The final ten degrees
Signs divide into three faces of ten degrees each, thirty six around the ecliptic. This is the closing face of Sagittarius, running from twenty degrees to the boundary at thirty.
The Sun crosses it in roughly ten days, normally from about 12 December to about 21 December. The upper edge is the winter solstice, which is why the published Sagittarius end date moves between 21 and 22 December from year to year. All decan boundaries drift like this by up to a day and a half, because the tropical year does not divide evenly into days, and a birth time shifts the answer further still.
Mid December birthdays sit comfortably inside the face; the trouble is only at the ends.
Saturn against Leo
The Chaldean order cycles through Mars, Sun, Venus, Mercury, Moon, Saturn and Jupiter without a break, starting from zero degrees of Aries. Counted all the way to the twenty seventh face, it arrives at Saturn.
The triplicity scheme takes no notice of that cycle. It shares a sign's faces among the signs of its own element in order, so the fire decans of Sagittarius go to Sagittarius, then Aries, then Leo. This last face therefore belongs to Leo, and to the Sun as Leo's ruler.
Saturn and the Sun are close to opposites in traditional terms, one associated with restriction and the other with display, so the scheme a writer uses changes the description of this decan almost completely. Since most popular articles quote a ruler without saying where it came from, this is a face where readers routinely encounter flatly contradictory accounts.
Each reading in turn
The Leo colouring is read as Sagittarius given a stage. The sign's interest in what is true in general is assumed to remain, but this face is described as wanting that view acknowledged by an audience rather than simply held. Traditional writing links it to teaching, to performance and to the confidence that comes from having said something in public and been believed.
The Chaldean Saturn is read as the check on all of that. Older texts treat Saturn in a fire sign as an imposition of limits on something expansive, so here it is interpreted as conviction that has had to survive contradiction, and as a preference for what can be demonstrated over what merely sounds right. The same placement is described as slow to grant its own enthusiasm, which is the same trait seen from the other side.
As always this is not restricted to the Sun. Any placement occupies a decan, and the Ascendant and the Moon are read this way as often as the luminaries. Decans descend from Egyptian star lists older than the twelve signs as we now use them, which gives the technique a real lineage, but it is a refinement applied to a chart rather than something a reading can be built on.
Solstice birthdays
Anyone born on 21 or 22 December sits at the point where Sagittarius becomes Capricorn, and the exact moment of the solstice differs each year. A degree either side is the difference between the last face of one sign and the first of the next.
The check above computes your actual solar longitude and reports the degree with the ruler each scheme assigns to it. That settles the question in a way no date range can, whichever edge of the decan you were born near.
It gives the neighbouring face as well, so you can see how narrow the margin was.
Questions people ask about this
What dates fall in the third decan of Sagittarius?
Roughly 12 to 21 December, with the upper edge at the winter solstice. The solstice moves between years, so a birthday on the 21st or 22nd needs calculating rather than assuming.
Is Saturn or the Sun the ruler of this decan?
Saturn in the Chaldean order and the Sun through the triplicity scheme, which assigns the face to Leo. The readings that follow from each are close to opposite, so it is worth knowing which one a source used.
Is Saturn here a bad placement?
The tradition describes it as restrictive rather than unfortunate, and restriction is not a verdict. What it produces depends on the house, the aspects and whether Saturn is otherwise well placed in the chart.
Does the Leo face change my Sun sign?
No. The Sun stays in Sagittarius. The triplicity decan is a shading applied to the sign, describing where the emphasis sits within it rather than substituting a different sign.
Do decans apply to the Ascendant?
Yes, and many practitioners read them there first. Every point in a chart sits in one of the thirty six decans, so the Moon and the rising degree are just as valid targets as the Sun.
Why is the decan system taken seriously at all?
Because it is documented and old, coming from Egyptian star lists later absorbed into Hellenistic practice. That history explains its standing, though it does not make it more important than the chart's main structure.