Stretching the System - Research Results

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Re: Stretching the System - Research Results

Post by Jim Eshelman » Mon Nov 20, 2017 7:49 am

Steve, there's no easy way to do this, and no way to plot them on a map with current tools. This sucks, because it turns out they are as strong as any other aspect we've been historically paying attention to mundane astrology (and probably natal, too). It's such a big deal that I'm currently working on a new edition of SMA that incorporates these and re-rates every chart referenced in the book (thousands of individual charts, keeping the rating standards consistent, and then reworking all the statistics on chart performance on the end).

Here is a compressed overview of what we're looking at.

Astrology uses a framework of three mutually-perpendicular great circles, the horizon, meridian, and prime vertical. We are used to the fact that planets on the horizon or meridian are angular, and we measure this through the third circle, the prime vertical. This includes measuring mundane conjunctions, oppositions, an d squares between planets on the horizon and meridian.

As a generalization: Relationships between any two of these circles is measured in the third (which is at right angles to it). If one planet is on the meridian and another planet on the horizon, they are square - at right angles to each other - measured along the prime vertical because the whole horizon and whole meridian are at right angles to each other as seen from the perspective of the prime vertical.

But it works the same (in principle) in other combinations. Please visualize this:

1. If one planet is on the meridian and another on the prime vertical, they are exactly square as measured along the horizon.

2. If one planet is on the horizon and another on the prime vertical, they are exactly square as measured along the meridian.

The good news: We have a way to measure along the horizon. It's called azimuth. It's exactly the framework for measuring the relationship between a planet on the meridian and one on the prime vertical.

The bad news: We have no direct way to measure along the meridian. I've had to invent a "fudge" that is close enough in most (maybe all) cases.

Another thing to mention in theory before I give you actual steps: Proximity to the horizon or meridian grants "foreground" or "angular" status. (We use that all the time, right?) But proximity to the prime vertical does not appear to do that. I've done different kinds of tests and, at least in mundane astrology where we have the most flawless chart times, neither ecliptical nor mundane contact with the Vertex "works" as a kind of angularity. It would be a gross error to treat it as if it does. However, we now know that planets mundanely on the Vertex-Antivertex form important aspects with planets on the horizon or meridian , and that often looks like they have angularity qualities! (But it's all in the geometry of the angularity.)



So... how do we find these with tools available to us such as Solar Fire?

First, see if there are planets within, say, 3° of the prime vertical. To do this, click Reports and look at the Azimuth column. If a planet is within 3° of 90° (Antivertex, due east) or 270° (Vertex, due west), you have something to work with. Second, note whether there are any planets mundanely on the horizon or meridian.

If you have more than one planet on the PV (within 3° of east or west in azimuth), they may form an aspect with each other - just run a Z-Analogue Azi (Azimuth) chart and read the orb (or read it right off the Azimuth column on the chart report).

If you have one or more planets on the PV and one or more closely conjunct MC or IC, also run the Azimuth analogue chart and read the aspect directly.

But if you have one or more planets on the PV mundanely, and one or more planets on the horizon, we have to look up two other factors and subtract them to get a close approximation of whether they have a mundane aspect measured along the meridian. To do this, compare the altitude of the planet on the horizon (get this from the Report on the chart) to the prime vertical amplitude (distance N or S of the PV) from an Z-Analogue PV Amp chart.

Here is an example of not finding such an aspect:

My natal chart for birthplace has Pluto at azimuth 87°13, or 2°47' before the Antivertex. This alerts me to a possible aspect to investigate, since I have Moon on horizon. But I can tell in a second that I won't find one because my Moon is 3°44' after the horizon (altitude -3°34'). To c0onfirm this, I run a Z-Analogue PV Amp chart and see Pluto, in amplitude, is only 2°22' before the Antivertex (rather than 2°47' as measured in azimuth). Pluto being 2°22' before the prime vertical in amplitude and Moon 3°44' after the horizon in altitude means that (within a small margin of error) they are 6°06' from a mundane square - and I'm looking for something within 3°. No aspect here.

