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1 WILLIAM LILLY AND HIS METHOD OF PRIMARY DIRECTIONS by Rumen Kolev, winter of 1998 A detailed research into the primary directions of William Lilly as given in his 'Christian Astrology', 1647, 'Regulus Publishing Co.', 1985. Pages 487-831. Published in March 1998 in the journal 'The Primary Directions' and in the Feb. 99 issue of the USA journal 'Considerations'. The title page of Andreas Argolus' 'TABULAE PRIMI MOBILIS' published in Rome in 1610. William Lilly most probably used the tables from this book for his calculations of primaries. WILLIAM LILLY AND HIS METHOD OF PRIMARY DIRECTIONS by Rumen Kolev The predictive methods of William Lilly can be found in his book, 'Christian Astrology', published in 1647. For the research made here, I used the edition of 'Regulus Publishing Co.' from 1985. Pages 487-831 deal exclusively with predictive techniques. All calculations and recalculations of primary directions and variables in this article are made with the computer program 'Placidus'. Lilly opens chapter 98 in his 'Christian Astrology' with an example chart (p.500). Pointing at the importance of a rectification for the 'judgement', he describes three ways to rectify a horoscope (p.502-519): Trutina Hermetis, Animodar and Accidentia Nati. Up to page 506 Lilly explains the first two methods. His conclusion ( p.506, bottom lines) is clear cut, '...neither the Trutine of Hermes, or this (Animodar), are of so sure foundation, as that Correction which is performed by Accidents (Accidentia Nati or rectification by past events with primary directions).' 6z 3z 37x William Lilly's Example Chart 19 September, 1616 ( Julian ), 2:24:30 PM, Geo. Lat. 53z N < 5z 1z 00x 44x 0z 21z 55x 44x R 1z RAMC = 222z 10x, MC = 14z 39x I, ASC= 6z 37x P RAMC = Right Ascension of MC. 02x 9z FIGURE 1 2 M WILLIAM LILLY M Recalculated with computer 29 September, 1616 ( Gregorian) UT = 2:14:05 PM, Geo. Lat. 53z N < 1z 35x RAMC = 222z 10x, MC = 14z 39x I, ASC= 6z 41x P FIGURE 2 William Lilly's Example Chart Long. Lat. RA Dec TABLE 1 Recalculated with computer Long. Lat. RA A06z 37xu0z 0x 186z 04x 02z 38xS A 06z 43xu0z 0x S 01z 44xE5z 0xN 058z 30x 25z 38xN S 01z 37xE 5z 11xN D 03z 34xu1z 32xS 182z 40x 02z 49xS D 05z 06xu1z 21xN F 06z 54xu1z 0xS 186z 43x 01z 50xS F 07z 58xu1z 16xN G 00z 54xT0z 28xN 123z 14x 20z 32xN G 00z 44xT 1z 05xN H 21z 55xO0z 37xS 261z 11x 23z 52xS H 21z 51xO 0z 05xN J 09z 02xW2z 58xS 037z 36x 11z 42xNJ 09z 00xW2z 40xS 186z 10x 058z 20x 185z 12x 187z 49x 123z 13x 261z 08x 037z 29x Dec 02z 40xS 25z 36xN 00z 47xS 01z 59xS 21z 05xN 23z 09xS 12z 00xN I reconstructed the horoscope by adjusting the right ascension of the MC. From the data above , it becomes clear that D and F are the planets seriously deviating from their positions in the computer recalculation. To a lesser extent, this is the case also with G and H. The positions of J, the S and the A are fairly exact. The S in the charts on pages 500 and 742 is in 1z 14x E. However, this must be a typographical error since on pages 512 and 774 the correct position of the S is given as 1z 44x E. 3 In the beginning of page 507 (chapter 100), Lilly mentions that some astrologers use transits or profections for rectification purposes and gently sweeps these aside as ineffective and dubious, '...as I could never find any verity or probability in either of those two wayes in my practice, so do I leave them to any who are desirous to practice them...' His kindness goes even further and he directs the 'desirous' to treatises by Origanus, John Schonar and Pezelius where these ways of rectification are explained. Done with that, Lilly swiftly and industriously turns himself to elucidate the method of rectification, which he holds for best, namely- through eminent past events and their correlation with primary directions (Accidentia Nati). On page 508 he writes: '...by (primary) direction (of the Asc., MC, the A, S and <[Pars Fortunae]) most of the affairs and contingencies belonging to every man or woman in a natural course of life are found out, both in quality What, and in measure of time When.' For rectification purposes Lilly advocates using primary directions to the Asc. and MC only, since the directions to the other three hylegiacall places do not change much with a change in the birth time1. According to Lilly, we should first procure ourselves with a list of prominent past events in the native's life, looking specifically for such events that can be associated with the symbolism of the Asc. or MC. For the ascendant these are: sicknesses, afflictions, injuries...of the body. For the MC: honours, marriage, promotions... 1- Some of the Placidian mundo interplanetary directions may have even higher time sensitivity than the directions to the Asc or MC. In the Placidian system, the directions used in the rectification are: 1. of planets to angles, 2. mundo parallels, 3. mundo rapt parallels and 4. planets mundo to house curves. Directions of type 1,3 and 4 change their hitdates with 1 year if we change the birth time with 4 minutes. The mundo parallels have the highest time sensitivity. It depends on several factors. Every mundo parallel has its own time sensitivity. It can reach as much as 4 years change in the hitdate for a 4 minutes shift in the birth time! Or 1 year for 1 minute! From what was practiced in the regiomontanian system, however, it is true that in this system only the directions to the Asc and MC are fitted for rectification purposes. These directions have a time sensitivity of 1 year change in the hitdate per 4 minutes shift in the birth time. The only mundo directions that were ever practiced in the Regiomontanus system were the mundo conjunctions and oppositions, but having low time sensitivity, they turn out to be useless for rectification. Other mundo directions like mundo parallels, rapt parallels et cetera, are theoretically possible in the Regio system. This was shown for the first time by Jerry Makransky in his book ' Primary Directions ' published in 1988. However, these directions were never practiced. Well, they probably deserve some testing at least ! 4 M WILLIAM LILLY M The events where the body (health) is concerned, should correspond with primary directions to the Asc. The events where the social position of the native is concerned, should correspond with primary directions to MC. Next, Lilly proceeds to the explanation how to calculate quickly the primary directions. He constructs a table with the ecliptical positions of what he deems the most important points. These points are such that when they come by primary direction on the horizon (ascendant) or the meridian (midheaven), a corresponding event is expected to happen. What are these points? According to Lilly, they are the big aspects of the planets, the Ptolemaic terms1, the housecusps (regiomontanian) and the antiscia and contra-antiscia of the planets. This table, however, can be useful only for directing the points with latitude zero and Lilly directs also points with a latitude, like the bodies of the planets or their places of opposition, antiscia and contra-antiscia with a latitude. It becomes more interesting on page 514, when Lilly practically rectifies or rather confirms that the given birth time is correct. Obviously his client, a certain merchant, is so young, that Lilly with great pains collects only 4 events: TABLE 2 1. 2. 3. 4. Came to a Master of quality A journey beyond sea of great concernment Sick of a burning Feaver Another Feaver and much Melancholly aged 16 years 07 months aged 20 years 04 months aged 20 years 10 months aged 24 years 11 months Since the first event concerns the social status of the native, Lilly logically looks for a primary direction to MC2. And since the event is a good one, he searches for the time when a 'good' zodiacal point has hit the midheaven. This time should be around the time of the event, maybe with a +-5 years deviation allowed, which will transcribe to a +- 20 minutes uncertainty in the birth time 3 . To check out the directions that could possibly fit in the nature of the first event, Lilly constructs a small table with directions of 7 points to MC. 1- There are 3 systems of terms: Egyptian, Ptolemaic and Chaldean. The majority of the ancient, medieval and renaissance astrologers used the Egyptian system of terms. Lilly used the Ptolemaic one. However, he was in an error, pushing the beginnings of the terms with 1 degree forward. 2- The date when a certain point will hit MC is calculated thus: the distance in right ascension is measured between MC and the point of question. This distance is converted in time of life with the formula 1 degree = 1 year which is the key of Ptolemy or 1 degree = 1 year 5 days 8 hours which is the key of Naibod, a key preferred by Lilly. 3- Or 5 years * 4 minutes = 20 minutes. 5 Four of them are terms of planets, one is the zodiacal contra-antiscion of Mars, another one is the 11th housecusp and the last one is a zod. ^G. The zod. ^G hits MC in 16 years and 7 months of age (Ptolemy key). Lilly underlines here the fact that G is the Lord of the 10th house and its ^ happens to be in the terms of H(ptolemaic). A recalculation with the computer for the reconstructed chart shows this direction to hit in age 16 years and 5 months. Directions to MC 14z 39x I, RAMC= 222z 10x obliquity =23.4876 William Lilly's Computer recalculation page 515 of for the reconstructed 'Christian Astrology' horoscope Promissor Position RA Arc Position RA Arc TABLE 3 15z 00x I 222z 31x 00z 21x 14z 00x I 221z 32x 00z 38xc1 22z 00x I 229z 35x 07z 45x 21z 00x I 228z 33x 06z 23x (07z 25x)2 terms of J 26z 00x I 235z 44x 13z 34x 27z 00x I 234z 42x 12z 32x (11z 30x)2 3 zod. CA of G 29z 06x I 236z 53x 14z 43x 29z 16x I 237z 03x 14z 53x 11 housecusp 30z 00x I 237z 48x 15z 38x 00z 12x O 238z 01x 15z 51x terms of H 00z 00x O 237z 48x 15z 38x 00z 00x O 237z 49x 15z 39x zod. ^G 00z 54x O 238z 45x 16z 35x 00z 44x O 238z 34x 16z 24x terms of F terms of D Lilly makes a mistake in determining the beginnings of the Ptolemaic terms. He pushes each term (except the first terms of the signs) with one degree forward. See chapter 99 or page 510 of the Regulus edition. However, he is not consistent. Sometimes he uses the correct Ptolemaic terms as in the table of the directions with Pars Fortunae on page 777. In other places he alternates between the correct Ptolemaic terms and those pushed forward. In other places there are gross errors- most probably typographical ones. Superscript explanations to the table above: 1- This direction calculated with the correct beginning of the term, turns out to be converse. Lilly computed only direct directions. 2- The arcs of the directions of the terms of D and J are typo errors. In brackets are given their correct arcs according to the data from the context. Look at page 515, for example, where Lilly correctly calculates the direction with the terms of D coming to 07z 25x,although in the table just above it, stands 07z 45xas its directional arc. 3- CA is the abbreviation for contra-antiscion. 6 M WILLIAM LILLY M The last direction in the list, the direction of the zodiacal ^G to the MC, is the direction which Lilly associates with the first event- the rise of the native to the title 'Master of Quality'. And since the hitdate with the key of Ptolemy is the same as the time of the event, 16 years and 7 months, Lilly has all reasons to keep in the back of his mind that the birth time given is most probably correct. At this point I would like to mention that Lilly, like all astrologers who lived in his times or earlier, directed only direct1. Doing so, I believe, they all were in a big error. Directions of planets mundo to the angles are very efficient, no matter whether they are direct or converse. Let's check it out ourselves. If we use the converse directions of planets to the angles (Asc., MC, IC, Desc.) on the example chart of Lilly, we can see two directions that perfectly match the first event from his list- the zodiacal and the mundo direction of H, the symbol for social status, converse to the ascendant. The first one means how many minutes before the birth, the ecliptical projection of H has been exactly on the horizon. The second one means the same, but for the body of H. Here 4 minutes = 1 degree distance = 1 year according to the key of Ptolemy. Calculated with the computer, the zodiacal direction of H converse to the ascendant hits when the native has been 16 years and 3.5 months old. The mundo one- when he has been 16 years and 5.5 months old ( with the key of Ptolemy ). To confirm that the birth time is correct, however, means not one direction only corresponding well with one event. Several directions should match important events. And important events should tie up with directions of low frequency only. The orb, in such case, can be around 1-3 months. To go back to Lilly, he does not fail to notice (page 517) that the zod. #A hits MC in the 23rd year of life (computer recalculation- 22 years 8 months) and the zod. #F- in the beginning of the 24th (computer recalculation- 24 years 6 days). When asked by Lilly, the merchant confirms that at this time he was 'with great esteem and successe'. 