1.
INTRODUCTION
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.
2. RATIONALE
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.
For example: calculate the position (longitude) of
the secondary sun for the current time and deduct from this the longitude
of the radical sun. This results in an arc that should be added to
the longitude of the radical MC and this gives the progressed (primary)
MC for that time, from which the other cusps can be calculated for
the local latitude of the birthplace.
I agree that of all keys published in literature the above formula
is by far the most reliable one, but in this article I want to publish
a correction on this formula.
The rationale behind this key is
usually given as follows:
Suppose the radical sun is exactly conjunct to the radical MC.
Then, when we want to calculate a progressed horoscope, we have
to calculate a secondary progressed chart for such horoscope.
For example if we need the positions for the tenth anniversary
we calculate a horoscope for the tenth day of life, for the moment
when the sun and the MC are conjunct again, since at that moment
exactly ten astrological days will have elapsed since birth.
It will be clear that in this way the sun and the MC progress
with the same speed and we maintain this as the right key, also
in those cases (almost all) where the sun and the MC at birth
are not conjunct: we simply keep their radical distance as a
constant arc and from this constant arc we progress the MC. But
is this correct? What if the radical sun is conjunct to the ascendant?
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 sunMC 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.
Intermediate remark: without mathematical proof, I will give
here an interesting fact: usually, the secondary sun progresses
at another speed than the primary one. But if you use this French
key, the primary sun will proceed at the same speed as the secondary
one. Now back to our problem.
3. PARADOX
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.
4. FORMULA
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:
Calculate the progression of the
secondary sun for the moment when one astrological day has passed
(i.e. when the sun has returned
to its radical position), then add this arc to the radical MC.
What if the radical sun is at a
random position, somewhere in a house? Then too one astrological
day will have passed when
the
sun returns to ‘the same place in the houses as at
birth. But how should we define (and calculate) this “same place
in the houses”?
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:
1. Convert the sun’s radical
position in the houses to its mundane longitude
2. Subtract the sun’s radical regular zodiacal position
from the one on the actual date
3. Add this arc to the result of (1). This gives the sun’s
desired mundane position.
4. Calculate the GMT on the secondary day for the moment when the
actual sun will have a mundane longitude equal to the result of
(3)
5. For this GMT on this secondary date, calculate the sun’s
zodiacal position
6. Subtract from this the sun’s radical longitude and
7. Add this arc to the radical MC.
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.
5. IMPORTANT NOTE
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.
