Wrong Math?

[SteveS]

Clay, in the Oct 1991 issue of AA you wrote in an article titled: More Math for Progressive Thinkers under Tertiaries:

To my knowledge, every available tertiary formula---in print or in software---is incorrect. The error is in equating “day” with “rotation”: the chart is progressed one civil day per lunar orbit, whereas it ought to be progressed one rotation per orbit.

Do you find your above statement to still be true today?

[Jupiter Sets at Dawn]

Steve, he posted here that he did. He mentioned in that thread about an incorrect chart that was published, so it might help you to go through that thread again and make notes.
https://solunars.com/viewtopic.php?f=46&t=2506&p=20627

[Jim Eshelman]

We discussed this when you brought it up last time

It's not that math is wrong necessarily, but that Clay has a different theory of what the formula should be.

It just so happens (because of the one number changed in the calculation formula) that you can get his approach in Solar Fire by setting progressions to Q1 and then running terts. (Changing between Q1 and Q2 just causes Solar Fire to shift the type of "day" it is using in progressions.)

It doesn't make a lot of difference - much less than in Q1 vs. Q2 secondaries. I did a side-by-side comparison on a thread some months ago and, bottom line, I couldn't tell from test events which one was better. About the same number of examples worked better for each. (Remember, there wasn't a lot of difference.)

Here's the thread where I tested:
https://solunars.com/viewtopic.php?f=48&t=1466

[SteveS]

Thanks Jim, i forgot we looked into this matter many months ago. Since I have again been looking at Clay's AA articles with him joining the forum, I am again reminded of this issue.

[Clay_Reed]

It doesn't make a lot of difference

The error for the "civil day" method in tertiaries (as opposed to my "rotation" method, never mentioned before I published it) is three progressed days per 82 real years, which is a lot.

Also, although I doubt angles are relevant for tertiaries, MAYBE they are -- and that huge error renders the subject impossible to analyze.

(Should repeat here: my formula posted elsewhere of multiplying number of civil days by 0.0365 and adding that to the radix date/time is an approximation, subject to an error of several hours; the precise method, which should be incorporated in software, is described in my AA article. I doubt it's relevant, but again it would be better to have the correct angles for someone who wants to really check it out.)

[Jim Eshelman]

You can deal with the math complexities by setting progressions to Q1 to match Clay's preferred rate. One Sidereal Day (0.9972695666666667 civil days) divided by one Sidereal Month (27.321661 civil days) = 0.0365 etc., the value he gave.

Historically, we have used one mean solar day (1 civil day) per Sidereal Month, which gives to 0.0366 etc.

To get Solar Fire to simply switch progressions from based on mean solar day to based on Sidereal Day, flip to Q1. This produces the tert formula he is recommending.

Angles are easy to handle, although everything I've seen says the rate is solar arc in longitude for MC then derive the Asc, and that birthplace and locale angles respond more or less equally.

[Clay_Reed]

You can deal with the math complexities by setting progressions to Q1 to match Clay's preferred rate. Angles are easy to handle, although everything I've seen says the rate is solar arc in longitude for MC then derive the Asc, and that birthplace and locale angles respond more or less equally.

It makes no sense to use "solar arc" for tertiaries.

You can't duplicate my exact formula by using Q1, as I said above. [edit: BUT you'll get an excellent approximate, good enough except for heavy-duty research.]

Try it: Is the MC the same at a given location for the tertiary as for the radix at the moment of the lunar return? Probably not. That means the computer program is wrong.

As for a moment between LRs, the Q1 setting will create errors in angles and the Moon, plus negligible errors in evrything else.

[Jim Eshelman]

It makes no sense to use "solar arc" for tertiaries.

The sense is the evidence. As part of a larger project, I took 50 well-timed charts, did terts with angles calculated two ways, with MC advanced either by mean solar rate in RA or solar arc in longitude. In a side-by-side comparison, the latter gave better or closer hits about three-fourths of the time.

You can't duplicate my exact formula by using Q1, as I said above. [edit: BUT you'll get an excellent approximate, good enough except for heavy-duty research.]

How much difference is there? Solar Fire simply shifts the definition of day length.

Try it: Is the MC the same at a given location for the tertiary as for the radix at the moment of the lunar return? Probably not. That means the computer program is wrong.

I wouldn't expect it to be consistently so, since lunar months are of varying lengths.

As for a moment between LRs, the Q1 setting will create errors in angles and the Moon, plus negligible errors in evrything else.

I'm curious how much, so here's an example I think you've calculated before (or I'll check any other you have at hand).

JFK born May 29, 1917, 3:00 PM, Brookline, MA (using: 42N19'54", 71W07'18").
Shot November 22, 1963, 12:30 PM CST, Dallas, TX (using: 32N47, 96W48)

Standard tertiary progression by Solar Fire (set at the Q2 default) gives Sun 26°51'50" Capricorn and Moon 28°49'39" Taurus. Switching Solar Fire setting to Q1 produces a tert with Sun 25°08'43" Capricorn and Moon 5°21'09" Taurus. How much does this differ from your calculations?