**MULTIPLE KEYS IN SYMBOLIC DIRECTIONS**

**(Published in “MEDIUM COELI” N° 8, 1997 and refreshed on 7/31/1999)**

**Dr. Spicasc (Dr. Carlos Raitzin)**

**In the present article I will display very clearly a detail of the precise results of my research, which were previously presented in a short article printed in 1993 in the magazine ATMA-JNANA.**

**I will include later extensions and improvements of these findings that I trust, will render ample service to serious and hard working astrologers. And I say findings because these keys have not been invented but found by myself starting on speculative hypothesis fully confirmed by later experiences.**

**I will devote this article to the foundations of these findings and promise some other writings in the future with more possible uses for practical cases.**

**For those who are taking the first steps in Astrology let us make it clear that symbolic directions are those that in the directional arc are measured on the ecliptics. If a native has Mars in his rectified radix at 16° of Aquarius and his MC at 14° of Cancer; moving this Mars 1grade per year in the direction of the signs (or direct) we will have the direction Mars trine MC when Mars gets to 14° of Pisces, that is to say exactly when the person is 28 years of age. If we move Mars on the opposite direction in respect to the signs (or converse) we will get the direction or aspect Mars opposition MC when the person is 32 years of age, when Mars get to 14° of Capricorn, always at the speed of one grade per year.**

**We call this to direct planet Mars and in that way we have two directions, a direct one when we move Mars along the signs and a converse one when we do it in the opposite direction.**

**If the information is precise (rectified chart with an error under or equal 3 seconds in the time of birth) both directions will correspond with normally concordant vital events (congruent) following the Theory of Determinations of the great Morin de Villefranche.**

**These findings have been widely tested during centuries and in fact, directions have proved to be the best experimental test for the validity of Astrology. Of course, in the former example we have considered precise grades for the sake of simplicity but in a practical case it will be necessary to take into account precise minutes and seconds in the arc. If we are not careful on that, the predicted dates for the future events will result erroneous. The Theory of Determinations is the only one that allows us to exactly predict what is going to be the nature of the events that will take place when the dates fall due in every direction in the life of the person.**

**In the case of the key (or angular speed) of a grade per year we will have that one month corresponds to 5 minutes in the arc, six days will be a minute in the arc and one day will be ten seconds in the arc, to which we will arrive through a simple proportion. This first key is generally called Ptolemy’s.**

**Our research consisted in pointing out the efficient keys in the symbolic directions, considering them as such to those that when due resulted congruent (concordant) with vital events observed in the strict sense of Morin de Villefranche and his Theory of Determinations. Naturally, I feel very grateful to the enormous group of friends who cooperated and helped to publish these old and new results, after having rectified their charts and observing their events in life on a daily basis, as well as comparing them with my predictions. All of them helped taking down notes of whatever happened to them. But I should point out three people who participated in a very active way. In the first place I want to mention my friend and disciple, the architect Estanislao Juan Kores, who produced his own rectifications and checked several thousands of directions in different cases. He even rediscovered the series Siriumc a short time after I did. We worked together to rectify the birth charts of Mozart and Beethoven, which were printed respectively in “Mercurio-3” (Barcelona) and “Ciencias Milenarias” (Buenos Aires).**

**In the second place, I would like to mention my wife and youngest daughter who typed tirelessly my manuscripts apart from keeping control on their own directions. My wife, Dr. Diana Romero de Raitzin, has practised a lot of very interesting rectifications using my multiple keys, among them those of the birth charts of S.S. the Dalai Lama and Dr. Martin Luther King (Jr.), both of them about to be printed in the magazine “Ciencias Milenarias”.**

**Our success has been so overwhelming and the results so solid and positive that the moment has come to publish them in detail together with some clarifications and commentaries on my experience for a more efficient use of the symbolic directions. My only wish is always the same: to help in the formation of a serious and well prepared school of Astrology in Argentina, based on experimental facts. Only in this way Astrology, which is today only an art or a pre science, will be considered a science. We can find in it real and solid facts but unfortunately they are often ignored.**

**It would be important to understand that the only possibility of progress is the experimental method, comparing the consequences of theory with the observed facts. This short article does not reflex at all the hard work we have been exercising for six years to arrive to this state of affairs.**

