Again with the same damn text as before, I suppose.  Lately I’ve been polishing up some of my own notes and personal texts that I don’t publicly share, one of which is my personal binder of divination texts I use for the Greek stuff I do, namely grammatomancy, astragalomancy, and some references to the Delphic Maxims that I like.  In the section I have on grammatomancy—much pared down from my De Grammatomanteia ebook, but refined to have more information and correspondences that I personally find useful—I’ve been trying to reorganize some of the information in a better way that reduces my reliance on external resources.  Of course, it’s mostly a “just in case” thing, and some of the stuff I don’t really use…but it doesn’t hurt to have.

One of the things I’ve been wrestling with is how much numerology stuff I want to include.  After all, numerology was considered pretty useful in classical times, and if nothing else, it’s informative and instructive to consider.  I’ve written about it before, specifically onomatomancy, literally “divination by names” (previously I called it “onomancy”, which isn’t wrong but isn’t as correct a term as I should be using).  I wrote three posts about it: one that overlaps numerology with stoicheia, one about using pythmēnes to determine winners, and one that uses particular numerological devices to determine the outcomes of events.  I’ve been debating whether to include summaries of these methods and their charts or rules in my divination binder for my temple, and it’s not a bad idea to, I suppose, though I’m unconvinced I really need to.  Still, it wouldn’t be bad to have, and having the stoicheia-based rules thrown in could be useful, so I’m leaning towards doing it anyway.  That’s what got me looking, once again, at the Circle of Petosiris, a particularly fun numerological tool to determine whether one will recover and live or succumb and die to an illness based on the numerological interactions between a person’s name and the lunar date on which they fall ill.

Get a drink and buckle up, dear reader.  This post got a bit longer than I had anticipated.

For some background on my resources for this, the first reference I found that discussed this particular device was Hugo Magnus’ Superstition in Medicine (1905).  Magnus touches on the topic briefly giving an outline of the topic, but he refers to two other texts: Marcellin Berthelot’s Introduction a l’étude de la chimie des anciens et du moyen age (1889) and a truly wondrous work, Auguste Bouché-Leclerq’s L’astrologie grecque (1899).  Indeed, it’s from Bouché-Leclercq that I ultimately got my images for the Circle of Petosiris, which he’s modified slightly to fix what he believes is an error in the original diagram.  Both of these Circles, however, ultimately come from MS Grec 2419 from the Bibliothèque nationale de France, which is a beast of a 15th century Greek manuscript that contains all sorts of magical, astrological, Solomonic, and other divinatory texts in Greek that I wish someone would translate at some point into English.

With that, let’s look at Bouché-Leclercq’s versions of the two Circles of Petosiris from MS Grec 2419.  Both of these Circles are found in MS Grec 2419, though I could only find them after looking hard; the way the BnF digitized the damn thing screwed up all the folio numbers.  All the same, let’s go with Bouché-Leclercq’s nicely-redone versions of the Circles, because the originals are rather messier and harder to read:

For comparison, take a look at what the Circles look like from the original text.  The two tables on either side of the Circle are, according to Bouché-Leclercq, computations of the days of the lunar month, though I’m not really sure what that means.  In either case, Bouché-Leclercq omits the tables, while Berthelot includes them in his own (faithfully reproduced) image.

 

If you take a closer look at both of these Circles (at least in Bouché-Leclercq’s versions), they have the same basic structure: a circle divided into four quadrants each filled with numbers, with a central middle column divided into an upper half and lower half also filled with numbers.  Thus, each circle contains six zones, and each of them are labeled with a particular outcome based on numbers; going clockwise from the 9 o’ clock position, these are Great Life (upper left), Average Life (upper central), Small Life (upper right), Small Death (lower right), Average Death (lower central), and Great Death (lower left).  Interestingly, the middle sections of the fancier Circle of Petosiris on the right aren’t labeled, but given the similarities and positioning between the Great and Small outcomes on either side, it can be inferred that the middle refers to Average.  In either case, the upper zones reflect outcomes of Life, and the lower zones the outcomes of Death.