1- In modern terminology, 'to direct direct' means to turn the celestial sphere in her natural direction of apparent rotation (east to west) and see the time when a certain point named Promissor will come to another point ( or curve or circle) which stays fixed on the sphere (the Significator). To direct converse, we do the same thing, but rotate the celestial sphere in the opposite direction (west to east). It must be kept in mind that the terminology of the primary directions up to the end of the 19th century was different and quite confusing. Although the notions of 'direct' and 'converse' directions existed, they meant then something very different from what they mean in the modern terminology. 7 Having found 3 directions corresponding well with events and periods, increases the confidence of Lilly in the initially given birth time. Now, to seal his ripening conclusions with the stamp of certainty, Lilly looks for directions to associate with the sicknesses of the native. Since the ascendant is the significator of the health, Lilly addresses himself to the directions to the ascendant (page 517). Lilly does not explain the mathematical algorithm of the computation1, but gives a ready table. The zodiacal +G (latitude = 0) comes to the eastern horizon (asc.) in 19 years 10 months and 10 days (computer recalculation- 19 years 8 months 18 days). This direction is the same as the ecliptical projection of G direct to the western horizon(desc.). Although with one year deviation, Lilly takes this direction to correspond with the 'Feaver' the native has had when 20 year and 10 months old. We should not forget, that for rectification, Lilly used the primary directions which are the fastest to compute, namely directions that can be computed with a table of houses or a set of special tables. In these times, many astrologers like Maginus, Argolus, Regiomontanus and others designed tables for speedy calculations. The most simple one which Lilly used in his preliminary rectification, is a table of all 360 degrees of the ecliptic and their corresponding oblique ascensions (OA) in different geographical latitudes. We find the OA of the point of interest and we subtract from it the OA of the ascendant. The result is the arc of the direction. The oblique ascension of the ascendant is simply RAMC + 90z. Directions to the ASC William Lilly's Computer recalculation page 517 of for the reconstructed 'Christian Astrology' horoscope TABLE 4 OAasc= 312z 10x ASC = 6z 37x P OAasc= 312z 10x ASC = 6z 41x P Promissor Antiscion of H ^J terms of H terms of G terms of J CA of S terms of J +G Position OA 08z 05x P 313z 34x 09z 02x P 314z 29x 13z 00x P 318z 10x 20z 00x P 324z 05x 26z 00x P 328z 38x 28z 16x P 330z 14x 00z 00x { 331z 26x 00z 54x { 332z 02x Arc 01z 24x 02z 19x 06z 00x 11z 55x 16z 28x 18z 04x 19z 16x 19z 52x 1- Look at the explanations beneath figure 3. 8 Position Arc 08z 09x P 01z 26x 09z 00x P 02z 16x 12z 00x P 05z 03x 19z 00x P 11z 05x 25z 00x P 15z 43x 28z 23x P 18z 08x 00z 00x {19z 14x 00z 44x {19z 43x M WILLIAM LILLY M All these directions are only the zodiacal. In his practice, Lilly of course also directed planets mundo (the bodies of the planets) to the ascendant and MC. We may assume, he supposed that the mundo direction of G to the descendant (in his terminology- the opposition of G to the ascendant cum latitudine) most probably would hit around the same time when the sickness of the native occurred. And indeed, on page 765 he gives the arc of this direction as 20 degrees 46 minutes which means 20 years 9 months and 6 days of age (computer recalculation- 21 years 9 months 24 days). Another important point here is the fact that the majority of the astrologers of this era and those who have lived earlier, ventured into prediction usually talking of future events taking place during a certain year of the life of the native and almost never specifying the season or the month. I guess, the reason of their caution was simply their experience, which showed them that the events generally deviated from the corresponding directions often with 1 or even more years. The real reason for this were, apart from the orbs of influence of the directions, the inexact positions of the planets they were working with and some astrologers of this time, as Placidus for example, have been aware of this. Working with the most powerful Placidian mundo directions, I have observed in my practice the average deviation between the hitdates of the directions and the events to be around 1-3 months. This concerns powerful directions and correspondingly big events. Such events occur no more than 3050 times in life. Of course, there were many instances of hits within days only. Some kinds of directions prove to be more exact, others less so. Talking about the direction of G to the descendant, William Lilly does not omit to write about the whole events-climate at that time- the native was not only sick with feaver, but also 'was robbed of some things, and in danger of losing more, and was also in danger of fire...' All of these events like a gang of naughty kids talk only of one thing- that their common father is nobody but a powerful direction of G! Here we notice that Lilly, like most other old masters of primary directions, knew that a strong primary direction triggers not only an isolated event, but also a period in which many events, small or big, may happen; all of them falling under the symbolism of the direction. I name this the 'multievent effect' of a direction. When we water a garden with a hose, there is a main current hitting the ground- like the kernel of a direction, materializing in the 'big event', but there are also many bigger and smaller sprinkles of water around- the multitude of smaller events spread out in time around the main 9 event. If, when rectifying a chart, we are not sure whether a particular direction is associated with a certain event, it pays off to ask for more events, no matter how small, which happened around the same time. Their symbolic integral will show us beyond doubt the common father of them all, just like in the case discussed by Lilly. N. Pole Zenith = Birthplace n izo r Ho OA of +G IC 14z39xW OA of Asc. Equator DA MC 14z39xI ASC 06z37xP Ecliptic +G 0z54x{ S. Pole FIGURE 3 On the figure above is shown the example chart of Lilly drawn in 3 dimensions, observed from point East. The observer is in the planes of the equator and the horizon. Because of the apparent rotation of the celestial sphere, the point +G which is in 0z54x{ (acc. to Lilly) will eventually reach the horizon. The arc of the direction Zod. +Gdirect = Z = OA+G - OAZ. OAZ = RAMC + 90z. OA+G = RA+G - AD+G. AD+G = arcsin [ tan ( δ+G ) * tan ( Φ ) ]. Here, δ is declination and Φ is the geographical latitude of the birthplace. The AD (ascensional difference) shows with how many degrees the day semi-arc of the point is greater or lesser than 90z. OA is for Oblique Ascension that shows the position of a certain point in relation to the horizon. 10 M WILLIAM LILLY M Horizon Equator Horizon +G(0z54x{ ) Diurnal Path of +G(0z54x{ ) ASC 6z37xP 9 8 7 10 11 12 Houses 1 2 Houses 6 5 4 Ecliptic Equator 2nd Regiomontanian 3rd howse-circles Diurnal Path of +G (0z54x{ ) 3 Horizon Meridian FIGURE 4 South Pole Diurnal Path of +G(0z54x{ ) Directional Arc Ecliptic Horizon +G(0z54x{ ) FIGURE 5 ASC 6z37xP A 3-Dimensional representation of the example horoscope of Lilly and the direction Zod. +Gd.= ASC. We can clearly see the Diurnal Path of the point +G (0z54x{ ). This is the circle around the Poles-axis along which the point moves due to the 24-hours apparent rotation of the celestial sphere. Wherever the diurnal path of the point crosses the horizon is where the point will rise. The arc measured in time (equatorial degrees) between the point and its point of rise (along its diurnal path) is the arc of the direction of the point to the ascendant ( the eastern horizon). The print-out is from the Program 'Placidus', version 2.0. The explanatory labels and arrows are superimposed. 11 Now, we can make a table with the directions and the events used by Lilly for the rectification. The key of transformation will be the key of Naibod, which Lilly employed in his practice. GREGORIAN GREGORIAN DATE ASSOCIATED HITDATE EVENT and AGE of event DIRECTION (Naibod) 1. Came to a Master of quality 16 y. 07 m. Apr. 29 1633 Zod. ^G= MC 2. A journey beyond sea of great concernment 20 y. 04 m. Jan 1637 none 3. Sick of a burning Feaver 20 y. 10 m. Jul 1637 Zod. +G= Asc 4. Esteem and Success 22.0 - 23.0 y Sep 1638 -Sep 1639 Zod. #A= MC Zod. #F= MC 4. Another Feaver and much Melancholly 24 y. 11 m. Aug 1641 none Lilly Jul 27 1633 Computer May 23 1633 Nov 26 1636 Oct 03 1636 Aug 21 1638 Oct 08 1639 Nov 29 1639 Feb 07 1641 If we take in account that any 4 minutes shift in the birth time would push the hitdates of these directions with 1 year backward or forward, it is clear that the birth time must be correct at least within +- 2 minutes exactness. This, however, will be true only in case we believe in the high efficiency of the directions used by Lilly1. I think that the zod. directions to the Asc. and MC have low to moderate efficiency and that there are more efficient directions: RE-RECTIFICATION OF LILLY'S EXAMPLE CHART WITH PLACIDIAN MUNDO DIRECTIONS Attempting to rectify the chart with the mundo Placidian directions can be an interesting and rewarding experience. We will compute with the key of Naibod. Obviously, the direction Mundo Hconv.= Asc should correspond with the obtaining of the master of quality 'degree'. The hitdate is June 16, 1633. In case we want it to hit exactly in the time of the event (April 29 1633), 1- In contrast, Placidus on page 211 (example 14) of his 'Primum Mobile' (Cooper's translation) declares the directions of zodiacal aspects to the ascendant and the midheaven 'altogether as nothing' ! Nowhere in this book of Placidus is there any evidence that he calculated and used zodiacal points to the angles ! Placidus preferred to work with the mundo directions which he amply computed in all his examples. 12 M WILLIAM LILLY M we should push the birth time back since the direction is converse. Working only with this direction, we will come to a rectified birth time of 2:13:34 PM or with 29 seconds earlier than the initial time. To check out the other events, I calculated only the four strongest types of directions in the Placidian system: mundo and zodiacal of planets to angles, mundo of planets to house curves and mundo parallels and rapt parallels with the S and the A. In each year of the life of the native, there are, on the average, only 2 directions of these kinds1. WITH RECTIFIED BIRTH TIME: 02:13:34 PM PLACIDIAN MUNDO DIRECTIONS Gregorian Gregorian EVENT and AGE DATE DIRECTION HITDATE (Naibod) 1. Came to a Master of quality 16 y. 07 m. Apr. 29 1633 Mundo Hconv.= ASC May 01 1633 2. A journey beyond sea of great concernment 20 y. 04 m. Jan 1637 Mundo Jdir.= #ASC Jan 02 1637 ( Mundo Jdir.= 3rd House Curve ) 3. Sick of a burning Feaver 20 y. 10 m. Jul 1637 Zod. +G= Asc Nov 20 1636 4. Esteem and Success 22.0 - 23.0 y Sep 1638 -Sep 1639 Mundo Ddir.= #MC Jul 22 1639 ( Mundo Ddir.= 8th House Curve ) 4. Another Feaver and much Melancholly and Scurvy 24 y. 11 m. Aug 1641 Mundo KAdir.