**My speculation started from the well known fact that the keys of one grade = one year (Ptolemy) and Dwadashamsa of two grades thirty minutes = one year, are proved to be very effective in the sense above mentioned. The logical question was if there were other reliable keys that would allow me to predict a greater percentage of facts in the life of the persons.**

**The idea came because the number of predictable facts through the well known efficient keys was small even when adding to symbolic directions the mundane primary directions (under the Ptolemy keys) and under the pole of the significator (under the Naibod key).**

**The primary directions in both cases cause the inconvenience of having a wider orb than the symbolic ones (that is to say, are less precise as regards coincidence in time with the date of the facts). That is why I believe it to be very often a great mistake to rectify birth charts with the primary directions, mainly because the calculations are more complicated and harder than the symbolic ones.**

**Let us remember that rectifying birth charts is a very common and essential part of the job of an astrologer who believes himself to be honest and competent. A radix would only be considered rectified when afterwards we can observe very clearly on several opportunities that the planet-cusp directions coincide with vital events when the date falls due and not in any other way. If an astrologer does not know how to calculate directions and rectifications he should complete his studies because otherwise his work would lack seriousness and depth.**

**That is why it is not correct to consider a chart as rectified if we have not tested it on numerous controls with planet-cusp directions that would show that such rectification has been well done. We have to remember that a correct rectification can only be achieved through these planet-cusp directions. The planet-planet directions are not useful in these cases because they do not allow us to detect subtle variations in their due date when the time of birth changes.**

**We still have the problem to determine if there are other efficient keys, but we have not been able to find them yet. There are enough reasons to believe that in the primary directions every individual has his own personal keys but it is not easy to determine these keys in each case. Our research in this other area is in full development.**

**As regards secondary directions we can say that their value is not really important in the way they are used today, being very small the percentage of coincidences with the real facts. This is not only a personal opinion but a solid experimental result corroborated by Gustav Schwickert and Jacques Reverchon. Perhaps, for these directions, we should go back to the calculating technique which used to be applied by Guido Bonatis based in the quotient meridian/semiarc distance (and not in the half hour) which made this astrologer famous in his time because of his very precise predictions regarding the dates of the events. But because people wanted to simplify the calculations, they have lost efficacy…**

**There are still further disillusions and very serious ones. Trying to predict more than they could astrologers have been incorporating a great number of sensitive points with very little value for the interpretation or for the directions and they have turned out to be completely useless and inefficient like asteroids, Chiron, Transpluto, corrected Lilith, Arabic points (including the part of fortune) fictitious planets from the Uranian Astrology of De Witte, Johndros’ points (Ecuatorial Ascendant and vertex), etc.**

**Very few times we can see efficacy in the directions with the nodes (medium) and the true nodes are simply useless.**

**Neither have I got any results with the directions according to the solar arc whether direct or converse except in the obvious and trivial case in which the directional arc coincides with that of the classical symbolic one of a grade = a year. On the contrary many times important things are disregarded like the aspects to the cusps and the determinations by antiscia. Trends are more powerful than the common sense of the experimental method…**

**I am not expressing an opinion but what I have long experimented with the passing of time and I feel satisfied that Alexander Marr expressed himself in a similar way (and perhaps more strongly) in an interview printed by the Spanish magazine “Mercurio-3”. Let us not forget that pseudo explanations are characteristic of pseudo sciences…**

**In such article Marr mentions something we are tired of repeating: “Those who work without rectifying the birth charts are joking with Astrology”…**

**Of course none of my affirmations should be believed in blind faith, on the contrary I encourage everybody to work on their own controls. And I say this because I am absolutely convinced that dogmatism in any way can block the human being and delay his progress in all aspects of life.**

**By the way, I will mention here a new and gigantic mistake which is very much in fashion today. There is a new group of “antiastrologers” who believe Astrology should not predict but only describe the general features of character and tendencies in an individual. Obviously this idea is not only equivalent to ignoring the nature of Astrology but also to throwing overboard all the accumulated findings along the centuries. My modest opinion is that those people are not using predictions because they are not prepared for that: their affirmations do not go further than “the grapes are green”...**