Just to make sure the Circles are fully understood, let’s take a closer look at the Greek script in each.  On the left, simple Circle, the central line says Πετοσίρου κύκλος, literally “circle of Petosiros” (spelling intentional on this one).  Around the edge, starting at the 9 o’ clock position and going clockwise, we get the

1. ἡ μεγάλη ζωή (“the great life”)
2. μέση ζωή (“middle life”)
3. ἡ μικρά ζωή (“the small life”)
4. μικρός θάνατος (“small death”)
5. μέσος θάνατος (“middle death”)
6. ὁ μέγας θάνατος (“the great death”)

The fancier Circle has a lot more going on inside it. Above the diagram, there’s the phrase κύκλος Πετοσίρεως, or “circle of Petosiris”.  On the horizontal, we have ὅροι ζωῆς καὶ θανάτου, literally “the borders of life and death”, a pleasant label for such a device, I suppose.  The “lobes” around the edge of the fancier Circle, starting at the 9 o’ clock position and going clockwise, indicate both the course of the Sun around the Earth in a single day as well as the four elements:

1. ἀρκτικός μεσόγειος (“Arctic [star] over the earth”, i.e. midnight)
2. πῦρ (“fire”)
3. ἀνατολή ὑπέργειος (“rising above the earth”, i.e. sunrise)
4. ἀήρ (“air”)
5. μεσημβρία μεσόγειος (“midday over the earth”, i.e. noon)
6. ὕδωρ (“water”)
7. δύσις ὑπόγειος (“setting under the earth”, i.e. sunset)
8. γῆ (“earth”)

In other words, if the fancier Circle of Petosiris were to be considered as a compass, north would be to the left, east at the top, south to the right, and west to the bottom.  The use of the elements here is interesting, as it might be thought to allocate certain elemental qualities to certain times of the day.  Continuing on, going around the outermost circle quadrant by quadrant, there are the following four messages:

1. οὗτοι ταχέως σώζουσιν (“these save from death quickly”)
2. οὗτοι ἐντός ἑπτά ἡμερῶν σώζουσιν  (“these save from death within seven days”, i.e. slowly)
3. οὗτοι ἐντός ἑπτά ἡμερῶν ἀναιροῦσιν (“these kill within seven days”, i.e. slowly)
4. οὗτοι ταχέως ἀναιροῦσιν (“these kill quickly”)

These line up with the text outside the circle and past the lobes, respectively μεγάλη ζωή (“great life”), μικρά ζωή (“small life”), μικρός θάνατος (“small death”), and μέγας θάνατος (“great death”).  It might be inferred, then, that the Average Life and Average Death zones would take effect in a span of three days or less, to use the same week-based timeframe for the Small Life and Small Death, while the Great Life and Great Death zones would take effect within a day.  It’s an odd timing system to use, I suppose, but it does offer a relative sense of scale.

Each quadrant also has a longer message in the innermost circle, though it’s repeated twice within each quadrant, once within each eighth-part of the circle:

1. ἀρκτικά ὑπέργεια του βοῥῥᾶ (“Arctic [stars] above the earth [in the region] of Boreas [i.e. the north]”)
2. μεσημβρία ὑπέργειος του βοῥῥᾶ (“midday [stars] above the earth [in the region] of Boreas [i.e. the north]”)
3. μεσημβρία ὑπόγειος του νότου (“midday [stars] under the earth [in the region] of Notos [i.e. the south]”)
4. ἀρκτικά ὑπόγεια του νότου (“Arctic [stars] under the earth of the [in the region] of Notos [i.e. the south]”)

These latter messages are probably supposed to represent the four parts of the day—viz. late night between midnight and sunrise, early day between sunrise and noon, late day between noon and sunset, early night between sunset and midnight—but these are given using kind of unusual astronomical phrases that I’m not fully certain I have right.  However, Berthelot doesn’t describe why these additions of times of day, positions of stars, or elements to the fancier Circle of Petosiris might be here, and they don’t seem to actually be used for numerological or onomatomantic divination; Bouché-Leclercq brings this up, and says that their inclusion is a “strange whim” and unknown how it might have been used.  However, based on some of the text (great life, small death, three zones of numbers per hemisphere, etc.), we have an almost identical setup of the basic arrangement of numbers, though Bouché-Leclercq says that the order is mysterious, i.e. it’s unknown why or how the numbers are arranged the way that they are.

