Blessed Feast of the Assumption of the Blessed Virgin Mary to all on the Gregorian Calendar, and Happy Feast of St. Stephen the Protomartyr for those on the Julian! In my neck of the woods, today is Sveti Stefan Vetroviti, as our nickname for St. Stephen is “the Windy” or “the Windswept”, in thanks to his continued syncretism with the god of wind, Stribog. This is a powerful feast of the zduhać, vertovnjak, oblačar, gradobranitelj, and zmajevit čovek class of weather-manipulating healers and sorcerers, given Stribog’s enduring patronage of their arts, through his fatherhood of the Vjetreni Vojvoda spirits and his own fights against the ala, hala, german, and aždaja. Moreover, it is a day not only associated with the collection of hagstones, but their deployment in charms for knotting the wind, protecting livestock, and providing homes for spirits.
One of our recent episodes on our podcast, The Frightful Howls You May Hear, featured an overview of some of the basic lore around hagstones from the British, Germanic, and Slavic contexts. We’ve been so overwhelmed by the outpouring of support, love, and engagement on the podcast from so many of you; the warm reception and incredible feedback we’ve received has truly nourished us in our creativity and excitement to share more. We are so deeply grateful to everyone who has sent in comments, shared their thoughts on the episodes, and signed up to support our Patreon where we post bonus content such as our show notes, Salt’s incredible monthly astrological almanac, our Q&As, and far more! Over the next few weeks, we hope to share with our readers here on the blog not only a little of what we’ve been up to behind the scenes, but also new offerings to come in the form of courses, mentorships, readings, charms, and far more. It’s truly been a blast for the three of us to share more regularly, via our bi-weekly episodes, aspects of folkloric and magical research we’ve been up to, as well as tidbits of our personal adventures and sorcerous journeys.
The Hagstone episode (also adding the YouTube link since we only made the channel a few episodes after the launch, and most of our viewers are on Spotify and Apple Music—so for those of you who prefer YT, we’re finally live!) came about while the three of us were scattered over the past two months, travelling for work, spiritual training, conferences, and everything in between. Even on my travels, I had been collecting them where I could see (or, in the case of their hissing, hear) them, and asked Salt and Key if they’d be interested in contributing some German and English sources to an introductory episode on these most reliable of magical companions.
One of several hagstones I found at the Colombia River Gorge recently.
I thought it might be helpful to share some of what we went over in the episode here as well, in honour of Sveti Stefan Vetroviti. While we covered a great many names that holed stones have been referred to across Europe, “hagstone” is the name we’ve all used with each other in English from the beginning, and it’s certainly the one that’s stuck in our common parlance, as well as across occult spaces. That being said, while the list of names is especially long, a sample of our favourites from the episode include mare stones, bitch daughter stones, witch stones, and adder stones in English; Lochsteine, Trutensteine, Schratensteine (see our episode on the Schrat for more on this one!), and Hühnergott in German; and a great many coming from the South Slavic dialects, of which I’ll provide below with their translations from Serbian:
Chicken god (pileći bog)
Identical in meaning to Hühnergott, which itself is believed to be a German neologism form Slavic languages, referring to their use in the protection of livestock and especially chickens by being hung over their coops
Dog’s heart (psećim srcem)
Dog’s god (psećim bogom)
Dog’s luck (pasja sreća)
These dog-related motifs are a reference to Veles, lord of cattle, wolves, agriculture, the wilderness, magic, the chthonic world, and far more
Perun’s arrow (Perunovom strijelom)
Thunderbolt (gromovnikom)
Thunderstone (gromovnički kamen or kamen groma)
These three come from the belief that these stones are formed when Perun, the god of thunder, order, and the heavenly realms, strikes the holes through with his furious lightning
Serpent stone (zmijski kamen)
from the belief that holed stones are black eggs from which basilisks are hatched
Snake’s poison (zmijski otrov)
Serpent’s egg (zmijsko jaje)
Witch’s stone (kamen veštica)
God’s eye (božje oko)
An example collected from a beach.
The uses for holey stones are all but endless. They protect livestock from curses, witches, and being ridden to the point of exhaustion by fairies, heal toothaches, headaches, and all manner of illnesses (in the Balkans, a common technique is to sandwich the afflicted area with a hagstone on either side, and conjure them to pass the pain through them and away, so that they may be disposed of later), ward against nightmares, and allow for the seating and ensoulment of spirits (in my tradition, this is typically done with seven-holed hagstones, which are especially prized). Some cultures recognize classifications of hagstones and their abilities and proclivities based on number of holes (with each having their own uses), whether they are seen as belonging to fire or water (based on their shape and hardness), whether they are male or female (less commonly used, but often having to do with roundness and pointedness), and in which location and weather conditions they were found. I went over a few variations from Slavic speaking countries with regards to these in the episode, though these classifications can become so detailed and so varied that they could take up their own chapbook!
One of our favourite charms that we shared, coming from Reginald Scot’s Discoverie of Witchcraft, is the famous “Man of Might” rhyme:
Tha mon o´ micht, he rade o´nicht wi´ neither swerd ne ferd ne licht. He socht tha mare, he fond tha mare, he bond tha mare wi´ her ain hare. Ond gared her swar by midder-micht she wolde nae mair rid o´ nicht whar ance he rade, thot mon o´ micht.
With the modern English being:
The man of might, he rode all night with neither sword, nor army, nor light. He sought the mare, he found the mare, he bound the mare with her own hair. He made her swear by mothers might that no more would she ride at night where once he, rode that man of might.
A common charm one can make from this cantrip is to braid horse hair (especially white horse hair, given that the “man of might” is none other than St. George in many understandings) through a hagstone while repeatedly uttering the verse, making an offering to your spirits and the good saint immediately after in thanks to empowering this anti-nightmare ward. I’ve made several of these for friends, family, and especially children’s cribs and found them to be exceptionally useful. The one which hangs over my and Salt’s bed is a two-holed hagstone, with the horsehair looping through the topmost hole, and the other being used to assist me to return to my body in dream and spirit flight.
A charm made in this manner using a hagstone I found while travelling.
Indeed, a very similar charm comes to us from the mid-16th century, as recorded by Thomas Blundeville of Norfolk in his The Order of Curing Horses Diseases (1566):
In nomine patris, &c. —-Patris et Filii et Spiritus Sancti Saint George our Ladyes knight, He walked day so did he night, Until he her founde, He her beate and he her bounde, Till truly her trouth she hym plight, That she would not come with the night, There as Saynt George our Ladyes knight Named was three tymes, Saint George.
Holed flint stones were typically hung, like iron, to ward people and horses alike from being ridden by night-mares—in the case of the latter, they could be placed around the manger or the neck of the animal. Blundeville considered this to be a “foolishe charme” that was to be written down while hanging a “flynte stone that hath a hole of his owne”, which was naught but a silly way to con money out of “playne folks purses”. Yet, much like Reginald Scot, in his very disdain he ultimately preserved for us this oral charm in writing, allowing us to make good use of it even now.
Another dreaming protection amulet, made from a hagstone, an iron key, crossed rabbit’s legs, and mandrake root.
While hagstones require no special ritual to make them “work” or to activate their virtues, there exists plenty of folklore with regards to how they should be acquired. J. Geoffrey Dent’s article “The Holed Stone Amulet and Its Uses” (1965) tells us that there is evidence from the South of England of beliefs that hagstones should be received as gifts, or, even better, stolen. Generational stones, that is, those which had been passed on throughout successive owners within a family, all used for the same purpose, are perhaps the most powerful through their repeated victorious efficacies, and presumably all the more potent if stolen. Yet in the Balkans, we repeatedly encounter the lore that hagstones indeed will only properly “activate” and bond with their owner if they are deliberately found within nature by them. I shared a few charms for how to actually go about and acquire them in this way, both with regards to luring them to you, such that spirits reveal their places and that you stumble upon them naturally, as well as how to seize their fortune once they are found in the episode.
