A CORRECTION ON THE SOLAR ARC KEY
IN PRIMARY DIRECTIONS
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by Wim van Dam
Through the ages, one of the main problems in astrology has been the right measurement of time in Primary Directions. Even if you don't use primary planets, you will probably use primary cusps. Then you progress the MC with about one degree a year and calculate the other cusps for this MC according to the local latitude. The aspects of these progressed - in fact primary - cusps to radical planets give highly important indications.
I will not dwell on the different measurements of time that have been proposed through the ages (for a short survey see Alan Leo, The Progressed Horoscope, p. 328 - 335), but I want to conclude that most authorities agree that the best results for progressing a chart are reached by adding the progression of the secondary sun to the MC.
The rationale behind this key is usually given as follows:
If in this case too we keep the distance constant in degrees between MC and sun for each consecutive secondary/progressed day after birth, then we get a surprise: the distance between the ascendant and the sun will increase each day. In some cases, the sun will retreat ever further into the progressed twelfth house. In other cases it will progress into the first house. And the other way round: if we calculate the progressed angles from the moment when, on each secondary day, sun and ascendant are conjunct, the progression of the MC, the key of time, will increasingly deviate from what we saw before.
In my point of view, if one is born at sunrise, with the sun conjunct to the ascendant, every astrological day after birth will be full but not when the distance sun-MC is the same as at birth, but when the secondary sun will be conjunct to the ascendant of that moment. For tropical areas this difference will be minimal, but even at moderate local latitudes (US, Southern Canada, Europe) the progressed MC will have progressed by quite a different measurement, which results into another, a different Key of Time. This difference may climb to several hours of time, equals tens of degrees on the MC, in the course of a lifetime, and I therefore maintain the view that this is not the correct measurement of time, although theoretically it is quite correct.
My good friend the late Swiss astrologer Erich Weil was rather fond of this key, he told me it is in use with many French astrologers and therefore he used to call it the French Method.
I have not been able to find out whether this key of time is the same one as "C.C. Massey's" method, described on p. 331 - 333 of Alan Leo o.c., for the simple reason that I do not understand this method. But it seems to be related.
For several years I was confronted with a nasty paradox: the usual key by far gives the best results but it is theoretically wrong, while the French method is theoretically sound but definitely gives wrong results. Often when I couldn't sleep, one could hear my teeth grinding.
However, what most people don't know is that a paradox is not an unsolvable contradiction but a seeming one. And one evening, while walking the dogs and as always pondering on this problem, I suddenly got the solution.
It will be helpful if we realize that there is yet another trap in the philosophy behind the usual method: as we saw, one day after birth the sun and the MC will still stand conjunct. This suggests that the MC and the sun travel together. In reality however, the Sun has progressed by about one degree in one day, while the MC will have made a complete round of 360 degrees + 1! In other words, it is not true that they progress together. They just meet again once each progressed day. The same happens when in the radix the Sun is exactly at the ascendant, or at any other cusp, or at any other position within the houses.
Therefore, what we really measure in the usual method is what progress the sun, independently and on its own, makes in the time it takes for that same sun and the MC together to take again their radical mutual position and then we add the arc the sun has made in that time to the radical MC. This formula provides us with the solution for the paradox: in the French method we should, in the same way, for the moment when the progressed sun is conjunct to the progressed ascendant again, not look at what position the actual MC is, but what progress the sun in that time has made from its own radical position and then add that arc to the radical MC. This way, the possible difference to the usual method in passed time since birth will still be the same couple of hours. But we do not look at the position of the MC at this moment (may be some tens of degrees off, giving a deviation of as many years) but at the progression, in that time, of the secondary sun, that in a couple of hours may differ by at most say 10 minutes of arc, equals only 2 progressed months!
Since deviations of time up to half a year are not uncommon in primary directions, it will be clear that here we have quite an acceptable key since it is theoretically correct and its results are roughly the same as with the usual key.
We now know how to calculate a progressed horoscope for the anniversary of a radix where the sun is exactly conjunct to the MC or to the Ascendant. Our formula is:
Quite unexpectedly and all of a sudden we see here one more practical application of the concept of mundane longitude as I exposed it in my article Mundane Longitudes. In this theory, we suppose that the arc of 360 degrees that the sun traverses through the twelve Signs of the zodiac in one year is equal (analogous) to its virtual movement around the earth, once more 360 degrees, in one day through the twelve Houses. The passage of the sun through one house (say the fifth one) somehow equals the passage of the sun through the thirty degrees of the fifth sign, Leo etcetera. We also applicate this principle to portions of houses: a planet halfway in the fifth house has got a mundane position of 15 Leo.