The only real difference in how these two Circles of Petosiris are used is by what number one divides by to obtain a remainder; when using the simple Circle, one divides by 29, while with the fancy Circle, one divides by 30.  This matches how the simple Circle only contains numbers from 1 to 29 (αʹ to κθʹ) while the fancier Circle goes from 1 to 30 (αʹ to λʹ).  We know that lunar months have either 29 days (a hollow month) or 30 days (a full month), so it struck me that the simple Circle should be used when one falls ill during a hollow month, and the fancier Circle during a full month; neither Berthelot nor Bouché-Leclercq suggest this, but this makes so much more sense, in that these two Circles can be used alongside each other, just not at the same time!  After all, both of these Circles appear in the same overall text (though perhaps not by the same actual author), so using one for one kind month and the other for the other kind of month makes some sense so that nothing is missed.  Using this idea, the simple Circle can be called the Hollow Circle of Petosiris for use with hollow months of 29 days, and the fancier one the Full Circle of Petosiris for use with full months of 29 days.

In this light, we can compare how the outcomes match between the two Circles:

Quality	Outcome	Hollow Month (29 days)	Full Month (30 days)
Bright	Great Life	2, 3, 7, 9, 11	2, 3, 7, 9, 10, 11
	Average Life	13, 14, 16, 17, 19, 20	13, 14, 16, 17, 19, 20
	Small Life	22, 23, 26, 28	22, 23, 26, 28
Dark	Small Death	1, 25, 27, 29	1, 25, 27, 30
	Average Death	4, 10, 15, 18, 21, 24	4, 15, 18, 21, 24, 29
	Great Death	5, 6, 8, 12	5, 6, 8, 12

Perhaps unsurprisingly, the outcomes of the hollow Circle and the full Circle are almost exactly the same!  There are only three differences between how the days are arranged between the two circles:

• Day 30 (which doesn’t exist in hollow months) is given to Small Death in full months
• Day 29 is given to Average Death in full months and to Small Death in hollow months
• Day 10 is given to Great Life in full months and to Average Death in hollow months

This further reinforces the notion that one circle really is meant for hollow months and the other for full months, and that the two Circles really belong to the same overall system, using one or the other based on the specific month of the illness.  In that sense, we can rearrange this table slightly to show how similar both systems really are:

Quality	Outcome	Hollow Month (29 Days)	Common	Full Month (30 Days)
Bright	Great Life		2, 3, 7, 9, 11	10
	Average Life		13, 14, 16, 17, 19, 20
	Small Life		22, 23, 26, 28
Dark	Small Death	29	1, 25, 27	30
	Average Death	10	4, 15, 18, 21, 24	29
	Great Death		5, 6, 8, 12

Note that the regions above the horizon in the full Circle, marked as above the Earth according to the time of day, are labeled in the table above as “Bright”, while the lower regions marked as below the earth are labeled as “Dark”.  This gives an interesting binary quality to each day of the month, which can also help predict how things overall turn out in addition to simple illnesses:

1. Take the name of the person, find the isopsephic value of the name, divide by the total number of days in the month, and find out whether the remainder is Bright or Dark according to the proper Circle of Petosiris for the type of month.
2. Find whether the given day of the lunar month on which one initiates a new project, task, or journey is Bright or Dark, according to the proper Circle of Petosiris for the type of month.
3. If both numbers are Bright, the whole of the project, task, or journey will be fortunate and good.
4. If both numbers are Dark, the whole of the project, task, or journey will be unfortunate and bad.
5. If the number of the person is Bright and the number of the day is Dark, the person will be in danger, but they will escape the danger.  More generally, fortune will occur under the appearance of misfortune.
6. If the number of the person is Dark and the number of the day is Bright, misfortunes will occur under the appearance of fortune, and although things appear to go well, hidden dangers and traps lie about.

