Directing through the Bounds is a special application of primary directions theory which could just as well be posted under the Medieval or Hellenistic boards on this forum. I post it here because it is first and foremost a technique involving primary directions.
At present, the best known treatment of this technique comes from Abu Ma'shar's Treatise on Solar Revolutions, available as a reprint from Project Hindsight.
The basic principle is simple. Not only can we direct planets and their aspects to significators like the Ascendant, but we can also direct the bounds to the significators.
Bounds (or 'terms') are unequal five fold subdivisions of each 30 degree zodiacal sign. There are several sets of bounds including one by Ptolemy and what are known as the Egyptian bounds which most Medieval astrologers use including myself.
Taking the Ascendant as an example, the practical impact of directing the bounds to the Ascendant effectively sets a stage on which planets and aspects function when they are also directed to the Ascendant. So there is a two step analysis.
If we just dealth with directing planets and their aspects, which is what virtually everybody does who uses primary directions today, then we really only get half the picture. Let's say we direct Mars/Gemini or one of its aspects to the Ascendant. We will get some kind of strife, maybe an identity theft, some lawyers involved, maybe a repetitive motion injury, depending on where Mars/Gemini falls in the chart. But if at the time the Mars/Gemini direction the directed Ascendant was in the bound of a benefic, then the effects might not be so deleterious. If the directed Ascendant fell in the bound of a malefic, they we would expect something more severe.
This accounts for the fact that the dexter sextile of Mars/Gemini directed to the Ascendant of the Regulus USA National Horoscope I published in December, when falling in the bound of Mars/Aries, triggered the Civil War. In this book 'America is Born: Introducing the Regulus USA National Horoscope' I present what is the most extensive empirical study of Directing through the Bounds every attempted or presented, that I am aware of.
If people have questions, I can give some more details here; otherwise check out the research.
World Class Research in Medieval Predictive Astrology