Here is an example of finding such an aspect:

In the current Capsolar for Washington, Saturn is azimuth 269°46', meaning she is 0°14' before due west (270°). The Capsolar has Uranus on MC and Jupiter on IC close enough that there might be something here. The easiest way to find out is to run an Azimuth analogue chart (or read azimuth straight from the chart report). Uranus, at azimuth 185°03', is 5°03' past Midheaven, and too wide an orb to be squaring Saturn. However, Jupiter, at azimuth 1°31', is only 1°31' past IC. Jupiter 1°31' past IC and Saturn 0°14' before Vertex are 1°45' from exact square measured along the third circle, the horizon. In the Azimuth analogue chart you can see this easily as:

Saturn 0°14' in 7th house
Jupiter 28°29' in 3rd house
1°45' square

And if this sounds tedious, just remember that I just did this for every solar ingress and every lunar ingress across over 300 events - something like 2,000 charts.
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Re: Stretching the System - Research Results

Post by Jim Eshelman » Fri Jan 19, 2018 10:26 am

As I work through the (already months-long) process of rewriting SMA to include this information, folding these new facts into the existing fabric, I notice a couple of things worth mentioning, that will affect how I deal with these going forward.

First, the category of non-foreground mundane aspects that exist only in the mundoscope are almost never worth listing in "hindsight" discussion of charts. They are too numerous and too vague. Although they gave sufficient positive points in the above testing, they completely muddy things in explaining charts in SMA.

Here is what I think is happening: I think these are indeed distinctive to a given location and, to some extent, really do filter one place from another for an event. However, they are nonetheless so weak - not being foreground - that they can't compete with the stronger factors on which we usually rely. More or less, this means that they are valuable for subtleties and shadings when they "go along with" the main indicators, but are going to get lost in the static otherwise. I had already mentioned above, and in other places, that they are a kind of "polish" technique, for the astrological analyst to use or not as he or she sees fit to refine what is already known from stronger factors.

In this sense, I will continue to use them in predictions. They are valuable to me there, where I can use or dismiss them at will based on how the rest of the chart hangs together. But I won't include them (except in a rare case of an exceptionally interesting example) in hindsight analyses.
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Re: Stretching the System - Research Results

Post by Jim Eshelman » Fri Jan 19, 2018 10:38 am

The second thing I am noticing is a different perspective on the category of non-angular planets aspecting angular planets.

I had originally looked at this category in the sense that an angular planet expresses itself not in some "pure" way (e.g., Venus always means peace and happiness), but in a sense expressive of all of the factors that modify it at that moment. In mundane astrology, almost entirely these "other factors" are aspects it receives. So, it is easy to find Venus closely angular for heart-breaking tragedies when it is aspected by Saturn or Pluto (or sometimes Neptune or Mars), even if the aspecting planet is, itself, not angular.

So I had been thinking of this as "which extra factors are modifying the angular planet."

But - at the moment (and subject to my changing my mind) - it isn't looking like that to me. Sure, much of the time, it looks exactly like that - but, for example, while afflictions to an angular benefic make things "less nice," it's not true that benefics aspecting an angular malefic make things better. I have charts of events where an afflicted Jupiter is quite appropriate, and often Jupiter is angular and afflicted; but, in other examples, Saturn is angular aspected by the Jupiter. These ae not "nice Saturn" events.

I'm currently thinking that there is a simpler premise here. (Or maybe it's more complicated. It's simple to me, and I know Mike has specifically done work with this.) The premise is that aspects have two scores, one derived from how close the aspect is, and the other from how angular the planets are. Multiply one by the other, and you get most of the effects we observe in real life. A partile aspect with both planets very closely angular would get the highest score. A partile aspect with neither planet angular would have it's (approx.) 100% strength multiplied by a very low percentage (for non-angularity) and would end up with a low score. But, if one planet were angular and the other not angular, the score would be somewhere in between.

Though I'm intellectually intrigued by the exact parameters of such precise quantification, I don't think we need it in practice. I think our usual rules of practice take care of it all for us.

In the specific scenario I am discussing - a non-angular planet aspecting an angular planet - I currently don't think the operative principle is that planet B is modifying planet A. I think, instead, that it is much simpler: (1) The strongest aspects are those close aspects where both planets are angular (2) The next strongest category of aspects are those where only one planet is angular.