In either case, it should be noted that there are slightly more Bright days than there are Dark days; there are always 14 Dark days every month, with 15 Bright days in hollow months and 16 Bright days in full months.  At least there’s a greater chance of success or survival than not, I suppose.

Yet another way that the Circles can be used is to determine which of two parties in a contest, fight, or battle will win.  Take the isopsehic values of each of their names, divide by 30, and find the remainder using the Full Circle of Petosiris to compare their respective results; the value with the better quality will determine the winner.  For instance, in the ever-popular onomatomantic example, Achilles (Αχιλλευς) has the isopsephic value of 1267, which gives a remainder of 7, landing in “Great Life”, while Hector (Εκτωρ) has a value of 1225, which gives a remainder of 25, landing in “Small Death”.  Though not as much is said about this method, several other

• Bright outcomes automatically become victorious over Dark outcomes.
• Especially in fatal conflicts, Dark outcomes indicate actual death, whether immediately or after a long-sustained injury or infection.
• If both parties end up in Dark outcomes, the one with the least bad result will survive the longest but both will lose.
• If both parties end up in Bright outcomes, the contest may be brought about to an amicable end, with the party with the better outcome having the upper hand.
• If both parties end up in the same outcome, the contest may be conceived of as equal and coming to a truce or stalemate, or we can resort to other numerological and onomatomantic methods instead (such as the pythmēnes method), though we could also use a simpler rule of just looking at the outcome numbers themselves and comparing directly with them, unless those two numbers are also the same.

In general, it seems like the Circle of Petosiris is actually a multipurpose numerological and onomatomantic tool of divination that can be used to not just determine the outcome of illnesses but of any general event, battle, or project.  What’s interests me and which can be another useful diagnostic tool, however, is the attribution of Brightness or Darkness to particular days.  After all, I already have a lunar calendar (well, really, lunisolar calendar), the Grammatēmerologion, which gives individual days of the lunar months to the letters of the Greek alphabet for prognostication and ritual planning.  If Bright and Dark days can be thought of as naturally tending to fortune or misfortune, respectively, especially for particular people based on their names, then it wouldn’t be hard to conceive of this as further enhancing the Grammatēmerologion system:

Day Number	Day Letter	Quality
		Hollow Month (29 days)	Full Month (30 days)
1	Α	Dark
2	Β	Bright
3	Γ	Bright
4	Δ	Dark
5	Ε	Dark
6	Ϝ	Dark
7	Ζ	Bright
8	Η	Dark
9	Θ	Bright
10		Dark	Bright
11	Ι	Bright
12	Κ	Dark
13	Λ	Bright
14	Μ	Bright
15	Ν	Dark
16	Ξ	Bright
17	Ο	Bright
18	Π	Dark
19	Ϙ	Bright
20		Bright
21	Ρ	Dark
22	Σ	Bright
23	Τ	Bright
24	Υ	Dark
25	Φ	Dark
26	Χ	Bright
27	Ψ	Dark
28	Ω	Bright
29	ϡ	Dark
30		—	Dark