Regardless of what you choose to say out loud (for ultimately many of these “charms” are oral prayers passed on that someone may have at some point invented, or, in the case of bajalice, received from a spirit), a good way to hunt them is to take off your left shoe, and walk barefoot along the shore or river while dropping one millet seed from your closed left fist into the ground at each step and repetition of your prayer. In this way, the spirits of the land are petitioned to receive your blessing of fertility, and accept your alm in exchange for revealing your prize.
A collection Salt and I brought home from a trip to Brighton Beach together.
Many of the oral charms we shared ultimately serve the purpose of bonding a stone to you, especially if they are not already claimed by one of your spirits. The three of us have often had the shared experience of bringing home a great many hagstones from a hunt only to find that 2/3rds of them had been immediately spoken for by our spirits, who wanted them for their own ends, vessels, and amulets. I’ve often had to string them in groups of seven, nine, thirteen, or twenty-one as soon as I’ve brought them through my door as a saint or house spirit immediately wanted them placed over an important threshold. In cases in which I’ve bought hagstones over Etsy, specifically because I was searching for particular numbers of holes that a spirit requested, I’ve left them before my spirits in small bird’s nests that I’ve collected for them, such that they can incubate, receive the rays of the sun, and lubricate their hissing through the maws of their gates.
If you listen closely for their hissing, the serpents below may even lead you to them by sidewalks in the cities.
While different aspects of lore disagree on whether or not the thread which hagstones are hung on should be knotted or not, the notion that they should be strung up with natural material (such as wool, linen, or hemp) is fairly universal. If I’m about to use mine to scry, I will often make use of a fairly well-known technique across the Balkans to whisper through the whole what I wish to see while moving it around my left palm with my right index finger. Afterwards, I will breathe through the whole, and place it to my right eye while closing the left, and then scry for the augury—or directly at the sky in the morning to witness the rising star, that it may be captured later within that very stone.
There’s so much more that could be said on their collection, uses, and enchantments, such that we’re already planning the next edition of our hagstone episode series. If there’s anything in particular any of our readers are curious about or would like to be included, please feel free to write to us below, and we’ll do our best to include some tips and folklore on each matter in the next installment! For now, happy hunting, and thank you all so deeply for supporting our podcast!
Paranatellonta and the formula for calculating rising and setting stars
The paranatellonta are another major feature of astrology that is occasionally utilized by classical authors, such as Firmicus Maternus, Manilus, and so on. We also find examples of these rising stars in later authors, influencing works such as the Astromagia of Alfonso and the Astrolabium Planum (or Astrological Optics as the English edition is known) of Johannus Angelus. They even find themselves appearing in the works of William Lilly and later renaissance authors, by their tables of “bright, dark and empty” degrees.
Now, the word paranatellonta (παρανατέλλοντα), literally “parallel rising” (or alternatively, συνανατέλλοντα, “synanatellonta” – rising simultaneously according to the Brill’s New Pauly) describes the rising of the fixed stars that occurs over the horizon. This is contrasted with the method of Ecliptic Projection given by Ptolemy, which sees use in various works including Anonymous 379 – in which, though he might imply use of the paranatellonta by his language, is in practice giving the ecliptic projections of the fixed stars in his work. This ecliptic projection method is also used by many astrologers today and in the classical period. It’s the most common and popular method of using the fixed stars, and itself one of much use and virtue.
Yet it is not the sole method of observing them, and, alongside the heliacal phases of the stars, the paranatellonta make up one of the three approaches to using the fixed stars in classical astrology.
Now, in ecliptic projections for the fixed stars, even if 8° Leo is rising in the Ascendant, it doesn’t mean that a fixed star whose ecliptic projection is at 8° Leo will also have its physical body also rising, because it is not directly on the Ecliptic (though some are and thus will). In other words, its body might be elsewhere, under or above the horizon. The paranatellonta however, refers to the more precise astronomical observation that we can use to determine the ascendant degree at the time a particular star’s physical body appears over the horizon. The name itself – co-arising, parallel rising, or rising alongside, however you spin it – is chosen because they rise at the same time as a particular degree of the zodiac, over the circle of the horizon. Thus they share a sympathetic relationship to the same said degree and exert their influence over it. The precise astronomical relationship here is going to be a subject in my upcoming Astrological Course, and we’ll leave those finer details for another time, though those familiar with the basics of astronomical coordinate systems will be able to understand these things just by what has already been written.
The concept of paranatellonta does indeed have a relationship to the “parans” of modern astrology, though there are also some distinctions and differences as well. Namely, as far as similarities go, the emphasis is upon the star’s physical body rising over the horizon (though we arguably also include culminating and setting stars as well) at the time of the Native’s birth.
As far as the differences, the first is that the paranatellonta emphasise the horizon. In other words, a star must be in the Ascendant or (arguably) culminating, setting and so on, to be considered relevant. It does not need to be regarding a planet to be effective or to have influence over the figure.
The second is that the paranatellonta are only effective at the time of birth itself – the exact measure of this seems to be based on the exact degree that the star co-rises with, if we consider the ‘images of the degrees’ given in Johannes Angelus & the Astromagia to give us an indication of this, although its worth thinking that Firmicus is clearly ascribing Sirius multiple degrees of influence as well. On the other hand, contemporary use of the parans considers them in relationship to the planets and horizon, and through a 24 hour period, whilst the paranatellonta emphasise the moment and degree of birth itself.
So we can see that the fundamental concept is very similar, and holds a similar basis; but there are distinctions as well.
Now, these paranatellonta also have a relationship with the decans, which makes sense considering that the decans were observed in relation to the horizon as well as their heliacal phases by the Egyptians, creating a nocturnal stellar clock – though we should distinguish the earlier Egyptian decans and the later use of decans in horoscopy.
We see them as especially important in judgements of physiognomy and the body in Astrology – which, is a far more important topic than is given credit at times. The body itself is a Nativity – a natal chart in and of itself – and the divinatory art of physiognomy as expressed in premodern Europe, much as chiromancy (or palmistry), was essentially looking at the celestial influences upon a person using the body as the medium and making divinatory statements based on their appearance. Likewise the paranatellonta are given a clear relationship to the body by Firmicus Maternus in his Mathesis – who, drawing on (I believe, as I am quoting from memory here) a lost work by Nechepso and Petosiris, gives the degrees that he calls full, and the degrees that he calls empty. These are related to the “bright, empty, dark, smoky” degrees found in later Astrological literature.
The list given by Firmicus Maternus includes Sirius as the most reliably identifiable star, and gives it to the 7th to 11th degrees of Cancer. However, the ecliptic projection of Sirius was in Gemini during the period Firmicus was writing, and the same for any sources he would have been using. On the other hand, if we look at the rising of Sirius over the horizon, during 100 BC the value we have is roughly 12 degrees of Cancer using the modern zodiac. Of course, there would naturally be offset from the zodiac used by our classical authors by some measure, but, it is still approximately close enough.
Correcting these tables (assuming they need it – as I think they do) is a difficult task; the paranatellonta vary as to which star rises, and which stars set over the horizon at any given time based on latitude. Thus any such efforts to do so would need to be able to calculate them for the given latitude as well as precession. Probably an impossible task, all in all.
