Where the Sun actually is
At noon on 10 September, in every year between 1930 and 2035, the Sun has stood between about sixteen and four fifths degrees of Virgo and eighteen and a fifth. That range is narrow because the calendar and the orbit are kept in step by the leap day, which pulls the date back roughly as fast as the missing quarter day pushes it forward.
Seventeen degrees places the birthday in the second of Virgo's three bands of ten, comfortably inside it rather than near either edge. The sign itself is not in question at all, since the Virgo boundaries are almost a fortnight away on either side and they move by hours, not weeks.
The Chaldean count
The older of the two schemes lays the seven visible planets in order of apparent speed, from Saturn as the slowest to the Moon as the fastest, and then deals them out one band at a time starting from the first degree of Aries. The sequence simply runs on through the whole zodiac, thirty six bands in all.
Counted that way, the second decan of Virgo falls to Venus. Tradition reads a Venus band inside an earth sign as the place where Virgo's exactness turns towards making things well, towards cultivation, arrangement and craft, rather than towards analysis for its own sake. That is a description handed down rather than a result of anything, and it should be read at that distance.
The triplicity count
The competing scheme ignores planetary speed and works from the element. Each sign's three bands go to the rulers of the three signs of its own element, taken in zodiacal order. For earth that is Taurus under Venus, Virgo under Mercury and Capricorn under Saturn, so Virgo's bands fall to Venus, then Mercury, then Saturn.
On that method the middle band belongs to Mercury, which is also the ruler of the whole sign. A reading built on it emphasises the sign's own qualities twice over rather than introducing a second planet. Neither scheme is checked against anything observable. They come from different sources and both survived, which is the whole of the explanation.
Holding the disagreement honestly
The useful move is to keep the measured part and the conventional part apart. The Sun's longitude on your birth date can be computed to the second and verified in any ephemeris. The name attached to the ten degrees it fell in cannot be verified at all, because there is nothing to check it against.
Most pages never mention that a choice is being made. They print one ruler, build a character sketch on it, and leave the reader believing a convention is a finding. Beyond the decan, the date still leaves the Moon with two possible signs and the rising sign with all twelve, so even a settled ruler would not carry the description very far on its own.
The practical approach is to read both attributions and see whether either says anything you can test against your own experience. Where they agree the tradition speaks with one voice, and where they diverge the divergence itself is the information. Treating the split as a defect misses the point, since it is simply what a long inheritance from several sources looks like.
Questions people ask about this
Which decan ruler applies to 10 September?
Venus under the Chaldean order and Mercury under the triplicity scheme. Both are in print, and neither is settled by observation, so the sensible answer names both.
What degree is the Sun on 10 September?
Between about sixteen and four fifths and eighteen and a fifth degrees of Virgo at noon, across the last century. Your own year, hour and place narrow it further.
Is 10 September firmly Virgo?
Yes. The date is roughly two weeks from either boundary, and the boundaries shift by hours rather than weeks, so no birth time or country changes it.
Why are there two decan systems at all?
They come from different traditions. The Chaldean order arranges planets by apparent speed and runs continuously from Aries, while the triplicity method groups signs by element and works within each one.
Does the decan change what my sign means?
Tradition treats it as qualifying the sign rather than replacing it. Virgo stays mutable earth under Mercury whichever band the Sun fell in.
How do I find which decan I am in exactly?
Work out your solar degree and see which ten degree band it lands in. The widget above computes the longitude from your year, time and birthplace.