This is kind of weird, though, when you look at it.  Some days that are given to really beneficial or naturally “bright” letters (like Alpha, “the god says that you will do everything well”, or Ēta, “the bright Sun who watches all watches you”) are given to be Dark, and vice versa (like Ōmega, given to Saturn, also has the comparatively awful oracle “you will have a worthless harvest, not a useful one”).  Additionally, the days that are given to obsolete letters (6, 19, and 29) or to unlettered days (10, 20, and 30) don’t really have much of a pattern as to which are Bright or Dark, even though it’s considered in the base Grammatēmerologion system that unlettered days are naturally considered unlucky or ill-favored for ritual or work.  I mean, I’m not really that surprised, considering how the Circle of Petosiris and the Grammatēmerologion system have no connection or shared logic behind them besides both relying on the use of a lunar month, and the fact that the Greek manuscript dates to the 1400s CE, but still.  Perhaps there is a logic behind how the Circle of Petosiris arranges days as Bright or Dark, or amongst the Great/Average/Small Life and Death categories, and I just don’t see it yet. At least I’m in good company of earlier scholars, I suppose.

It’s trying to figure out that order that reminded me of one of the first reasons why I ever learned about the Circle of Petosiris, namely the Sphere of Dēmokritos from PGM XII.351—364, something I mentioned in the original post about this stuff.  It’s a much simpler system, but the underlying method is the same: take the value of the person who has fallen ill, add to it the number of the day of the lunar month, divide by thirty, and take the remainder.

Unlike the more complex Circle of Petosiris with its threefold division of either life or death, the Sphere of Dēmokritos gives only two outcomes: if the result falls in the upper part of the table from PGM XII.351—364, the person will live, and if in the lower section, they will die.

• Live: 1, 2, 3, 4, 7, 9, 10, 11, 13, 14, 16, 17, 19, 20, 23, 25, 26, 27
• Die: 5, 6, 8, 12, 15, 18, 21, 24, 22, 28, 29, 30

On a whim, if we redefine “live” as Bright and “die” as Dark, I decided to compare how the Sphere of Dēmokritos matches up with our Circle of Petosiris scheme:

Day	Letter	Hollow Circle	Full Circle	Sphere of Dēmokritos
1	Α	Dark	Dark	Bright
2	Β	Bright
3	Γ	Bright
4	Δ	Dark	Dark	Bright
5	Ε	Dark
6	Ϝ	Dark
7	Ζ	Bright
8	Η	Dark
9	Θ	Bright
10		Dark	Bright	Bright
11	Ι	Bright
12	Κ	Dark
13	Λ	Bright
14	Μ	Bright
15	Ν	Dark
16	Ξ	Bright
17	Ο	Bright
18	Π	Dark
19	Ϙ	Bright
20		Bright
21	Ρ	Dark
22	Σ	Bright	Dark	Dark
23	Τ	Bright
24	Υ	Dark
25	Φ	Dark	Dark	Bright
26	Χ	Bright
27	Ψ	Dark	Dark	Bright
28	Ω	Bright	Dark	Dark
29	ϡ	Dark
30		—	Dark	Dark

The overlap here is, frankly, astounding; in general, of the thirty days of the Sphere of Dēmokritos, eight are different from either the Hollow or Full Circles of Petosiris (days 1, 4, 10, 22, 25, 27, 28, and 30), and if we just limit ourselves to the Full Circle of Petosiris, the overlap is even greater where only four days are different (days 1, 4, 25, and 27).  For one text that dates back to the fourth century and another that’s dated to the fifteenth, that’s incredible.  The striking similarities between these systems shows that either they were developed independently using a similar method that happened upon similar results, or (perhaps and hopefully) more likely, that the Sphere of Dēmokritos is an earlier form of the Circle of Petosiris, or closely-related to one of the Circle’s forebears, with only a few changes/copyist errors slipping in along the way and the Circle developing a finer gradation of results from a simple “live” or “die” outcome.

In fact, if you think about it, consider how the numbers are arranged in the Sphere of Dēmokritos: an upper and a lower half, with the upper half indicating life and a lower half indicating death, with three groups of numbers in each half: one on the left, one on the right, and one in the middle.  Consider where the overlaps apply even in how these numbers are arranged: in the Great Life section in the upper left of the Circle of Petosiris, you have 2, 3, 7, 9, and 11; in the Sphere of Dēmokritos, the upper left column has 1, 2, 3, 4, 7, and 9, with 1 and 4 being known as flipped in brightness and with 11 being found in the middle column of the Sphere.  If you plot not only what the overlaps are but where they occur, you have essentially same system, just represented in a more rectangular format!