This gives us a most valuable tool to further refine our solar key, for it means the sun's (mundane) movement through one house, small or large, is equal to its zodiacal movement through one sign. Which means that, for example, its movement through one thirtieth of a house, be this large or small, equals its movement (transit) through one degree of the zodiac. This principle can be applied to almost any housing system but as usual I have found it fruitful with Placidus.
Suppose we have the radical sun exactly at the MC, the tenth house, and its radical longitude is at exactly 0 Leo, and we want to calculate the data for a given date when the actual transit sun is at 0 Cancer, which is its radical position minus one sign. Then we must calculate at what GMT on the secondary day the actual sun was at the cusp of the (tenth minus one = ) ninth house and for that moment calculate its zodiacal longitude. Minus the longitude of the radical sun is the desired arc. Because of the changes in the sun's position in the houses for the same GMT on consecutive secondary days, the relationships between the secondary GMT and the day of the year will vary from year to year.
In order to find the moment on a secondary day, corresponding to a given day of life then, we should find the moment in GMT when the sun's actual mundane longitude, its position in the houses, deviates from its radical mundane longitude by as many degrees as the transit zodiacal sun on the date of life is distant from the radical one. For this moment in GMT calculate the sun's actual secondary zodiacal longitude. Deduct from this the sun's radical longitude, add this to the radical MC and you have got the progressed MC for that date, hello Earth, are you still there? Defined step by step we should proceed as follows:
Together with the accurate definition of steps 1 through 7 (you don't think I stated them off the cuff, do you?), it took me about half a year of my spare time to incorporate this into my computer program, "Morinus", inclusive the reversed task: given (calculated) the secondary date and the GMT when a direction is full, to what actual date will that GMT correspond? By now, you should be able to define the necessary steps yourself.
Once having programmed it, I did some testing on this key and indeed it usually seems to give better results - if and when there are differences between the two keys, for as stated above the difference usually is no more than a few months so it is not essential in daily practice. But of course, after all these years of grinding one's teeth it is most satisfying to use a key that is both theoretically sound and gives good results- at last.
Oh. well.. I have to admit there is one problem that I did not mention above. It is quite possible that, since primary directions are technically full within six to ten hours after birth, we should only reckon with the sun's progression on the day of birth. Meaning, for each year of life the relationship between a certain GMT and a day in the year would be the same. The difference with the progressed solar arc can be up to some degrees at higher age. I did some initial research on this but the results were rather disappointing (To be honest, I had expected this would prove to be a better key but I got higher deviations in time than with the progressed solar arc). I hope to report on this later, after more research. For the moment my conclusion is that the progressed solar arc, corrected for the true astrological day as described above, gives the most accurate results in primary directions technique. This leads us to the important conclusion that primary and secondary directions, though at first sight not related at all, maintain some unknown and for me incomprehensible relationship.
Since the technique is based on a corrected definition of the secondary day, it may be applied to secondary directions as well (and to solar arc directions). Somehow, this application for secondaries, without the link with the key for primary directions, was described in Alan Leo, o.c., p. 334, 5, but only for whole years and without my steps 1 through 7. Especially for the secondary moon this method gives some interesting results. But here I have to add an important remark : not only should we correct the definition of a secondary day, we also should correct the secondary moon for parallax. (For the technicians: based on the radical RAMC, not on the actual one at the actual GMT on the progressed day. Astronomically illogical, astrologically quite acceptable.)
I will give here an example of the position of the secondary moon in my horoscope for the date of my B.A. , September 30th 1971. The secondary moon, radical ruler of nine, at that date was in a sextile to the radical sun, ruler of ten and positioned in nine, at 2 Leo 58. Quite applicable, but the moon's position was not at 2 Libra 58, it was at 1 Libra 38, off by one degree and twenty minutes of arc, equals eighty minutes equals some 40 days off. If we apply only the corrected definition of the secondary day we get 1 Libra 58 and if we correct just the moon's parallax we get 2 Libra 23. If we apply both corrections, we get a secondary moon at 2 Libra 48 - off by only 10 minutes of arc equals 5 days. With the solar arc of the day of birth as a constant measure results vary from 1.40 to 2.25 Libra, a meagre result.
Q.E.D. Step by step we refine astrology. But what a long way we still have before us.
AUTHOR: Wim van Dam