the clock at solar noon, if this occurs while standard time is in effect. And it will be 2:00 PM if daylight saving time is in effect.
It is therefore possible to find noon at 2:00 PM!
We demonstrate this methodically below. Next, we present an application we developed in Geogebra to find the date(s) corresponding to a given location.
1. The method
We saw (same place) that the difference between solar time and standard time is a round number if the location’s longitude and the equation of time cancel each other out.
And we obtained a map of France showing the locations where this is possible four times a year, twice a year, or never:
From there, we need to determine whether the days when the equation of time cancels out the longitude fall during daylight saving time (because if it’s standard time, it will be 1:00 PM and not 2:00 PM).
2. The application (programmed in Geogebra)
When the equation of time is zero, solar noon is exactly 12:00 PM for locations on the Greenwich Meridian. We know the dates: April 15, June 13, September 1st, and December 25.
So we see that for these locations, noon can occur at 2:00 PM three times a year (November 3 falls during standard time, so noon occurs at 1:00 PM, which is less interesting).
To find the days, simply move the curve above up or down and locate the intersection with zero, then keep only the days that fall during daylight saving time.
In the window below, use the mouse to click on the point on the ruler on the left and drag it to the longitude you want between 5°E and 5°W, and see at the bottom which days you can find noon at 2:00 PM!
The following map results from this application:
Two things can be noted on this map:
- Zone between 1.6° East and 3.5° East
In this zone, the equation of time cancels out the longitude twice, but this always occurs while daylight saving time is in effect. Therefore, you cannot see noon at 2:00 PM there! This is particularly the case in Paris.
- Meridians 1.6° East and 0.9° West
These locations are special because, theoretically, they should experience noon at 2:00 PM once and twice a year. We have therefore drawn these meridians in light blue (once) and red (twice).
However, in practice, the application cannot find a day when the two intermediate extrema (July 25 and May 13, respectively) are perfectly tangent to the 0 line.
We explain this as follows: the red curve is not a continuous curve; it is a set of points (the value of the equation of time at noon for every day of the year). According to this definition, there is no day on which the equation of time is exactly zero. For example, here is the raw data used to plot the equation of time curve for 2026:
Date | Time of Meridian Transit |
06/12/2026 | 11:59:52 |
06/13/2026 | 12:00:05 |
06/14/2026 | 12:00:17 |
June 13 has been chosen as the day when the equation of time is zero, but at noon, it is actually 5 seconds.
So, on June 13, if you are on the Greenwich meridian, noon will not be at 2:00 PM, but at 2:05 PM!
Nevertheless, we have chosen this day because 5 seconds is generally an acceptable margin of error for a sundial.
When there are two points of intersection between the curve and y=0, it is generally not noon, but the day is correct and is provided by the app.
Note: this does not work for a single point of intersection (where the curve is locally tangent to y=0). Consequently, the app cannot find “the”
day when noon occurs at 2:00 PM on the 1.6° East and 0.9° West meridians. We have nevertheless colored them blue and red, respectively.
It’s also worth noting that if we were to aim for that level of precision, we’d have to recalculate the days every year due to small fluctuations in the equation of time. We also can’t rule out the possibility that the date of the switch to standard time plays a role. You’ll see this for yourself when you play around with the app. Have fun!