**Going back to our main issue, our first experiments to find efficient keys in symbolic directions starting by the well known ones were a complete failure. My method in research was of the type of an idealistic naive: if there are two efficient keys, why not more? In this way I tried without success among others, the arithmetic and geometric medias and the golden section: when the dates fell due there were no concordant events. Please note that I am not saying that general affirmation that the directions “were not producing any effects”. Directions do not produce anything and Astrology includes nothing of the kind: planets are only indicating vital moments. Ignorant people who keep talking about energy, vibrations and waves (never spotted or measured by anybody) will only discredit our discipline and show the incredible lack of knowledge and misunderstanding of the principles of Astrology on behalf of the so called astrologers.**

**We have heard so many false notions that many astrologers have ended up believing firmly in them… But believing in, never testing and knowing… and this happens in all areas of life.**

**In that moment a simple cinematic analogy helped us to better understand the problem and solve it. Let us assume that symbolic directions are generated by a material point that runs along the ecliptic with constant angular speed equal to Ptolemy’s key, one grade/one year; and along a second material point that runs in time along the ecliptic with constant angular speed and equal to the dwadashamsa key, two grades thirty minutes/one year (called dwada because it is equal to the twelfth part of a sign). Let us suppose now a third material point that runs along the ecliptics with such angular speed that goes round the ecliptics twice in the period of time taken by the first movement together with the time taken by the second movement (each one only once). Calling angular speed of the first movement w1 and w2 to that of the second we will have, in simple reasoning, that if we call angular speed of the third movement w, this will be given by**

**1/w = (1/w1 + 1/w2)/2**

**that is**

**w = 2/(1/w1 + 1/w2) = 2w1w2/(w1 + w2)**

**The amount w is called the harmonic media from w1 and w2 (we prefer to spell harmonic with h to avoid confusions with other concepts). This is a result of the following: the time taken by the first material point is T1 = 360 grades/w1 (grades/year). The time taken by the second material point is T2 = 360/w2 and in due course the third material point will take T = 360/w where this last speed w is the unknown factor.**

**As T = (T1+T2)/2, substituting we have**

**360/w = (360/w1 + 360/w2)/2 = 360(1/w1 + 1/w2)/2**

**(Note that T is the average or arithmetic media of T1 and T2)**

**WE CAN SEE THAT THE FIRST “SECRET” IN MY DISCOVERY CONSISTS IN FINDING THE AVERAGE OF THE SPINNING TIMES T1 AND T2 (AND NOT THE ANGULAR SPEED).**

**Of course, this is like Columbus egg, it is very simple once you have done it.**

**Now, simplifying the factor 360 in both members you get the preceding formula.**

**For the case of the two efficient keys long known we have,**

**w1 = 360/360 grades/year = 1grade/year = 10/10**

**w2 = 360/144 grades/year = 2,5 grades/year = 10/4**

**being it easier (as we will see later) to use the same numerator 10 to work with them.**

**Then we have**

**w = 2/(1/w1 + 1/w2) = 2/(10/10 + 4/10)**

**= 20/(10 + 4) = 20/14 = 10/7 grades/year**

**= 1° 25’ 43” /year.**

**This value is the harmonic media of w1 = 1°/year and of w2 = 2° 30’ /year.**

**In the experiences made with it in real cases it proved to be a key fully efficient and this meant the opening of a big door.**

**The consequence is simple and interesting, when the angular speed is constant w the movement will be two spins round the circuit in the length of time 2T = T1 + T2.**

**If we want to discuss more deeply the idea of harmonic media and numeric examples we can consult Moroney’s book “Hechos y Estadisticas” (Eudeba)**

**Writing down the three efficient keys we now have numerator equal 10 in the three cases:**

**10/4 10/7 10/10**

**We can see that the denominators are found in arithmetical progression 4, 7, 10. This led me to a more ambitious hypothesis which is the following:**

**Shall we get other efficient keys if we continue the arithmetical progression?**

**The series to be considered is here,**

**10/4, 10/7, 10/10, 10/13, 10/16, 10/19, 10/22,…**

**Our careful experiments with clients who had had their radixes accurately rectified led us to the categorical conclusion that all these keys are efficient as far as our observations arrived (key in the fortieth order).**

**Then I faced new questions which I will shortly mention in the following lines. I called this first succession of keys Spicasc thinking that only with these new keys the problem would be solved completely, which of course was not as you will see in the next paragraph.**

