(See appendix in the end)

1. Introduction

The peak of an astrograph is called or meant to represent the highest point that the sun can reach on the horizon of the observer, wherever he or she may be, and, because the observer’s east point must appear on our left, not right side, the cusp of the astrograph will always represent the south, whereas the base or diametrically opposite place, the north. (Reverse this description in charts of or from the southern hemisphere.) [1]

Because all astrograph is also called or summoned to represent the perspective of the observer on their local horizon, respecting diurnal movement or primary motion constitutes a sine qua non of rigorous astrographic measurement. It is therefore necessary to take note or record the ascensional times of each point of the ecliptic (i.e. zodiacal degrees) lying upon the horizon of the observer in accordance with time (clock), latitude (city), and time of year (date), for they will mark the six periods or the six stages of ascension and descension which they accomplish at that latitude at that time, that is, they will mark the cusps of the houses, for every sixth part of the diurnal arc of each zodiacal degree or point constitutes a cusp (six different degrees in all for six different total trisections). [2] Hence we dub the points of the ecliptic and/or the cusps as ‘the footprints/footsteps of the sun’.

2. Description of a circumpolar phenomenon

A. The cardinal points, in turn, will mark the region of the horizon through which the sun or the ecliptic ascends, culminates, sets, and anticulminates, whereas the intermediate directions or points (northeast, northwest, southeast, southwest) represent the rest of the regions of the horizon that the ecliptic (zodiacal belt or path of the sun) also crosses. Even though none of these other directions separate the day from the night as does the east and the west points, they do distinguish or mark different stages or periods of ascension (from the north point to the south point) or descension (from the south point to the north point) and are therefore also important.

B. In this sense, only the observance of the diurnal movement to which we referred earlier can make it possible for an astrograph to indicate — with utmost precision — the points on the horizon, other than the cardinal points (angles), through which the sun or the ecliptic can appear upon a polar latitude (reflecting thereby the living conditions appropriately) [3], where the spherical trigonometry that inspires our calculations (independently of the model of houses) begins to fail, save we appeal to a natural measurement of the local sky (hour arcs, not great circles).

C. Whilst in a fair amount of latitudes of the planet we will be able to confirm the rising and setting of the sun or the ecliptic on the east and west points, respectively, in many others we will observe that it accomplishes its diurnal movement a little north of due east (during the morning) and due west (during the afternoon) when it is summer, or a little south of due east (during the morning) and due west (during the afternoon) when it is winter. Should it be the summer solstice (in the northern hemisphere), it will rise and set to the northeast and northwest, respectively. Should it be the winter solstice (in the northern hemisphere), it will rise and set to the southeast and southwest, also respectively, whereas during the equinoxes (spring and autumn) it will rise and set, always, due east and due west independently of latitude on the globe.

D. Whatever segments of the ecliptic (i.e. signs) the sun occupied when it so behaved, these will exhibit the same behaviour in an astrograph, despite the fact that the sun no longer occupies those signs or ecliptic segments, for they retain its diurnal motion.[4]

E. As during summer and during winter the sun occupies the segments of the ecliptic that lie north (tropic of Cancer) and south (tropic of Capricorn) of the equator of our planet, at the north pole (75º-90º N) we will not see the summer signs abandon the upper portion of the horizon (for the sun never abandoned it when it occupied them) nor the winter signs abandon the lower portion of the horizon (for the sun never abandoned it when it occupied them)[5].

F. This is the reason for which, when employing the animation function of our software, we observe that these signs ingress into the horizon and egress from it through a different region or direction, that is, without needing or having to cross the east and west points, ASC and DES, as other segments will cross them, either directly (more or less perpendicularly) or in retrogradation (parallel to the horizon).

G. At 75º N, the signs Sagittarius and Capricorn will enter or ingress into the “upper” portion of the horizon (without ever emerging sufficiently), not through the east (ASC) but the south or a little east of due south (tenth house), whereas the opposite signs, Gemini and Cancer, will enter the “lower” portion of the horizon (without ever sinking sufficiently), not through the west (DES) but the north or a little west of due north (fourth house). This is why or how, in the former case, the upper hemisphere of the chart is reduced to only one house, the twelfth or the seventh, whereas in the latter, the first or the sixth, whilst the rest collapses.

H. In order to be able to reflect this astrographically, it is necessary that the ecliptic (Zodiac) shows a retrograde motion (parallel ascension for the observer on the local horizon) at the east and west points, that is, for the ecliptic to behave like this before showing us the region of the horizon through which the aforementioned signs can “ingress into the other side of it”, north and south, not east and west, respectively (although they will never reach sufficient altitude above or below it).