But we can see here the relationship the fixed stars and paranatellonta have with the appearance. This is resembling to the decans who themselves, in astrological literature, tend to represent the corporeal form or body of a thing that they signify, as well injury to the same by disease or accidents. We find examples of this relationship in the works of Sahl Bin Bishr (again quoting from memory, please comment if a correction is needed!) who cites Al Andrazaghar on the use of the Face-Lord in judging appearance and also Julian of Laodicea, recently translated by the Horoi project. Thus we see that the co-arising stars have a strong share and influence over the body of the Native, as well as their activity and behaviour.
This brief cursory look is just a beginning, but I leave you with the formula below – so that you can calculate the time that a particular fixed star might rise or set over the horizon, as well as the formula to determine which stars will rise or set.
Notes to the Formulary
A quick note: I do not have a background in mathematics, save for entry level programming in Javascript, BASH & a small amount of C#. As such please forgive my crude formatting and the fact that I am probably breaking several mathematical conventions. Furthermore, I wish to note my sources used here. Firstly, I have drawn upon the formula given by Robson in her work on the Fixed Stars, and the formula for the Ascendant and Midheaven given by Radixpro. I have removed the conversion of LST to RAMC (or vice versa) in both cases as a result, and redacted Robson’s use of the Logarithmic Trigonometry since it is unnecessary – though those who wish to make use of them will find modernized formula for these logarithmic tables following the example as a helping hand to those who are interested in using parans and calculating them by hand.
The Formula
Sin-1 (Tan (δ) x (Tan (φ)) = AD
90N + AD = H
or
90S – AD = H
α – H = Rising RAMC
α + H = Setting RAMC
sin RAMC / cos RAMC x Cos ε = ƛMC
Tan–1 (cos RAMC / -(sin ε x tan φ + cos ε x sin RAMC)) = ƛAsc
1. Breakdown of the Formula
First we need to take the declination of the fixed star (δ), the right ascension of the fixed star (α), and the terrestrial latitude (φ).
2. Calculate the Ascensional Difference (AD) for the star, as follows:
Sin-1 (Tan (δ)) x (Tan (φ))
In the windows calculator for example, this is as follows:
Tan δ x Tan φ = Dif
Sin-1 (Dif) = AD
3. Use one of the following, depending on whether the star is southern or northern
90N + AD = H
or
90S – AD = H
4. Calculate the rising RAMC of the star as follows, using the Right Ascension (α)
α – H = Rising RAMC
5. Calculate the setting RAMC of the star as follows, using the Right Ascension (α)
α + H = Setting RAMC
6. Now we calculate the MC, before calculating the Ascendant; so that we can determine the rising time of the star. This is a simple formula, divided into a few steps, and should give you the chance to familiarize yourself with these calculations before the more complicated Ascendant. The formula is as follows: to calculate the zodiacal longitude (ƛ) of the MC, using the RAMC we calculated above, and the obliquity of the ecliptic, which we can approximate to 23.4371 for modern dates but ideally, we use a more precise amount, especially in dealing with trigonometry.
ƛMC = sin RAMC / cos RAMC x Cos ε
Simplified, it is as so:
Step 6.1:: sin RAMC = SinRam
Step 6.2: cos RAMC x Cos ε = CosRE
Step 6.3: SinRam / CosRE = Result
Step 6.4: tan-1 (Result) = ƛMC
Note that if the RAMC is under 180, it will fall between 0 Aries and 29°59’ of Virgo. If it is greater than 180, then it will be between 0° Libra and 29°59’ of Pisces. If it is not meeting these requirements, add or subtract 180 as necessary to produce the result sought.
7. Now we use the following formula to calculate the Ascendant from the RAMC. To do this we need our RAMC from earlier steps, and terrestrial latitude (φ) from step 1. Finally we need the obliquity of the ecliptic (ε). This can be found easily online or via its own relevant formula. Then we consider the following formula:
Tan–1 (cos (RAMC) / -(sin ε x tan φ + cos ε x sin RAMC)) = ƛAsc
However, we can simplify this as follows into six steps.
7.1: cos RAMC = CosRam
7.2: sin ε x tan φ = sintanEL
7.3: cos ε x sin RAMC = cossinERAM
7.4: sintanEL + cossinERAM = Negative Number1
7.5: – Negative Number1 = Negative Number2
7.6: CosRam / Negative Number2 = Result
7.7: Tan-1 Result = ƛAsc
From this we have our ascendant axial degree – and remember that 00.00 is 0 Aries; Whilst 359.99 is 29.59’ of Pisces. It must be in a sign following, or to the left; of the MC. So if the result is not appropriate, then you must apportion 180 to the ascendant longitude as necessary.
Examplum
Let us take the star of Regulus, on 7 Sep 2022; and as for our local horizon, let us say that the Native is from Winchester, Hampshire.
1. First we need to take the declination of the fixed star (δ), the right ascension of the fixed star (α), and the terrestrial latitude (φ). [I have also included the obliquity of the Ecliptic (ε) since we will need it later.]
φ: 51°05’ or 51.08 North
δ: 11°51’ or 11.85
α: 10h9m32s, or 152.25
ε: 23.4382260812
2. Calculate the Ascensional Difference (AD) for the star, as follows:
Sin-1 (Tan (δ)) x (Tan (φ))
In the windows calculator for example, this is as follows:
Tan δ x Tan φ = result
Sin-1 (result) = AD
Let us take the Ascensional difference, by observing the formula given, and it gives us:
tan(11.85) x tan(51.08) = result 0.2598493562969941021326313835425
We then use the arcsin on result to generate our AD:
sin-1 0.2598493562969941021326313835425 = AD 15.061123671264834812596990682949 (or 15°03’)
3. Use one of the following, depending on whether the star is southern or northern
90N + AD = H or 90S – AD = H
Now, since the star of Regulus is of northern declination; and we likewise are northern, we add his ascensional difference to 90, so we can make H.
4. Calculate the rising RAMC of the star as follows, using the Right Ascension (α)
α – H = Rising RAMC
Then following this, we calculate the RAMC of the star by subtracting the same from his RA, and it gives us a sum of 47.18887632873516518740300931705 in RAMC. Thus the midheaven shall have the Right-Ascension of 47 degrees and 11 minutes, when the star rises over the Ascendant. Note that we will dispense with looking for the setting time (step 5) here to keep the example simple.
6. Now we calculate the MC, before calculating the Ascendant; so that we can determine the rising time of the star. This is a simple formula, divided into a few steps, and should give you the chance to familiarize yourself with these calculations before the more complicated Ascendant. The formula is as follows, to calculate the zodiacal longitude (ƛ) of the MC, using the RAMC we calculated above, and the obliquity of the ecliptic, which we can approximate to 23.4371 for modern dates but ideally, we use a more precise amount, especially in dealing with trigonometry.
ƛMC = sin RAMC / cos RAMC x Cos ε
Simplified, it is as so.
Step 6.1:: sin RAMC = SinRam
Step 6.2: cos RAMC x Cos ε = CosRE
Step 6.3: SinRam / CosRE = Result
Step 6.4: tan-1 (Result) = ƛMC
So, using the RAMC to determine the longitude of the midheaven in the zodiac, we must proceed as follows:
The Sine of the RAMC is 0.73359794075541645499224468998881
The obliquity of the ecliptic is 23.4382260812 and when cosined and multiplied with the cosine of the RAMC, it gives us 0.62351091696510862919932339243141.
So, we divide this sum from the sine of the RAMC, giving us 1.1765598978220749303357600844386. Make an arc-tan with it and we are given 49.637609676335657842990870332858.
Converted to DMS (this means at the time of the stars rising) it will be at 49°38’ degrees of absolute longitude. IE: 19°38’ Taurus will be on the MC.
