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Progressing the Angles
     A comment on directing,
     by David McCann

The following article, first published in The Traditional Astrologer magazine (Issue 3, Winter 1993), was written to provide commentary to a serialised reproduction of H.S. Green's 1905 text Directions and Directing. It raises some salient points regarding the progression of angles which will be useful even to astrologers who lack access to Green's work.

H.S. Green's explanation of secondary directions has one serious flaw: he did not know how to direct the angles properly. In King Edward VII's horoscope this led to an error of 14° in the progressed ascendant for his 59th birthday. It's a common enough mistake: Alan Leo and Margaret Hone used the same method as Green; Ronald Davison and Chester Kemp used a different method, which gave an error of 3° in this case; Robert de Luce knew what he was doing, though not the quickest way of doing it.

The first point to make is that the 'progressed angles' are not progressed at all. Look at it this way. The Sun moves 1° per day, so the secondary progressed Sun moves by 1° per year. The Midheaven moves right around the zodiac every day, so the progressed midheaven will move 1° per day, not 1° per year. Such a fast moving point is naturally of little use and Placidus, who seems to have invented secondary directions, only progressed the planets. The 'progressed angles' are really directed angles, using primary directions.

To understand what we are doing, we must first think about days. When the earth has made a complete revolution on its axis, the meridian will have returned to the same point in the sky: this period is the sidereal day.

Imagine that it is noon, with the Sun on the Midheaven at 1° Aries. After one sidereal day has elapsed, the midheaven will be at 1° Aries again, but it will not yet be noon, for the Sun will have moved to 2° Aries. Thus the tropical day, between successive noons, is longer than the sidereal day by the time taken for the Midheaven to catch up with the Sun: about 4 minutes. The distance moved by the midheaven in a tropical day is therefore a complete circle plus the distance moved by the Sun, so in a period of one day it appears to have moved at the same rate as the Sun.

Ptolemy, in his primary directions, directed the MC by 1° of right ascension for each year. Renaissance astrologers, seeing how the midheaven and Sun appear to have the same daily motion, replaced Ptolemy's measure by the motion of the Sun. Naibod used its mean value; Maginus and Tycho Brahe the actual motion on the day of birth; Kepler the Sun's actual motion on successive days after birth, reckoning a day for a year. His idea undoubtedly inspired secondary directions. As Green suspected, the two systems are 'part of one whole' and the 'progressd horoscope' combines progressed planets with directed angles.

Green went wrong by mistaking mean time for true (or apparent) time. We have seen that a day consists of the time taken for the Earth to rotate on its own axis, plus the time taken for the Midheaven to catch up with the Sun. The former is fixed in length but the latter is not, for the speed of the Sun varies, as can be seen from the ephemeris.

The difference between two successive days may be only a matter of seconds, but this is still unacceptable for accurate clocks. Moreover, seconds soon add up to minutes. The true day is therefore replaced by a fictitious mean day, of average length. Mean time is the time measured within this mean day - convenient for time keeping but of no astrological significance. King Edward VII was born at a time of year when the discrepancy between mean and true time is at its greatest. On his birthday, true noon occurred at 11:44 am mean time and the given mean time of birth - 10:48 am - corresponded to a true time of 11:04 am. After 59 days, true noon was at 12:06 pm mean time, so that the true time of 11.04 am corresponded to a mean time of 11:10 am. Thus Green cast the progressed chart for a time that is 22 minutes early. The exact difference is 22mins 31secs, giving the correct midheaven as 3° 53' Capricorn and the Ascendant as 10°11' Aries.

Fortunately, it is not necessary to make conversions between mean and apparent time in order to calculate the progressed angles. After its conjunction with the Sun at noon, the MC moves on at a constant speed in right ascension. Thus time can be expressed as the distance from the Sun to the MC, measured in right ascension. To cast our progressed charts for the same time as the birth chart, we only have to keep the same distance in right ascension between the Sun and the MC.

The right ascension of the MC is simply the local sidereal time. For the King's nativity that was 14hrs 01min 43secs. Finding the right ascension of the Sun is equally simple. Since the Sun and MC have the same right ascension at noon, the right ascension of the Sun is the sidereal time at which its zodiacal position would be on the 10th cusp, which can be found from any table of houses. In this case it is 14hrs 57mins 44secs. The MC is therefore 56mins 01secs behind the Sun. In the progression for the 59th birthday, the right ascension of the Sun is 19hrs 12mins 57secs.

Thus the Local Sidereal Time must be 18hrs 16mins 56secs, giving a Midheaven of 3°53' Capricorn. This technique will still work if you prefer the modem method of using noon (or midnight) positions, rather than calculating a progressed chart for the time of birth.

The mistake made by Davison and some others involved keeping the Sun and the MC at a constant distance in longitude. This is incorrect because the Sun-MC arc is supposed to be measuring the time of the chart, and only right ascension does this. The falsity of the method is proved by the result of using it: a Midheaven of only 2°33' Capricorn.

There is another lesson here. Too often modem astrologers seem to think that the only criterion of truth is "it works for me". In this case, of three suggested methods, only one was found to be valid: by the simple expedient of taking the trouble to think out exactly what we are trying to do.

David McCann, who lives in London, is an expert on the history and philosophy of astrology. His articles have been published in many international journals of astrology and he was a regular contributor to the Traditional Astrologer magazine, where this article first appeared.

© David McCann
This short feature was first published in The Traditional Astrologer Magazine, issue 3, Winter 1993, pp.39-40.

More on Houses

See also: Regiomontanus Cusps from Placidus Tables

More articles by David McCann