Recently I revisited multiple texts pertaining to the houses and the methods by which they are discerned or measured for the purpose of being able to look at things with a fresher set of eyes after a little over a decade of having learnt the trigonometry that characterise them. While at the time looking at the sky and imagining the natural division of the horizon sufficed to discard all other exercises of measurement, the past three years have revealed the persistent or otherwise stubborn adherence amongst many astrologers to the historical justifications for these diverse methodologies, that is, to the reason why other methods were devised.

Upon revisiting this literature, I find not a coherent exercise today either. Only by considering the available tools and the prevailing astronomical or physical understanding of the periods in which these methods were conceived can one comprehend the rationale inspiring such divisions of the local horizon. In this sense, reading the arguments for these methods in the twentieth or twenty-first century, these appear valid from a perspective different from observational truth; that is, these arguments are congruent with a specific epoch rather than the one in which they are articulated, an era that has afforded us a more profound and consequently more accurate understanding of the celestial sphere and its mechanics. Consider, for instance, the argument put forth by Mr. Dane concerning the Campanus method of house division in the accompanying passage. (See paragraph, followed by our observations.)

Reference: The Elements of House Division (1977), by Ralph William Holden, Raven Dreams Press (repr. 2023, Colorado, USA), page 93.

There is only one problem (profound methodological inconsistency or contradiction) in defending this, however. Should we have righteously recognised that the houses are not within the Zodiac, why force or impose a thirty-degree division onto or within the horizon? The horizon is not the Zodiac, one may respond to Mr. Dane. The horizon is the physical medium through which the Zodiac or its properties manifest upon the Earth, as later implied in the same sentence, and this energetic spill does have or is subject to the rhythm of diurnal displacement, whereby each cusp is defined by the precise moment an ecliptic point reaches or touches, intersects or crosses a specific segment of the horizon, be it the eastern horizon (Ascendant) or the local meridian (Midheaven), or each one-sixth of the angular distance travelled by the Sun (total change of combined local horizon degrees) when it occupied said point of the ecliptic (one-sixth of the diurnal arc of that cuspal degree).

This can only be found to be consistent not only with the notion of spacetime (within the realm of the classical, not quantum, physics of celestial mechanics) but also with Kepler’s Second Law of Planetary Motion. In the same manner as bodies sweep equal areas in equal amounts of time, each diurnal arc (point of the ecliptic or Zodiacal degree) subtends or sweeps equal amounts of combined local horizon degrees in equal amounts of time. To have us honour or uphold oblique, (Placidus or natural), not right (Regiomontanus) nor vertical (Campanus), ascension relative to both the first and the tenth houses, whereas not for the rest, introduces a methodological contradiction.

Yes, strictly speaking, from a Newtonian perspective, Campanus would accurately partition horizontal space, whereas Regiomontanus would more precisely address horizontal spacetime. However, Regiomontanus does not accurately represent the ecliptic relative to the horizon, as the ecliptic, whose points one seeks to delineate, is not confined to the East-West cardinal points. Instead, it exhibits a sinuous or wave-like behaviour resembling that of a serpent (horizontally in polar regions, vertically in equatorial or tropical regions, and diagonally in temperate regions). Regiomontanus makes a sounder attempt to quantify this property (spacetime) by employing the celestial equator as its primary frame of reference; the celestial equator appears inclined relative to the horizon, thereby somewhat mirroring the ecliptic’s tilt. Nevertheless, similar to Campanus’ prime vertical, it remains anchored to the East-West cardinal points. Despite this, it continues to utilise the celestial equator, thereby employing two distinct methodologies for different house cusps, as it still recognises oblique (not right) ascension solely for the first and tenth house cusps.

This should indicate that no method more unanimously considered astronomically or physically valid exists for discerning house cusps than this one: recognising the length of any house as equivalent to one-sixth of the diurnal/nocturnal arc of the cuspal degree completing that journey, especially if we concur that aspectual relationships occur across the ecliptic rather than within the houses, even if, contingent upon latitude, some may exhibit the behaviour or produce the effect of a different aspect (a relativistic phenomenon, mundane aspects, first noted by Ptolemy and Lilly, and more recently discussed by a colleague, Anthony Louis).

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We will not touch upon this topic (i.e. which method of house division would honour or uphold the current understanding of the celestial sphere the most faithfully, and its implications) in the coming months, as the remaining observations will be included in a future paper we are co-authoring. We are to shift our attention to an essay that revisits the polar houses, which we hope to have published this summer (it is almost completed).