Note, that if we consider the Swiss ephemeris table of houses for the right ascension of the Midheaven, the answer is approximately the same. (Possibly give or take an insignificant deviation of a few minutes – I haven’t interpolated the table of houses).
Intermission
Now, before we move onto calculating the Ascendant (which is more useful if we would construct a table, for example) we ought to examine the figure, and determine the evidence to show that this works.
Here we have the Chart as I have designed it. We can see the Ascendant is 29’45’’ Leo. The Midheaven is at 19’38’’ of Taurus, as we observed earlier.
Now, if we look at the ‘parans’ in the Solarfire program reports, we can see that connecting to and rising over the Ascendant is Regulus, with only about a minute’s difference to our manual calculation.
In this respect then, we can see that it works effectively for the calculations. But still, if we had the wish to construct a table, for example, then it is good that we know the rising degree as well.
Back to our example!
7. Now we use the following formula to calculate the Ascendant from the RAMC. To do this we need our RAMC from prior steps, and terrestrial latitude (φ) from step 1. Finally we need the obliquity of the ecliptic (ε). This can be found easily online or via its own relevant formula. Then we consider the following formula
Tan–1 (cos (RAMC) / -(sin ε x tan φ + cos ε x sin RAMC)) = ƛAsc
However, we can simplify this as follows, into six steps.
7.1: cos RAMC = CosRam
7.2: sin ε x tan φ = sintanEL
7.3: cos ε x sin RAMC = cossinERAM
7.4: sintanEL + cossinERAM = Negative Number1
7.5: – Negative Number1 = Negative Number2
7.6: CosRam / Negative Number2 = Result
7.7: Tan-1 Result = ƛAsc
So in this example, we have our RAMC, and we make the cosine of it to be as follows which we will save for later. (Cosine of the RAMC: 0.67958374121178950478721381305492)
Now we take the sine of the Obliquity of the Ecliptic and multiply it via the tangent of the Terrestrial Longitude, and it gives us this result. 0.49259755429671712792119030118711
We then take cosine of the obliquity of the ecliptic, and multiply this via the sine of the RAMC. This gives us the following. 0.67306837551544119543796432811591
We add these two values together to produce the following:
1.165665929812158323359154629303
But we then negate it, so that it is written as such instead:
-1.165665929812158323359154629303
Now we take that Cosine of the RAMC, and divide it by the negative number:
And this we make the arctan, or tan-1 and the value that is returned will be our absolute longitude. However, in this example we must also add 180 Degrees, since the result is -30 and would place us elsewhere.
Converted to degrees this is 149 degrees and 45 minutes, 28 seconds of absolute longitude. So we thus know the Ascendant will have the 29th Degree of Leo, 45 minutes and 28 seconds, just as it is also affirmed in the figure above. And if we wished to include it in a table for the same star, we could do so.
Co-Latitude and which stars can rise or set
Note that not every star will rise and set however, depending on the latitude we look. Therefore we must look to its colatitude:
1. Determine the Co-Latitude. This is found by subtracting the latitude of a place from 90. Thus, Alexandria has the latitude of 32°10’ (or 32.17 decimal).
90° – 32°10’ = 57°50’N
2. Any star with a greater declination than the co-latitude in the same hemisphere cannot set. Any star with a greater declination than the co-latitude in the other hemisphere cannot rise. As an example, if our co-latitude for Alexandria is 57°50N, then a fixed star at 58°N cannot set; and a fixed star at 58°S cannot rise over the horizon.
A final note on Robson’s formularies
Though I don’t consider the aspects with the paranatellonta, I wanted to make a note for those who are interested in using the above formula for their own use of parans. The formula given by Robson was making use of logarithmic tables, and converting these to a calculator can be troublesome. Whilst I won’t give the full formula here, as a helping hand for the interested parties who might want to use the same, the method of deriving the logarithms is as follows. For example, if we wanted to observe the logarithmic tangent of a particular stars declination:
log(tan(δ)) + 10 = LTδ
In the Windows calculator this would be as follows (make sure you are using scientific mode):
Tan δ = δt
log δt = δtl
δtl + 10 = LTδ (logarithmic tangent of the declination)
If any readers, students, and fellow astrologers are interested in using these formulas in their publications and programs, you have my permission and encouragement to do so! All I’d ask you to give me a shout out as well, and ideally a link to either this article/our blog, or the website of our upcoming platform for hosting classes, soon to be featuring work from myself, Sfinga, and Key: mercurii-school.com. The website isn’t live yet, but expect updates very shortly on the first course: a 106 lesson tour of traditional astrology and magic by yours truly. I named my sources, and would appreciate being named in turn!
Many thanks for your time, and I hope you find this useful!
Happy New Year everyone! I’m B. Key. After a July 2021 guest post describing the evocation of Faust’s Mightiest Sea-Spirit, Sfinga and Salt, two of my best friends, graciously invited me to become a third author for this blog. To kick things off, I decided to develop a brief miscellany of sorcerous chemistry and external alchemy. By day I’m a biochemist, so this blend of interests never fails to stir the spirit to put pen to paper.
—
For the past two millennia, alchemy, with its myriad and diverse cultural interpretations, has been practiced in an uninterrupted and ever evolving march toward inner and outer reunification with divinity. Forming medicines and other precious substances from baser materials, lengthening our lives to the point of immortality, wielding magic, commanding spirits, and deepening our connection to the Gods are not without pitfalls. In these ~2200 years, the chase continues to leave the fragmented notes and the emperors, philosophers, physicians, and chemists who penned them in behind, all reunified with the divine in death, instead of life.
To pick up the fragments of the past and piece them back together again, and to add our own scrap to the pile in hopes that one may, some day, craft from it the Philosopher’s Stone, drink from the Font of Life, see Gold in the crucible instead of Lead, is unto itself a goal both most high and tantalizingly attainable. From these records, we find a both a “science simply composed of one and by one, naturally conjoining things more precious, by knowledge and effect, and converting them by a natural commixtion into a better kind” (Roger Bacon, The Mirror of Alchemy), as well as “…the knavery and confederacy of conjurors, the impious blasphemy of enchanters, the fruitless beggerly art of alchimistry, and the horrible art of poisoning” (Reginald Scot, The Discoverie of Witchcraft).
For Hermes said of this Science: Alchemy is a Corporal Science simply composed of one and by one, naturally conjoining things more precious, by knowledge and effect, and converting them by a natural commixtion into a better kind.
Roger Bacon, The Mirror of Alchemy
Ahead is a small collection of personal techniques, selected to demonstrate sorcerous applications, both duplicitous and sincere, of chemical materia and the synthesis thereof. With the guidance and inspiration of spirit and deity, each of these works will take on a life of its own, as all things shall, and become a gateway to new endeavors, each as disparate and expansive as the notes left behind.
A disclaimer: The following experiments involve the use of strong acids, caustic solutions, powerful oxidizing agents, heavy metals, and their products. It is extremely dangerous to attempt any of the following, especially if you do not have formal laboratory training and an environment with the equipment and space to carry out these experiments in a contained and professional manner. Of special concern is the experiment by which one can see a serpent—if deciphered and enacted, the byproducts and waste created by this reaction are extremely dangerous, highly toxic, difficult to clean, require specialized facilities to dispose of, AND some may be regulated in your municipality.
To have 30 Pieces of Silver Take up your Copper, and wash it in a mixture of good vinegar and salt in excess until impurities have fled. In a good flask, dissolve lye, about 12 grams, into 100 ml of water that has been distilled, and heat, but do not boil. Once warm, add granules and fragments of Zinc. Dry your Copper of vinegar, and add it to the lye, atop the Zinc.