It’s at this point that I’m getting really hooked now, because now I want to know what the logic is behind why the numbers of the lunar month are arranged the way they are on the Circle of Petosiris.  After a bit, it seems like one of the few (maybe the only?) text that discusses this topic is Otto Neugebauer and George Saliba’s 1989 paper On Greek Numerology (Centaurus, vol. 31, pp. 189—206).  Neugebauer and Saliba document a number of instances of the Circle of Petosiris that are extant in a variety of texts, including the Sphere of Dēmokritos, and even claim that the list of lucky and unlucky days of the Egyptian calendar given in PGM VII.272—283 is a highly corrupted version of this same system.  Neugebauer and Saliba go over about a dozen manuscripts, but they don’t go into depth on how significantly different the Circles of Petosiris of each might differ.  My idea of using one such Circle for hollow months and another for full months makes sense (though I could just as easily use the Hollow Circle for both and just add on day 30 where we’d expect in the Full Circle and make no other changes), but who’s to say whether such a combined approach might ever have been used, especially if there were so many other variations available?  That Bouché-Leclerq inter alia share two such Circles, one based on the number 29 and another based on the number 30, might just be a coincidence of fate and philology.

What’s interesting from Neugebauer and Salida’s paper is something that I glossed over as unimportant at the beginning of this post.  Recall those tables by the Hollow Circle of Petosiris from MS Grec 2419?  Bouché-Leclercq says that those are “computations of the days of the lunar month”.  Neugebauer and Saliba, based on a hint from some of Paul Tannery’s chapter on fragments of similar numerological devices in from Notices et extraits des manuscrits de la Bibliothèque nationale et autres bibliothèques (1886, vol. 31, part 2, pp.231—260), figured out that the large numbers are the numerological equivalents of the actual names of the dates of the lunar month plus an extra word or phrase.  For instance, in the first row of the left table, there’s the number ͵αφπθ = 1589.  Neugebauer and Salida reckon this to be the equivalent of the words ΠΡΩΤΗ (1288) and ΣΕΛΗΝΗ (301), which together add to be 1589.  Indeed, they find that the numerical values of each row are equivalent to the spelled-out name of the date plus the word for Moon in Greek, as the text itself indicates: “reckon also the name of the Moon if it falls from conjunction to full-moon”.  Likewise, the values in the right table all have the number 138 added as a constant, which is explained as “the number of the waning-moon”, literally the word “hollow” (ΚΟΙΛΗ).   Thus, the top row of the right table, day 16, we would expect then to be “sixteen hollow” or ΕΞ ΚΑΙ ΔΕΚΑΤΗ and ΚΟΙΛΗ: 5 + 60 + 20 + 1 + 10 + 4 + 5 + 20 + 1 + 300 + 5 = 431, then 431 + 138 = 569.  Indeed, we find the number φμθʹ, which is 569.

If we were to develop a complete reproduction of this kind of table, then we’d end up with the following.  Where there is more than one set of values for a given day, this shows that there were different ways to write out the name of the day based on the given source of the specific Circle method, e.g. day 16 could be written as ΔΕΚΑΤΗ ΕΚΤΗ or it could be written as ΕΞ ΚΑΙ ΔΕΚΑΤΗ.  I know some of these aren’t necessarily what’s used in modern Greek, but they are attested in the literature Neugebauer and Saliba reference as well as other classical sources.