**The first doubt was if such keys would give such directions so that anything would be easy to explain. IT IS NOT AT ALL LIKE THIS and it is necessary to practically experiment with these keys before we can say any opinion in respect to them. The number of directions rapidly diminishes with slight fluctuations when we add the order number of the key, and there are facts which are left without a congruent explicatory direction when they are limited to the use of such keys, even if we add the symbolic directions to the primary ones of both types already mentioned. To confirm what I am saying I invite the readers to make the calculations and controls, which is the only way to really find out what we are talking about.**

**But, what is absolutely surprising, is that with the new keys, the congruency or concordance of directions and facts turned out to be absolutely complete following the Theory of Determinations while we could observe this in all the cases.**

**But there were more surprises: any key in the succession Spicasc is harmonic media between the former and the following in the succession as you will be able to test with a simple addition and also, considering five keys in the succession, the central one is harmonic media of the following four. This can easily be shown but I will not do it here because I do not want to be very long.**

**I considered these facts since the moment I spotted them as an expression of universal and complete harmony, as René Guénon use to say.**

**The Supreme Mind is showing us His Geometry through experience, the Sublime Architect of the Universe who is behind life in the world with his perfect and fair order.**

**But my surprise grew bigger when in the Spicasc succession I bumped into some keys which had already been recommended by other authors, that where in turn rendered like special cases within the general law.**

**I think it is worth mentioning which ones. The key XIII from Table I is**

**10/40 = 15 minutes/year**

**being this “the key of death” from Carter.**

**Addey introduced “the golden section” as a key of one grade very near the key V from Table I, that is 10/16. But something that brought me another insight was the following: Frankland suggested as a key 4/7 which is the harmonic media of our keys V and VI. This took me to the hypothesis that harmonic medias of two successive keys from the Spicasc succession can also be considered efficient keys. This was a new succession that I called Numeha which can easily be obtained starting from the Spicasc keys calculating harmonic medias from each pair of successive keys in it.**

**The Numeha succession resulted into**

**20/5, 20/11, 20/17, 20/23, 20/29, 20/35, …**

**We can see that if we equal the numerators in 20 the denominators will also grow in arithmetic progression of ratio 6, while in the Spicasc the ratio in the progression is 3. This is only an apparent difference as we will later see.**

**This new series Numeha was immediately put into practice to check concordance of directions and vital facts. And again, to my surprise, the keys resulted as efficient as the Spicasc ones.**

**Naturally, at this point, we will comment on some topics related to them. In the first place, these tests were only possible in a wide range thanks to the systematic use of the computers. From all the programmes available at present, the one specially indicated for this work was Blue Star Plus of Matrix. The best programme and the most useful to rectify is at present Solar Fire from Astrolabe, beginning from its 4.07 version.**

**Of course it will be very important to use the cusps of the intermediate houses in the programme Blue Star as input-points since the directions from the planets to the cusps are the only ones that will allow us a very precise rectification. It is absolutely necessary to highlight again that the only valid cusps in symbolic directions are those of Placidus. This last idea is a solid and experiential fact which I discovered along the many years of practice and controls and not because of a simple question of personal and subjective preferences.**

**Nonetheless I should mention here that the indisputable validity of Placidus domification method has been established for latitudes of both hemispheres of the Earth from the Equator to the Polar Circle. Beyond the Polar Circle we still have to experiment with tests on natives of those areas but they are not easy to be found.**

**The topocentric cusps are only a proximity to those of Placidus, a proximity which is more and more deficient when the latitude rises. As soon as the slightest differences appear between them, the control of the due dates of the directions and the dates of the vital facts definitely favour Placidus. There is an old Chinese proverb that says “a fact is more valid than a thousand subtleties”…**

**The use of the auto-jobs of the Blue Star programme is specially easy and comfortable when we have to deal with multiple keys and it turns out to be a real must due to the incredible volume of the calculations. Through the auto-jobs the work gets very comfortably automated.**

**After the overwhelming success of the Numeha keys we faced a new question: what would happen if I got a new succession starting from these ones and following the same procedure? Then I started to get the harmonic media of every pair of successive terms of the Numeha and … I came back to the Spicasc succession. I would state it like this, the successions Spicasc and Numeha are harmonic combinations between them because each one of them is obtained calculating harmonic medias of the successive terms of the other one.**