Your Copper shall be Silver, after half of an hour. On Holy Wednesday, take up this silver in your left hand, ideally during the darkness of Tenebrae, and kiss an icon of Christ. Turn, and do not look back until you arrive at a potter’s field. Bury the coins, begging the spirits of place take them, which they will refuse if all is done properly. Leave the place, and return only to unearth them at the dawn of Easter Sunday. Know that these coins are now of great use in trafficking with spirits, especially those who shun the Lord. To have Gold from this Silver, heat it upon a plate.
To Transmute Lead into Gold Add Aqua Fortis to an equal measure of pure water, and toss in some Lead shot. Heat until the Lead is gone. Boil pure water, and add to this one gram of Potassium Iodide, a splash of good vinegar, and the humor of Lead. As this cools, it shall take on the luster of Gold, until Gold itself falls like snow out of the menstruum. It shall snow for one day and one night, until it can be recovered.
To Have Stigmata Baptize the Salt born of Potash and Sulfur and apply him to your palm. Take up the stone Molysite, reduce him to dust, baptize him, and apply him to the other. Pray fervently, and know stigmata shall appear without damage to the hand.
To See an Evil Serpent Hear, O my son, and receive my sayings, this secret of secrets, hidden from the eyes of all but God. Hear, O my son, the Serpent of the Garden has not strayed far from his Bride our Mother. Hear, O my son, that His sons Salt and Mercury stalk the Earth. Hear, O my son, that those same serpents conjured to thwart Moses may be called through our Art at great peril to Body and Soul!
Aqua Fortis, itself distilled, shall feast upon Mercury, and emit a miasma so potent as to ravage the lungs of beasts. From him, his brother, Salt, shall be born a Red Oroboros. Boil Him to free the White tail from a Black mouth and return him to the Water of His birth, but know that he too will bring an equally perilous miasma.
Baptize Him, and with Him cast Salt born from the marriage of Potash and Sulfur. Know, O my son, A plague of Fog shall descend upon the land, and know He is in it. Take Him into the desert, as Enoch, and exorcise him with Fire. An Evil Serpent shall appear before you, and know He will escape you by shedding His skin. Hear, O my son, that all parts of Him are corruption.
Michael Maier, Mary the Jewess, from Symbola Aurea Mensae Duodecim Nationum (1617)
To Know the Weather by means of a Wonderful Vessel Add 900 mL of good spirits (100 proof vodka works well), three blocks of Camphor, 30 grams of Saltpeter, and 30 Grams of Sal Ammoniac to a pot and heat until all is dissolved. Decant this liquid into a clear glass vessel, leaving some air, and seal. Allow to rest outdoors for a night, and know the liquid inside now produces wonderful omens by which to know the weather, which are as follows:
If it is clear, the weather will be as clear
If it is cloudy, the weather will be as cloudy
If it is cloudy and there are small stars, the weather will be perilous
If there are stars, expect fog. If it is winter and the sun shines, expect snow
If there are large flakes throughout, it will be overcast, and may bring snow
If there are crystals at the bottom, expect frost
If there are threads near the top, expect wind
To refresh the vessel, heat him in a bath until the liquid within is clear of all debris, and let him rest overnight once more. Know the vessel must always rest outdoors away from sunlight, lest he cease to function.
To Harm and Bring to Obedience Those Spirits That Conjure Tempests Before The Circle(twice proven) Mix together 6 parts saltpeter, 4 parts sugar, some Sulfur, and some Asafoetida, then cast some of this upon the fire with this exorcism:
Abraham got up early in the morning to the place where he stood before the Lord, and he looked toward Sodom and Gomorrah, and toward all the land of the plain, and beheld, and, lo, the smoke of the country went up as the smoke of a furnace into the eyes and nose and mouth and lungs of NN. And it came to pass, when God destroyed the cities of the plain, He destroyed the enchantments, beguilements, deceptions, deceits, and of NN and filled the eyes and nose and mouth and lungs of NN with the Fire and Brimstone which is prepared for all rebellious disobedient obstinate and pertinacious spirits.
To have a Luminous Phial Heat almond oil in a vessel. Add to it phosphorous, 12 grains per half ounce of oil. Allow the oil to cool, then decant into phials until mostly, but not entirely filled. When uncorked, the phial shall glow.
To Have Mercury MIx a liter of pure water with about 400 grams lye. Add Sulfur, about 50 grams. Apply heat until he is gone, then allow to cool. It will appear as Blood. Add Cinnabar and wait. Add Aluminium, pounded thin, by parts until it is in excess. Add an equal volume of pure water. Allow to rest for one night, then decant the menstruum. Wash him with water; repeat until impure mercury is seen. To purify him, wash him in a bath of Potassium Permanganate. Again with water until pure. Wash in a bath of diluted Aqua Fortis. Wash again with water until pure. Filter and recover the Mercury, now pure.
To have a Pigment favored by Venus and her Spirits MIx 256 grams of Blue Vitriol with 700 ml pure water in a flask and heat. Mix 96 grams of Soda Ash with 300 ml of pure water in a flask and heat. Once both are liquefied, add the second to the first in many small parts. Allow to rest for one night, then recover the pigment by filtration. Boil away the fluid that passes through the filter to yield strong Natron.
To have the Oil of Vitriol Burn Sulfur and Saltpeter together in the presence of steam.
A reading list and selection of sources: Henry Cornelius Agrippa, Joseph H. Peterson – Three Books of Occult Philosophy (2000) Al-Razi, Gerard of Cremona – Liber Luminis luminum (1974) Roger Bacon – The Mirror of Alchemy (1597) Henry Beasley – The Druggist’s General Receipt Book, 9th Edition (1886) T. L. Davis – Pyrotechnic Snakes, Journal of Chemical Education (1940) Ekmeleddin İhsanoglu (ed.) – Cultural Contacts in Building A Universal Civilization: Islamic Contributions (2005) Jerry Alan Johnson – Daoist Mineral Magic (2006) Jerry Alan Johnson – Daoist Internal Alchemy: Neigong & Weigong Training (2014) David A. Katz – An Illustrated History of Alchemy and Early Chemistry (1978) Albertus Magnus, Joseph H. Peterson – Egyptian Secrets of Albertus Magnus (2006) Lawrence M. Principe – Chymists and Chymistry: Studies in the History of Alchemy and Early Modern Chemistry (2007) Reginald Scot – The Discoverie of Witchcraft (1584) Christopher Warnock, Nicholaj de Mattos Frisvold – The Book of the Treasure of Alexander: Ancient Hermetic Alchemy and Astrology (2012) Martha Windholz (ed.) – The Merck Index: An Encyclopedia of Chemicals and Drugs, 9th Edition (1976)
The following series of posts is intended to be a basic guide to the various cycles of the seven planets within Medieval Astrology, including both Persian-Arabic and Latin sources. In particular, throughout this we will be paying special attention to the motion of the planets, and the role this plays in their condition, which goes beyond just retrograde and direct! For this post, we’ll be observing what we call “ascending in the apogee of the eccentric” or the deferent circle.
So to begin with, we most often find the techniques relating to the apogee alongside a scattering of other techniques in medieval texts. We can find them in works such as Abū Maʿšar’s Great Introduction (Yamamoto and Burnett, 2019), Al-Qabisi’s Introduction to the science of Astrology (Dykes, 2010), Al-Biruni’s Book of instruction in the elements of the art of Astrology (Wright, 1934), and also Ibn Ezra’s work On Nativities (Sela, 2013). It is especially prominent in works of Medieval Perso-Islamic Astrology, however by the 1500’s in Europe, it seems to have considerably fallen out of favor and to have been ignored as a dignity or power of the planet.
