Graham,

As far as I can see, your steps A-J seem to be exactly what I am suggesting. I am glad we understand each other at last!

If we include secondary motion, which is not entirely uniform, using whole diurnal/nocturnal arcs rather than semi-arcs could cause a slight difference. But this is not really to do with different house systems. The proportional semi-arc method of directions is the same irrespective of which system of house division one employs. (The Placidus house system is based on this method of direction, not the other way around. Before Placidus, astrologers directed by the same method while using house systems such as Alcabitius or Porphyry.)

Martin
Thanks for clarification. This remark of yours is interesting:

The Placidus house system is based on this method of direction, not the other way around. Before Placidus, astrologers directed by the same method while using house systems such as Alcabitius or Porphyry.

In another thread in this forum, "planetary hours calculator", Andrew Bevan argues that since planetary hours are Placidean, they should only be used if you use Placidus houses. Otherwise he feels that the houses you use (e.g. Regio) should be bisected to get your own "house-compatible" "hours". (Hope I've summarised fairly).

I thought when reading this that it was not right, and now I understand why. Planetary hours are what Placidus houses are based on, not the other way around. Their logic is very much the same as the logic behind primaries - the hours are based on the primary day and night temporal arcs of the sun.

As for including secondary motion, I've worked out that we can easily make a rough "rule-of-thumb" adjustment for the Moon's directions (the ones which vary most, of course) :
Use your favourite program to calculate primary-motion-only directions (Solar Fire or whatever: I like to use one with parallax) and adjust the hit dates as follows:
- if Moon is promissor, add 1 yr per 27 yrs, 6 months per 14 yrs, 3 months per 7 years;
- if Moon is significator, subtract as above.

Graham

Graham,

Yes -- Ptolemaic directions and planetary hours are both based on diurnal and nocturnal (semi-) arcs, and Placidus (like some others before him) took this as a basis for house division. Regiomontanus, reading Ptolemy differently (and wrongly), invented a new model of directions to suit the 'rational method' of house division; but as far as I know, he left planetary hours alone.

As for including secondary motion, I've worked out that we can easily make a rough "rule-of-thumb" adjustment for the Moon's directions (the ones which vary most, of course) :

That's very useful. Thanks!

Ptolemaic directions and planetary hours are both based on diurnal and nocturnal (semi-) arcs, and Placidus (like some others before him) took this as a basis for house division. Regiomontanus, reading Ptolemy differently (and wrongly), invented a new model of directions to suit the 'rational method' of house division; but as far as I know, he left planetary hours alone.

This is a fascinating discussion.

However, I'm confused, because what you've written above appears to contradict what's been written elsewhere by Mike Wackford or Rudiger Plantiko, who seem to think that the Placidus method of house division reflects Ptolemy's ideas about domification.

From your previous comments, I take it you prefer the methods of Porphyry or Alchabitius? Is this correct?

Hello Andrew,

However, I'm confused, because what you've written above appears to contradict what's been written elsewhere by Mike Wackford or Rudiger Plantiko, who seem to think that the Placidus method of house division reflects Ptolemy's ideas about domification.

From your previous comments, I take it you prefer the methods of Porphyry or Alchabitius? Is this correct?

Personally I tend to favour Alcabitius on purely empirical grounds, but from the textual evidence there seems little doubt that Ptolemy had equal houses in mind. This (if I may quote myself, from another thread) is how Ptolemy defines the suitable places (houses) for the apheta/hyleg in Tetrabiblos III.10 (Robbins's translation, slightly edited to make it more literal):

'the twelfth part [Ptolemy's usual synonym for 'zodiacal sign'] surrounding the ascendant, from five degrees above the actual horizon up to the twenty-five degrees that remain, which are rising in succession to the horizon; the part sextile dexter to these 30 degrees, called that of the Good Daemon; the part in square, the mid-heaven above the earth; the part in trine, called that of the God [?]'

There is certainly no quadrant system, Placidean or otherwise, described in the Tetrabiblos. I don't have a problem with that, however, as I am not a Ptolemy-worshipper. But Placidus was determined to read all his inventions (houses, secondary directions, mundane aspects, etc) into Ptolemy's text. That's what theological training does to you!