Simple, yes? And it puts a different spin on this category of aspects, consistent with what I am seeing in case-by-case instances. (Single case, yes; but I'm looking at hundreds of such cases, one by one.)
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Re: Stretching the System - Research Results

Post by Jim Eshelman » Fri Jan 19, 2018 6:10 pm

Today, as I've been grinding through updating chapters of SMA. I've found some examples of the impact of PVP aspects ("Prime Vertical Parans," i.e., mundane aspects formed between a planet exactly on the prime vertical and one on the horizon or meridian).

My favorite of the day is the Arisolar before the 1965 Watts Riots. With a dormant Cansolar, the Arisolar was the reigning solar ingress and was previously rated -2 (Very Bad). It had Jupiter exactly on IC and a mundane Moon-Mercury opposition - not what we would expect from the signature event of '60s urban violence with 35,000 rioters, 34 deaths, over 1,000 injuries, over 3,400 arrests, and $40 million in damages (equal to more than $300 million in today's dollar).

That's not a "Jupiter is the only angular planet, and we all sing Kumbaya at church camp" event.

But when I check to see if any planets are exactly on the prime vertical, I find that, yes, indeed, they are, and the aspects they form between themselves and (especially) the Jupiter are quite remarkable. Here is a map of key planets' azimuth positions. (Pluto is wider than I count, but I thought it would add to the display.)

I look at this chart, and only three words are needed to wrap up all my thoughts: "explosive violence" and "looting." More word would round it out, but those words do catch all the main points.
Watts.jpg
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Re: Stretching the System - Research Results

Post by SteveS » Sat Jan 20, 2018 2:18 am

Bingo! 8-) research.

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Re: Stretching the System - Research Results

Post by staragewiz » Mon Jan 22, 2018 11:29 am

Jim,

Please direct me to your post on calculation for the prime vertical chart in Solar Fire.

Had it before from your previous site and have mislaid the formula and
file you provided. I have SF ver.9 and don't know why they haven't
included the PVC calc. for their latest upgrade?

thanks,

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Re: Stretching the System - Research Results

Post by Jupiter Sets at Dawn » Mon Jan 22, 2018 12:09 pm

Typing Solar Fire Prime Vertical into the search box (above) got me this thread:
http://solunars.com/viewtopic.php?f=8&t=1539&p=9445

which lead me to this thread:
http://solunars.com/viewtopic.php?f=9&t=1544

Are either of those what you're looking for? If not, do try the search box. I doubt Jim has this at his fingertips, and you are more likely to know what you're looking for than he is.

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Re: Stretching the System - Research Results

Post by Jim Eshelman » Mon Jan 22, 2018 12:17 pm

staragewiz wrote:
Mon Jan 22, 2018 11:29 am
Please direct me to your post on calculation for the prime vertical chart in Solar Fire.
Do you mean the mundoscope? (Which, to be clear, is not what I was showing above.) The raw calculations are accomplished by clicking the "Harmonic Chart" button (or F6) and picking Z-Analogue Prime Vertical from the Chart Type list.

Regarding displaying the mundoscope, in the Solar Fire Tips forum I have several chart blanks, especially this: http://solunars.com/viewtopic.php?f=9&t=14
I have SF ver.9 and don't know why they haven't included the PVC calc. for their latest upgrade?
They've had it as Z-Analogue Prime Vertical since at least SF 5.

Now, if you meant, instead, what I was writing about above, that wasn't a mundoscope. That was an azimuth map to show mundane aspects between one planet on the meridian and another on the PV.
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Re: Stretching the System - Research Results

Post by Jim Eshelman » Sun Jan 28, 2018 4:06 pm

I've now finished layering these new aspects into every chart in the SMA catalogue. For the next edition of the book, I have a lot more events to add, but - before that - I'm going to update the "Quantifying the Techniques" chapter just using the existing charts with their new scores. (I reassessed the score of every single chart. Most of them stayed the same, since these new factors were mostly nuances, or reinforced the general message; but some of them got new scores, and I think they were nearly all improved scores.)