What does ascending in the apogee mean? Essentially, it refers to the planet and its distance to the earth. The further away from the terrestrial earth a planet is, the more dignified it was considered. Conversely, a planet closer to us, becomes closer to the nature of the terrestrial, more corruptible and perishable. This technique then, aims to assess whether a planet is close to us, or distant from us, in order to judge its strength and quality. It is a laborious process, but alongside the Solar Phases and strength by Latitude(and planetary dragons, otherwise called nodes) they comprise some facets of Astrology that are often neglected today. Hence I have selected them to be the first in this series of posts.
Now, to understand this technique, we do need to know some Astronomical terms. Geocentric Astronomy, especially in this period, often draws on the Almagest of Ptolemy (usually accompanied by a lengthy commentary from its translator) and what we are engaging with here relies on the model presented by Ptolemy (Toomer, 1984). In particular we need to understand epicycles, and the deferential Circle. I am not going to present the entire theory of epicycles here, as it would distract from the main points. However, hopefully some explanation in the form of the following diagram will be sufficient.
As you can see, the circle of the deferent encircles the eccentric point in the centre. Conversely, the epicycle moves itself along the circle of the deferent. When a planet is “outside” the deferent circle (far from the earth) we call the planet direct. When a planet is “inside” the deferent circle via his epicycle, we call him retrograde; when he’s on the circle itself, we say he is in his stations. The deferent ring moves around the Ecliptic, which means each part of the deferent has its own “Zodiacal Longitude,” i.e: 0 degrees of Aries, 5 degrees of Cancer and so on, with the “Start” always beginning at the Vernal Equinox, or 0 Aries. The next part that is important for us to note is that the centre of this epicycle is called the mean longitude of a planet. This mean longitude, or the middle of the epicycle, moves across the deferent in its standard secondary motion, from east to west. Its motion is uniform, constant, unceasing and unchanging in Ptolemaic thought. It does not retrograde, there is no tangible body to be found here. It is an invisible axis point around which the planet circles, whilst the epicycle itself circles around the eccentric point. This uniformity of movement, is also the reason we use the mean longitude in considerations like the solar revolutions.
Now, in the above diagram, you’ll note that we also defined the apogee and perigee of the eccentric circle. But we also need to note that there is an apogee and perigee of the epicycle. They are depicted in our image, marked as PE and AE. These are based on the location relative to us on the earth. The pink line cutting through the middle of the epicycle, is known as the apsidial axis in modern Astronomical terms. The same term is applied to the one cutting through the deferent.
Thus, we have two apogees and two perigees. The first is the epicycle’s apogee; the second is the deferent’s apogee. We’re going to talk about the deferent’s apogee for now, saving the epicycle’s apogee for the future, as the calculations are considerably laborious and involve us having to find the verus locus of the planet using tables of anomalies if we want to make use of the technique itselfvia Ptolemy. Whilst I do intend on writing on this topic, it is more properly treated on its own once we have become acquainted with the calculation of mean longitude, which is a pre-requisite for the calculation of the “epicycles” anomalies and how we might consider this, in Modern Astronomy where there is no such thing as an epicycle.
I also want to add a brief note here. Judging from Al-Biruni’s work, it was common for contemporary astrologers to mainly emphasize the deferential motion. On the one hand, he criticizes this and seems to consider the epicycle’s apogee more important. On the other, it does show that the deferential apogee was thought to play an important role in the planetary motions regardless. When we look in these older texts and see the various terms “equation of centre” and “increasing in number,” these are referring to the tables of anomaly used to calculate a planets true position in the epicycle. Conversely, the tables of mean motion are relatively easy to understand with a little engagement, and so I have chosen to start with the deferential motion.
Finding the Degree of the Mean (Eccentric) Apogee
With this out of the way, how do we find the degree of the deferent’s apogee? In Islamic Astronomy, we find one method presented by Al-Biruni, building on Ptolemy’s theory and adjusting it for precession. The theory he puts forth in his The Book of Instruction in the Elements of the Art of Astrology is that the planetary apogee (upon the deferent) moves according to precession. The rate of motion for the deferent is the rate of precession. According to Al-Biruni, that is 1˚ for every 66 Arabic years, or 64 years in the Gregorian calendar; Astrologers today typically use 1˚ per 72 years for precession of the fixed stars, we also have the modern Astronomical rates of procession which are as follows.
The Apsidial lines of the planet’s today follows the following key, according to Mohammed Mozzafari.
Below is an example of Biruni’s calculations. The year in which he wrote this portion of his text was 1029AD, or 420AH. Thus we can surmise (sticking to his technique) the following longitudes for the apogee of the deferent. You can also find alternative values in Introductions to Traditional Astrology (Dykes, 2010).
Planets and their Deferent Apogee, a table according to Al-Biruni
Apogee Longitude in 420 AH; According to Biruni
Apogee Longitude Values adjusted for precession according to Al-Biruni
Year: 2020 Key: 1˚ per 64 Gregorian Years Value added: 15˚29’
Perigees (180˚ from the Apogee)
Saturn
6˚48′ Sagittarius
22˚17’ Sagittarius
22˚17’ Gemini
Jupiter
16˚43′ Virgo
02˚12’ Libra
02˚12′ Aries
Mars:
08˚33’ Leo
24˚02’ Leo
24˚02’ Aquarius
Sun
24˚32′ Gemini
09˚01’ Cancer
09˚01’ Capricorn
Venus
24˚32′ Gemini
09˚01’ Cancer
09˚01’ Capricorn
Mercury
23˚43′ Libra
08˚12’ Scorpio
08˚12’ Taurus
*Note, there may be some inaccuracy as pertaining to the precise minute ’ of the table. However, the degree itself should be fine.
A planet is considered to be in its eccentric apogee when its mean longitude (the middle of it’s epicycle) is within the eccentric apogee. The same, of course, applies for the perigee. Thus, we cannot for this technique apply the true longitude of the planet as we usually see it in our Astrological software, but instead must calculate this ourselves via the mean longitude of the planet.
Calculating the Mean Longitude of the planets
I will now present the following method, utilized by Ptolemy, in observing the mean longitude of the planets. Following it will be a modern table of the orbital cycles of the planets using modern astronomy, usable should you wish to adapt these values to more modern ones. I’d also note that mean longitude has other uses than simply the relationship of a planet with the apogee of the deferent, including a role in the mean conjunctions of Saturn and Jupiter, often phrased as the “Great Conjunctions,” as Ben Dykes succinctly puts forth [here]. There is also the option of calculating these mean longitudes using Ptolemy’s values online, thankfully due to this excellent [tool].
Abbreviations used in calculation:
Difference in Time = DT
Difference Times Motion = DTM
Stored Value = SV; this is the number you add to the next calculation
Preserved Value = PV; this is the final value of that particular position.
DTMF = Difference Times Motion Final, i.e.: DTM + SV, (Do not calculate this for sixths, simply use the DTM)
Formula
Calculate difference in time, IE: How many days and hours between the two dates?
Consult the table below, starting from the far right hand side. Take the value on the far right there and times it by the DT. This is called the DTM, or difference times motion.
Then divide the value of DTM by 60, take the integer of this answer, and add it to the next calculation. We call this the SV, stored value. (an integer is a whole number, IE: You need to ignore decimal places and make sure not to round it up or down)
Then take the same DTM, and modulus 60, this gives us the remainder, or how much is left in this time.
Then move onto the next calculation (IE: From sixths to fifths) and repeat the process, making sure to add the SV from the previous before calculating the remainder.
The formula is as follows, and an example is provided also.
