Meridian Distance or PVL in Jupiter rainfall data

[Jim Eshelman]

In the massively important studies of astronomical factors corresponding to terrestrial weather in which Donald Bradley participated in collaboration with Max Woodbury, Glenn Brier, and others at New York University, one commonly overlooked detailed has caused me minor uncertainty for decades.

Bradley published these results, in a popular form, in a two-part article "Crashing the Atmospheric Science Barrier" in American Astrology in the later 1960s after Woodbury and Brier's professional reputations were no longer at stake, Part I dealt with noncontroversial matters like lunar phase and other lunar motion matters that conventional meteorology could accept. However, Part II dealt with things that were privately discussed in meteorological circles at the time but could never have been published without putting academic reputations at stake: specifically, angularity in Caplunar ingresses!

I've recently had the opportunity to read part of the unpublished academic papers that were written. These shed some light on a couple of obscure points in the public, popular presentation in American Astrology.

Specifically, I speak of Figure 8 of the that article pair which shows Jupiter's relationship to Caplunar angles for nearly 50,000 maximum precipitation records. The peaks at 0°, 90°, 180°, and 270° - the angles - are stunning and unmistakable. (So far so good.) But the labelling is confusing: At the bottom of the chart, these positions are labelled as MC, Asc, IC, and Desc; yet the caption of the table reads, "Complete U.S. rainfall history 1871-1951 in terms of Jupiter's hour angle at commencement of every sidereal month."

Hour angle? Waitaminute... "hour angle" means the distance between Jupiter's right ascension and the RAMC. It's purely a right ascension (equatorial) measurement. If that is literally true, the 90° intervals should have been labelled MC, EP, IC, and WP, not with Asc and Desc. Which did they use? Perhaps, I have long thought, he meant the hour angle of the PV position (a reasonable usage if explained, which it was not). What does the graph really show?

I can't say for sure yet, but I did learn a couple of useful things. First, in the initial presentation of the data, the measurement was indeed hour angle - measurement along the equator in RA only. Second is the process that started them down this road.

[Jim Eshelman]

I don't have the information or calculation resources to replicate the entire 50,000-record study, but I can easily go back to the beginning... to what started all of this.

Based on a spot-check Bradley had done (and published in AA) a few years earlier, they took twelve events: the maximum 24-hour precipitation date (over a catalogued 50-year span) in New York City for each of the 12 months of the year. For example, they took the rainiest day in NYC in January for that 50-year period, and then the rainiest day in February, etc. This overcame seasonal variations in rainfall and measured "rainiest" against expected seasonal norms. They then plotted Jupiter's hour angle - yes, hour angle - in the Caplunar immediately preceding each date.

The eventual 50,000-record mega-study, btw, did exactly the same thing but for every weather recording station in the United States that had been tracking daily precipitation non-stop for the whole 50 years. But let's go back to NYC. Those we dates were:

Jan 4, 1944
Feb 11, 1886
Mar 25, 1876
Apr 5, 1886
May 7, 1908
Jun 14, 1917
Jul 26, 1872
Aug 16, 1909
Sep 23, 1882
Oct 8, 1903
Nov 15, 1892
Dec 13, 1941

Though 12 cases is small for a final conclusion, it was enough to get Federal funding managed through a significant university in the hands of two of the most prestigious statisticians and meteorological researchers of all time.

Theo original (unpublished) paper is absolutely clear that, in their academic presentation, they used Jupiter's hour angles. I'm curious whether HA (equatorial) or mundoscope (PVL) positions have the stronger effect - at least, for the New York City sample. I will compare them.

[Jim Eshelman]

Using Solar Fire, I calculated the 12 Caplunars. For greater accuracy, I'll now recalculate them with TMSA. I'm using the longitude and latitude that the American Atlas records for New York, NY, which is likely the central post office in Manhattan, 40N42'51", 74W00'23".

For display purposes, I will overlap the quadrants and begin with the cadent cusps (so that the angular cusps fall near the center of the illustrations). I will preserve the house information (i.e., confirming the actual quadrant, in case that matters or we want it later), but display circles superimposed. The two sections below tabulate Jupiter in RA (hour angle of Jupiter, as conventionally defined: equator) and Jupiter in PVL (hour angle of Jupiter's circle of position along the prime vertical).