Day	Name		Modifier		Sum
	Word	Value	Word	Value
1	ΠΡΩΤΗ	1288	ΣΕΛΗΝΗ	301	1589
2	ΔΕΥΤΕΡΗ	822	ΣΕΛΗΝΗ	301	1123
3	ΤΡΙΤΗ	718	ΣΕΛΗΝΗ	301	1019
4	ΤΕΤΑΡΤΗ	1014	ΣΕΛΗΝΗ	301	1315
5	ΠΕΜΠΤΗ	513	ΣΕΛΗΝΗ	301	814
6	ΕΚΤΗ	333	ΣΕΛΗΝΗ	301	634
7	ΕΒΔΟΜΗ	129	ΣΕΛΗΝΗ	301	430
8	ΟΓΔΟΗ	155	ΣΕΛΗΝΗ	301	456
9	ΕΝΑΤΗ	364	ΣΕΛΗΝΗ	301	665
	ΕΝΝΑΤΗ	414			715
10	ΔΕΚΑΤΗ	338	ΣΕΛΗΝΗ	301	639
11	ΕΝΔΕΚΑΤΗ	393	ΣΕΛΗΝΗ	301	694
12	ΔΩΔΕΚΑΤΗ	1142	ΣΕΛΗΝΗ	301	1443
13	ΔΕΚΑΤΗ ΤΡΙΤΗ	1056	ΣΕΛΗΝΗ	301	1357
14	ΔΕΚΑΤΗ ΤΕΤΑΡΤΗ	1352	ΣΕΛΗΝΗ	301	1653
15	ΔΕΚΑΤΗ ΠΕΜΠΤΗ	851	ΣΕΛΗΝΗ	301	1152
	ΠΕΝΤΕ ΚΑΙ ΔΕΚΑΤΗ	809			1110
16	ΔΕΚΑΤΗ ΕΚΤΗ	671	ΚΟΙΛΗ	138	809
	ΕΞ ΚΑΙ ΔΕΚΑΤΗ	434			572
17	ΔΕΚΑΤΗ ΕΒΔΟΜΗ	447	ΚΟΙΛΗ	138	585
	ΕΠΤΑ ΚΑΙ ΔΕΚΑΤΗ	755			893
18	ΔΕΚΑΤΗ ΟΓΔΟΗ	453	ΚΟΙΛΗ	138	591
	ΟΚΤΩ ΚΑΙ ΔΕΚΑΤΗ	1539			1677
19	ΔΕΚΑΤΗ ΕΝΑΤΗ	702	ΚΟΙΛΗ	138	840
	ΕΝΝΕΑ ΚΑΙ ΔΕΚΑΤΗ	480			618
20	ΕΙΚΟΣΤΗ	613	ΚΟΙΛΗ	138	751
21	ΕΙΚΟΣΤΗ ΠΡΩΤΗ	1901	ΚΟΙΛΗ	138	2039
22	ΕΙΚΟΣΤΗ ΔΕΥΤΕΡΗ	1435	ΚΟΙΛΗ	138	1573
23	ΕΙΚΟΣΤΗ ΤΡΙΤΗ	1331	ΚΟΙΛΗ	138	1469
24	ΕΙΚΟΣΤΗ ΤΕΤΑΡΤΗ	1627	ΚΟΙΛΗ	138	1765
25	ΕΙΚΟΣΤΗ ΠΕΜΠΤΗ	1126	ΚΟΙΛΗ	138	1264
26	ΕΙΚΟΣΤΗ ΕΚΤΗ	946	ΚΟΙΛΗ	138	1084
27	ΕΙΚΟΣΤΗ ΕΒΔΟΜΗ	742	ΚΟΙΛΗ	138	880
28	ΕΙΚΟΣΤΗ ΟΓΔΟΗ	768	ΚΟΙΛΗ	138	906
29	ΕΙΚΟΣΤΗ ΕΝΑΤΗ	977	ΚΟΙΛΗ	138	1115
30	ΤΡΙΑΚΟΣΤΗ	1009	ΚΟΙΛΗ	138	1147

