Where the position actually is
Before the schemes can be compared the position has to be pinned down. At noon in each year from 1930 to 2035, the Sun on this date stood between roughly twenty five and twenty six and a half degrees of Libra. There is no year in the sample where the sign is unclear and none where the figure leaves that band.
Past twenty degrees puts it in the third of the sign's three ten degree faces, the one running from twenty to thirty. That much both schemes agree on. What they disagree about is which planet governs the band.
The Chaldean route to Jupiter
The Chaldean method runs the seven visible planets in order of apparent speed, from Saturn as the slowest through Jupiter, Mars, the Sun, Venus, Mercury and the Moon, then repeats. Starting at the first face of Aries with Mars, the sequence is walked continuously through all thirty six faces of the zodiac. Counting round in that fashion, the closing face of Libra lands on Jupiter.
The strength of this method is that it needs no reference to anything but the order itself, and it produces a single unbroken chain across the whole zodiac. Its weakness is that the result has no obvious relationship to the sign the face sits in, so a face can end up attributed to a planet with nothing else to do with the sign around it.
The same order underlies the planetary hours and the sequence of the days of the week, which is part of why it survived. It is a structural device rather than an observation, and it was never presented as one.
The triplicity route to Mercury
The other scheme divides each sign's three faces among the three signs of its own element, taken in zodiacal order. Libra is air, so its faces go to Libra, then Aquarius, then Gemini. The closing face is the Gemini one, and Gemini is ruled by Mercury, which is how that attribution arrives.
This method has the advantage of keeping the face inside its element, so the reading stays connected to the sign rather than jumping elsewhere. Its cost is that it produces different answers from the Chaldean chain almost everywhere, and a source that quotes one without naming the scheme has settled the question silently.
The two schemes do coincide at a few points around the zodiac, which occasionally lets a page present an attribution as uncontested when it is only accidentally agreed. That is not the case here. For the closing face of Libra the schemes genuinely part, and the planet you end up with depends entirely on which route was taken.
What to do with the disagreement
Neither attribution can be checked against anything observable, so there is no test that decides between them. What is checkable is the degree itself, and both schemes are working from the same degree. Treat the ruler as a label a tradition applies rather than a fact about the sky, and note which tradition you are reading.
The rest of the chart is untouched by all of this and is also unfixed by the date. The Moon can sit in any sign on this birthday depending on the year and can change sign during the day itself, and the ascendant runs through all twelve signs every twenty four hours. The widget above returns your exact solar degree from your year, hour and birthplace, along with how far that placement stood from the nearest sign boundary.
Questions people ask about this
What sign is 19 October?
Libra. Every year sampled at noon from 1930 to 2035 places the Sun clearly inside the sign, with the change into Scorpio still four days or so away.
Which decan is 19 October in?
The third decan of Libra, the band from twenty to thirty degrees. Both traditional schemes agree on the band and disagree on the planet attached to it.
Is Jupiter or Mercury the correct ruler?
Both are traditional. Jupiter comes from the Chaldean order of the planets and Mercury from the triplicity scheme by way of Gemini. Neither can be tested, so the honest answer names the scheme.
What degree of Libra is this birthday?
Between about twenty five and twenty six and a half degrees at noon over that century. The exact figure for one birth depends on the year, the hour and the birthplace.
Does the decan change how the sign is read?
In the older material it adds a second layer of attribution rather than replacing the sign. The position remains fully Libra whichever face it falls in.
Why does the degree barely change between years?
Because the quarter day shortfall in a common year is corrected by the leap day every fourth February. The annual creep and the leap correction offset one another over the cycle.