A separate question is whether the progression rate is
even throughout the year or
uneven. Secondary progressions traditionally are calculated at an
even rate. At different times in the 1950s and '60s, it was thought that this time varied according to the speed of transiting Sun (which changes throughout the year). This would never be perceptible without quotidian angles to consider, since it isn't uneven enough to change planet motion so that people normally would notice.
This variable rate was referred to an RAAS argument:
right ascension of the apparent Sun. In the early 1960's (because
alpha is a symbol for right ascension), this was sometimes called the
alpha-Q. By the late '60s, Fagan began attaching the prefix
Neo- to any Q method that used RAAS (Neo-SNQ, Neo-SQ).
The invariable (even) rate was referred to an RAMS argument:
right ascension of the mean Sun. The term "mean Sun" is based on the exact way of calculating this by hand (pre-computer) and makes a nice verbal contrast to "apparent Sun" of the other math. Also, because of historic usage, these terms were never changed and are still familiar. All RAMS means is that time flows evenly - at the same even, invariable rate - no matter what time of the year.
We can perhaps most simply call these the
mean and
apparent rate.
All the comparisons I have done favor the mean rate, not the apparent. Fagan favored the apparent rate at the end of his life and, if this was going to be a phase, he didn't live long enough to grow out of it. Bradley's research pointed to the mean rate, which is also the basis of the Capsolar quotidian
that he used to rectify the boundaries of the zodiac. Duncan felt that we damn well better find out experimentally which was better because, if it turned out to be the apparent rate, then this would require significant revision of Bradley's rectification of the zodiac!
Don wrote me about this on January 4, 1971:
...your letter, again hitting onto the solar-anomaly question, calls for a quick and forthright reply. Virtually everybody who becomes swept up in technical astrology gets snared in this question and few are able to straighten themselves out alone. It is mainly a matter of semantics, not mathematics.
The term "fictitious time" is itself fictitious if you confuse revolutions with rotations! Even Cyril in his dotage couldn't separate the two logically, though of course he knew better in his brighter years. GET THIS STRAIGHT: What is called fictitious time in astronomy RUNS AT THE SAME PACE AS SIDEREAL TIME -- and by pace I MEAN LINEARLY. The Earth turns, for all practical purposes within one part in millionths, EXACTLY AT THE SAME RATE WHETHER IT IS AT APHELION OR PERIHELION. THE SIDEREAL ROTATION OF THE EARTH IS UNIFORM, AND IT IS SURELY THE SIDEREAL (THAT IS, CELESTIAL) SPHERE WHICH IS THE TRUE FRAME OF REFERENCE.
It is pitiably simple to establish whether the Q charts should be rotated sidereally or in terms of the solar anomaly. Study just a few cases (a lot aren't necessary) of events occurring in October-November for February-born people, and you have a big surprise coming. Reverse the process, studying progressed charts by both methods for autumn-born people with the events in February. The flow of time is uniform in astrology as well as in physics. [emphasis added]
Ken Bowser prefers the apparent rate at least for SQ (thus, the Neo-SQ). I've never noticed (and never asked him) whether he thinks the SNQ should be calculated this way as well. We have a mismatch. I could claim I've looked at it enough (but it's not really enough) or that my conclusion was Bradley's conclusion but, really, we need to do a LOT more day-to-day and special event looking. This just won't happen until we have the software tools to put in everybody's hands.
If a user picks
apparent instead of
mean, we need a different approach. Maybe you can think of a better one mine below; this is what I came up with on first try: It's the "more complicated" way mentioned on the last post (which may, therefore, be the best single-approach model for all of these). Remember, these might be progressions of both the natal Q (SNQ) and the SSR's Q (SQ).
Q2 Rate
- Subtract birth JD from event JD to get age: Take the integer for whole years. (For the SQ, the answer will always be zero.) - You won't use the non-integer part of this age.
- Calculate the epochs of the current and next SSRs. Subtract to get the length of the current sidereal year.
- Calculate RA of transiting Sun and RA of SSR Sun. Subtract and divide by 360° to get the percentage of the current year that has elapsed per the apparent solar rate. Multiply by 24:00:00 to get the part of a day that has elapsed (time increment). (Shorter form: Dividing by 360 and multiplying by 24 can, of course, be squeezed into one step.)
- Add the age (whole years treated as days) and the time increment to the birth epoch to get the progressed epoch. (Technical note: I have left a possible error in this that will never exceed 3.35 time-seconds, i.e., less than 0°01' on angles.)
Q1 Rate
Same as the method recommended for Neo-Q2 right above, with one modification (bold below):
- Subtract birth JD from event JD to get age: Take the integer for whole years. (For the SQ, the answer will always be zero.) - You won't use the non-integer part of this age.
- Calculate the epochs of the current and next SSRs. Subtract to get the length of the current sidereal year.
- Calculate RA of transiting Sun and RA of SSR Sun. Subtract and divide by 360°... then multiply by 24:00:00 to get the part of a day that has elapsed (time increment).
- Multiply age + time increment by 0.997269566 to convert Q2 rate to Q1 rate.
- Add the result (treated as days) to the birth epoch to get the progressed epoch.