Besieged
A planet is besieged when it stands between Saturn and Mars, hemmed in on both sides with no benefic between. It describes a matter or a person with no clear way out, and it's testimony rather than a verdict.
The fuller picture
The condition worth learning is the strict version, and it's about aspects rather than mere position: a planet separating from the hard aspect of one malefic and applying to the hard aspect of the other is besieged. It has just come through one difficulty and is walking into another. Read on the person asking, that describes somebody with no good option available; read on the thing asked about, a matter hemmed in from both sides.
Two details in that definition do real work. The first is that the malefics are Saturn and Mars specifically, not any two unpleasant planets. The second is the qualification our own short definition carries from Bonatti — no benefic intervening. A Jupiter or a Venus standing between the two malefics, in aspect or in place, is the escape route, and its presence is what the condition denies. Both halves are easy to lose, and a besiegement claimed without either is usually just a planet that happens to have malefics on both sides of it.
Our engine tests something looser than that, and you should read its besiegement findings with the difference in mind. We work in ecliptic longitude only: a planet is besieged when it sits between Mars and Saturn on the shorter arc, with the whole enclosure inside sixty degrees. There is no test of whether either contact is separating or applying, no test of aspect at all, and no test for an intervening benefic. So the condition we report is enclosure by position rather than the aspectual sandwich the doctrine describes. It is a defensible reading — enclosure between the malefics is a real traditional condition in its own right — but it is not the same predicate, and it will report besiegements the strict test rejects.
The strongest technique attached to this in the source is corroboration by house, and it is worth copying. In the worked reading a besieged Moon is backed up by Saturn, the South Node and Pluto all gathered on the fourth cusp, which puts the trouble in the home. The besiegement says the matter is hemmed in; the houses say where. One condition rarely means much on its own, and the habit of looking for a second, unrelated testimony pointing at the same place is what turns it into a reading.
It also pays to notice readings that stand next to besiegement without being it. There is one chart where a significator is described as escaping the evil of the South Node through the evil of retrogradation — caught between two bad things, and taking one of them — and the author is careful to say that this is not besiegement in the classical sense. The temptation to stretch the word to cover any planet with a difficulty on each side is exactly what makes it useless.
Finally, and this matters more than the mechanics: a besieged planet is not a verdict. It is grave testimony about the condition of one planet, and grave testimony still gets weighed against the contacts, the receptions and the houses. Our own notes carry it as an open question whether besiegement should ever be as decisive as a void Moon, and the standing position is that conditions of this kind weigh and never gate. If a chart can be cast it can be read.
In your chart
Every chart in iHorary is checked for a planet enclosed between Mars and Saturn, and the finding is kept only when the besieged planet is one your question turns on — the ruler of your own house or the ruler of the matter. It is then recorded as negative evidence to be weighed with everything else, never as a denial that ends the reading. The besieged planet carries a Besieged chip among its condition chips, with the score that condition contributed, though the chip names the planet rather than the actor it stands for — the significator list is what tells you which planet carries you and which carries the matter. Read it beside the planet's own dossier, which gives its dignity, its house, its motion and its distance from the Sun, since a besieged planet that is otherwise strong is a different case from one that is afflicted on every count.
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