To be clear, for the vast majority of charts there were no changes at all due to the new factors. However, when they made a positive difference, it was often a HUGE difference. (Example: major financial market collapse with a Week chart that had Jupiter exactly angular; but now we know that the angular Jupiter was aspecting Saturn and Pluto. Big difference!) I'm curious how the overall pattern of scores changes, which is why I'm diving into an extra recalculation of everything in the "Quantifying the Techniques" chapter.

I'll post any significant changes here.

Though Capsolar scores overall remained at 89% "correct" (+1 or higher), Capsolars for 1st quarter (when it was also a Quarter chart) leapt from 89% to 97% - 32 out of 33 non-dormant examples. This is a gigantic improvement.

When the Capsolar is dormant or zero in the first half of the year, the flowing-through Cansolar now shows 96% effective instead of 93%.

Caplunars, overall, remain 92% effective. Interestingly, we previously had a 2% advantage during the first week of the Caplunar when it was also the Week chart (94% effective), and that is now down to 92%. However, when the Caplunar is the Week chart it is qualitatively better than for the month as a whole (more +2 scores and higher).

These are all the categories affected. There were not dramatic changes, but the solar ingresses, in particular, tended to improve in some ways.
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Re: Stretching the System - Research Results

Post by SteveS » Mon Jan 29, 2018 3:41 am

Thanks Jim. :)

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Angular Planets Aspected by Non-Angular Planets

Post by Jim Eshelman » Sun Feb 04, 2018 1:50 pm

[Here is the current draft of the description of these aspecs that I will be adding to the next edition of SMA.]

Close conjunctions, oppositions, and squares of non-angular planets to angular planets are valid supplemental factors. They are modifiers, providing additional details that the core system may lack. By themselves, they do not drive distinctive events.

Historic working methods only consider planets that are foreground or conjunct one of the secondary angles (except that Moon aspects are always valid). Non-angular planets are treated as if they do not even exist. Aspects, historically, have only been taken between foreground planets. This still seems the best way to assess the basic meaning of an ingress chart.

However, research now has confirmed what we suspected from the beginning, that aspects of non-angular planets to an angular planet have value.

One theoretical explanation of these aspects’ importance is that the full condition of an angular planet needs to be considered in its interpretation. Aspects routinely modify the nature of an angular planet. Throughout this book, we will see Venus closely angular for tragic events that are in no sense benefic, positive, pleasant events, provided Venus is aspected by planets such as Saturn and Pluto that interweave tragedy with the Lesser Benefic’s powerful emotions. We will see Jupiter angular for events of enormous economic loss when it aspects, say, Mars or Pluto.

This is obvious enough when Venus or Jupiter and its modifying planet are both foreground. However, we have many examples where a non-angular planet makes this modifying aspect and is the only visible factor that brings the ingress in alignment with the event. Other times, the chart is already on the right track, but one of these supplemental aspects enhances it; for example, an explosion occurs with Uranus closely foreground and square a non-angular Mars: The chart is good enough just with the Uranus, but clearer and more specific with the Mars aspect.

Another theoretical argument explains the importance of these aspects differently. It is more technical; more casual readers may want to skip this paragraph. One way of viewing overall aspect strength is that it is a combination of the closeness (orb) of the aspect itself plus the relative angularity of the two planets. For example, one might assign a score to the aspect based on its orb (100% when exact, and tapering down from there), and another (strength, expressiveness) score to each planet for its proximity to the angles (also 100% at exact contact, and then dropping off bilaterally). Multiplying these three numbers (aspect orb score, Planet A angularity score, and Planet B angularity score) would give a final score for the aspect that reflects both its own intensity (aspect orb) and the likelihood of its external expression (planet angularity). It is easy to see that the aspects that score highest are close-orbed aspects where both planets are foreground. The second highest scoring group of aspects, though, would be close-orbed aspects where at least one planet is foreground. That, in fact, is the exact situation we are discussing with the present category of aspects, and it explains case-by-case observations that the non-angular planet is not always the modifier: A non-angular Jupiter aspecting an angular Saturn does not make it “a better Saturn.” Rather, it brings the expression of a Jupiter-Saturn aspect per se into the mix of a chart that is already primarily Saturnian.