The reason why these tables are given in MS Grec 2419 and other texts is due to a particular way of using the Circle of Petosiris that I wasn’t taking into account earlier.  The method I thought would be used—perhaps biased by my first encounter with this sort of technique from the Sphere of Dēmokritos from PGM XII.351—364—would be to take the value of the person’s name and the actual number of the lunar date, sum them together, divide by the number of days in the lunar month, and use the remainder.  Rather, it seems that instead of using the raw number (perhaps as a later development, or as an alternative technique?) one would use the value of the actual name of the lunar date instead, and in most cases (there’s at least one manuscript that doesn’t do this) modified by whether the date was during the waxing or waning moon.  The benefit to using the numbers in the table above, whether of the name itself or the name plus a modifier, has the benefit of making more erratic the results of dividing and taking the remainder in a discontinuous, semi-unpredictable way (1589, 1123, 1019, 1315, …), as compared to the sequential order of the actual numbers of the days of the lunar month (1, 2, 3, 4, …).

That means we have several methods to use now for the Circle of Petosiris, although several of them can be ignored because they confuse adding pure numbers with names of numbers.  In any case, we’d take the same approach: come up with a sum, divide by the number of days in the lunar month, and find the remainder among the zones of the proper Circle of Petosiris:

1. Add the value of the name of the person to the number of the lunar day.
2. Add the value of the name of the person to the number of the lunar day plus the number of the day of the week.
3. Add the value of the name of the person to the number of the lunar day plus the value of the name of the day of the week.
4. Add the value of the name of the person to the value of the name of the lunar day.
5. Add the value of the name of the person to the value of the name of the lunar day plus the number of the day of the week.
6. Add the value of the name of the person to the value of the name of the lunar day plus the value of the name of the day of the week.
7. Add the value of the name of the person to the value of the name of the lunar day plus a modifier.
8. Add the value of the name of the person to the value of the name of the lunar day plus a modifier and the number of the day of the week.
9. Add the value of the name of the person to the value of the name of the lunar day plus a modifier and the value of the name of the day of the week.

The same could likewise be done by comparing the value of the name of the person against the number of the lunar date or the value of the name of the date, after dividing and taking the remainder of each by the number of days in the lunar month, and seeing where each remainder falls to compare them.

This is all well and good, and Neugebauer and Saliba have done some pretty intense work to correlate and investigate all the variations in these weird sums and modifiers found where there are such tables with Circles of Petosiris.  However, in an incredibly disappointing conclusion, they finish their paper by saying that “obviously one should now explain how these numbers were classified into strong, medium, and weak ones…our attempts in this direction did not lead to any convincing result.”  As the mathematician and historian Joel Kalvesmaki says on this specific point, they “solved many important problems but left many more outstanding”.  What we’re likely relying on is a fundamentally old tradition of lucky and unlucky numbers within the context of lunar dates, and it doesn’t seem to be clear to anyone why the Circle of Petosiris or the Sphere of Dēmokritos or other such techniques arrange the numbers the way they do.  Neugebauer and Saliba suggest that “since these numbers represent lunar dates, it is plausible to search for astrological motivations”, although Kalvesmaki makes a good point that such a kind of system of days can have any number of mutually-nonexclusive origins: making observations from experience and experiment, informative myths, zodiacal considerations, and the like.

It seems that, unfortunately, I’m at a dead end with this sort of investigation.  Unless I get access to a wide number of manuscripts dating back some two millennia and somehow pick up classical and medieval Greek, I doubt I can get much further along this line of thinking.  I suppose the only thing left is to experimentation.  One easy way would be to use the comparison method: take the value of my name and compare it to any of the combinations above: the number of the lunar day as reckoned from the Noumēnia in my Grammatēmerologion with or without the number of the day of the week added, or the value of the name of the day according to the table with or without the modifier value with or without the value of the name of the number of the day of the week.  I suppose it wouldn’t be hard to write a simple program to do just that, then keep a running log of how good or bad a given day is.  It’s not as satisfying as discovering some long-lost ancient logic or system, but picking out patterns can be just as sweet once you sift through the salt.