Ages back I spent a fair amount of time studying primaries using Alan Leo's The Progressed Horoscope, and extracted the main chapters from the text, converting his log formulas to trig formulas. He explains, with examples, the basics of constructing a speculum as well as the variety of ways in which primary directions are calculated: zodiacal, mundane, direct, converse, with and without latitude, etc. He also covers the various opinions surrounding them.

If you haven't read him yet but are curious about primary directions, I've uploaded the extract as a PDF, Alan Leo Primary Directions, on archive.org.

That's very generous of you, Jane. All the same, I would caution against using Alan Leo as a source for understanding primary directions, especially in a traditional context. Leo himself didn't really understand them (as noted with some acerbity by contemporaries of his such as A.J. Pearce), delegated some of the more intricate aspects of them to associates like H.S. Green, and still managed to get things wrong, as when, in the present book, he gives two mutually incompatible 'rationales of converse directions' (failing to recognize that the two descriptions would lead to a difference of more than 20 years in the arc of direction). Holden put it well in his History of Horoscopic Astrology (p. 195):

Leo was also responsible for a major shift in astrological predictive techniques. Prior to his appearance on the scene, primary directions had been the favorite tool of the astrologer. But primaries are bothersome to calculate […] Leo’s solution to the problem was to produce what he called “the progressed horoscope.??? This is a mixed bag of secondary directions and zodiacal primaries […] His technique was soon adopted by most Western astrologers, since it was easier and quicker. Thereafter, the use of primary directions rapidly declined to a low level from which it has never recovered (despite the recent advent of computers to do the hard work).

Hi Martin,

Have to admit to having a soft spot for Leo, he was my only source on primary directions for 20 odd years. I have never read any of Pearce's (Zadkiel II's) work so can't really comment on anything he said or did.

Leo's The Progressed Horoscope may have made secondary progressions more popular;however, he does explain how primary directions both zodiacal and mundane, direct and converse, are calculated even though he did not appear to be impressed by the theory surrounding converse directions or the nomenclature used (here I sympathize with him).

There are better explanations, and formulas, available today; I doubt anyone does primaries by hand anymore given the software available but sometimes it's good to know where those algorithms came from.

janegca wrote:Leo's The Progressed Horoscope may have made secondary progressions more popular;

Not only that; he more or less invented them, at least in the form he presents them, although I doubt he meant to. I don't think he had actually read Placidus (who invented the secondary directions, as they were originally called, and used them in a much more circumscribed manner, as a mere adjunct to primary directions).

however, he does explain how primary directions both zodiacal and mundane, direct and converse, are calculated even though he did not appear to be impressed by the theory surrounding converse directions or the nomenclature used (here I sympathize with him).

Yes, but again, he didn't properly understand what he tried to explain, which makes the undertaking a perilous one. His formulae may all be correct (I haven't gone over them), but some of his explanations aren't.

I do agree about the value of being able to calculate directions by hand and understanding what one is doing. (So much so that I teach an entire course on it.)

Hi Martin,

Yes, but again, he didn't properly understand what he tried to explain, which makes the undertaking a perilous one

You may well be right, I haven't closely read his explanations in a number of years.