= n (Desc) Sep 05 1641 n (Desc) = rapt parallel around the western horizon 1- The number of directions that Lilly used for the rectification is roughly the same as the number of the placidian mundo directions that I used. The frequency of a certain kind of direction is an important parameter in its evaluation as in respect to its possible strength i.e. its suitability to correlate with big events. The lower the frequency of a kind of direction (i.e. it happens more seldom) the bigger the possibility that it could correspond with big events. A common mistake of many astrologers is to take techniques with very high frequency as transits, for example, and try to correlate them with big events. On the other hand, it is true, that not any technique with low frequency corresponds to big events! Big events, however, necessarily should correspond to a technique with a low frequency. 13 Done with the rectification, Lilly proceeds with explanations how to erect a chart in the Regiomontanian house systems and other topics. On page 651 he starts the section 'The Effects of Directions' which is the last section of the book. Lilly writes about the authorities in the field he drew fromRegiomontanus, Maginus, Leovitius, Manginus, Zobulus and Argolus. Lilly explicitly states, 'At this day we use no method in Directions but Argolus...' From this alone, we can safely conclude that most probably he directed regiomontanian as far as the fact that all these authors directed as per Regiomontan though at least one of them, Maginus, knew how to direct also as per Ptolemy1. Unlike Morin or Naibod, Lilly is honest and a real scholar enough to admit that his method of directing (Argol) is different from what Ptolemy left i.e. directing by 'Diurnall and Nocturnall Horary times'2. On pages 652-654, Lilly gives rules for interpreting a direction: 1. We should consider whether the direction is 'good or evil'. Good aspects mean good directions and evil aspects- evil directions. 2. The significator or the point that stays still3 signifies what area of life will be affected or the persons who will be affected. How? The significator does this first by his symbolic meaning (Lilly uses the phrase 'of himself'). If, for example, the significator is the S, then what will be affected is the family life, the journeys, the wife, the older sister or the mother of the native. On the second place Lilly puts what the significator means 'by Accident' i.e. the house it is in or the house it rules. If in the 8th, it may mean inheritance or somebody lately deceased et cetera. 1- In his book 'Tabulae Primi Mobilis' published in Venice in 1604, Ioannes Antonius Maginus explains in canons 46-48 the Ptolemaic method of directing. It is the same as that which was later developed by Placidus and became known as the semi-arc method. Maginus also explains and exemplifies the Ptolemaic house system (page 25) which now is known as the Placidian house system. Placidus was born in 1603. 2- 'Diurnal (Nocturnal) Horary Times' is a term from 'Tetrabiblos' chapters 14 and 15 (Modes of Prorogation) where Ptolemy de facto describes what is today known as Placidian primary directions (semi-arc method). The 'Diurnal ( Nocturnal ) Horary Times' as a term was replaced somewhere in the 19th century by the term 'day ( night ) semi-arc'. Both have the same meaning. 3- Most of the old authors from the 15-17th centuries accepted as significators only 5 points: the ASC, MC, the A , the S and < [ Pars Fortunae]. William Lilly, however, employed as significators all planets. 14 M WILLIAM LILLY M The point that is being moved or the promissor1 signifies, symbolically and through a house position or rulership, the cause of the event: things and persons. If it is F, the cause of the event may be a young and charming woman. If G- a young and energy driven man. In this respect, Lilly seems to subscribe more to the Cardanian teaching, that the planetary symbolism has to have priority in the interpretation rather than the Morin's accidental determinations. An example to illustrate the difference: According to Morin, for instance, a direction of H or its aspects to the ascendant may mean decease or even death, if H happens to be in the 12th, 8th or 6th house or has rulership over them. In contrast to this, Cardan teaches that this is but impossible, because of the essential nature of H as a benefic. It seems as if Lilly sides more with Cardan. On page 654 starts chapter 157 where Lilly discusses the duration and the strength of the directions. He writes, ' when both of them (significator and promissor) are in their Essentiall Dignities (in signs of rulership, exaltation...) and in angles, the effects of their direction shall be evident and manifest...'. In chapters 158-165 Lilly interprets zodiacal aspects, terms, house cusps and fixed stars directed to all 5 classical significators. In chapter 166, Lilly discusses three different keys for transforming the directional arc into time of life. The Ptolemy key equates 1 degree to 1 year. The key of Naibod equates 1 degree to 1 year 5 days and 8 hours. The key of Tycho Brahe measures the travel of the A in RA for the birthday and equates this to 1 year. William Lilly, turns out, used Naibod as the most exact key and Ptolemy for initial orientation. From here on, up to page 741 (chapter 175), Lilly writes about the profections, the solar return chart and the transits. From chapter 175 to chapter 185 Lilly gives a short interpretation of the example chart. Then on page 765 he gives tables with primary directions to the five hylegiacal places- the Ascendant, the MC, the A, the S and <. 1- The notation of the other old authors, which they inherited, by the way, from Ptolemy, is misleading and confusing. They directed only direct or with the rotation of the celestial sphere. The significator of a direction was called not the point that stayed still, but only one of the five classical significators: the ASC, MC, the A, the S or <, no matter whether it was fixed or moved. Happily, W.Lilly has simpler and easier to understand notation. 15 DIRECTIONS TO THE ASCENDANT Pages 765-768 of the tables are a table with the directions to the ascendant. Altogether they are 104. The meaning of these directions is to compute the time after birth when a certain point, the Promissor, due to the apparent rotation of the celestial sphere, will rise i.e. will hit the eastern horizon. This time can be measured in hours and minutes as well as degrees and arcminutes. The simple conversion formula is 24 hours = 360 degrees. The timearc is accepted in Astrology to be measured in degrees. The algorithm is, first to calculate the AD (Ascensional Difference) of the promissor from its declination and the geographical latitude of the birth, then its OA (Oblique Ascension) and then to find out the directional arc by subtracting the OA of the Promissor from the OA of the Ascendant. The logic and the algorithm 1 were already given in the explanations under Figure 2. Now we will proceed with a full analysis. First, what are the points which Lilly directs to the eastern horizon (the ascendant) ?? They are: Modern terminology Terminology of Lilly # of such directions 1. planets MUNDO to... Ad corpus... cum latitudine 1 ( of J ) (or The bodies of the planets to... ) 2. planets Zodiacal to... Ad corpus... 1 ( of J ) + 1 of / (The zodiacal projections of the planets to...) 3. The zodiacal oppositions Ad +...cum latitudine 3 ( of G, D and F ) of the planets with latitude to... Directions #3 are the same as the directions of the bodies of the planets to the western horizon (descendant) i.e. planets MUNDO to the descendant. Here, Lilly takes the zodiacal opposition of a planet by longitude and assigns to it the latitude of the planet with the reverse sign. 4. The zodiacal oppositions Ad +... 4 ( of G, D, A and F ) of the planets ( latitude = 0 ) 5. The major aspects of Ad ^... 15 the planets ( #, % and ^ ) 6. The minor aspects of Ad !... 43 the planets ( !, @, $, &, *, _, 36z and 108z ) In Lilly's notation: 72z ($) is a heart, 36z is a heart with a line at the bottom, 108z is a heart with a triangle at the bottom, 150z (_) is designated with $ , 144z (* ) is two hearts, 45z (@ ) is a square with a 'T' over it , 135z (&) is a square with a 'C' over it. 1- The directions of points to the ascendant and MC are explained in detail in my book ' Primary Directions ', volume 1. 16 M WILLIAM LILLY M Modern terminology Terminology of Lilly # of such directions 7. The Ptolemaic terms Ad ter. ... 21 8. The zodiacal antiscia Ad Ant. (CA) ... 6 and contra-antiscia of the planets 9. The antiscia and Ad Ant. (CA) ... cum latitudine5 contra-anrtiscia of the planets with latitude 10. The zodiacal projections of stars Lucid. Lyrae aust. (Vega) 1 11. The housecusps (regiomontanian) Ad Domum... 3 (of 2,3 & 4) 1 ANTISCIA & CONTRA-ANTISCIA ACC. TO LILLY What did Lilly understand by the terms ' antiscia and contra-antiscia ' and ' antiscia and contra-antiscia cum latitudine' ? The antiscion (Ant.) of a point is its mirror image around 00 R when the point is in the northern signs (or around 00 P if it is in the southern signs). The latitude of the antiscion is the same as that of the original point. The contra-antiscion (CA) is the mirror image around 00 U and has the same latitude, but with the opposite sign. So, 'antiscion and contra-antiscion' of a planet apply to the ecliptical projection of the planet, while 'antiscion and contra-antiscion cum latitudine' apply to the body of the planet i.e. here also the latitude is observed. Antiscion of S cum FIGURE S Moon latitudine 6 1z44xE, Contra-Antiscion of S 28z16xR, b=5z00xN b=5z00xN 28z16xP, b=0z Zod. projection of the Moon Antiscion of S Contra-Antiscion of S cum latitudine 28z16xP, b= 5z00xS 28z16xR, b=0z 1z44xE, b=0z Q W E R T Y U I O P { } In directions, the effects of the antiscia of a planet were considered as if they were the planet itself. The contra-antiscia were treated as if they were + of the planet. I was able to recalculate with the computer all 104 directions to the ascendant present in the table of Lilly. They were recomputed on the reconstructed chart. Now we will proceed by presenting a table with all 104 directions calculated by Lilly, showing the points, their coordinates and the directional arcs- according to Lilly and according to the computer recalculation on the reconstructed chart. 1- Argolus, whom Lilly claims to follow, computed the coordinates of the antiscia and the contra-antiscia in the same way as explained here. However, he directed only ant. and contra-ant. with latitude. 'Pandosion Sphaericum', Andreae Argoli, Patavii, 1653. 17 Table with the Directions to the ASC William Lilly's Computer recalculation pages 765-768 of on the reconstructed 'Christian Astrology' horoscope OAasc= 312z 10x ASC = 6z 37x P OAasc= 312z 10x ASC = 6z 41x P Arc of Arc of # Promissor Position Direction Position Direction * 1 %F S. 06z 54x P 0z 00xN 00z 14x 07z 58x P 0z 00xN 01z 15x 08z 05x P 0z 00xN 01z 24x 08z 09x P 0z 00xN 01z 26x 2 Ant.H 3 ^J D. 09z 02x P 0z 00xN 02z 19x 09z 00x P 0z 00xN 02z 16x * 4 Ant.Hcum lat08z 05x P 0z 37xS 02z 39x 08z 09x P 0z 05xN 01z 16x 5 6 7 8 * Zod. Lucid. Lirae 10z 00x P 0z 00xN 03z 14x ter.H 13z 00x P 0z 00xN 06z 00x &S D. 16z 44x P 0z 00xN 09z 14x ter.G 20z 00x P 0z 00xN 11z 55x * 9 108zJ D. 10 108zD S. 11 !H S. 12 108zA S. 13 108zF S. 14 ter.J 21z 02x P 21z 34x P 21z 55x P 24z 37x P 24z 54x P 26z 00x P 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 12z 44x 13z 08x 13z 24x 15z 26x 15z 39x 16z 28x 09z 58x P 12z 00x P 16z 37x P 19z 00x P 0z 00xN 0z 00xN 0z 00xN 0z 00xN 03z 10x 05z 03x 09z 06x 11z 05x 21z 00x P 23z 06x P 21z 51x P 24z 43x P 25z 58x P 25z 00x P 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 12z 41x 14z 18x 13z 20x 15z 30x 16z 25x 15z 43x 1- S. and D. are abbreviations from the Latin 'Sinister' and 'Dexter', accordingly- Left (east of the planet) and Right (west of the planet) aspects. East of the planet means also that the aspect is measured in the direction of succession of the zodiacal signs. This notation comes from the fact that when we observe the sky facing South, the East will be on our Left. And if you want to see the ecliptic without breaking your neck, you better watch the sky facing South ( in the northern geo. latitudes ). 