Date A – Date B = DT
DT x TableValue = DTM
DTM + SV = DTMF (Ignore this step the first time, IE: when calculating sixths)
DTMF / 60 = SVn(make sure only to use the Integer value, ignoring decimals)
DTMF % 60 = PV
The Example
For our example let’s say we are calculating the mean longitude of Jupiter. Let us say that the difference in time for our hypothetical motion to keep things simple, is measuring between 5 precise days. Thus, we observe the table of his daily motions as follows:
Degrees
Minutes
Seconds
Thirds
Fourths
Fifths
Sixths
0
4
59
14
26
46
31
The Example calculation with notae:
Sixths
5 x 31 = 155, thus we say that Jupiter moves 155 sixths in this time period.
Each time the number reaches 60, we add 1 to the next calculation. (IE: Fifths) and keep the remainder with the sixths. To see what we add to the 5ths, and what we keep in the sixths when we make our new table, consider the following calculations for the SV and the PV. If you wish, you may choose to ignore the PV until you begin to calculate the motion in seconds as we don’t typically consider them in the chart. But if you plan on observing new dates based on your new calculations as the starting date in the future, it might be wise to keep them.
Sixths, Calculating the Stored Value/SV
To see what you add to the next value, take the number obtained and divide it by sixty. Ignore decimals and use the actual integer or whole number given, (do not round it upwards, ever.)
155 / 60 = 2.58333333, so we will add 2 when we calculate the fifths.
Sixths, Preserved Value/PV
155 % 60 = 35, so our final value for sixths, if we were going to make a new table, is 35 Sixths.
Fifths
5 x 46 = 230 + 2 = 232
232 / 60 = 3.86666 (so SV = 3)
232 % 60 = 52 (So we keep 52 in our fifths position)
Fourths
5 x 26 = 130 + 3 = 133
133 / 60 = 2.216666666666667 (so SV = 2)
133 % 60 = 13
Thirds
5 x 14 = 70 + 2 = 72
72 / 60 = 1.2
72 % 60 = 12
Seconds
59 x 5 = 295 + 1 = 296
296 / 60 = 4.93333333333 (so SV = 4)
296 % 60 = 56
Minutes
4 x 5 = 20 + 4 = 24
24 / 60 = 0.4
We do not have any SV, so we do not need to calculate a PV. The total motion in minutes, is therefore 24
Degrees
0 x 5 = 0
Since there was no SV when we observed the Minutes, we do not add anything here and his motion in degrees remains zero. Thus, Jupiter, in the course of five days has not moved a full degree of mean longitude
With this, our final table for five days of motions, now looks something like this. You’ll note I haven’t included the thirds and fourths in his final position. However it is certainly valuable when they do, and are desirable when calculating over very long periods of time.
Jupiter
Degrees
Minutes
Seconds
Thirds
Fourths
Fifths
Sixths
Starting Point 3˚2’3” Aries —› Position now
3
26
59
–
–
–
–
Amount of mean motion he has moved in 5 days:
0
24
56
12
13
52
35
Adjusting to more precise values – Minutes & Julian Days
Now, most of the time when we consider two different dates, they will typically be more than five days apart, and also making use of hours, minutes, etc. When we want to consider the mean longitude over for a long period of time, to begin with, it is typically it is best if we use the smallest value we have (i.e. the hourly mean motions of the planets). Thus, you’ll note that what I described as difference in time does not necessarily equal to one day, but can also apply to hours, minutes, seconds and so on.
Ptolemy gives us hourly values, which is more than enough for most purposes. So, if we were to consider the above calculation for 5 days, rather than DT = 5, DT now = 120 (5 sets of 24 hours). But what if we need to calculate minutes? Well, a minute is a 1/60 fraction of an hour. Thus we just need to divide the hourly motion by 60 to get the result for one minute of mean motion.
Therefore, if we are considering a nativity, and the birth was at 5 hours and 20 minutes, we would calculate the first 5 Hours as was said above. For the remaining 20 minutes, we would calculate them separately, and then we would divide the result.
A quick way of calculating this formula would be to take the hourly mean motion and divide by 60. Then multiply the resulting answers based on how many minutes you had left, as per the following brief and easy formula.
Formula for Adjustments by minute
Mean motion per hour / 60 = Motion per minute.
Motion per minute x number of minutes desired = final result for the adjustment.
IE: We want to add on 15 minutes to our previous calculation.
Now, Jupiter’s hourly motion in seconds = 12”.
Therefore:
12 / 60 = 0.2
0.2 x 15 = 3
Therefore, we would need to add 3 more seconds to the calculation for Jupiter’s mean longitude. If we obtain a decimal number, but no integer (i.e. 0.35584484 as a random example) we can take the decimal number, multiply it by 60, and add the integer from that number to the next table, though this shouldn’t be a common occurrence for most planets.
Julian Days
The most precise way to calculate difference in time, when it is over a long period of time, is using Julian Days. This doesn’t refer to the Julian Calendar, but rather a system created in order to count days, with day 0 beginning from the date January 1, 4713 BC in the Julian Calendar. This topic has been spoken about at length by others elsewhere (see here) and so there isn’t much need for me to explain it, however if you are learning astrology I do advise at least attaining a cursory understanding of them, if not the formula as it is the preferred dating system in astronomical systems.
With that, here are the tables of mean motion, taken from G.J Toomer’s edition of Ptolemy’s Almagest.
Table of motion via mean longitudes for the seven planets taken from the Almagest (Toomer, 1984)
Note on the tables: Mercury and Venus in the Ptolemaic system are considered to share the same mean motion with the Sun, which is the centre of their epicycle. Hence Mercury never has more than 28 degrees of elongation from him, and Venus 48 degrees. Their difference with the Sun lies not in their mean longitude, but in the true and apparent longitude (that is, in motion along the epicycle). I would also note that when a planet moves over 360˚, Ptolemy keeps the remainder, much as we have done. Thus the Moon’s yearly motion in mean longitude is not the large number she actually travels, but her difference in location from the starting point from where we begin our measurement.
Saturn
Degrees
Minutes
Seconds
Thirds
Fourths
Fifths
Sixths
Yearly motion
12
13
23
56
30
30
15
Monthly (30 day) motion
1
0
16
45
44
25
30
Daily Motion
0
2
0
33
31
28
51
Hourly Motion
0
0
5
1
23
48
42
Jupiter
Degrees
Minutes
Seconds
Thirds
Fourths
Fifths
Sixths
Yearly motion
30
20
22
52
52
58
35
Monthly (30 day) motion
2
29
37
13
23
15
30
Daily Motion
0
4
59
14
26
46
31
Hourly Motion
0
0
12
28
6
6
56
Mars
Degrees
Minutes
Seconds
Thirds
Fourths
Fifths
Sixths
Yearly motion
191
16
54
27
38
35
45
Monthly (30 day) motion
15
43
18
26
55
46
30
Daily Motion
0
31
26
36
53
51
33
Hourly Motion
0
1
18
36
32
14
39
Sun/Venus/Mercury
Degrees
Minutes
Seconds
Thirds
Fourths
Fifths
Sixths
Yearly motion
359
45
24
45
21
8
35
Monthly (30 day) motion
29
34
8
36
36
15
30
Daily Motion
0
59
8
17
13
12
31
Hourly Motion
0
2
27
50
43
3
1
Moon
Degrees
Minutes
Seconds
Thirds
Fourths
Fifths
Sixths
Yearly motion
129
22
46
13
50
32
30
Monthly (30 day) motion
35
17
29
16
45
15
0
Daily Motion
13
10
34
58
33
30
30
Hourly Motion
0
32
56
27
26
23
23
Mean Longitudes of the Planet’s from January 1st, 2020, 12pm, Greenwich, England (Ptolemy method)
Julian day: 2458850.0000000
(Starting from 0 Aries, the vernal equinox)
Sun: 271˚ 25’ 48”
Moon: 342˚03’20”
Saturn: 287˚14’42”
Jupiter: 275˚58’26”
Mars: 214˚59’33”
Venus: 271˚ 25’ 48”
Mercury: 271˚ 25’ 48”
You may use these to calculate the mean longitudes of the planets at your own desired date. Note that these are considered using Ptolemy’s values, and so there are certainly arguments one can put forth that they are outdated. On account of this I have calculated a corrected mean motion of the planets using better values from NASA. Note that they may still lack precision.