We need to distinguish types of aspect for this purpose. Beyond conjunctions, oppositions, and squares, I have seen individual examples of a semi-square or sesqui-square to an angular planet, and often these have seemed valid. (They still need to be formally studied.) However, the same cannot be said about trines and sextiles. Despite an occasional splendid example, I have seen numerous bad examples – charts that would be seriously derailed if a trine or sextile were considered. The few good examples, therefore, are coincidences: A single example may impress us, but ultimately is random. All substantial evidence I have seen reinforces that trine and sextile aspects simply do not operate in these ingresses. Semi-squares and sesqui-squares are promising, but, not yet having been systematically studied, are not incorporated into our working methods.

In the Summary section for each chart in this book, I list aspects by non-angular planets to angular planets in parentheses, to show their secondary (supplemental) importance. As with other factors, I include them in the textual discussion only when they strongly further the discussion of the chart.
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Non-Foreground Mundane Aspects

Post by Jim Eshelman » Sun Feb 04, 2018 2:36 pm

[Here is the current draft of the description of these aspecs that I will be adding to the next edition of SMA.]

Mundane aspects have proven their worth overwhelmingly. In solar and lunar ingresses, mundane aspects stand equal to ecliptical aspects under the same conditions, with no distinctions in strength or interpretation. However, one category of mundane aspect warrants more attention:

1. Neither planet forming the aspect is foreground or otherwise angular.
2. An aspect of the same planet pair does not exist ecliptically.

Mathematically, mundane aspects differ from ecliptical aspects in one important respect: They are geographically distinctive. Even if they exist for large portions of the globe, they rarely exist for all parts of the globe. Therefore, in a sense resembling angularity, they distinguish one region from another to help localize events, at least when foreground. Are non-foreground mun-dane aspects important because they are locale-distinctive?

Examination of all ingresses for events in this book shows a weak effect for such aspects. Their role is quite narrow: They seem not to disclose the type of event, but may give supple-mental details and “background information” about incidental conditions of the event. For ex-ample, a severe ingress may have a mundane-only Venus-Jupiter aspect when the severity affects the elite (e.g., celebrities or the rich). If the aspect is at odds with the basic nature of the ingress, it may have no evident expression at all; but, where it can fit into the “main story,” it lends embellishment.

I have only rarely found them worth mentioning in the analyses that follow. I do not list them routinely. They are not a significant part of this book. Where they have value is in prediction: I give them credence when writing forecasts based on these ingresses.

Despite being locally distinctive, they do not affect dormancy: Even with striking non-foreground mundane aspects in a dormant ingress, the prior ingress typically flows through.
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Re: Stretching the System - Research Results

Post by SteveS » Sun Feb 04, 2018 2:53 pm

8-) :)

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The Prime Vertical & Vertex

Post by Jim Eshelman » Sun Feb 04, 2018 5:36 pm

[Here is the current draft of the description of these aspecs that I will be adding to the next edition of SMA.]

Most dramatic of the new developments in Sidereal ingress theory is a new category of aspect based on at least one planet being on the prime vertical. In a sense, these are just mundane aspects (with which we are already familiar), but taking a large view of the celestial sphere. Though I could have called them, simply, “mundane squares,” it seems that a new name is needed so that the reader can follow along more easily. I have termed them Prime Vertical Parans (PVP).

Life would have been simpler if these aspects had failed; but they did not. They are not easy to see in a chart, and only half of them can be visually diagrammed with existing tools. For you to understanding them, both you and I will have to take extra care with the explanations. If you are not comfortable with positional astronomy and the various reference systems of the celestial sphere, you should at least strive for understanding the concept of these aspects to avoid confusion when they are mentioned. And, perhaps regrettably, they will be mentioned frequently be-cause they stand fully equal to the familiar ecliptical aspects already known to us. (In the stack Summaries, in the chapters that follow, I list them simply as another aspect.)

We will build up to their explanation slowly with discussions of other factors that did not prove of value in these charts.

What is the Vertex?

As Ascendant and Descendant are the points of the ecliptic that intersect the horizon, and MC and IC are the points where the ecliptic intersects the meridian, Vertex and Antivertex (as usually understood) are the opposed intersection points of the ecliptic and the prime vertical. The name Vertex comes from the term “prime vertical.”