4- Lilly did not give the coordinates of some points in his tables with directions. In such cases I give in italic the coordinates which, most probably, Lilly used. The comparatively large difference between the arc of Lilly and the recalculated one, comes from the inexact latitude of Jupiter Lilly worked with. I recalculated the direction with the data of Lilly ( 08z 05x P 0z 37xS ) and came to a directional arc of 02z 36x 14c. 5- This is the star VEGA. Lilly directed the zodiacal projections of the stars and not the stars proper (which would be mundo directions). Why did he do this ? Most probably because it was much easier. Anyway, a mundo direction of Vega to the ascendant is but impossible since in this case Vega happens to be circumpolar (always above the horizon). 9- A sesquiquintile ( quintile and a half ) of Saturn. 18 M WILLIAM LILLY M Table with the Directions to the ASC William Lilly's Computer recalculation Arc of Arc of # Promissor Position Direction Position Direction 15 36zHS. 27z 55x P 0z 00xN 17z 49x 27z 51x P 0z 00xN 17z 45x 16 CA S 28z 16x P 0z 00xN 18z 04x 28z 23x P 0z 00xN 18z 08x 17 ter.J 00z 00x {0z 00xN 19z 16x 00z 00x {0z 00xN 19z 14x * 00z 54x {0z 00xN 19z 02x 00z 44x {0z 00xN 19z 43x 18 +G 19 ^S D. 01z 44x {0z 00xN 20z 24x 01z 37x {0z 00xN 20z 18x * 00z 44x {1z 05xS 21z 49x 20 +G cum lat.00z 54x {0z 28xS 20z 46x 03z 34x {0z 00xS 21z 36x 05z 06x {0z 00xN 22z 32x 21 ^D S. 06z 37x{0z 00xN 23z 29x 06z 43x {0z 00xN 23z 31x 22 ^A S. 23 ^F S. 06z 54x {0z 00xN 23z 39x 07z 58x {0z 00xN 24z 16x 24 @H S. 06z 55x{0z 00xN 23z 40x 06z 51x {0z 00xN 23z 36x 25 ter.D 07z 00x {0z 00xN 23z 43x 06z 00x {0z 00xN 23z 05x 26 %J D. 09z 02x {0z 00xN 24z 55x 09z 00x {0z 00xN 24z 53x * 27 CAJ cum lat.20z 58x {2z 58xN 26z 09x 21z 00x {2z 40xN 26z 44x 28 ter.F 13z 00x{0z 00xN 27z 10x 12z 00x {0z 00xN 26z 36x 29 108zS D. 13z 44x {0z 00xN 27z 34x 13z 37x {0z 00xN 27z 30x * 30 CAS cum lat.28z 16xP 5z 00xS 28z 31x 28z 23xP 5z 11xS 28z 59x 31 &D S. 18z 34x{0z 00xN 30z 08x 20z 06x {0z 00xN 30z 53x 32 CAJ 20z 58x {0z 00xN 31z 19x 21z 00x {0z 00xN 31z 20x 33 ter.H 21z 00x {0z 00xN 31z 21x 20z 00x {0z 00xN 30z 50x 34 &A S. 21z 37x {0z 00xN 31z 39x 21z 43x {0z 00xN 31z 41x 35 &F S. 21z 54x {0z 00xN 31z 48x 22z 58x {0z 00xN 32z 18x 18- The directional arc here is again a typo error. The true arc should be 19z 52x. Lilly gives the OA of the point as 332z 02x. Since the OA of the ascendant is 312z 10, theirdifference has to be 19z 52x. Within the data of Lilly, the recalculation of the directional arc comes to 19z 49x 52c. 20-Within the data of Lilly, the recalculated directional arc is 20z 43x 35c. 27- The directions of points with latitude, in the tables of Lilly, do not have a longitude nor a latitude given, but only their OA. I assign to these points the coordinates which I suppose, most probably, Lilly used. For example, a recalculation using the supposed data Lilly used, shows for this direction an arc of 26z 12x 35c. This result is very close to the arc of Lilly and ergo, confirms our theory about how Lilly computed the positions of the antiscia and contra-antiscia with latitude. 30- With the data of Lilly the recalculation of the directional arc results in 28z 28x 27c. 19 # Promissor Table with the Directions to the ASC William Lilly's Computer recalculation Arc of Arc of Position Direction Position Direction 36 #H S. 37 Domum 2 38 ter.G 39 $J D. 40 *D S. 41 ter.F 42 *A S. 43 *F S. 44 _G D. 45 %S D. 46 _D S. 47 $H S. 48 / 49 _A S. 50 _F S. 51 *G D. 52 ter.H 53 #J D. 54 ter.D 55 & G 56 $S D. 21z 55x {0z 00xN 23z 30x{0z 00xN 26z 00x {0z 00xN 27z 02x {0z 00xN 27z 34x {0z 00xN 00z 00x } 0z 00xN 00z 37x } 0z 00xN 00z 54x } 0z 00xN 00z 54x} 0z 00xN 01z 44x } 0z 00xN 03z 34x } 0z 00xN 03z 55x } 0z 00xN 05z 50x} 0z 00xN 06z 37x } 0z 00xN 06z 54x} 0z 00xN 06z 54x} 0z 00xN 09z 00x } 0z 00xN 09z 02x } 0z 00xN 15z 00x } 0z 00xN 15z 54x } 0z 00xN 18z 44x } 0z 00xN 21z 51x {0z 00xN 23z 35x {0z 00xN 25z 00x {0z 00xN 27z 00x {0z 00xN 29z 06x {0z 00xN 00z 00x } 0z 00xN 00z 43x } 0z 00xN 01z 58x } 0z 00xN 00z 44x } 0z 00xN 01z 37x } 0z 00xN 05z 06x } 0z 00xN 03z 51x } 0z 00xN 07z 36x } 0z 00xN 06z 43x } 0z 00xN 07z 58x } 0z 00xN 06z 44x } 0z 00xN 08z 00x } 0z 00xN 09z 00x } 0z 00xN 14z 00x } 0z 00xN 15z 44x } 0z 00xN 18z 37x } 0z 00xN 31z 46x 32z 36x 33z 16x 34z 13x 35z 11x 35z 35x 35z 54x 36z 27x 35z 55x 36z 18x 37z 49x 37z 17x 38z 53x 38z 31x 39z 02x 38z 31x 39z 03x 39z 28x 41z 32x 42z 14x 43z 46x 57 Ant F cum lat. 23z 06x } 1z 00xN 43z 32x 58 ter.G 21z 00x } 0z 00xN 44z 20x 59 %H S. 21z 55x } 0z 00xN 44z 42x 22z 02x } 1z 16xN 20z 00x } 0z 00xN 21z 51x } 0z 00xN 42z 40x 43z 55x 44z 39x 60 Ant F 61 Ant.A 62 @J D. 23z 06x } 0z 00xN 23z 23x } 0z 00xN 24z 02x } 0z 00xN 45z 09x 45z 16x 45z 32x 22z 02x } 0z 00xN 23z 17x } 0z 00xN 24z 00x } 0z 00xN 44z 43x 45z 13x 45z 29x 63 Ant D 26z 26x } 0z 00xN 46z 28x 24z 54x } 0z 00xN 45z 50x 31z 49x 32z 35x 33z 46x 34z 15x 34z 30x 35z 36x 35z 52x 36z 00x 36z 00x 36z 23x 37z 16x 37z 20x 37z 52x 38z 30x 38z 37x 38z 37x 39z 30x 39z 31x 41z 57x 42z 19x 43z 26x * 57- The antiscion of F with a latitude, acc. to the data Lilly used, should be in 23z 06x } 1z 00xS. However, if we direct this point we'll come to an arc of 46z 45x 47c. If we try with the point 23z 06x } 1z 00xN., the directional arc will be 43z 31x 19c. Obviously, Lilly made a mistake assigning to the point the latitude of F with the opposite sign ( 1z 00xN. ). Having done so, he came closer to the correct arc ! 20 M WILLIAM LILLY M Table with the Directions to the ASC William Lilly's Computer recalculation Arc of Arc of # Promissor Position Direction Position Direction 64 ter.J 27z 00x } 0z 00xN 46z 41x 26z 00x } 0z 00xN 46z 16x 65 ter.H 00z 00x } 0z 00xN 47z 50x 00z 00x } 0z 00xN 47z 50x 66 ^G D. 00z 54x Q 0z 00xN 48z 10x 00z 44x Q 0z 00xN 48z 07x * 07z 58x Q 1z 16xS 52z 59x 67 +F cum lat. 06z 54x Q 1z 00xN 48z 27x 68 #S D. 01z 44x Q 0z 00xN 48z 30x 01z 37x Q 0z 00xN 48z 27x * 24z 54x } 1z 21xN 43z 40x 69 Ant D cum lat.26z 26x } 1z 32xS 48z 55x 03z 02x Q 0z 00xN 49z 00x 03z 00x Q 0z 00xN 49z 00x 70 36zJ D. 03z 34x Q 0z 00xN 49z 12x 05z 06x Q 0z 00xN 49z 49x 71 +D 72 +A 06z 37x Q 0z 00xN 50z 24x 06z 43x Q 0z 00xN 50z 26x 73 +F 06z 54x Q 0z 00xN 50z 30x 07z 58x Q 0z 00xN 50z 56x 74 ter.F 07z 00x Q 0z 00xN 50z 33x 06z 00x Q 0z 00xN 50z 10x 75 !J D. 09z 02x Q 0z 00xN 51z 21x 09z 00x Q 0z 00xN 51z 21x 76 108zH S. 09z 55x Q 0z 00xN 51z 42x 09z 51x Q 0z 00xN 51z 40x * 77 +F cum lat. 06z 54x Q 1z 00xS 52z 07x 07z 58x Q 1z 16xS 52z 59x 78 108zG D. 12z 54x Q 0z 00xN 52z 52x 12z 44x Q 0z 00xN 52z 49x 79 ter.D 15z 00x Q 0z 00xN 53z 43x 14z 00x Q 0z 00xN 53z 19x 80 @S D. 16z 44x Q 0z 00xN 54z 25x 16z 37x Q 0z 00xN 54z 22x 81 Domum 3 18z 34x Q 0z 00xN 55z 09x 18z 27x Q 0z 00xN 55z 08x 82 ^H S. 21z 55x Q 0z 00xN 56z 33x 21z 51x Q 0z 00xN 56z 33x 83 ter.G 22z 00x Q 0z 00xN 56z 35x 21z 00x Q 0z 00xN 56z 11x 84 36zS D. 25z 44x Q 0z 00xN 58z 11x 25z 37x Q 0z 00xN 58z 08x 85 ter.J 27z 00x Q 0z 00xN 58z 35x 26z 00x Q 0z 00xN 58z 19x 86 ter.F 00z 00x W 0z 00xN 60z 04x 00z 00x W 0z 00xN 60z 04x 87 %G D. 00z 54x W 0z 00xN 60z 28x 00z 44x W 0z 00xN 60z 25x 88 !S D. 01z 44x W 0z 00xN 60z 51x 01z 37x W 0z 00xN 60z 48x 67- Recalculating with what should be logically the Lilly's data, namely 06z 54x Q 1z 00xN, the directional arc results in 48z 53x 23c. 69- Computer recalculated with coordinates 26z 26x } 1z 32xS , the arc is 48z 55x 23c. 77- '+F cum lat.' shows up as directions number 67 and 77. Directing the point 06z 54x Q 1z 00xS with the computer gives an arc of 52z 07x. However, the point +F cum lat. should has 1z 00xN as a latitude and not 1z 00xS. Without doubt, this is an error. Lilly has omitted the direction of +D cum lat. 21 Table with the Directions to the ASC William Lilly's Computer recalculation Arc of Arc of # Promissor Position Direction Position Direction 89 _D D. 03z 34x W 0z 00xN 61z 46x 05z 06x W 0z 00xN 62z 26x 90 _A D. 06z 3?x W 0z 00xN 63z 09x 06z 43x W 0z 00xN 63z 12x 06z 54x W 0z 00xN 63z 17x 07z 58x W 0z 00xN 63z 48x 91 _F D. 06z 55x W 0z 00xN 63z 18x 06z 51x W 0z 00xN 63z 16x 92 &H S. 93 ter.D 09z 00x W 0z 00xN 64z 19x 08z 00x W 0z 00xN 63z 49x 09z 02x W 0z 00xN 64z 20x 09z 00x W 0z 00xN 64z 19x 94 Zod. ~J 95 *D D. 09z 34x W 0z 00xN 64z 36x 11z 06x W 0z 00xN 65z 23x 12z 37x W 0z 00xN 66z 09x 12z 43x W 0z 00xN 66z 13x 96 *A D. 97 *F D. 12z 54x W 0z 00xN 66z 18x 13z 58x W 0z 00xN 66z 52x 98 Domum 4 14z 39x W 0z 00xN 67z 13x 14z 39x W 0z 00xN 67z 13x 99 *H S. 15z 55x W 0z 00xN 67z 53x 15z 51x W 0z 00xN 67z 52x 100 ter.H 16z 00x W 0z 00xN 67z 57x 15z 00x W 0z 00xN 67z 24x 101 &D D. 18z 34x W 0z 00xN 69z 22x 20z 06x W 0z 00xN 70z 15x * 102 Mundo J 09z 02x W 2z 58xS 69z 30x 09z 00x W 2z 40xS 68z 55x 103 72zG D. 18z 54x W 0z 00xN 69z 34x 18z 44x W 0z 00xN 69z 28x 104 &A D. 21z 37x W 0z 00xN 71z 07x 21z 43x W 0z 00xN 71z 12x THE DIRECTIONS TO THE ASCENDANT- CONCLUSIONS Working with the data he had, Lilly calculated the arcs fairly exactly. The mistakes: direction # 18. The errors: # 57 and the controversy around the double show-up of the direction +F cum lat. to the ascendant in directions # 67 and # 77. One of them, most probably, has come in place of the omitted direction +D cum lat. to the ascendant. To the technical errors, I would include also the fact that Lilly has pushed the beginnings of the Ptolemaic terms with one degree forward. Further, I would question the assertion of Lilly that ' At this day we use no method in Directions but Argolus...'. Argolus directed the zodiacal aspects with a latitude. Lilly directed them with a latitude zero. Argolus1 directed the Egyptian terms. Lilly directed Ptolemaic terms. 102- Computer recalculated with the coordinates of Lilly, 09z 02x W 2z 58xS , the arc comes to 69z 26x 36c. 1- 'Tabulae Primi Mobilis', Andreae Argoli, Romae 1610. 'Pandosion Sphaericum', Andreae Argoli, Patavii, 1653. 22 M WILLIAM LILLY M DIRECTIONS TO MC We will turn our atention now to Lilly's directions to the MC. He tabulated 54 such directions: # of directions 1. Planets mundo to MC: 1 ( of H ) 2. Planets zodiacal to MC: 1 ( of H ) 3. Planets mundo to IC: 1 ( of S ) ( or The zod. +of planets with a latitude to MC ) 4. Planets zodiacal to IC : 1 (of S ) ( or The zod. +of planets with latitude = 0 to MC ) 5. Major aspects of planets (lat. = 0 ): 8 6. Minor aspects of planets (lat. = 0 ): 22 1 7. Ptolemaic terms : 11 8. Zod. antiscia and contra-antiscia of planets: 2 ( of H and G ) 9. Zod. antiscia and contra-antiscia with latitude: 2 ( of H and G ) 10. Zod. projections of stars: 2 ( Antares & Vega ) 11. Housecusps ( regiomontanian ): 3 ( of 11, 12 and the asc. ) Table with the Directions to the MC William Lilly's Computer recalculation pages 769-771 of on the reconstructed 'Christian Astrology' horoscope RAMC= 222z 10x MC = 14z 39x I Arc of Arc of # Promissor Position Direction Position Direction 1 36zH D. 15z 55x I 0z 00xN 01z 16x 15z 51x I 0z 00xN 01z 12x 2 @D S. 18z 34x I 0z 00xN 03z 55x 20z 06x I 0z 00xN 05z 29x 3 108zG S. 18z 54x I 0z 00xN 04z 15x 18z 44x I 0z 00xN 04z 06x 4 ter.D 21z 00x I 0z 00xN 06z 23x 21z 00x I 0z 00xN 06z 23x 5 @A S. 21z 37x I 0z 00xN 07z 00x 21z 43x I 0z 00xN 07z 06x 6 @F S. 21z 54x I 0z 00xN 07z 17x 22z 58x I 0z 00xN 08z 23x 7 !H D. 21z 55x I 0z 00xN 07z 18x 21z 51x I 0z 00xN 07z 15x 8 ter.J 27z 00x I 0z 00xN 12z 32x 27z 00x I 0z 00xN 12z 32x 9 CAG 29z 06x I 0z 00xN 14z 43x 29z 16x I 0z 00xN 14z 42x * 10 CAGcum lat.29z 06x I 0z 28xN 14z 50x 29z 16x I 1z 05xS 14z 37x 1- Surprisingly, the terms Lilly directed to MC are the correct Ptolemaic terms and not those pushed with 1 degree forward, which he employed to the ascendant. 