What this is. Recently, a dear colleague, Philip Graves, shared whatever fragments he could have found on the explanation of the Placidus method of house division set forth by two renowned astrologers or authors, Colin Evans and Charles E.O. Carter, in my effort to prove that said method of house division has long been misconstrued due to wrongful explanations by respected individuals (otherwise exceptionally able or talented and highly competent). Unfortunately, the practitioners that followed (contemporary astrologers, some of which could be our very colleagues, teachers, and/or friends) took for granted the correctness of the descriptions and have irresponsibly reproduced them. That is, they have not occupied themselves with first-hand corroborations, even with the availability or the help of current technology (e.g. Stellarium, WinStar, Solar Fire Gold, Meridian, Janus, Borealis’ 3D software, etcetera).

I myself was taught plenty under Carter and another bit under Evans, Raphael, Sepharial, and Weiss’s texts when I turned 11 (even though I did not undertake a profound study until the age of 26). However, I overlooked their words on house division because my teachers recommended that I learn physics first. They did, however, advise caution, and said that they, for their part, did not rely in house cusps different from the ones that either ascensional times or the celestial equator would produce, recognising or characterising the latter as astronomical, whereas the former as astrophysical. Even though I have occupied myself during the last year with explaining (in an unpublished essay prefaced by Anthony Louis) the reason for which polar regions constitute the ultimate test any particular method of house division can undergo, after my physical studies I understood the reason for which they advised as much.

I trust that you will as well after considering this. If that is not the case, that you will at least have conducted a few exercises, so that neither my words nor those of the authors aforementioned are reproduced without first-hand corroborations. The truth does not fear verification. Only lies would.

• PART ONE | Charles E.O. Carter

Philip Graves wrote,

“Carter has a few words that are critical of the Placidus system in his book Essays on the Foundations of Astrology (1947). Page 158 reads:

«However, this system [i.e. Placidus] has been fiercely (the adverb is not too strong) attacked on the same grounds as that of Porphyry, i.e., because the angles are determined by one method and the intermediate cusps by another. It is obvious that, except at the equinoxes, the Sun does not rise exactly between midnight and noon: why then, if the horizon is on the cusp of the 1st house, should the other cusps be determined by an equal division of the time taken by the Sun to pass from angle to angle?» (Underline is mine)

This constitutes, you must excuse me, a gross misunderstanding of the mechanism of action by which Placidus house cusps are ascertained, as we have iteratively explained since 26 September 2024.

First, the angular cusps are not revealed by “one method,” whereas the non-angular cusps “by another.”[1] All are revealed by ascensional times alone, even if some houses can, yes, be ascertained in a geometrical manner, as it is the case of the 10^th House cusp, which can be discerned (also) by means of the local meridian, and the 1^st House cusp, in turn, by the physical point of reference we regard as the plane of the local horizon. How is this so? Because time or motion precedes space. The MC is not, simply, the degree transiting the local meridian; it is first and foremost, exactly three-sixths of the diurnal arc of the point of the ecliptic constituting it, that is, said Zodiacal degree would have become the MC exactly three-sixths after having crossed the local horizon or been the ASC.

Second, the Placidian intermediate cusps are not ascertained, in any way whatsoever, by a supposed “equal division of the time taken by the Sun [i.e. a given degree or point of the ecliptic] to pass from angle to angle.” (This is so in the method of Alcabitius and of Koch.) In a Placidus-measured chart or astrograph, each cuspal degree constitutes a unique, distinct, or separate trisection. That is, unlike in Alcabitius or in Koch, each house within a quadrant does not measure the same amount of time. Each measures a different amount of time, namely: one third (1/3) of whatever amount of time that cuspal degree would have invested in moving from one angle to the next. It is precisely because “it is obvious that, except at the equinoxes, the Sun does not rise exactly between midnight [IC] and noon [MC],” that this type of measurement conducts as much as six (6) separate trisections, not one (like, again, Alcabitius or Koch conduct). Each cuspal degree represents or portrays a trisection of its own ascensional, seasonal, or daylight time.

Third. This constitutes the very reason for which everything is governed by time or motion, not space (i.e. time or motion constitutes our primary source of truth). Let us get it right. Placidus enforces or applies the same physical principle—which any supporter of a particular method of house division knowingly or unknowingly recognises concerning the cusp of the first house—to all ASCs impartially or equitably, that is, to all degrees that may be ‘dawning’ or ‘rising’ over each region (i.e. house). Because there is not a physical point of reference such as the local meridian or the surface of the horizon, it must rely upon the original (and natural) author of those two points, that is, upon time or motion. As Abraham Ibn Ezra correctly portrayed it (in accord with to Shlomo Sela’s 2014 prestigious English translation), it is, indeed, “the method of rising times.”