**This possibility was then closed and it was necessary to think in something else. But the solution to keep making progress soon came and faced us with new questions where we have no answers yet. If we write the Spicasc succession with a numerator equal 20 (that is to say if we multiply numerator and denominator by two) we will clearly have:**

**20/8, 20/14, 20/20, 20/26, 20/32, 20/38, …**

**With this simple trick we have come to the same numerators as those for the Numeha series and the denominators will be now in arithmetic progression of ratio 6.**

**If we now put together both groups of terms, those of the Spicasc succession changed like this and those of the Numeha succession, we will get a new group that once in order looks like this,**

**20/8, 20/11, 20/14, 20/17, 20/20, 20/23, …**

**We can now see that the denominators are now organized into an arithmetic progression of ratio 3.**

**We can now calculate harmonic medias of every pair of successive terms of this new succession. We can get it very easily**

**40/7, 40/13, 40/19, 40/25, 40/31, 40/37, …**

**We can easily see that, with a constant numerator equal 40, the denominators are again in arithmetic progression of ratio 3. I called this new succession Siriumc (do not look for mysterious explanations, I simply have Sirium in the MC and Spica in the AC of my birth chart) and I started immediately experimental research concerning the concordance of directions and vital events of many persons. The results were, at the beginning, quite enigmatic. In some symbolic directions of this type I could not always see concordant events when the time was due while other directions with the keys of this succession Siriumc were not only efficient but also corresponded with certain vital events of unexpected importance which were produced with enormous precision of date like the corresponding ones of the Spicasc and Numeha keys. As time passed I came to the conclusion that the keys of the Siriumc succession are extremely efficient and should be used if we want to get a complete directional system.**

**Later the accountant Ortolani continued with this research obtaining new series of very interesting keys but the corresponding directions only align with events of minor importance. The process of generating a series of keys would be then exhausted except in one case. We are speaking of the key of 11°/ a year obtained by Daniel Lanfranco which has produced interesting results and is still being studied. What is interesting about the Lanfranco key is that it is not one of my multiple keys nor is it arrived at through them in the habitual way.**

**I would like to mention something else regarding the orb of the Spicasc, Numeha and Siriumc symbolic directions. When the charts are properly rectified the events are presented in due date with an orb of 2 days at the most in 98% of the individual cases and even the same day of the partile in many opportunities.**

**But there is a remanence of 2% that corresponds to “persons with a long orb” in whom the orb appears inexplicably longer and where the congruent events can be delayed or anticipated up to 5 days when the directions are due. I cannot clear this up because it is an empirical fact. Obviously in normal cases the orb of the symbolic directions is considerably less than the usual one of the primary directions.**

**Because of all this, it is essential to rectify the charts before calculating the directions if we do not want to incur in nonsense. Naturally, if we want to rectify a chart, it is essential to experiment at the base with the first keys of the three successions, something that in my experience is the most advisable. But it will not be enough to explore, it will be necessary to go deep into the interpretative foundations of the directions. And this is precisely what we get in the Theory of Determinations by Morin, which is badly or little known by most of the students, practitioners, teachers and supporters.**

**Of course these techniques we are dealing with are not for those hurried or untidy astrologers who calculate charts without the exact time… These people will not get any benefits of these new directional keys. And it is very sad to see in our country at the most half a dozen astrologers capable of rectifying a birth chart with precision and accuracy.**

**Everything else, as we have seen, is nothing but wishful thinking or cheating to naive people.**

**Only a small fraction of the symbolic directions as well as the primary directions of any key are not made real in personal cases. Morin used to speak about this in his time when solar returns and transits which were not congruent could neutralise directions in a way that nobody would get surprised.**

**There is another practical limitation and this is the present condition of Astronomy of position and the astrological software. If we knew exactly, (with cents of a second in the arc for every instant in time) the position of the planets of the solar system, everything would be better and we would be able to go much further. But this is not the case now and with the software at hand we can only get as near as key 40 for any of the three successions Spicasc, Numeha and Siriumc.**