10- Lilly should have directed the point 29z 06x I 0z 28xS. The arc calculated with this point is 14z 35x 29c. Calculated with 29z 06x I 0z 28xN, the arc is 14z 48x 28c. 23 Table with the Directions to the MC William Lilly's Computer recalculation Arc of Arc of # Promissor Position Direction Position Direction 11 Domum 11 30z 00x I 0z 00xN 15z 38x 00z 12x O 0z 00xN 15z 50x 00z 00x O 0z 00xN 15z 38x 00z 00x O 0z 00xN 15z 38x 12 ter.H * 13 +S cum lat.01z 44x O 5z 00xS 16z 20x 01z 37x O 5z 11xS 16z 09x 14 ^G S. 00z 54x O 0z 00xN 16z 35x 00z 44x O 0z 00xN 16z 25x 15 +S 01z 44x O 0z 00xS 17z 27x 01z 37x O 0z 00xS 17z 19x 03z 34x O 0z 00xN 19z 22x 05z 06x O 0z 00xN 20z 59x 16 #D * 04z 24x O 0z 00xN 20z 15x 17 Zod. Antares 04z 30x O 0z 00xN 20z 21x 18 #A S. 06z 37x O 0z 00xN 22z 34x 06z 43x O 0z 00xN 22z 41x 06z 54x O 0z 00xN 22z 53x 07z 58x O 0z 00xN 24z 01x 19 #F S. 20 ter.H 08z 00x O 0z 00xN 24z 03x 08z 00x O 0z 00xN 24z 03x 21 _J D. 09z 02x O 0z 00xN 25z 09x 09z 00x O 0z 00xN 25z 07x 22 ter.D 14z 00x O 0z 00xN 30z 28x 14z 00x O 0z 00xN 30z 28x 23 Domum 12 14z 46x O 0z 00xN 31z 19x 14z 51x O 0z 00xN 31z 23x 24 *J D. 15z 02x O 0z 00xN 31z 25x 15z 00x O 0z 00xN 31z 32x 25 $D S. 15z 34x O 0z 00xN 32z 09x 17z 06x O 0z 00xN 33z 48x 26 &G S. 15z 54x O 0z 00xN 32z 31x 15z 44x O 0z 00xN 32z 20x 27 $A S. 18z 37x O 0z 00xN 35z 28x 18z 43x O 0z 00xN 35z 34x 28 $F S. 18z 54x O 0z 00xN 35z 47x 19z 58x O 0z 00xN 36z 54x 29 ter.J 19z 00x O 0z 00xN 35z 52x 19z 00x O 0z 00xN 35z 52x * 30 Mundo H 21z 55x O 0z 37xS 38z 01x 21z 51x O 0z 05xN 38z 58x 31* Zodiacal H 32 &J D. 33 *G S. 34 ter.G 35 ter.F 36 _G S. 37 _S D. 21z 55x O 24z 02x O 24z 54x O 25z 00x O 00z 00x P 00z 54x P 01z 44x P 0z 00xS 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 39z 03x 41z 19x 42z 17x 42z 23x 47z 50x 48z 50x 49z 45x 21z 51x O 24z 00x O 24z 44x O 25z 00x O 00z 00x P 00z 44x P 01z 37x P 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 38z 57x 41z 17x 42z 05x 42z 23x 47z 50x 48z 38x 49z 35x 13- Recomputing with Lilly's data i.e. 01z 44x O 5z 00xS, the arc comes to 16z 19x 48c. 17- The arc of the mundo direction of Antares to the Meridian (MC) is 19z 20x. 30- Recomputing with 21z 55x O 0z 37xS, the arc comes to 38z 58x 58c. I was not able to figure out the genesis of this error. 31- Recomputing with 21z 55x O 0z 00x , the arc comes to 39z 01x 26c. 24 M WILLIAM # Promissor 38 39 40 41 42 43 * 44 %D S. ter.D ascendant %A S. %F S. *S D. Ant.H Table with the Directions to the MC William Lilly's Computer recalculation Arc of Arc of Position Direction Position Direction 03z 34x P 06z 00x P 06z 37x P 06z 37x P 06z 54x P 07z 44x P 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 51z 45x 54z 23x 55z 04x 55z 04x 55z 23x 56z 18x 05z 06x P 06z 00x P 06z 41x P 06z 43x P 07z 58x P 07z 37x P 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 53z 23x 54z 22x 55z 06x 55z 09x 56z 30x 56z 07x 08z 05x P 0z 00xN 56z 38x 08z 09x P 0z 00xN 56z 42x 08z 09x P 0z 05xN 56z 42x * 45 Ant.Hcum lat.08z 05x P 0z 37xS 46 ^J D. * 47 Zod. Vega 48 49 50 51 52 53 54 ter.H &S D. ter.G 108zJ D. 108zD S. !H S. 108zA S. LILLY M 56z 40x 09z 02x P 0z 00xN 57z 40x 09z 00x P 0z 00xN 57z 38x 10z 00x P 0z 00xN 58z 43x 09z 58x P 0z 00xN 58z 40x 12z 00x P 16z 44x P 19z 00x P 21z 02x P 21z 34x P 21z 55x P 24z 37x P 60z 53x 66z 00x 68z 25x 70z 35x 71z 08x 71z 30x 74z 22x 12z 00x P 16z 37x P 19z 00x P 21z 00x P 23z 06x P 21z 51x P 24z 43x P 60z 52x 65z 50x 68z 24x 70z 32x 72z 46x 71z 27x 74z 29x 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN THE DIRECTIONS TO MC- CONCLUSIONS The directions to MC seem to be computed OK, excepting directions # 10 and 30. A question, however, arises, why did Lilly use here the correct Ptolemaic terms after arguing in chapter 100 (Page 510) that they should be pushed with one degree forward and after using these revised terms in his directions to the ascendant. The astrologers who worked with the correct Ptolemaic terms Lilly accused in a 'vulgar Errour' ! Yet, he himself takes now a seat among them !... This inconsistency is so simple and easy to notice that, I guess, Lilly was not in his best shape writing the final and most complicated chapters. The nature of the mistake points at a tired man in a big hurry... 44- Recomputing with Lilly's coordinates, 08z 05x P 0z 00x, the arc is 56z 37x 45c. 45- Recomputing with Lilly's coordinates, 08z 05x P 0z 37xS, the arc is 56z 40x 15. 47- Lilly directed the zodiacal projection of the star and not the star proper (which would be a mundo direction). The arc of the star mundo to MC is 53z 43x. 25 THE INTERPLANETARY DIRECTIONS Finished with the directions to the ascendant and MC, Lilly goes on with a list of directions to the A. He tabulated only results, without explaining the algorithm. I was almost sure that he directed regiomontanian. However, to play it safe, I decided to check out the Poles of the planets computed by Lilly and given in the final page of the chapter (p.831). Basically, there were only two possibilities: Lilly directed either regio or Lilly directed placidian under the pole. No other systems of primaries were known and practiced in these times. I know of one exception though- the system of primaries developed by Cardan. However, Cardan first, apparently did not have any followers and second, there were neither 'Poles' nor 'Circles of Position' in his system. The term 'Circle of Position', which Lilly used, is much more reminiscent of the regio way of directing. Expecting to confirm the regio credo of Lilly, but open-minded, I calculated with the program the regio and the placidian Poles of the Planets in the example horoscope: COMPUTER CALCULATED Lilly's Placidian Regio Planets 'Circle of Position' Pole Pole A S D F G H J < 40z 00x 28z 56x 39z 23x 40z 00x 24z 31x 40z 49x 41z 00x 28z 52x 38z 59x 39z 00x 27z 34x 37z 54x 51z 00x 47z 51x 51z 18x 52z 00x 43z 54x 51z 32x 08z 00x 48z 00x 04z 54x 41z 08x 08z 36x 47z 49x The results confirmed my suspicion- Lilly directed regio. The regio algorithm of computation of interplanetary directions is too lengthy to be given here in full detail. That's why I'll restrict myself only to explaining the meaning of the regio directions. The presentation of the full regio algorithm is a topic for a separate article. We already know that, according to the modern terminology, the Significator in a primary direction is the point which stays fixed on the celestial sphere. The significators in the interplanetary directions, used by the old 26 M WILLIAM LILLY M astrologers, were the A, the S and <. Only few authors used as significators also the rest of the planets. Now, assuming that the significator stays still and the whole sphere, with all its points, turns around the axis of the cel. poles, the question is: When will a certain point (the Promissor) arrive to a conjunction with the significator ? Regiomontanus' answer was- When the point, carried with the apparent rotation of the celestial sphere, reaches the house circle1 that goes through the significator. This house circle should go through 3 points: the significator and the two crosspoints of the Horizon with the Meridian. North Point of the Horizon Horizon Meridian North Pole Regio housecircle tru the Sun FIGURE 7 Meridian Regio 9th house house-circle Regio housecircle tru the Sun Equator Meridian Horizon SUN Horizon South Point of the Horizon A 3-Dimensional representation of the example horoscope of Lilly and the house circle through the A. See how the Meridian, the Horizon, the house circle through the A and all house boundaries join at the North and South points of the horizon. The print-out is from the Program 'Placidus', version 2.0. 1- A house circle is a great circle passing through the two crosspoints of the Horizon with the Meridian ( the North and South Points of the horizon ). A great circle is a circle on the celestial sphere whose plane goes through the center of the sphere. 27 Regio housecircle tru the Sun Meridian Equator SUN Horizon Diurnal Path of H FIGURE 8 Directional Arc of Mundo H=A ( REGIO ) Equator 9 10 8 7 H Houses11 6 12 Horizon 1 5 Houses 2 4 3 Diurnal Path of H South Meridian Regio housePole circle tru the Sun A 3-Dimensional representation of the interplanetary Regiomontanian direction Mundo. Hd.= A in the example horoscope of Lilly . We can see the Diurnal Path of H. This is the circle around the Poles-axis along which H moves due to the 24-hours apparent rotation of the celestial sphere. Wherever the diurnal path of Hcrosses the house circle through the A is where H will come into conjunction (acc. to Regio-montanus ) with the A . The directional arc is the arc between H and this point. It is measured in time (equatorial degrees) The print-out is from the Program 'Placidus', version 2.0. The explanatory labels and arrows are superimposed. DIRECTIONS TO THE SUN A The directions of points to the house circle through the Sun are 70: Points # of directions 1. Planets mundo: 1 ( of H ) 2. Planets zodiacal: 1 ( of H ) 3. Planets mundo (to the night arc of the house circle): 2 ( of S and J ) ( or The zod. +of planets with a latitude to the day arc of the circle ) 28 M WILLIAM LILLY M 41. Planets zodiacal (to the night arc of the house circle): 2 ( of S and J ) ( or The zod. +of planets with latitude = 0 to the day arc of the circle ) 5. Major aspects of planets (lat. = 0 ): 9 6. Minor aspects of planets (lat. = 0 ): 30 7. Ptolemaic terms: 15 8. Zod. antiscia and contra-antiscia with latitude: 1 ( of G ) 9. Zod. antiscia and contra-antiscia of planets: 1 ( of G ) 10. Zod. projections of stars: 3 ( Antares, Spica & North Scale) 11. Housecusps ( regiomontanian ): 5 ( of 9, 10, 11, 12 and the asc. ) I was able to recalculate with the program 62 of the 70 directions. The 8 directions left out are the 3 directions with stars and 5 with half-quintiles and sesqui-quintiles. Table with the Directions to the SUN A William Lilly's Computer recalculation pages 771-774 Circle of Position= 40z 00x, Pole= 39z 23x, OD (Oblique Descension)= 183z 51x OD = 183z 59x OD is under its own Pole # Promissor 1 _J S. 2 $H D. 3 ter.H 4 $G S. 5 &S S. 6 Zod. Spica 7 Domum 9 * 8 ter.F 9 #H D. Position 09z 02x U 09z 55x U 11z 00x U 12z 54x U 16z 44x U 18z 33x U 18z 34x U OD is under its own Pole Arc of Direction 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 01z 25x 01z 57x 02z 35x 03z 42x 05z 59x 07z 05x 07z 06x 19z 00x U 0z 00xN 21z 55x U 0z 00xN 07z 21x 09z 08x Arc of Position Direction 09z 00x U 0z 00xN 09z 51x U 0z 00xN 11z 00x U 0z 00xN 12z 44x U 0z 00xN 16z 37x U 0z 00xN 01z 22x 01z 52x 02z 33x 03z 36x 05z 56x not recomputed 18z 27x U 0z 00xN 07z 03x 19z 00x U 0z 00xN 21z 51x U 0z 00xN 07z 23x 09z 09x 1- The house circle through the A has two arcs: one is above the radical horizon ( day-arc); the other is below the radical horizon (night-arc). The radical A is above the horizon and that's why Lilly directs the points to the day-arc of the Solar housecircle. To direct a point to the night-arc of the regio house circle through the A is the same as to direct its + (with the opposite latitude) to the day arc. The directional arcs are always equal. 8- This should be the terms of D and not of F. A typo error. 