• PART TWO | Colin Evans

Graves also wrote,

“20th-century author, Colin Evans, the editor/rewriter in 1953 of Waite’s Compendium of Astrology […] I remember a particularly strong attack on Placidian cusps there. On p. 46 of the 1953 edition, Evans says (p. 93):

«This is the only system that is not geometrical: does not divide the entire celestial sphere into areas, equal or unequal, by lines meeting at any two opposite points (which would be poles of whatever primary circle might be used as basis of a system of house-division. No such primary circle is the basis of the Placidus system).» (Italics are mine)

Here, Evans is completely spot on. Furthermore, makes us not the only ones asserting this: Placidus does not employ or lets itself by guided by geometrical or otherwise arbitrary constructs of any kind. It is a natural method of house division inasmuch as it relies upon seasonal time alone, ratifying thereby its claim according to which it cannot be any more topocentric than that, that is, true to the local horizon.

• PART THREE | Colin Evans

Graves wrote once more,

“Going back to Evans, you may find this relevant, in Chapter VI, p. 45:

«This system is therefore based upon artificially equalised subdivisions of the naturally unequal amounts of time a degree of the Zodiac spends in each quadrant.» (Underline is mine) [2]

This confounding is alarming. First, Evans has confounded or conflated the naturally unequal amounts of time that each Placidian house within a quadrant constitutes with the naturally equal amounts of time that a given degree invests in each quadrant and/or house (of the same hemisphere, upper or lower). In this sense, “Artificially equalised subdivisions”? Alcabitius and Koch are the methods whereby the three houses within a quadrant have the same duration, as it has assigned to all of them one-third of the amount of time that the ascending (Alcabitius) and midheaven (Koch) degree invests in displacing from the horizon to the midheaven.[3]

Second, a diurnal arc may—correctly—have been trisected equally, but each portion of said trisection will not constitute each house within the quadrant, in which case each would possess the same amount of time (e.g. Alcabitius, Koch). Each house within a quadrant will or shall measure a different amount of time: that of the cuspal degree responsible for the house in question. Therefore, it is natural by all accounts, not artificial, inasmuch as it has recognised the actual length of that diurnal arc in that local horizon (i.e. latitude). Put simply, Evans misunderstood the way in which the principle of seasonal time is applied or otherwise exploited.

Third. Had the last part been written “[…] the naturally unequal amounts of time each degree of the zodiac spends in each quadrant,” as opposed to “a degree,” all would have been portrayed correctly. However, any given degree does spend an equal amount of time in each (upper or lower) quadrant and/or a house (need only conduct the exercise to verify it, that is, measure the length or duration of any one degree above the horizon, divide it by six, and advance the time every one-sixth of the actual length in order to confirm that said degree does appear at or loom over each subsequent house). It is each degree (i.e. a separate one) that spends, in each quadrant and/or house, an amount of time different from the previous and/or the subsequent degree, for each day the sun does exhibit a different apparent angular speed (i.e. each point of the ecliptic constitutes a solar footprint, yes), the very reason for which Placidus occupies itself with conducting six separate trisections. It is characterised as a simultaneous measurement of all cuspal degrees or as a simultaneously uninterrupted timing of all.

• PART FOUR | Skycript / Deborah Houlding

Skyscript or Deborah Houlding, for their part, even though they correctly made reference to “the great theoretical strength” that the Placidus method of house division possesses due to the fact that its houses are the very product of seasonal hours, for which reason they are “inextricably linked to both the idea behind Planetary Hours and the most ‘natural’ system of Primary Directions” (Wackford, M.), she or her advisors incorrectly described the very method of which they speak, later conflating it with the procedure by which Alcabitian houses are ascertained also. Because the two methods were conflated, neither one would have been correctly described. Have a close look!

“Every cusp marks a degree that the ascendant will move to at a subsequent planetary hour,” it reads. No, every Placidian cusp marks or constitutes one-sixth of its own daylight (seasonal) time. Therefore, one-sixth (i.e. two planetary hours) of its own diurnal arc shall mark the point upon the horizon that said degree would have reached or “will move to” every two subsequent planetary hours, producing thereby a—natural—house (i.e. not geometrically derived). Should a diurnal arc (say, 00º Leo 00’) measure 16 hr (i.e. 960 min) in Kodiak, Alaska on 12 August 2024, each seasonal hour (one-twelfth) of that degree alone would have a duration of 1.33 hr. or 80 min, whereas each one-sixth, 2.66 hr. or 160 min. Therefore, every 160 min, that degree representing that diurnal arc in that latitude would, yes, appear at each subsequent house every two seasonal hours, beginning from the horizon. (For reference, said degree would have loomed over the horizon at 4:30:05 a.m. local time. Please conduct the exercise in order to fully understand.)