Modern tables of orbital periods
Here is a modern table of the planetary orbits, taken from NASA’s planetary fact sheets for those who’d prefer more precise values. Note that I have included the inferiors here, but we need to remember: their mean longitude were considered equal to the Sun in Geocentric astronomy/astrology and so those particular values aren’t all that useful for our purposes in this particular context.
Planet
Days to complete a revolution in the Tropical Zodiac
Saturn
10,746.94
Jupiter
4,330.595
Mars
686.973
Sun
365.24217
Venus
224.695
Mercury
87.968
Moon
27.3217
The formula of correction and notes to the table
Here follows the formula I have used in order to calculate this corrected longitude; with thanks to my friend, B. Key for his help in determining the best way to go about these initial corrections.
I will also note, that where the table has said year, it refers to a solar or tropical year, and thus is 365.24217 days, rather than simply 365 days.
Terms used:
VT = Value of time (I began with the solar year, 365.24217, to calculate daily motion)
PO = Planetary orbit (in days) value, as above
FR = Fraction result
POS = Position
POSI = Position Integer (IE: The integer number preceding a decimal point in POS)
POSD = Position Decimal points. (IE: the numbers following the integer)
NTPOSI = Integer to place in next table (as as POSI)
NTPOSD = Decimals to round to get the next tables POSD.
Formula for year
Year (or time)/ PO = FR
FR x 360 = POS
POS % 360 (if the POS is over 360. IE: the Moon)
Place POSI within table (the whole number)
POSDx60 = NTPOSI and NTPOSD
Repeat process until yearly table is filled out.
Formula for time when under one year in length
1 unit = days
365.24217 / 365 for tabledays;
tabledays x30 for months;
tabledays / 24 for hours
Therefore, years values in table: time = 365.24217
Month values in table: time = 30.019904383561643835616438356164
Days values in table: time = 1.0006634794520547945205479452055
For hours: time = 0.04169431164383561643835616438356
Corrected Tables of Mean Motion in Longitude for the Seven Planets
Saturn
Degrees
Minutes
Seconds
Thirds
Fourths
Fifths
Sixths
Yearly Tropical motion
12
14
5
27
14
25
17
Monthly (30 day) motion
1
0
20
10
27
30
35
Daily Motion
0
2
0
40
20
55
1
Hourly Motion
0
0
5
1
40
52
17
Jupiter
Degrees
Minutes
Seconds
Thirds
Fourths
Fifths
Sixths
Yearly Tropical motion
30
21
44
34
35
16
37
Monthly (30 day) motion
2
29
43
56
16
3
0
Daily Motion
0
4
59
27
52
32
6
Hourly Motion
0
0
12
28
39
41
20
Mars
Degrees
Minutes
Seconds
Thirds
Fourths
Fifths
Sixths
Yearly Tropical motion
191
24
2
52
37
5
17
Monthly (30 day) motion
15
43
53
39
40
2
4
Daily Motion
0
31
27
47
19
20
4
Hourly Motion
0
1
18
39
28
18
20
Sun, Mercury, Venus
Degrees
Minutes
Seconds
Thirds
Fourths
Fifths
Sixths
Tropical year
360
0
0
0
0
0
0
Monthly (30 day) motion
29
35
20
32
52
36
9
Daily Motion
0
59
10
41
5
45
12
Hourly Motion
0
2
27
56
42
44
23
Moon
Degrees
Minutes
Seconds
Thirds
Fourths
Fifths
Sixths
Tropical year
132
33
17
38
18
37
32
Monthly (30 day) motion
35
33
8
50
49
12
7
Daily Motion
13
11
6
17
41
38
24
Hourly Motion
0
33
21
19
37
3
7
Corrected Mean Longitudes of the Planetsfor January 1, 2000, 12:00PM
With this information in our hands, it’s time to actually see whether according to what we have calculated so far, if a planet isascending in the apogee of its eccentric circle (that is, the deferent). This is a fairly easy process, as what we do in this consideration is observe the meanlongitude of the planet, and whether it is ascending (moving towards the apogee) or descending (moving towards the perigee). The values for these have already been given (using historical, not corrected values). Thus, quadrants 1 and 2 represent a planet descending from its apogee. It is a place of weakness, with quadrant 2 weakest of all, and quadrant 1 more like one who is descending towards weakness. Quadrants 3 and 4 represent the climbing of the planet, that is to say, it is a place of strength, and quadrant 4 is stronger than 3, because 3 is more like a recovering from weakness. Thus we might decide to label them as follows, in the same manner we see the Solar Phases treated in Guido Bonatti’s Liber Astronomiae (Dykes, 2010):
Quadrant 1) Strength moving towards weakness;
Quadrant 2) Most Weak
Quadrant 3) Weakness moving towards Strength;
Quadrant 4) Most Strong.
The Effects of a planet ascending in its Apogeeand its implications
Ibn Ezra in his Book of Reasons (Sela, 2007) says of a planet ascending in its eccentric circle (the deferent) that for the planet, it is the same to a horseman as having a horse with excellent legs. Further, a planet in its apogee is close to the zodiac, thus it resembles a soul; when it is low (besides its perigee) and close to the earth, it is more like a body instead. We see then that we have two conditions, one of strength and one of weakness. These two conditions are divided between moving towards strength, or being naturally strong and continuing in increase; likewise, we also see decrease in strength, followed by weakness.
This motion within the deferent here is essentially very much like the solar phases of the planets (their relationship in distance with the Sun), in that this cyclical and uniform motion reflects a period of motion and travel. From strength to weakness to strength once again. It is unceasing and unchanging, undisturbed. In much the same way, the motion of a planet by its latitude (southern or northern within the ecliptic belt) also follows the same pattern. A planet ascending to become northern is strong, especially when beside its ascending dragon (called the mean north node of the planet). A Planet descending is sapped of strength, especially when besides its descending dragon (called the mean south node of the planet). Indeed, the mean nodes are calculated from the apogee’s longitude! So we can see there is a correlation between these techniques.
Now, each of these two topics (both solar phases, and latitude/nodes) will receive more discussion in time, and I do also intend on writing on the calculation of a planet’s true position, so that we might consider its place in the epicycle and its relation to the epicycle’s apogee. However for now, hopefully this will suffice. Astrology is one of my most beloved passions, and I deeply enjoy discussing and teaching its mechanisms.
If you would like to purchase any astrological services from me, I offer long, in-depth, customizable and clear readings on this page. It would be my honour to be of service to you!
References:
Ptolemy, G.J. Toomer, The Almagest (1984). Abū Maʿšar, Al-Qabisi, Benjamin Dykes, Introductions to Traditional Astrology (2010). Abū Maʿšar, Keiji Yamamoto, Charles Burnett, The Great Introduction to Astrology (2019). Al-Biruni, Ramsey Wright, The Book of Instruction in the Elements of the Art of Astrology (1934). Abraham Ibn Ezra, Schlomo Schea, On Nativities and Continuous Horoscopy (2013). Abraham Ibn Ezra, Schlomo Schea, The Book of Reasons (2007). NASA, Planetary Fact Sheets, https://nssdc.gsfc.nasa.gov/planetary/planetfact.html.
With Cunning & Command 