**Through this experience we can arrive at a very interesting indirect proof of the validity of Astrology which will be worth speaking about: if we rectify a birth chart using only one, two or three particular keys of any of these successions, it will stay rectified for all of the keys of the three types and also for the primary directions in both types, as you will confirm with the coming results. It is an experimental proof that the time of birth of an individual is a unique and precise instant, making it a precious and fundamental step in showing the validity of the foundations of our discipline in a definite and solid way. It will be easy to imagine how foolish it would be if we had to use a different time of birth for every key and type of direction…**

**It is vital in this moment to make a very important observation. With these findings astrologers will have at hand a great variety of efficient directions as ever before. My multiple keys have at least ten times more of predictive power than all the primary directions of any kind altogether. But this has a handicap that will be easy to see. If all these keys and directions are efficient (and they are) it implies that the destiny of all beings is planned since the moment of his birth with an enormous degree of precision.**

**We have seen through these directions that determinism is more important than we used to suspect. The consequence is that little is left to chance in our lives. Of course this brings back the typical fight between determinism and free will, but we will speak about that in future writings. Because of this, more than one will say that I am a fatalistic in my position but I am just the opposite.**

**Count Leon Tolstoi, in a moment of deep sadness, held a point of view we are not able to share: “The only absolute knowledge that we are allowed to reach is that human life has no meaning”. The multiple keys give us the most certain testimony against these sombre and cynical thoughts because we will have to face the evidence that every human life has been planned in minute detail by the Cosmic Mind. What would be the purpose of such precision if it were not by a transcendental reason inherent and inseparable of the human condition?**

**All this issue of free will against determinism is not so simple and will demand fine distinctions. Actually, destiny is like a stratified field of analogies that may be lived in many different levels at every instant depending on the depth of the spiritual life and the power of will of every human being. This will lead us directly and inevitably into Esoteric Astrology. Those who are interested can read my article “The sixth dialogue”, published in ATMA-JNANA with the pen name of SARASTRO.**

**But one thing is real and true: there are no plans without a planner and Astrology faces us with the sublime reality of God’s existence.**

**There is another consideration of a speculative and philosophical kind that we will mention now, and which is not very pleasing perhaps. We will soon realize that as each of the three successions have infinite keys we will never get to know all our directions and surprise will always be on the way.**

**Socrates and his “ignorabimus” in the words of the philosopher Paul du Bois-Reymond comes to our mind….**

**TABLES FOR SYMBOLIC MULTIPLE KEYS**

**TABLE I**

**KEYS FOR THE SPICASC SUCCESSION**

**0 10/1 = 10 GR 00 MIN 00 SEC/YEAR**

**I 10/4 = 02 GR 30 MIN 00 SEC/YEAR (dwadashamsa)**

**II 10/7 = 01 GR 25 MIN 43 SEC/YEAR**

**III 10/10 = 1 GR 00 MIN 00 SEC/YEAR (Ptolemy)**

**IV 10/13 = 0 GR 46 MIN 09 SEC/YEAR**

**V 10/16 = 0 GR 37 MIN 30 SEC/YEAR**

**VI 10/19 = 0 GR 31 MIN 35 SEC/YEAR**

**VII 10/22 = 0 GR 27 MIN 16 SEC/YEAR**

**VIII 10/25 = 0 GR 24 MIN 00 SEC/YEAR**

**IX 10/28 = 0 GR 21 MIN 26 SEC/YEAR**

**X 10/31 = 0 GR 19 MIN 21 SEC/YEAR**

**XI 10/34 = 0 GR 17 MIN 39 SEC/YEAR**

**XII 10/37 = 0 GR 16 MIN 13 SEC/YEAR**

**XIII 10/40 = 0 GR 15 MIN 00 SEC/YEAR (Carter)**

**XIV 10/43 = 0 GR 13 MIN 57 SEC/YEAR**

**XV 10/46 = 0 GR 13 MIN 03 SEC/YEAR**

**XVI 10/49 = 0 GR 12 MIN 15 SEC/YEAR**

**XVII 10/52 = 0 GR 11 MIN 32 SEC/YEAR**

**XVIII 10/55 = 0 GR 10 MIN 55 SEC/YEAR**

**XIX 10/58 = 0 GR 10 MIN 21 SEC/YEAR**

**XX 10/61 = 0 GR 09 MIN 50 SEC/YEAR**

**.......................**

**NB, Code 0 is included only as a reference, because even though it is efficient, it is not advisable for the beginners. And this is all due to the idea that the use of a proliferation of directions is said to “explain” any event or mix up the user. The same can be said about the first key of the Numeha succession as well as the first key of the Siriumc succession.**

