Yes. Here are the main points to know:
1. Both points
average the same speed.
2. Both points
start the year at the same spot and
end the year at the same spot.
3. Differences, therefore, fall in between the start and stop of the year.
4. The
mean rate moves at a smooth, even rate. The
apparent rate moves at an irregular, variable rate.
The two different approaches (abbreviated "Mean" and "Apparent") respectively use the rate of the
Right Ascension of the Mean Sun (RAMS) and the
Right Ascension of the Apparent Sun (RAAS). This was easier to explain in the days when everyone was working out of an ephemeris, but is easy enough to explain now.
RAMS moves at the same rate as the Sidereal Time column of an ephemeris. In fact, in a noon ephemeris, it is identical with the ST column (and in a midnight ephemeris is 12 hours different). It reflects the mean (average) motion of the Sun, as if the Sun moved at exactly the same rate every day.
But the Sun does NOT move at the same rate every day. When it is around 0° Capricorn it moves about 61'/day, and when at 0° Cancer it moves 57'/day. It speeds up and slows down throughout the year as the Earth passes through different parts of its
elliptical (not circular) orbit.
The
Mean Sun approach uses the steady, even
average Sun rate. Another way to say this is that the SSR or ingress precession follows an even flow of time. The
Apparent Sun rate does not show time flowing evenly. It speeds up and slows down, and the
rate at which it does this is the Sun's actual apparent motion.
The difference between MS and AS is called the
equation of time. This Wikipedia article has a couple of nice graphs showing how this difference fluctuates during the year:
https://en.wikipedia.org/wiki/Equation_of_time
It's the difference between
standardized time zone time and
sundial time. In fact, before time zones, mechanical clocks moved people from sundial time (apparent rate) to
Local Mean Time (mean rate).
Fagan always felt that the PSSR needed to flow at the apparent solar rate, and Bradley followed that definition. This puts it at odds with the SNQ and SQ, except that, at the end of his life, Fagan started thinking the SNQ and SQ also should use the apparent rate. He put the word
Neo- in front of them to indicate this. Thus, the SQ is progression of the SSR by the mean solar rate, and the Neo-SQ is the progression of the SSR at the apparent rate. I long ago confirmed Bradley's determination that the SNQ and SQ work by the mean rate, but Siderealists always continued calculating the PSSR by the apparent rate as first defined. My push now is to finally test and confirm (1) how well the PSSR works at all and (2) whether it has a mean or apparent solar argument.
Over half the complexities that have kept people from using the PSSR come from this Apparent Sun issue. That's why the Stahl and Omega ephemerides had the ASSI column, an average increase for calculating the PSSR that just needed a little correction but mostly would give you the PSSR by subtracting two numbers and adding a third - a very fast process.