29 Table with the Directions to the SUN A William Lilly's Computer recalculation Arc of Arc of # Promissor Position Direction Position Direction 10 ter.G 24z 00x U 0z 00xN 10z 25x 24z 00x U 0z 00xN 10z 29x 11 *S S. 25z 44x U 0z 00xN 11z 30x 25z 37x U 0z 00xN 11z 30x 12 ter.G 00z 00x I 0z 00xN 14z 12x 00z 00x I 0z 00xN 14z 19x 00z 54x I 0z 00xN 14z 47x 00z 44x I 0z 00xN 14z 48x 13 %G S. 01z 44x I 0z 00xN 15z 19x 01z 37x I 0z 00xN 15z 23x 14 _S D. * 15 +J cum lat. 09z 02x I 2z 58xS 16z 31x 09z 00x I 2z 40xN 23z 46x 03z 34x I 0z 00xN 16z 31x 05z 06x I 0z 00xN 17z 42x 16 !D S. 17 ter.G 06z 00x I 0z 00xN 18z 08x 06z 00x I 0z 00xN 18z 18x 18 !AS. 06z 37x I 0z 00xN 18z 33x 06z 43x I 0z 00xN 18z 47x 06z 54x I 0z 00xN 18z 45x 07z 58x I 0z 00xN 19z 38x 19 !F S. 20 @H D. 06z 55x I 0z 00xN 18z 46x 06z 51x I 0z 00xN 18z 53x 21 +J 09z 02x I 0z 00xN 20z 12x 09z 00x I 0z 00xN 20z 22x 22 36zD S. 09z 34x I 0z 00xN 20z 35x not recomputed 23 North Scale .09z 48x I 0z 00xN 20z 45x not recomputed 24 36zA S. 12z 37x I 0z 00xN 22z 41x not recomputed 25 36zF S. 12z 54x I 0z 00xN 22z 53x not recomputed 26 ter.F 14z 00x I 0z 00xN 23z 39x 14z 00x I 0z 00xN 23z 53x 27 MC 14z 39x I 0z 00xN 24z 08x 14z 39x I 0z 00xN 24z 21x 28 36zH D. 15z 55x I 0z 00xN 25z 00x not recomputed 29 !D S. 18z 34x I 0z 00xN 26z 58x 20z 06x I 0z 00xN 28z 24x 30 108zG S. 18z 54x I 0z 00xN 27z 13x not recomputed 31 ter.D 21z 00x I 0z 00xN 28z 48x 21z 00x I 0z 00xN 29z 05x 32 @A S. 21z 37x I 0z 00xN 29z 16x 21z 43x I 0z 00xN 29z 38x 33 @F S. 21z 54x I 0z 00xN 29z 29x 22z 58x I 0z 00xN 30z 36x 34 !H D. 21z 55x I 0z 00xN 29z 30x 21z 51x I 0z 00xN 29z 44x 35 ter.J 27z 00x I 0z 00xN 33z 29x 27z 00x I 0z 00xN 33z 48x 36 CAG 29z 06x I 0z 00xN 35z 11x 29z 16x I 0z 00xN 35z 40x 15- Here Lilly again makes an error. He did not write the coordinates of the point he directed, but a little detective work will show that he has directed 09z 02x I 2z 58xSouth. If we recompute the direction with this point, the arc will result in 16z 49x, which is very close to Lilly's result. In his speculum, however, the latitude of J is 2z 58xSouth and the lat. of +J with a latitude should be 2z 58xNORTH. Directing 09z 02x I 2z 58xNorth gives arc of 23z 50x. 30 M WILLIAM LILLY M Table with the Directions to the SUN A William Lilly's Computer recalculation Arc of Arc of # Promissor Position Direction Position Direction 37 ter.G 00z 00x I 0z 00xN 14z 12x 00z 00x I 0z 00xN 14z 19x 38 %G S. 00z 54x I 0z 00xN 14z 47x 00z 44x I 0z 00xN 14z 48x 00z 00x O 0z 00xN 35z 58x 00z 00x O 0z 00xN 36z 16x 39 ter.H 00z 54x O 0z 00xN 36z 41x 00z 44x O 0z 00xN 36z 54x 40 ^G S. 01z 44x O 0z 00xN 37z 23x 01z 37x O 0z 00xN 37z 37x 41 +S 42 #D S. 03z 34x O 0z 00xN 38z 56x 05z 06x O 0z 00xN 40z 38x 43 Antares 04z 30x O 0z 00xN 39z 45x not recomputed 06z 37x O 0z 00xN 41z 35x 06z 43x O 0z 00xN 42z 04x 44 #A S. 06z 54x O 0z 00xN 41z 51x 07z 58x O 0z 00xN 43z 10x 45 #F S. 08z 00x O 0z 00xN 42z 50x 08z 00x O 0z 00xN 43z 13x 46 ter.F * 47 +S cum lat.01z 44x O 5z 00xN 43z 13x 01z 37x O 5z 00xS 31z 12x 48 _J D. 09z 02x O 0z 00xN 43z 46x 09z 00x O 0z 00xN 44z 07x 49 ter.D 14z 00x O 0z 00xN 48z 23x 14z 00x O 0z 00xN 48z 46x 50 Domum 12 14z 46x O 0z 00xN 49z 01x 14z 51x O 0z 00xN 49z 35x 51 *J D. 15z 02x O 0z 00xN 49z 22x 15z 00x O 0z 00xN 49z 44x 52 $D S. 15z 34x O 0z 00xN 49z 53x 17z 06x O 0z 00xN 51z 46x 53 &G S. 15z 54x O 0z 00xN 50z 12x 15z 44x O 0z 00xN 50z 26x 54 $A S. 18z 37x O 0z 00xN 52z 51x 18z 43x O 0z 00xN 53z 22x 55 $F S. 18z 54x O 0z 00xN 53z 08x 19z 58x O 0z 00xN 54z 36x 56 ter.J 19z 00x O 0z 00xN 53z 14x 19z 00x O 0z 00xN 53z 38x 57 Zod. H 21z 55x O 0z 00xN 56z 09x 21z 51x O 0z 00xN 56z 31x 58 Mundo H 21z 55x O 0z 37xS 56z 54x 21z 51x O 0z 05xN 56z 37x 59 &J D. 24z 02x O 0z 00xN 58z 21x 24z 00x O 0z 00xN 58z 44x 60 *G S. 24z 54x O 0z 00xN 59z 16x 24z 44x O 0z 00xN 59z 30x 61 ter.G 25z 00x O 0z 00xN 59z 22x 25z 00x O 0z 00xN 59z 47x 62 ter.F 00z 00x P 0z 00xN 64z 43x 00z 00x P 0z 00xN 65z 08x 63 _G S. 00z 54x P 0z 00xN 65z 43x 00z 44x P 0z 00xN 65z 56x 64 _S D. 01z 44x P 0z 00xN 66z 36x 01z 37x P 0z 00xN 66z 54x 47- Lilly makes an error. He should have used 01z 44x O 5z 00xSouth for the point +Swith a latitude. Instead, he used a lat. of 5z 00x North. How do we know this, if Lilly did not give the coordinates he used ? Regio-Directing 01z 44x O 5z 00x North to the A( with all other data as in the chart Lilly used ) gives arc of 43z 24x. If we direct the point 01z 44x O 5z 00xSouth, we'll get 31z 33x. 31 Table with the Directions to the SUN A William Lilly's Computer recalculation Arc of Arc of # Promissor Position Direction Position Direction 65 %D S. 03z 34x P 0z 00xN 68z 39x 05z 06x P 0z 00xN 70z 42x 06z 00x P 0z 00xN 71z 24x 06z 00x P 0z 00xN 71z 43x 66 ter D 67 Ascendens 06z 37x P 0z 00xN 72z 06x 06z 41x P 0z 00xN 72z 35x 68 %A S. 06z 37x P 0z 00xN 72z 06x 06z 43x P 0z 00xN 72z 38x 06z 54x P 0z 00xN 72z 25x 07z 58x P 0z 00xN 74z 03x 69 %F S. 07z 44x P 0z 00xN 73z 22x 07z 37x P 0z 00xN 73z 39x 70 *S D. THE DIRECTIONS TO THE SUN A- CONCLUSIONS In the directions to the A, Lilly used the correct Ptolemaic terms. The errors are in directions # 15 and 47. These are directions with +J with a lat. and +S with a lat. Lilly took the wrong signs for the latitudes. That this may has been his own method of directing, cannot be a viable argument, since at other places he took the correct sign. The +of a planet with a latitude has to have the same latitude as the planet, but with the opposite sign. If the point + is opposite the planet in longitude, why not also in latitude?! This practice and the practice of assigning a latitude to the aspects, is something I could trace through Argolus, Maginus and Gauricus back to Regiomontanus1 (1436-1476). DIRECTIONS TO THE MOON S The directions of points to the house circle through the Moon are 54 and all of them are erroneous. The reason is a mistake in Lilly's calculation of the Oblique Descension (OD) of the Moon under its own Pole (40z) which he gives as 74z 16x. The OD of the Moon under its own Pole, which we'll note as ODS S , is calculated as follows: ODS S = RAS + ADS S(Ascensional Difference of the Moon under its own Pole). The ADSS computed with Lilly's data gives 23z 33x or ADS S = arcsin[ tan( δ S ) * tan(Pole S ) ]= =arcsin[ tan(25z 28x) * tan(40z) ]= 23z 33x. Ergo, the ODSSof Lilly should be = RAS + ADSS= 58z 30x + 23z 33x = 82z 03x. No matter how much I strained my brains, I was not able to figure out the genesis of this most serious error of Lilly. Maybe he just took the wrong entry from the tables of Argolus. The correct ODSSis with 7z 47x greater than that of Lilly. We can expect the correct arcs to be so much shorter. 1- 'Tabulae Directionum et Profectionum Clarissimi Viri..', I. Regiomontani, 1551 32 M WILLIAM LILLY M The 54 points Lilly directs to the Moon are as follows: Points # of directions 1. Planets mundo: 1 ( of G ) 2. Planets zodiacal: 1 ( of G ) 3. Planets mundo (to the day arc of the house circle): 1 ( of H) ( or The zod. +of planets with a latitude to the night arc of the circle ) 4. Planets zodiacal (to the day arc of the house circle): 1 ( of H) ( or The zod. +of planets with latitude = 0 to the night arc of the circle ) 5. Major aspects of planets (lat. = 0 ): 12 6. Minor aspects of planets (lat. = 0 ): 19 7. Ptolemaic terms: 11 8. Zod. antiscia and contra-antiscia with latitude: 2 ( of H and S) 9. Zod. antiscia and contra-antiscia of planets: 2 ( of H and S) 10. Zod. projections of stars: 2 ( Aldebaran and Praesepe ) 11. Housecusps ( regiomontanian ): 2 ( of 6 and 7 ) Table with the Directions to the MOON S William Lilly's Computer recalculation pages 774-776 Circle of Position= 40z 00x, Pole= 40z 49x, ODSS= 74z 16x ODSS= 82z 47x Arc of Arc of # Promissor Position Direction Position Direction 1* ^D D. 2 Aldebaran 3 ^A D. 4 ^F D. 03z 34x E 04z 30x E 06z 37x E 06z 54x E 0z 00xN 0z 00xN 0z 00xN 0z 00xN 05z 59x 07z 09x 09z 47x 10z 08x 05z 06x E 0z 00xN 00z 03xc. not recomputed 06z 43x E 0z 00xN 01z 57x 07z 58x E 0z 00xN 03z 29x 5* ter.H 6 !J S. 07z 00x E 0z 00xN 09z 02x E 0z 00xN 10z 15x 12z 44x 07z 00x E 0z 00xN 09z 00x E 0z 00xN 7* ter.F 8 Domum 6 9 36zJ S. 10 108zD D. 14z 00x E 14z 45x E 15z 02x E 15z 34x E 18z 47x 19z 39x 20z 01x 20z 40x 13z 00x E 0z 00xN 09z 38x 14z 51x E 0z 00xN 11z 52x not recomputed not recomputed 0z 00xN 0z 00xN 0z 00xN 0z 00xN 1-The recalculated direction is converse. 5-The terms in direction #5 are the correct Ptolemaic. 7- The correct Ptolemaic terms of F start in 13z 00x E. 33 02z 18x 04z 46x # Promissor Table with the Directions to the MOON S William Lilly's Computer recalculation Arc of Arc of Position Direction Position Direction 11 @G D. 12 108zA D. 13 108zF D. 15z 54x E 0z 00xN 18z 37x E 0z 00xN 18z 54x E 0z 00xN 21z 04x 24z 16x 24z 36x 15z 44x E 0z 00xN 12z 56x not recomputed not recomputed 14* ter.J 21z 00x E 0z 00xN 27z 03x 26z 00x E 0z 00xN 24z 50x 15* +H cum lat. 21z 55x E 0z 37xS 27z 27x 21z 51x E 0z 05xS 20z 01x * 16 +H 17 @J S. 18 36zG D. 21z 55x E 0z 00xN 24z 02x E 0z 00xN 24z 54x E 0z 00xN 28z 06x 30z 31x 31z 30x 21z 51x E 0z 00xN 20z 07x 24z 00x E 0z 00xN 22z 35x not recomputed 19* ter.G 20 ter.G 21 !G D. 22 !S S. 23 %D D. 24 Domum 7 25 %A D. 26 %F D. 25z 00x E 00z 00x R 00z 54x R 01z 44x R 03z 34x R 06z 37x R 06z 37x R 06z 54x R 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 31z 37x 37z 10x 38z 10x 39z 03x 41z 00x 44z 10x 44z 10x 44z 30x 20z 00x E 00z 00x R 00z 44x R 01z 37x R 05z 06x R 06z 41x R 06z 43x R 07z 58x R 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 17z 58x 29z 16x 30z 04x 31z 01x 34z 43x 36z 22x 36z 24x 37z 40x 07z 00x R 0z 00xN 44z 36x 20z 00x R 0z 00xN 49z 17x 27 * ter.F 14-From 20z 00x E begin the Ptolemaic terms of G and not of J . The terms of J start in 26z 00x E. A typographical error ? 15- Let us assume that Lilly is correct and ODS S = 74z 16x. If we direct 21z 55x E 0z 37xN. to this 'assumed' Moon, we'll get an arc of 28z 40x. If we direct 21z 55x E 0z 37xS. we'll get 27z 26x . The result of Lilly is 27z 27x . Ergo, Lilly directed the point 21z 55x E 0z 37xS. This is an error. The correct latitude of the point +H with a latitude is 0z 37xN since radical H , acc. to Lilly, has a latitude of 0z 37x South. Here, Lilly directs an erroneously calculated '+Hwith a latitude' to an erroneous S . Remarkably, the +H -error diminishes the error in the arc due to the ODS S -error with 01z 13x ! Still, the difference from the correct arc is more than 07z. 16- Working with Lilly's data for everything and recomputing with 21z 55x E 0z 00xN, the arc results in 28z 03x. 19- See the explanations under the line on this page for the direction # 14. 27-From 06z 00x R begin the Ptolemaic terms of H and not of F . The terms of F start in 20z 00x R. 34 M WILLIAM # Promissor LILLY M Table with the Directions to the MOON S William Lilly's Computer recalculation Arc of Arc of Position Direction Position Direction 28* CAH cum lat. 08z 05x R 0z 37xS 44z 59x 29 36zS S. 07z 44x R 0z 00xN 45z 21x 08z 05x R 0z 00xN 45z 43x 30 CAH 31 #J S. 09z 02x R 0z 00xN 46z 11x 08z 09x R 0z 05xS 37z 46x not recomputed 08z 09x R 0z 00xN 37z 52x 09z 00x R 0z 00xN 38z 44x 32* ter.D 33 @S S. 13z 00x R 0z 00xN 16z 44x R 0z 00xN 50z 37x 54z 10x 13z 00x R 0z 00xN 16z 37x R 0z 00xN 42z 42x 46z 09x 34* ter.H 35 $J S. 20z 00x R 0z 00xN 21z 02x R 0z 00xN 57z 14x 58z 11x 06z 00x R 0z 00xN 21z 00x R 0z 00xN 35z 39x 50z 11x 28z 23x R 23z 06x R 21z 51x R 24z 43x R 25z 58x R 27z 00x R 27z 51x R 28z 23x R 00z 00x T 5z 11xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 63z 21x 52z 04x 50z 57x 53z 29x 54z 33x 55z 26x 56z 09x 56z 36x 57z 56x 00z 44x T 1z 05xN 59z 53x 36*AntS cum lat.28z 16x R 37 $D D. 21z 34x R 38 _H D. 21z 55x R 39 $A D. 24z 37x R 40 $F D. 24z 54x R 41 ter.J 27z 00x R 42 *H D. 27z 55x R 43 Ant.S 28z 16x R 44 ter.J 00z 00x T 45* Mundo G 5z 00xS 58z 39x 0z 00xN 58z 40x 0z 00xN 58z 59x 0z 00xN 60z 22x 0z 00xN 61z 37x 0z 00xN 63z 25x 0z 00xN 64z 12x 0z 00xN 64z 27x 0z 00xN 65z 57x 00z 54x T 0z 28xS 66z 06x 28-Lilly should have directed this point with latitude 0z 37xN. Working with Lilly's ODSS, the arc of the CA with lat. 0z 37x N is 46z 28x . With lat. 0z 37x S , the arc is 44z 58x . 32- This is the correct beginning of the Ptolemaic terms of D in R. 34- See the explanations under the line for the direction # 27 on page 34. 36- It is unfathomable why Lilly takes here 5z 00xS for the latitude of the point when it is obvious that it should be 5z 00x N, equal to the latitude of the radical S (according to Lilly's data). At least, this is what the logic and Argolus cry in one voice. Working with Lilly's ODSS, the arc of the antiscion with lat. 5z 00xN is 70z 45x. With lat. 5z 00xS, the arc is 58z 40x. 45- Taking all parameters as given by Lilly and recomputing with 00z 54x T 0z 28xN, the arc results in 67z 12x. Working, however, with 00z 54x T 0z 28xSouth, the arc is 66z 05x. Lilly again has taken the wrong sign for the latitude, since G in his chart has latitude of 0z 28x North ! 35 # Promissor * 46 47 48 49 50 51 52 53 54 Zod.G #S S. Praesepe #D D. ter.D #A D. #F D. &H D. %J S. Table with the Directions to the MOON S William Lilly's Computer recalculation Arc of Arc of Position Direction Position Direction 00z 54x T 01z 44x T 02z 03x T 03z 34x T 06z 00x T 06z 37x T 06z 54x T 06z 55x T 09z 02x T 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 66z 42x 67z 23x 67z 38x 68z 51x 70z 46x 71z 15x 71z 28x 71z 29x 73z 06x 00z 44x T 0z 00xN 58z 32x 01z 37x T 0z 00xN 59z 15x not recomputed 05z 06x T 0z 00xN 62z 01x 06z 00x T 0z 00xN 62z 43x 06z 43x T 0z 00xN 63z 16x 07z 58x T 0z 00xN 64z 13x 06z 51x T 0z 00xN 63z 22x 09z 00x T 0z 00xN 65z 01x THE DIRECTIONS TO THE MOON S- CONCLUSIONS Basically, since Lilly made a gross error computing the Oblique Descension of the S under its own Pole, all directions to the S are wrong. At closer scrutiny, it turns out, the directions numbered 15, 28, 36 and 45 contain other errors. All these directions are directions of points with a latitude and Lilly took the wrong signs for them. Another thing is the directions with terms, numbered 14, 19, 27 and 34. Here Lilly made mistakes in the rulers. This, of course, may be errors of the printer. Still another thing is that some of the terms are the correct Ptolemaic terms (#5) and some (#7) are those of Lilly ( Ptolemaic terms pushed with 1 degree forward ). DIRECTIONS TO PARS FORTUNAE < On page 777, Lilly puts in a table directions to <. For the longitude of < Lilly gives 00z 36x Y ! It is again a difficult task to understand why Lilly took 00z 36x Y for the longitude of < when, in the chart, it is correctly placed in 01z 44x Y. The latitude of the point is clearly zero, since Lilly gives its declination as 11z 19x North and the point 00z 36x Y can have such a declination only with latitude zero. In this way, I will sweep aside the bold suggestion of Dimitar Kojouharov that Lilly maybe used the Placidian < which is situated on the diurnal path of the S. If < that Lilly used, was the Placidian < then it should have had the declination of the S, namely 25z 38x North. 