Of the two intersections of the ecliptic and prime vertical, Vertex is that which falls on the western half, and Antivertex on the eastern half, of the celestial sphere. In fact, better definitions of Vertex and Antivertex would express them as half-circles on the celestial sphere. As Ascend-ant is actually the entire eastern half of the horizon (any planet crossing that semi-circle is rising), Descendant is the entire western half of the horizon, and MC and IC are not points but, rather, halves of the meridian… so might we better define Vertex as the half of the prime vertical west of the meridian. Similarly, Antivertex is the half of the prime vertical east of the meridian.

For all points on the globe, the horizon, meridian, and prime vertical are three mutually perpendicular great circles on the celestial sphere. Each is in a plane at right angles to both the other two. The prime vertical is that great circle that rises due east, sets due west, and passes through zenith and nadir. It intersects the meridian at zenith and nadir, and the horizon at eastpoint and westpoint.

It is along the prime vertical that planet positions are measured in the mundoscope, and along the prime vertical that a planet’s proximity to horizon or meridian is measured to determine the degree of its angularity. That is, the prime vertical is the framework in which the foreground, middleground, and background condition of planets is measured; therefore, the prime vertical itself partakes of none of these per se. Though often described as an angle, like Ascendant or Midheaven, Vertex stands apart from Ascendant and Midheaven’s most distinctive feature, the ability to imbue a planet with angularity or bring it into the foreground of awareness and action.

Vertex in Natal Astrology

Pioneering work with Vertex by L. Edward Johndro and Charles Jayne led them to character-ize its actions as fated. This became widely adopted. I credit their observations while rejecting their conclusions, simply because I reject the idea of “fate” in the sense of an imperceptible force outside of a person impelling them on an unchosen lifepath. However, I naturally accept that there are events and circumstances that seem fated. If arising from a person’s own choices, these must necessarily be unconscious choices, simply because what makes them seem fated is that the person has no conscious awareness of having caused them.

This matches what we would expect from Vertex, based on the more rudimentary observations above. Proximity to the horizon or meridian measured along the prime vertical naturally confers conscious expression to planets; therefore, the prime vertical itself cannot partake of gradient conscious expressiveness. Similarly, Vertex and Antivertex can be in any part of a horoscope’s quadrant, from near the horizon to near either end of the meridian, meaning that it is the only “angle” (so-called) that is not necessarily foreground.

In short, the essential nature of Vertex and Antivertex is characterized by unconscious actualization. Planets on these “angles” manifest acutely, but unconsciously. Action arises without conscious participation. Events actualize without easily traceable motivation and appear fated, forced by some unknown power; but the power, as with everything else shown in a horoscope, is oneself.

Vertex in Mundane Astrology

Initially it was unclear, therefore, what power this factor might have in mundane astrology where collective mind swells into events. First impressions, as we began the SMA project, were that Vertex is easily ignored and, if of any value at all, is of minor value at best.

In natal astrology, we are used to taking conjunctions and oppositions to Vertex in celestial longitude (in eclipto) with no more than a 3° orb, and squares to it (which are ecliptical conjunctions with Southpoint and Northpoint, the meridian’s intersections with the horizon) with orbs of no more than 2°. In 2015, I began a side project examining planet contacts to Vertex in Sidereal solar and lunar ingresses and quotidians. The results were discouraging. For the same sample tragic events that fill most chapters of this book, and which show a strong tendency to have malefics dominate the angles, Vertex did not have a majority of malefic contacts. In fact, Jupiter and Ve-nus more frequently contacted Vertex in the relevant ingresses and quotidians than Mars and Saturn. Were any conclusion to be drawn from that study, it likely would have been that Vertex’s action is to suppress or bury a planet’s expression; but even these effects were too mild (too little statistical abnormality) to warrant drawing a firm conclusion.

The only conclusion drawn was that employing Vertex and its companion points as if they were angles is unwarranted. The larger question was shelved for a later time.

Mundane Contacts with Vertex

Occasionally, I would think about how best to measure contacts to Vertex mundanely. We have two potentially useful measurements available in current astrological software, but we do not have one of the most important.

