In this post I am going to contrast the Alcabitius semi-arc system of house division with the Placidus house system.
Both Alcabitius and Placidus are time-based house systems, as opposed to Porphyry, which is purely an ecliptic-based system.
In Porphyry, we start at the point of the ascendant (the point where the horizon meets the ecliptic) and measure the number of degrees along the ecliptic to the MC (the point where the ecliptic meets the local meridian). We trisect that into three equal houses and in this way get the cusp positions for the tenth, eleventh and twelfth houses, and by extension for the fourth, fifth and sixth houses. Easy!
Then we measure the number of degrees from the MC to the descendant and trisect THAT! That will give us the house cups for the seventh, eighth and ninth houses, and by extension the first, second and third houses. Note that in the chart above, houses 7, 8 and 9 are smaller than houses 10, 11 and 12.
To a certain extent, using the local meridian in Porphyry takes into account the latitude of the native in that unless one was born on the equator, the distance from the horizon to the midheaven (MC) will not be the same as from the MC to the descendant.
Let’s contrast Porphyry with how the Alcabitius house system is calculated:
In Alcabitius, instead of simply trisecting the ecliptic between the ascendant point and the MC, we trisect the amount of time the Sun takes to rise along the ecliptic from the ascendant to the MC.
So for example, in Paris today the Sun rose over the horizon at 7h33m13s and reached its culmination at the MC at 13h54m26s. So, we subtract the time of the Ascendant from that of the MC and find that it took 6 hours 21 minutes and 13s for the Sun to travel from the ascendant to the MC.
Here is the chart of the Sun rising on 1st April 2021 over Paris:
Using the Alcabitius system, we simply divide the total time by three to get the eleventh and twelfth house cusps. 6h21m13s divided by 3 = 2h 7m 4.33s. We take the quotient of the division (2h7m4.33s) and add it to the time of the ascendant (7h33m13s). By doing this, we learn that the Sun was at the cusp of the 12th house at 9:40:17.33s.
To get the time the Sun arrived at the 11th house cusp, we simply add 2h7m4.33s to the time of the 12th house cusp, which would be at 11:47:21.65s
Then, with the help of basic high school trigonometry, we determine what degrees on the ecliptic the Sun would have been on at the times we just calculated, and we have our house cusps!
Here is a chart of the Sun culminating over Paris. Because of the latitude, the culmination point is not directly above our head, but slightly to the west. Because of this, notice that houses 7, 8 and 9 are smaller in ecliptic degrees than houses 12, 11 and 10:
And now, we finally arrive at the Placidus house system!
Placidus is very similar to Alcabitius, but it takes Alcabitius a step further.
By trisecting or dividing the ecliptic in three equal parts from the ascendant to the MC (and then again from the MC to the descendant), Alcabitius is not taking into account that the twelve signs of the zodiac do not necessarily have the same ascension times as they pass over the ascendant: Depending on the native’s latitude, some signs take long to pass over the ascendant than others!
Straight versus crooked signs:
As we saw in the last blog, because of the earth’s tilt in relation to the ecliptic, in the northern hemisphere Cancer, Leo, Virgo, Libra, Scorpio and Sagittarius take longer to pass over the ascendant than the other six signs, and are called “signs of long ascension” or “straight signs” or “signs of right ascension”. The other six signs are Capricorn, Aquarius, Pisces, Aries, Taurus and Gemini, and are called signs of “short ascension”, or “crooked signs. Because of the earth’s tilt, the crooked signs actually appear to be flatter or “stooped” than the other signs, and as a result, they go by faster as they pass by the horizon due to the earth’s daily rotation.
In the southern hemisphere, the perspective is reversed, so what is a “long sign” in the northern hemisphere becomes a “short sign” in the southern hemisphere!
Going back to the northern hemisphere now: Even with the six “long ascension” signs, the ascension times are not uniform. The duration of the ascension time very much depends on what latitude the native is placed on. So a native born in Chicago at 11am will have a different set of ascension times than a native born in Houston, which is further south and obviously at a different latitude.
So the beauty of Placidus is that it takes into account of the latitude of the native when determining the ascension time each sign takes to go over the horizon at the time of birth.
As with Alcabitius, we measure the time it takes for the Sun to go from the Ascendant and MC and divide the total by three. Let’s say the quotient of this division is 2 hours 33 minutes 15 seconds.
And then we go a step further in Placidus:
We physically measure where the Sun will be in its rotation on the ecliptic 2h33m15s after it was at the point of the ascendant. Where the Sun will be on the ecliptic depends entirely what latitude the native is on using Placidus, for as we have seen, some astrological signs take longer for the Sun to pass through than others, even though they all have the same longitudinal width of 30° on the ecliptic!
If we have a long ascension sign like Libra on the horizon, the sizes of the houses will look quite different than if we have a sign of short ascension on the horizon, such as Aquarius.
Here are two chart cast for the same place and time using Alcabitius and Placidus.
Have a look to compare the difference:
Note that the Sun took longer to move (in a diurnal direction) through Placidus than it did through Albitius. In Alcabitius, the Sun arrived at the twelfth house cusp at 20° Leo 03′. In Placidus, the Sun arrived seven degrees earlier, at 27° Leo 44.
The reason for the discrepancy is because in Alcabitius we are simply trisecting the distance between the Ascendant and the MC. Each of the three houses have the same number of degrees. In Placidus, the length of time it takes for the Sun to pass through each of the signs is taken into consideration, hence the differences when we compare the cusps.
To conclude, both Alcabitius and Placidus are timed-based house systems, with Placidus being more concerned with the native’s latitude than Alcabitius and is thus more sensitive to the native’s location. In this way it is more geocentric or earth-based.
Speaking of earth-based house systems, it would be difficult to imagine a celestial circle that is more earth-based than the celestial equator, which is simply the earth’s equator projected out to the celestial sphere.
There are a number of house systems that are based on the longitudinal degrees of the equator, rather than the ecliptic. Perhaps the best known of them is the Regiomantanus house system. This was the system used by William Lilly. We’ll be taking a look at how Regiomontanus is calculated in the next installment.