36 M WILLIAM LILLY M For the Oblique Descension of < under its own pole, Lilly gives 165z 30x. Working with the data Lilly used, the correct < is in 01z 44x Y and its OD under its own pole of 48z would be 166z 04x 30c. The < of the recalculated chart is in 01z 35x Y and its OD under its own pole is 165z 55x , not far away from Lilly's 165z 30x. In the end of the table ( page 780 ), Lilly writes ' Some direct the < converse, or against the succession of Signs, you do no more but subduct the Promittor from the Significator, and so go backwards.'... Here, the suggestion of Lilly is that we just compute the OD of the points which are situated in direction of decrease of the longitude (as to the <) and subtract their OD's from the OD of the <. So, all OD's are to be computed under the pole of the <. Doing so, we actually direct the points against the celestial rotation until they come to the house circle passing through <. Well, to direct < converse, in the manner of Regiomontanus, is actually not so easy as Lilly wants it. Regiomontanus did it by directing < , with the celestial rotation, until < reached the house circle passing through the other point. If, for example, we want do direct < 'conversely' to ^G, in the way Regiomontanus practiced it, we first have to compute the Pole of ^G with a complicated algorithm, then its AD (Ascensional Difference) under its own pole and then its OD under its own pole. Then we have to compute the OD of < under the pole of ^G. And finally we will find the directional arc by subtracting the OD of ^G from the OD of <. Both OD's are computed under the pole of ^G. The whole exasperating procedure has to be repeated for each other point that we want to direct < to. This is how Regiomontanus directed <1. The 93 points Lilly directs to Pars Fortunae are as follows: Points # of directions 1. Planets mundo: 4 ( of F, D , A and H ) 2. Planets zodiacal: 4 ( of F, D , H and ? ) 3. Planets mundo (to the night arc of the house circle): 2 ( of Jand S) ( or The zod. +of planets with a latitude to the day arc of the circle ) 4. Planets zodiacal (to the night arc of the house circle): 2 ( of Jand S) ( or The zod. +of planets with latitude = 0 to the day arc of the circle ) 5. Major aspects of planets (lat. = 0 ): 10 6. Minor aspects of planets (lat. = 0 ): 39 1- 'Tabulae Directionum et Profectionum Clarissimi Viri..', I. Regiomontani, 1551 37 7. Ptolemaic terms: 18 8. Zod. antiscia and contra-antiscia with latitude: 3 ( of F, D and G) 9. Zod. antiscia and contra-antiscia of planets: 3 ( of F, D and G) 10. Zod. projections of stars: 3 ( Spica, North Scale and Antares ) 11. Housecusps ( regiomontanian ): 4 ( of 9, 10, 11 amd 12) Table with the Directions to Pars Fortunae < William Lilly's Computer recalculation pages 777-780 'Circle of Position'= 48z 00x, Pole= 47z 49x, OD<<= 165z 30x OD<<= 165z 55x Arc of Arc of # Promissor Position Direction Position Direction 1 36zA D. 00z 37x Y 0z 00xN 00z 01x not recomputed 2 36zF D. 00z 54x Y 0z 00xN 00z 10x not recomputed * 00z 54x Y 0z 00xN 00z 10x 00z 44x Y 0z 00xN 00z 27xc. 3 !G S. 4 %S S. 01z 44x Y 0z 00xN 00z 35x 01z 37x Y 0z 00xN 00z 01x 5 !D D. 03z 34x Y 0z 00xN 01z 34x 05z 06x Y 0z 00xN 01z 52x 6 108zH D. 03z 55x Y 0z 00xN 01z 45x not recomputed 7 ? 05z 50x Y 0z 00xN 2z 45x 07z 36x Y 0z 00xN 03z 08x 8 !A D. 06z 37x Y 0z 00xN 03z 09x 06z 43x Y 0z 00xN 02z 42x 9 !F D. 06z 54x Y 0z 00xN 03z 18x 07z 58x Y 0z 00xN 03z 20x 10 36zG S. 06z 54x Y 0z 00xN 03z 18x not recomputed * 11 ter.F 07z 00x Y 0z 00xN 03z 21x 07z 00x Y 0z 00xN 02z 50x 12 ^J S. 09z 02x Y 0z 00xN 04z 23x 09z 00x Y 0z 00xN 03z 52x 13 @G S. 15z 54x Y 0z 00xN 07z 46x 15z 44x Y 0z 00xN 07z 13x 14 ter.J 18z 00x Y 0z 00xN 07z 49x 18z 00x Y 0z 00xN 08z 19x 15 108zS S. 19z 44x Y 0z 00xN 09z 37x not recomputed 16 %H D. 21z 55x Y 0z 00xN 10z 40x 21z 51x Y 0z 00xN 10z 12x 17 CAF 23z 06x Y 0z 00xN 11z 14x 22z 02x Y 0z 00xN 10z 17x 18 CAA 23z 23x Y 0z 00xN 11z 22x 23z 17x Y 0z 00xN 10z 52x 19 ter.G 24z 00x Y 0z 00xN 11z 40x 24z 00x Y 0z 00xN 11z 13x 20 &J S. 24z 02x Y 0z 00xN 11z 41x 24z 00x Y 0z 00xN 11z 13x 3-The recalculated direction is converse. 11-All terms directed to the < are the correct Ptolemaic. Only the terms of G in dir. # 42 are pushed forward with a degree. Lilly forgot to direct the terms of Hin Y. 38 M WILLIAM # Promissor LILLY M Table with the Directions to Pars Fortunae < William Lilly's Computer recalculation Arc of Arc of Position Direction Position Direction 21* CADcum lat. 26z 26x Y 1z 32xN?? 12z 10x 22 23 24 25 26 27 * CAFcum lat. 23z 06x Y CAD 26z 26x Y ter.J 00z 00x U #G S. 00z 54x U *J S. 03z 02x U Zod.D 03z 34x U 1z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 0z 00xN 12z 38x 12z 49x 13z 30x 14z 55x 15z 56x 16z 11x 24z 54x Y 1z 21xS 09z 44x 22z 02x Y 24z 54x Y 00z 00x U 00z 44x U 03z 00x U 05z 06x U 1z 16xS 08z 29x 0z 00xN 11z 39x 0z 00xN 14z 05x 0z 00xN 14z 26x 0z 00xN 15z 31x 0z 00xN 16z 32x 1z 16xN 0z 00xN 0z 00xN 0z 00xN 28* Mundo F 29 ter.F 30 Zod.A 31 Zod.F 06z 54x U 06z 00x U 06z 37x U 06z 54x U 1z 00xS 16z 23x 0z 00xN 17z 20x 0z 00xN 17z 38x 0z 00xN 17z 46x 07z 58x U 06z 00x U 06z 43x U 07z 58x U 32* Mundo D 33 _J S. 34 $H D. 35 ter.H 36 $G S. 37 &S S. 38 Spica 39 Domum 9 40 ter.D 03z 34x U 09z 02x U 09z 55x U 11z 00x U 12z 54x U 16z 44x U 18z 33x U 18z 34x U 19z 00x U 1z 32xN 18z 21x 0z 00xN 18z 47x 0z 00xN 19z 13x 0z 00xN 19z 44x 0z 00xN 20z 39x 0z 00xN 22z 31x 0z 00xN 23z 24x 0z 00xN 23z 26x 0z 00xN 23z 38x 05z 06x U 1z 21xN 18z 26x 09z 00x U 0z 00xN 18z 24x 09z 51x U 0z 00xN 18z 49x 11z 00x U 0z 00xN 19z 22x 12z 44x U 0z 00xN 20z 13x 16z 37x U 0z 00xN 22z 07x not recomputed 18z 27x U 0z 00xN 23z 02x 19z 00x U 0z 00xN 23z 19x 19z 42x 16z 58x 17z 18x 17z 54x 21-What was the point Lilly directed for 'CA Dcum lat.' is unfathomable. I tried with 6 pairs of coordinates which Lilly may have used, but could not come close to his result. 22-Computing with the data Lilly used and with the point 23z 06x Y 1z 00xN gives arc of 12z 38x. This time, Lilly used the correct latitude for the point. 28-Computing with the data Lilly used and with the point 06z 54x U 1z 00xS gives arc of 16z 21x. 32- If we compute with the coordinates for D Lilly had for the chart, namely 03z 34x U 1z 32x South, we will come to an arc of 14z 01x. If we compute with 03z 34x U 1z 32x North, we'll get 18z 22x. So, after erring first in the position of D and then in < , taking the wrong sign for the latitude of D , brings Lilly almost on top of the correct result !! Small errors tend to cancel out. Sometimes, thanks God, even big ones do !! 39 Table with the Directions to Pars Fortunae < William Lilly's Computer recalculation Arc of Arc of # Promissor Position Direction Position Direction 41 #H D. 21z 55x U 0z 00xN 25z 07x 21z 55x U 0z 00xN 24z 45x 42 ter.G 25z 00x U 0z 00xN 26z 41x 24z 00x U 0z 00xN 25z 52x 25z 44x U 0z 00xN 27z 03x 25z 37x U 0z 00xN 26z 41x 43 *S S. 00z 00x I 0z 00xN 29z 19x 00z 00x I 0z 00xN 29z 01x 44 ter.G * 09z 00x I 2z 40xN 38z 00x 45 +J cum lat. 09z 02x I 2z 58xS 29z 47x 46 %G S. 00z 54x I 0z 00xN 29z 48x 00z 44x I 0z 00xN 29z 25x 47 _S S. 01z 44x I 0z 00xN 30z 15x 01z 37x I 0z 00xN 29z 54x 48 !D S. 03z 34x I 0z 00xN 31z 15x 05z 06x I 0z 00xN 31z 50x 49 ter.H 06z 00x I 0z 00xN 32z 27x 06z 00x I 0z 00xN 32z 20x 50 !A S. 06z 37x I 0z 00xN 32z 58x 06z 43x I 0z 00xN 32z 45x 51 !F S. 06z 54x I 0z 00xN 33z 08x 07z 58x I 0z 00xN 33z 28x 52 @H D. 06z 55x I 0z 00xN 33z 09x 06z 51x I 0z 00xN 32z 50x 53 +J 09z 02x I 0z 00xN 34z 21x 09z 00x I 0z 00xN 34z 05x 54 36zD S. 09z 34x I 0z 00xN 34z 39x not recomputed * 55 Zod. N. Scale 09z 48x I 0z 00xN 34z 47x not recomputed 56 36zA S. 12z 37x I 0z 00xN 36z 28x not recomputed 57 36zF S. 12z 54x I 0z 00xN 36z 40x not recomputed 58 ter.F 14z 00x I 0z 00xN 37z 18x 14z 00x I 0z 00xN 37z 05x 59 MC 14z 39x I 0z 00xN 37z 45x 14z 39x I 0z 00xN 37z 29x 60 36zH D. 15z 55x I 0z 00xN 38z 30x not recomputed 61 @D S. 18z 34x I 0z 00xN 40z 12x 20z 06x I 0z 00xN 40z 59x 62 108zG S. 18z 54x I 0z 00xN 40z 25x not recomputed 63 ter.D 21z 00x I 0z 00xN 41z 38x 21z 00x I 0z 00xN 41z 35x 64 @A S. 21z 37x I 0z 00xN 42z 13x 21z 43x I 0z 00xN 42z 04x 65 @F S. 21z 54x I 0z 00xN 42z 24x 22z 58x I 0z 00xN 42z 55x 66 !H D. 21z 55x I 0z 00xN 42z 25x 21z 51x I 0z 00xN 42z 09x 67 ter.J 27z 00x I 0z 00xN 45z 56x 27z 00x I 0z 00xN 45z 45x 68 CA G 29z 06x I 0z 00xN 47z 27x 29z 16x I 0z 00xN 47z 24x 69 Domum 11 30z 00x I 0z 00xN 48z 11x 00z 12x O 0z 00xN 48z 06x 45-Lilly directs here + J with the wrong latitude, 2z 58x South, instead of 2z 58x North. Directing +J with lat. 2z 58xS gives arc of 29z 50x. With 2z 58xN: 38z 46x. 56-Lilly writes this star as ' Luc. Lanc. aust.', South Scale. However, by its coordinates, it is clear that it should be 'Luc. Lanc. borealis', North Scale. 40 M WILLIAM LILLY M Table with the Directions to Pars Fortunae < William Lilly's Computer recalculation Arc of Arc of # Promissor Position Direction Position Direction 70 ter.H 00z 00x O 0z 00xN 48z 11x 00z 00x O 0z 00xN 47z 57x * 29z 16x I 1z 05xS 45z 41x 71 CA Gcum lat. 29z 06x I 0z 28xN 48z 15x 72 ^G S. 00z 54x O 0z 00xN 48z 48x 00z 44x O 0z 00xN 48z 31x 01z 44x O 0z 00xN 49z 27x 01z 37x O 0z 00xN 49z 11x 73 +S 74 #D S. 03z 34x O 0z 00xN 50z 53x 05z 06x O 0z 00xN 51z 55x 51z 36x not recomputed 75 Zod. Antares 04z 30x O 0z 00xN 76 #A S. 06z 37x O 0z 00xN 53z 19x 06z 43x O 0z 00xN 53z 13x 77 #F S. 06z 54x O 0z 00xN 53z 33x 07z 58x O 0z 00xN 54z 15x 78 ter.F 08z 00x O 0z 00xN 54z 28x 08z 00x O 0z 00xN 54z 17x 79 _J D. 09z 02x O 0z 00xN 55z 20x 09z 00x O 0z 00xN 55z 08x * 21z 55x O 0z 00xN 25z 07x 80 –S cum lat. 01z 44x O 5z 00xN 57z 02x 81 ter.D 14z 00x O 0z 00xN 59z 38x 14z 00x O 0z 00xN 59z 29x 82 Domum 12 14z 46x O 0z 00xN 60z 23x 14z 51x O 0z 00xN 60z 16x 83 *J D. 15z 02x O 0z 00xN 60z 35x 15z 00x O 0z 00xN 60z 24x 84 $D S. 15z 34x O 0z 00xN 61z 04x 17z 06x O 0z 00xN 62z 21x 85 &G S. 15z 54x O 0z 00xN 61z 22x 15z 44x O 0z 00xN 61z 04x 86 $A S. 18z 37x O 0z 00xN 63z 55x 18z 43x O 0z 00xN 63z 53x 87 $F S. 18z 54x O 0z 00xN 64z 11x 19z 58x O 0z 00xN 65z 04x 88 ter.J 19z 00x O 0z 00xN 64z 14x 19z 00x O 0z 00xN 64z 08x 89 Mundo H 21z 55x O 0z 37xS 66z 13x 21z 51x O 0z 05xN 67z 04x 90 Zod. H 21z 55x O 0z 00xN 67z 07x 21z 55x O 0z 00xN 66z 56x 91 &J D. 24z 02x O 0z 00xN 69z 15x 24z 00x O 0z 00xN 69z 06x 92 *G S. 24z 54x O 0z 00xN 70z 09x 24z 44x O 0z 00xN 69z 52x 93 ter.G 25z 00x O 0z 00xN 70z 15x 25z 00x O 0z 00xN 70z 07x 71-Lilly directs the CA of Gwith the wrong latitude i.e. 0z 28x North, instead of 0z 28x South which is the opposite of the latitude of the radical G. Directing the CA of G (within Lilly's data) with South lat. gives arc of 46z 48x; with North lat.: 48z 16x 80- Lilly directs the +S with latitude 5z 00x North which is the lat. of the radical S. He should have directed +S with latitude 5z 00x South. Within Lilly's data, the arc of +S with lat. 5z 00x South, directed to <, is 41z 06x; with lat. 5z 00x North: 57z 02x. 41 THE DIRECTIONS TO PARS FORTUNAE <- CONCLUSIONS The errors are, as usual with Lilly, in the directions of points with latitude: # 21, 32, 45, 71 & 80. Lilly directed to < the correct Ptolemaic terms. THE FINAL PAGES The final pages of the book ( 781-829) are a detailed predictive analysis for 22 'future' years ( 29th to 50th of native's life). In the analysis Lilly employs primary directions, solar return and profections in this order. The primaries