Analemma
Because the Earth has a slightly elliptical orbit, the Sun's arrival at the meridian varies during the year. Tycho did not have good clocks, so the arrival of the Sun on the meridian was the definition of 'noon'. We would now call that arrival time 'local solar noon'. With today's clocks, we can record the time of meridian passage accurately. The wiki for the equation of time states:
"The right time was originally considered to be that which was shown by a sundial. When good mechanical clocks were introduced, they agreed with sundials only near four dates each year, so the equation of time was used to "correct" their readings to obtain sundial time. Later, as clocks became the dominant good timepieces, uncorrected clock time, i.e., "mean time", became the accepted standard."
The details on how I made my solar measurements can be found on an earlier page. The following plot shows my measurements of the time of meridian passage (fraction of a UT day) over one year, and the corresponding altitude of the Sun at that passage. This shape is called the 'analemma'.
My solar data was pretty ratty at the start. I was still trying to understand the instrument and its oddities. A look at the error in my data (solar altitude minus JPL Horizons value) showed that before August 2020 my measurements were unstable. After that, the instrument became much steadier. Here is a plot of my raw errors over time:
The data before August is ignored, and all analyses operate on the post-August data. It is easy to see the plot that the decent data starts after MJD 222. I isolated that data and found that the average error from the JPL ephemeris was about -0.037 degrees (about 2 arc minutes) and added that in to my measures to form the alt_final column in the spreadsheet. This improved my latitude estimate but had no effect on my estimate of the obliquity.