Which face this is
Cancer runs from zero to thirty degrees and divides at ten and at twenty. On 19 July, taken at noon in every year from 1930 to 2035, the Sun has stood between roughly twenty six and twenty seven and a half degrees. That is well inside the third face, with no year coming close to either edge of it.
Someone born in early July, with the Sun in the first ten degrees, shares the sign with you and not the face. The difference is not decorative. In the older material the face carries its own ruler and its own descriptive notes, which is the whole reason the division exists. Thirty six faces divide the zodiac where twelve signs would leave it coarse, and the finer grid is old enough to predate most of what is written about sun signs today.
The two rulers on offer
The Chaldean order steps through the seven visible planets from slowest apparent motion to fastest and repeats across all thirty six faces from the start of Aries. Worked through, the closing face of Cancer comes out as the Moon, the same body that rules the sign.
The triplicity scheme does something else entirely. It hands the three faces of a sign to the three signs of its element in order, so the faces of Cancer go to Cancer, Scorpio and Pisces, and the last of them therefore answers to Jupiter. Both schemes are old, both are still in print, and no amount of argument has retired either. Any source giving one ruler without naming its scheme has left something out.
What is read into it, and what is not
The Moon reading is usually described as an intensification of the sign, the lunar themes of memory and attachment arriving without a second planet to shade them. The Jupiter reading, by way of Pisces, is described as broader and less bounded. Both are interpretive conventions carried down in writing, not findings, and they are useful mainly because they are specific enough to disagree.
What is not on offer is a claim about your life. A face is a coordinate band. The tradition attaches meanings to it, this page reports those meanings, and nothing in either the position or the attachment predicts an event or fixes a character. Held at that weight the material is worth reading. Held any tighter it stops being defensible.
The rest of the chart, and where to get it
The face is still solar. It says where the Sun was, and the Sun is one body among ten or so that a chart accounts for. The Moon moves through about thirteen degrees a day, so its sign can turn over inside your birthday. The ascendant moves a full sign every two hours or so, and depends on latitude as well as the clock.
The widget above takes your year, hour and birthplace and returns your exact solar degree along with the distance to the nearest boundary. On 19 July that distance sits at around three days of Cancer, comfortably settled, and the widget states it rather than asking you to take a range on trust. A stated margin can be argued with, which a rounded date range cannot.
Questions people ask about this
What decan is 19 July?
The third decan of Cancer, the band from twenty to thirty degrees. The Sun sits around twenty six to twenty seven and a half degrees there, depending on your year.
Who rules that decan?
The Moon in the Chaldean face order, Jupiter in the triplicity scheme by way of Pisces. Both systems are still in use and a source should say which one it is following.
Does the decan change my sun sign?
No. It is a subdivision inside the sign, not an alternative to it. A 19 July Sun is in Cancer under either scheme.
Why is the decan rarely mentioned?
Because it needs a position rather than a date range, and most birthday pages work from the range. Once the degree is computed the face follows immediately.
Could 19 July ever be Leo?
Not at any hour in the years sampled. The Sun still has about three degrees of Cancer to cross, which is around three days.
Is the third decan of Cancer better or worse than the others?
Neither. The tradition describes each face differently and does not rank them. Any source grading them is adding something the older material does not contain.