Therefore, it is Alcabitius, not Placidus, that would have proceeded as follows:

• the 12^th House cusp marks the degree that would have culminated 4 daylight hours since the ascending degree crossed the horizon, whereas
• the 11^th House cusp marks the degree that would have culminated 2 daylight hours since the ascending degree crossed the horizon, because

Alcabitius would have determined the total amount of time the ascending degree would have invested in becoming the MC since it became the ASC in order to have each house within the corresponding quadrant constitute one-third of that same, not a separate, amount of time. Koch, in turn, would have determined the total amount of time the culminating degree would have invested in becoming the MC since it became the ASC in order to have each house within the corresponding quadrant constitute one-third of that same, not a separate, amount of time. Again, please conduct the exercise in order to fully understand this.

The Woodlands, TX
19 Aug 2025, 2:19 a.m.

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[1] It is a method such as that of Regiomontanus—you can confirm this were you to conduct the measurement yourself—that actually employs two distinct methodologies or frames of reference, for it begins prescinding from the poles of its own grand circle (celestial equator) in order to be able to rescue the ascensional time of the ASC by following the surface of the local horizon from the north point to the south, or vice versa. Then shifts to a strict spatial equipartite division of the celestial equator in order to draw great circles from it onto the ecliptic to have them meet it somewhere. This is necessary inasmuch as, were it to draw said great circles from the poles of the celestial equator (the grand circle constituting its primary frame of reference for most non-angular cusps), the central line would have intersected the ecliptic through the East point of the horizon at a different angle, that is, whereupon the ecliptic is not necessarily crossing it. Rarely, actually, as she’s a serpent exhibiting a wave-like behaviour, a hula-hoop. You need more than geometry to catch all ascendants (cusps) within the chart exactly. You need timing. This is why Placidus houses need rely upon only one variable alone, ascensional times (even if the ASC and the MC can be ascertained, also, not necessarily originally, geometrically).

[2] Full quote reads (as transcribed by dear Philip Graves): “Applied to other Degrees and Signs. But at the geographical latitude of London, for instance, 0° of Gemini, as a random example, takes nearly eight hours going through each diurnal semi-arc (or backwards through the two quadrants from I to X and from X to VII), and only about four hours going through each of the other two semi-arcs (or quadrants of the chart), under the earth. So, for London, Placidus makes 0° Gemini cusp I at S.T. 20h.0m., XII at 22h.37m., XI at 1h.14m., X at 3h.51m., taking about 2h.37m. from cusp to cusp above the earth, and then at the shorter interval of about 1h.24m. (all these times are only roughly approximate) he makes it reach in turn each of the remaining cusps below the earth. This system is therefore based on artificially equalised subdivisions of the naturally unequal amounts of time a degree of the zodiac spends in each quadrant.” Again, it seems that, as happened to many and continues to happen to others, Evans confounded or conflated the cusps of Alcabitius with those of Placidus. Alcabitius would have proceeded as Evans describes, and likewise Koch (in the opposite direction). Placidus, in turn, would have exploited only one interval of that amount of (seasonal) time, which would actually correspond to 00º Gemini (yes, just checked for the city of London; that is the diurnal and nocturnal seasonal time, respectively, of said degree). It (Placidus) would then have continued the exercise with an interval of another, separate, not the same, degree (i.e. each cuspal degree responsible for a house) in order to be able to respect and therefore reflect the unequal amounts of time that each degree invests in each house and/or quadrant. Example. Had 00º Gemini been the cusp of the 12th House, said house would measure one-third of that degree’s diurnal semi-arc, whereas the 11th House, in turn, one-third of a different degree, one third of the diurnal semi-arc of the 11th House cuspal degree, and so forth relative to any or all houses. This is not so in Alcabitius/Koch, for they proceed how Evans indicated. That is, each Alcabitius/Koch house within the quadrant would have measured one-third of one degree alone, not three separate ones. Placidus does recognise the unequal amounts of time each (not a) degree spends in each house and quadrant, and the equal amounts of time a certain degree does spend in each house and/or quadrant of the same hemisphere (upper or lower).

[3] One has to wonder… How can otherwise highly competent individuals not notice that they are describing three or at least two methods of house division in the same exact manner. As if one were to confound the equipartite division of the celestial equator (Regiomontano) with that of the prime vertical (Campano de Novara).

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Related publications:

Bustamante Segovia, David:
Illustration of the Placidian Mechanism of Action (DOI 10.5281/zenodo.1445256)
https://zenodo.org/records/14452568

Wackford, Michael:
It’s the Oblique Sphere, Stupid!
https://mail.skyscript.co.uk/polar_oblique.html