**TABLE II**

**KEYS FOR THE NUMEHA SUCCESSION**

**I 20/5 = 4 GR 00 MIN 00 SEC/YEAR**

**II 20/11 = 1 GR 49 MIN 05 SEC/YEAR**

**III 20/17 = 1 GR 10 MIN 35 SEC/YEAR**

**IV 20/23 = 0 GR 52 MIN 10 SEC/YEAR**

**V 20/29 = 0 GR 41 MIN 23 SEC/YEAR**

**VI 20/35 = 0 GR 34 MIN 17 SEC/YEAR (*)**

**VII 20/41 = 0 GR 29 MIN 16 SEC/YEAR**

**VIII 20/47 = 0 GR 25 MIN 32 SEC/YEAR**

**IX 20/53 = 0 GR 22 MIN 38 SEC/YEAR**

**X 20/59 = 0 GR 20 MIN 20 SEC/YEAR**

**XI 20/65 = 0 GR 18 MIN 28 SEC/YEAR**

**XII 20/71 = 0 GR 16 MIN 54 SEC/YEAR**

**XIII 20/77 = 0 GR 15 MIN 35 SEC/YEAR**

**XIV 20/83 = 0 GR 14 MIN 27 SEC/YEAR**

**XV 20/89 = 0 GR 13 MIN 29 SEC/YEAR**

**XVI 20/95 = 0 GR 12 MIN 38 SEC/YEAR (**)**

**XVII 20/101 = 0 GR 11 MIN 53 SEC/YEAR**

**XVIII 20/107 = 0 GR 11 MIN 13 SEC/YEAR**

**XIX 20/113 = 0 GR 10 MIN 37 SEC/YEAR**

**XX 20/119 = 0 GR 10 MIN 05 SEC/YEAR**

**.......................**

**(*) Frankland-Sepharial: naronic key. Read Carter in “Symbolic Directions in Modern Astrology”. This key is harmonic media between those of 10/16 and those of 10/19 from the Spicasc succession.**

**(**) subdwadashamsa key 12/144 = 30/12 x 12 = 0° 12’ 30’’ is very near this one.**

**It is used in Hindu Astrology.**

**TABLE III**

**KEYS FOR THE SIRIUMC SUCCESSION**

**I 40/7 = 5 GR 42 MIN 51 SEC/YEAR**

**II 40/13 = 3 GR 04 MIN 37 SEC/YEAR**

**III 40/19 = 2 GR 06 MIN 19 SEC/YEAR**

**IV 40/25 = 1 GR 36 MIN 00 SEC/YEAR**

**V 40/31 = 1 GR 17 MIN 25 SEC/YEAR**

**VI 40/37 = 1 GR 04 MIN 52 SEC/YEAR**

**VII 40/43 = 0 GR 55 MIN 49 SEC/YEAR**

**VIII 40/49 = 0 GR 48 MIN 59 SEC/YEAR**

**IX 40/55 = 0 GR 43 MIN 38 SEC/YEAR**

**X 40/61 = 0 GR 39 MIN 21 SEC/YEAR**

**XI 40/67 = 0 GR 35 MIN 49 SEC/YEAR**

**XII 40/73 = 0 GR 32 MIN 53 SEC/YEAR**

**XIII 40/79 = 0 GR 30 MIN 23 SEC/YEAR**

**XIV 40/85 = 0 GR 28 MIN 14 SEC/YEAR**

**XV 40/91 = 0 GR 26 MIN 22 SEC/YEAR**

**XVI 40/97 = 0 GR 24 MIN 45 SEC/YEAR**

**XVII 40/103 = 0 GR 23 MIN 18 SEC/YEAR**

**XVIII 40/109 = 0 GR 22 MIN 01 SEC/YEAR**

**XIX 40/115 = 0 GR 20 MIN 52 SEC/YEAR**

**XX 40/121 = 0 GR 19 MIN 50 SEC/YEAR**