One that we have available is azimuth, a measurement of the position of planets and other celestial bodies around the circle of the horizon. Defining mundane crossing of Vertex or Antivertex as a planet’s exact intersection with the prime vertical, azimuth easily gives us the points of exact crossing: a planet intersecting the prime vertical has an azimuth of either 270° (due west, Vertex) or 90° (due east, Antivertex).

Another approach is to use prime vertical amplitude, which measures distance of a planet north or south of the prime vertical much as altitude measures position above or below the horizon. Altitude is useful for measuring proximity to the horizon especially because, when a body is very close to the horizon (the cases that matter most to us), altitude is always very close to the distance from the horizon in prime vertical longitude (i.e., in the mundoscope). When PV amplitude is 0°, the planet is exactly on Vertex or Antivertex.

Either of these measurements determines perfectly when a planet is exactly on Vertex or Antivertex. They do not, however, give matching, or necessarily the most useful, information about how much a planet has moved away from Vertex. Probably the ideal measurement for this is one for which astronomy does not have a name, since it has no use to astronomers. It would be a measurement in terms of the meridian circle that matches what azimuth is to the horizon and PV longitude is to the prime vertical.

1. Azimuth is measured around the horizon by drawing a great circle through a point passing through the horizon’s poles – which are zenith and nadir – at right angles to the horizon.
2. Prime vertical longitude is measured around the prime vertical by drawing a great circle through a point that passes through the PV’s poles – which are southpoint and northpoint, the intersections of the horizon and the meridian – at right angles to the PV.
3. The new measurement, which (for lack of an existing name) I will call meridian longitude, would be measured around the meridian circle by drawing a great circle through a point that passes through the meridian’s poles – which are eastpoint and westpoint, the in-tersections of the horizon and prime vertical – at right angles to the meridian.

Since we do not have this calculation available, we must fake it. If the goal is simply to de-termine whether a planet is mundanely conjunct Vertex or Antivertex, we can nearly always get a usefully accurate measurement (within the 3° maximum tolerance I recommend) by consulting azimuth and PV amplitude, which should agree within a few minutes. Only if they diverge more widely should we be suspicious of whether we have an accurate measurement.

Since ecliptical conjunctions to Vertex failed in mundane astrology, and contacts to the me-ridian and horizon in solar and lunar ingresses work mundanely instead of ecliptically, these per-spectives opened the door to reexamining Vertex contacts by viewing them mundanely.

Initial Observations

First impressions were discouraging. For example, several examples presented themselves from the start showing that close contacts to Vertex do not raise a dormant ingress into activity. In case after case, the two primary characteristics of a dormant ingress persisted: (1) The rest of the chart, e.g., close aspects among widely foreground planets, were not expressive. (2) The prior non-dormant ingress flowed through and continued to be important.

This first impression already distinguishes Vertex contacts from contacts with other angles. Either Vertex contacts are not operative at all, or they are too weak to overcome dormancy, or there is a qualitative difference that prevents it. In any case, we learned immediately that we cannot think of Vertex simply as another angle.

In a non-dormant ingress, close Vertex-Antivertex contacts gave mixed impressions, some-times seeming to delightfully fill in a missing piece, and sometimes being dumb notes. From the pilot testing, it simply was not clear whether these planets were lit up much as if they were angu-lar.

Some of the best examples, though, had something in common: They coexisted with planets close to the horizon or meridian (which we would expect in a nondormant ingress), and about the same distance from the angles (which would be expected for the close contacts needed to over-come dormancy, compared to the similar 3° used for Vertex contacts).

Looking further, a promising line of inquiry opened. Ignoring for the moment the question of whether a planet is in some fashion empowered or actualized by being on Vertex or Antivertex mundanely, the geometry of these intersecting great circles meant that two planets about the same distance on the same side of any two of the main reference circles – meridian, horizon, and prime vertical – would form a close mundane square. As the meridian, horizon, and prime vertical all square each other, planets exactly on them also would square each other – in one or an-other available reference circle.