Jupiter in RA
15°18' H12
28°17' H3
29°39' H9
==========
0°27' H10
1°25' H10
1°26' H1
23°01' H1
--------------
2°39' H11
4°15' H2
12°46' H8
13°40' H2
14°11' H8

Jupiter in PVL
26°48' H3
27°27' H12
29°30' H9
==========
0°26' H10
1°41' H10
2°19' H1
14°19' H1
29°37' H1
--------------
5°04' H2
10°41' H11
13°41' H8
15°40' H8

[Jim Eshelman]

Jupiter in PVL came out ahead but only a little. This is no surprise since (1) we value the major angles more than the minor ones and yet (2) we consider both to be valid.

On a simple count, PVL has six occasions of Jupiter within what we would consider foreground, while RA has only five; yet, that extra one just above Ascendant is outside "immediate foreground" (Class 1 angularity) by a small amount. It's also interesting that the ones along the meridian (on MC or IC), which theoretically could be measured either way, are sometimes closer in RA.

A simple assessment of which are closer: The average orb of the five foreground Jupiters by RA is 1°44'. For Jupiter by PVL, the five closest average 1°30'. (If the sixth wider one is included, the average is 1°47'.) There is slight orb advantage to the PVL measurement (either a tighter orb, or one additional angularity for about the same orb).

Finally, I want to see whether either approach adds granularity to the shape of the angular curve through the whole quadrant by clearly identifying weakest areas; and how the two compare. In other words: Is there a discernible background and where is it? The designations indicate the first, second, and third decanates of cadent, angular, and succedent houses, respectively.

Jupiter in RA
C1: 0
C2: 1
C3: 2
A1: 3
A2: 0
A3: 1
S1: 2
S2: 3
S3: 0

Jupiter in PVL
C1: 0
C2: 0
C3: 3
A1: 3
A2: 1
A3: 1
S1: 1
S2: 3
S3: 0

Jupiter in both lists has obvious clumping either side of the angles. The RA list is then more even, clumping in early succedent resembling that near the angles . The PVL list also has an anomalous high mid-quadrant, though what is most eye-catching - even exciting - is that the only sectors with 0 occurrences are those converged on the cadent cusps (the last succedent decanate and the non-foreground cadent areas). Though this does not exactly match our current theories, it is extremely close to them - and with only 12 examples.

Perhaps this can be made clearer with three-sector moving totals:

Jupiter in RA
C1: 1
C2: 3
C3: 6
A1: 5
A2: 4
A3: 3
S1: 6
S2: 5
S3: 3

Jupiter in PVL
C1: 0
C2: 3
C3: 6
A1: 7
A2: 5
A3: 3
S1: 5
S2: 4
S3: 3

The PVL pattern is clearest: The single lowest score (distinctly dropping off from those on either side) is the first cadent decade - the immediate background - with the two on either side being two of the three next-lowest. The two highest scoring are the two straddling the angle. Though there remains an unexpected upward blip mid-quadrant, it does not rise to the level of the two that straddle the angle. The two decanates we currently regard as foreground average 6.5; the four that we currently regard as middleground average 4.0; and the three we currently regard as background 2.3. That's good scaling!

Notice, however, that this favors a cadent cusp = background for ingresses, whereas we have been presuming a mid-quadrant theory. This isn't definitive and is nonetheless worth noting. (The mid-quadrant area, defined by the three succedent decanates, averages 3.0, which is higher than the current-cadent theory produces [2.3].)

The RA model was never expected to show a full foreground-background cycle and, in fact, does not. The first two-thirds of the pseudo-succedent areas have scores just as high as the two decanates straddling the angles. Its only real commonality with the PVL 'curve' is that the first cadent decanate is lowest. Replicating the ranking that was undertaken for the PVL figures, the two RA decanates we might regard as foreground average 5.5; the four that would be middleground average 4.0; and the three would be background 3.0. That's still scaled properly, though less differentiated than the PVL curve (foreground and background are less pronounced). To test a mid-quadrant background theory, the three succedent decanates average 4.7, which is quite high and makes no sense.)

[Jim Eshelman]

I still don't know for sure what the labels on the published graph mean, though I do know how the original measurement was done for the first academic paper.

Along the way, while digging through this, we've found what appears to be a confirmation that the current model of foreground, middleground, and background zones measured along the prime vertical seems to be exactly or at least approximately correct except this single (small) study suggests that ingresses should follow the same model, not the mid-quadrant background theory we currently use.