seem to be the most important tool for Lilly. In many instances Lilly states that if the solar return and the profections are of the same character as the current primary directions- they strengthen them; if of the opposite- they may cancel the weak primaries or soften the strong primary directions. In these analyses Lilly used directions to all planets and not only to the five classical significators ( Asc, MC, A, S and < ). On the last page (831) Lilly tabulates the Poles and the Oblique Descensions or Ascensions of J, H, G, F and D. Let us compare their values with those of the computer: Planets LILLY's Pole OD or OA COMPUTER CALCULATED Pole OD or OA A S D F G H J < 40z 00x 183z 51x 39z 23x 183z 59x 40z 00x 74z 16x 40z 49x 82z 47x 41z 00x 183z 05x 38z 59x 184z 35x 39z 00x 182z 57x 37z 54x 186z 15x 51z 00x 149z 02x 51z 18x 151z 59x 52z 00x 295z 03x 51z 32x 293z 41x 08z 00x 35z 57x 08z 36x 35z 38x 48z 00x 165z 30x 47z 49x 165z 55x Asc. MC 53z 00x 53z 00x 312z 10x 222z 10x 53z 00x 53z 00x 312z 10x 222z 10x It seems, only the OD/OA of the Asc., MC , A, J and < have values close enough to the computer recalculations. Consequently, only the directions to these significators have a chance to be approximately of the same arcvalues in Lilly as well as according to the computer. I will analyze only Lilly's calculations for two years, before my final conclusions and wrap up. 42 M WILLIAM LILLY M Table with the Directions to various Significators for the period 18 Sept. 1644 to 18 Sept 1645 ( Julian calendar ) with the key of Naibod William Lilly's page 781 Computer recalculation Hitdate of Hitdate of # Promissor Significator Direction (Julian ) Direction (Julian ) 1 108z J D. = H 28 Jan 1645 not recomputed < 21 Feb 1645 10 Jan 1638 2 Zod. Ant S = 3 Zod. CA F = G 05 Mar 1645 23 Sep 1641 = J 05 Mar 1645 27 Apr 1645 4 !J S. 5 +H = S 24 Mar 1645 14 Feb 1637 6 Zod. CA A = G 18 Apr 1645 10 Apr 1642 7 Terms D = D 12 May 1645 24 Oct 1645 8 108z D S. = H 01 Jul 1645 not recomputed 9 Terms G = G 25 Jul 1645 27 Jul 1642 10 &J S. = G 01 Aug 1645 28 Jul 1642 11 CAScum lat. = ASC 29 Aug 1645 17 Feb 1646 As expected, most of the directions computed by Lilly deviate a lot from the computer calculated hitdates. The most important directions for Lilly are #2 and #5 which are directions to the hylegiacal points < and S. His interpretation of Zod. Ant. S = < is: '..much converse and dealing with vulgar people of Lunar condition, and some profit by Saylors, Widdowes, Gentlewomen....profit by dealing in forraigne parts...' All of the above is under the symbolism of the S. The interpretation of +H = S is: '..slight joviall disease by drinking ( +Hfalls in the 6th house and H is in the 12th )...unkindness of acquaintance ( H rules 11th )...not safe to visit any imprisoned friends ( H in the 12th )...Men represented by H..to be much prejudiciall to the Native this year..Gentlemen, Clergy, Lawyers..( H as a symbol )' Zod. CAA = G: '..prejudice in matter of Inheritance or Patrimony ( A Lord of the 8th ) by means of Kindred or Soldiers ( G Lord of 3rd )' 108z D S. = H, '..delight in Books..to be grave, austere and religiously inclined..' In all interpretations, Lilly skillfully combines the meanings of the planets as symbols and the meaning of the houses they are connected with ( through a position or a rulership ). 43 for the period 18 Sept. 1646 to 18 Sept 1647 ( Julian calendar ) William Lilly's page 787 Computer recalculation # Promissor Significator Hitdate (Julian ) Hitdate (Julian ) 1 Zod. CA F = G ?? 23 Sep 1641 2 +J cum lat. = < Dec 1646 10 Apr 1655 = < Dec 1646 26 Jul 1646 3 % G = F ?? 22 Sep 1644 4 Terms D 5 @S conv. = < ?? 05 Dec 1647 = ASC Apr 1647 20 Jan 1648 6 & D 7 _ S S. = < May 1647 19 Jan 1647 = F July 1647 20 Apr 1645 8 @ A = MC Aug 1647 17 Aug 1647 9 Terms D Directions #2 and #3 are the most important for Lilly. Discussing +Jcum lat. = <, Lilly writes, '..the Native shall suffer in his Wealth and Estate ( < ) by ancient Saturnine men or in things as Land, Rents, annuities ( J )...impoverish..by means of the Dead ( radical < in 8th )...+J is in Signes fixed which argue..the continuance of the matter...all crumbshouldered or splea-footed signified by J prove enemies...'. For &D= ASC Lilly says, '...vexed by Mercuriall men...Atturneys, Merchants, Factors, agents forreigne...' In the beginning of his analysis for the next 1647-1648 year Lilly writes, ' It's not probable that the malice of the last yeers aspects...will be quite extinguished...' This brings home that a strong direction was for Lilly not only an event, but also a period. THE INTERPRETATION The interpretation of Lilly follows some simple rules. The Significator shows 'the matter' or what will be affected by the direction. It is the ' what ' of the direction. On pages 653-654 Lilly explains: ASC - Life and Body, Affections and Manners of Body and Mind. S - Journeys, Matrimony, Wife, Women, relatives. A - Health, Honour, Father, favour of great persons. MC- Honour, Offices, friendship of Nobility, Kings.Trade, Profession, Mother < - Riches. J - Ancestors, Inheritances, Buildings, Possessions, Fears, Jealousies. H - Glory, Children, Renowne, Riches, Religion, Sobriety. G - Animosity, Victory, War, Lawsuits, Brethren. F - Matrimony, Love, Pleasure, rich Ornaments, Maids, Women D - Wit, Understanding, Trade, Industry, Negotions, Journeys, lesser Brethren. To the pure symbolism of the significator Lilly adds also its accidental 44 M WILLIAM LILLY M meaning through the houses it is connected with. The promissor shows ' the manner and the quality ' or the nature of the event as well as the person it will come through. It is the ' how '. If, for example, you have %D = < then watch out for lawyers ( D ) reaching for your pockets ( < ). If, on the contrary, you have ^F = S then you may relax in you home ( S ) and expect a visit from a nice creature ( F ). If Nirvana is what you want, then do not miss your L = ASC. Lilly inspected the promissor closely. What is it ? In which house and sign is it ? Is there anything else in the same house or sign ? He also examined the region around the promissor. Were there other important points, neighbours of the promissor: aspects, antiscia, terms, planets... Let us say, we are deciphering the direction ^F = <. According to Lilly, we should see where is the promissor ^F and also the original promissor which is casting the aspect, namely F. Assume F is in the 2nd house in 18z16xT and ^F is in the 5th house in 18z16xO. Let us say F rules the 11th and the 4th houses. We have now a full description of the accidental determinations of the promissor: 2, 11, 4 and 5. Lilly would not doubt to say: ' Much favour from Gentlewomen (F) and friends (11) in respect to immobility and money (<, 4, 2). Lilly also watched the chronological order of the directions. The directions came to life in front of his inner eye. One event or succession of connected events was unfolding in time through several directions coming close one after the other. If we had %D = < and after couple of months the ^F = S, Lilly would say that ' much relief will come from the vexations of the Atturneys ( %D ) through a young and beautiful woman ( ^F ), friend of the native (11th house)..". Important were also the other points around the promissor. Let us assume that a well aspected H is close to the point ^F. This will certainly change things. The region will become brighter. No matter that the direction H = S may ensue after couple of years, the very presence of H around our promissor will strengthen the direction of ^F. And this was the interpretation style not only of Lilly, but of all master astrologers of the renaissance. Different authors looked for different things, but the principles were the same: The region around the promissor is important. A strong direction is an event, but also a period. The directions are internally connected and influence each other, just like the events in our life. The primary directions are not only a predictive tool, but they give the key to the way how our potentiality develops in time, the way the karmic seeds ripen in interconnection, the way our archetypes, dormant in our psyche, unfold. 45 To illustrate the method, I like to think of the significator as a wayfarer (technically it stays fixed), as a part of us or as one of our faces traveling through the celestial sphere. Now it advances through a deep forest inhabited with ghastly creatures ( if the region is dotted with %J, +G , &: ..), now it comes to the palace of repose ( a region with F, #H , ^S ..). THE TECHNICAL PERFORMANCE OF LILLY It is obvious that the calculations of Lilly contain many errors. You may say this comes from the times he lived in. I don't think so. I have checked out authors who have lived a century and more earlier and they were much exacter. So, what are the shortcomings of Lilly ? I will readily enumerate them: 1. Lilly, it turned out, could not cope with the latitudes. Almost every direction of a point with a latitude is calculated erroneously. 2. Lilly invented a new set of quasi Ptolemaic terms, but was not consistent employing them. 3. Lilly made a gross error computing the OD of the Moon. 4. Lilly did not explain anywhere the mathematical algorithm he was following, nor did he gave any example calculations. From the nature of the errors I concluded that Lilly was more probably fabulously absent-minded or stressed-out in a haste rather than a bad matematician and a sloppy calculator. Or at least that's what I'd like to believe in! What is the charm and boldness of Lilly ? 1. Lilly computed hundreds of directions. 2. Lilly gave clear rules and examples for the interpretation.. 3. Lilly wrote the final chapters when a plague was in a full swing in London, 'visiting' also his own house, as he stated in the end of the book. A PERSONAL OPINION After all these calculations and recalculations, a question arises: What is the efficiency of the system Lilly used ?! I have checked almost all systems of primary directions and my preliminary conclusion is that the efficiency of the Regiomontanian zodiacal directions is low. It seems, the zodiacal directions in any system, be it Placidian, be it Regio or else, are not the most efficient. The directions to the Asc. and MC, Lilly computed, may have some limited efficiency. I prefer to work, for now, exclusively with the Placidian mundo directions that I hold for the most efficient and mind-blowing system of primaries. For a final conclusion more research is necessary. 46 M WILLIAM LILLY M THE SYSTEM OF LILLY A WRAP-UP 1. Lilly deemed the primary directions as the most reliable predictive tool in natal astrology. 2. Employed the primary directions as the most reliable tool for rectification of the birth time as well. 3. Directed Regiomontanian. 4. Used the Ptolemy key for initial orientation and the Naibod key for more exact results. 5. Directed only direct ( with the rotation of the celestial sphere ). To the < he directed points also against the diurnal rotation. 6. Lilly directed: Planets and their +with a lat. ( mundo ) Planets and their +with zero latitude ( zodiacal ) J ASC Antiscia and contra-ant. with a lat. and with lat. = 0 H MC Aspects with zero latitude ( zodiacal ) TO A G Zodiacal projections of stars F S Regiomontanian housecusps D < Ptolemaic terms 7. Employed also solar return chart and profections. They could influence the weak primaries. 8. Interpreted, combining the symbolic meanings with the accidental ( house ) determinations of the Significator and the Promissor. 9. A Strong primary direction meant for Lilly an event as well as a period. Bibliography 1. 2. 3. 2. 3. 4. 5. 6. 7. 8. 9. ' Tabulae Directionum...', ' Tabulae De Primo Mobili...', ' Directiones...', ' Tabulae Primi Mobilis...' , ' Tabulae Primi Mobilis... ' ' Pandosion Sphaericum ' ' Operum, Tomus Quintus...', ' Christian Astrology ', ' Primary Directions ', ' Primum Mobile ', ' Primary Directions ' vol. I, I. Regiomontani, 1551 Lucae Gaurici, Romae 1557 Lucae Gaurici, Romae 1557 I. Antoniis Magini, Venitiis 1604 Andreae Argoli, Romae 1610 Andreae Argoli, Patavii 1653 Hieronymi Cardani, Lugduni 1663 W. Lilly, Regulus Publishing Co., 1985 J. Makransky, Dear Brutus Press, 1988 Placidus , I. for Study of Cycles, 1983 Rumen Kolev, Zenith 1997 47