In fact, it would be the third reference circle that would let us measure the first two. Think for a moment about mundane aspects used throughout this book, shown in the mundoscope. A planet near the horizon, and another planet near (and on the same side of) the meridian, are found to be square when measured along the third circle – the prime vertical. It takes all three of these mutually perpendicular great circles to form the aspect.

Similarly, a planet near the meridian, and another planet near (and on the same side of) the PV, form a square aspect when measured along the third circle, the horizon, i.e., in azimuth.

Finally, a planet near the horizon, and another planet near (and on the same side of) the PV, form a square aspect when measured along the third circle, the meridian, using the measurement I previously labelled meridian longitude. For cases very close to the circles, we can estimate this difference by comparing the altitude of one planet (to show its distance from the horizon) to the PV amplitude of the other (to show its distance off the PV).

PVP Aspects: Mundane Aspects Involving Prime Vertical

Tabulating all cases (in the events following) where one or more planet was within 3° of the prime vertical, we then identified those where the planet formed a close mundane square to a planet on the horizon or meridian. Again, this was done by measuring PV-to-meridian aspects in azimuth, and PV-to-horizon aspects by subtracting the PV amplitude of one to the altitude of the other. Results were very encouraging: This measurement provides additional, elaborative aspects to planets already closely foreground in a solar or lunar ingress.

Additionally, with two or more planets within 3° of due east (Antivertex) or due west (Ver-tex) in azimuth, conjunctions and oppositions in azimuth – mundane aspects entirely in terms of the prime vertical – were found to be of great value. In fact, these provide some of the most striking examples of the entire study.

For planets within 3° of due east or due west, I term mundane aspects formed by two or more planets along the prime vertical, or a planet on the PV with another on the horizon or merid-ian, Prime Vertical Parans (PVP). They will be casually referenced throughout this book as “PVP aspects.” Their exist is consistent with all other observations to date concerning the Vertex. For example, these planets are irrelevant to the issue of dormancy. These aspects explain why some Vertex contacts seem strongly validating of an event, and others seem irrelevant: If they do not form a PVP aspect to a foreground planet, they are not involved in the chart.

I have not yet tested these for quotidians because quotidian angularity is taken ecliptically. It is a different factor, best saved for a separate investigation.

Also, current stages of this examination have not tested squares to Vertex. Properly, these are conjunctions with Northpoint and Southpoint. They are believed to be taken ecliptically in the same way that conjunctions to Zenith and Nadir are taken ecliptically (as squares to Ascendant). However, when a planet is exactly square Vertex in eclipto, it is always square it along the Prime Vertical. (It took seeing actual examples in the mundoscope to alert me to check the spherical geometry of this and, yes, it holds up.) This, too, is best saved for a later, separate examination.

Examples

We have scores of examples of this type of aspect, with almost no instances of such an aspect seeming wrong. As might be expected, there are many that could be argued one way or the other – they are “good enough” without at all being necessary to make the point. What is captivating is just how many truly compelling examples arise.

For example, several examples arose from the vehicular catastrophe events. In the Week chart for the Clipper Tradewind crash, Mercury and Mars are 0°05' apart in PV amplitude and 0°02' apart in azimuth. They form a mundane square with Saturn on Descendant. In the Lac-Mégantic train derailment, which obliterated most of a town, we add a Saturn-Pluto square to an already angular Saturn. In the Sewol sinking, the already-sufficient Month chart, with Mercury 0°01' from IC, adds a Mercury-Pluto square.

For the New London school explosion, the tepid Quarter chart, with Moon on IC (consistent with an event involving children, but saying little else) adds a 0°19' Mars-Uranus conjunction in azimuth, in mundane square to that Moon.

Most of the deaths of U.S. presidents (especially the assassinations) gained from this approach. One striking example is the Year chart for President Kennedy’s murder. In a Capsolar already featuring a closely angular Jupiter-Pluto opposition, we add a partile Mars-Uranus conjunction (0°24' apart in PV amplitude) in mundane square to the Jupiter-Pluto for the explosive surprise and violence of the year’s biggest event.

These examples, and scores more, provide a prima facie case for the validity of this type of aspect. The rest of the examples are detailed throughout the chapters following.
Jim Eshelman
www.jeshelman.com

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