I. For the purpose of understanding this phenomenon better, see our future (April 2025) publication: “Polar Astrology. On Why Some Methods of House Division ‘Fail’ in the Polar Regions, According to the Unaware or Uninformed” (Bustamante, David; Wackford, Michael. April 2025. Zenodo/PhilPapers).
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[1] In the southern hemisphere, as we lay our eyes upon the horizon with the east to our right side, we are looking towards or have our sight pointing to the north, whereas in the northern hemisphere, as we lay our eyes upon the horizon with the east to our left side, we are looking towards or have our sight pointing to the south. What is to be considered even more important to understand, so as to avoid both confusion and wild inventions, is that the MC will always represent the upper, not lower, culmination of the sun and the celestial bodies, whereas the IC, in turn, the lower, not upper, culmination of the sun and the celestial bodies, without mattering that, only in the polar circles, it is possible to experience the MC below, not above, the horizon, while the IC, in turn, above, not below, the horizon, at certain times of the day, for these emulate the behaviour of the sun in said regions.

[2] The cusp of the 9th house, for example, represents four-sixths of the diurnal arc of whatever degree constitutes it (provided the chart has been calculated under the natural method of house division, Placidus). The seasonal hours of that degree (or of the sun had it occupied it) will be necessarily equivalent to those of the diametrically opposite degree below the horizon. Thus, four sixths (4/6) of the diurnal arc of the former will constitute four sixths (4/6) of the nocturnal arc of the latter.

[3] The houses reflect the physical or geographical properties of the seat of the birth or event, whatever it may be. Our life — be it social, family, professional, or even sexual — at the equator is not and would never be the same as at 35º N or S, much less 70º N or S (within the polar circles), where our organism and life in general change radically, depriving us both of the consumption and production of certain foods and of the execution or enjoyment of certain activities, be these personal, socioeconomic or sociopolitical. In these regions, zodiacal degrees become depleted by houses and some may be deprived of zodiacal activity (‘disappear’), but this is entirely normal and to be expected. There is no guava and cheese dessert, flan, custard, mantecado, or dessert whatsoever that can justify the substitution of reality (i.e. truth) with the illusion of fiction (i.e. a lie).

[4] Let us remember that the zodiac is nothing but the ecliptic and that the ecliptic is nothing but the path of the sun, for which reason the signs are not constellations but the twelve months of the year. See our molecular theory of the ecliptic (i.e. physical or meteorological basis of the tropical Zodiac) here https://zenodo.org/records/10463825 (Zenodo.org) or here https://philarchive.org/rec/BUSJAD (PhilPapers).

[5] This may serve as experimental information for those interested in vindicating astrology as a natural science after it was expelled from the universities. That is, what does not exist in extreme latitudes? A, B, and C. What do the segments or degrees that do not touch the horizon line represent? Is there a relationship between the former and the latter? Should there be one, we will have been able to take a big step towards vindicating the discipline. All that remains is to design the experiment properly and always start from proven, not false or uncertain, premises.

APPENDIX

1. The first case describes the behaviour of the sun during the polar summer. The second case describes the behaviour of the sun during the polar winter. Whatever signs or degrees of the ecliptic (zodiacal belt) are occupied by the sun during that time, they will exhibit the same behaviour from an astrographical point of view (use the ‘animation’ of your software).

2. During polar summer, when the day ends and begins at the same point, due north (during midnight), the IC will adhere to the DES as the summer signs will fall from the south (where they had culminated) to the north in order to, not hide, but kiss the horizon and resume their course upwards (twelfth house). In this sense, anticulmination will take place above, not below, the horizon, producing certain anomalies thereby in the lives of those born during said instant (when the MC relieves the ASC of its duties, as the IC relieved the DES of its).

3. During the polar winter, when the morning ends and the afternoon begins at the same point, due south (at noon), the MC will adhere to the ASC as the winter signs will ascend from the north (where they had anticulminated) to the south in order to, not rise, but kiss the horizon and resume their course downwards (sixth house). In this sense, culmination will take place below, not above, the horizon, producing certain anomalies thereby in the lives of those born during said instant (when the IC relieves the DES of its duties, as the MC relieved the ASC of its).

4. The meeting place, contact point, or point of encounter between heaven and Earth or the portal of entry of the entity into the physical world does not occur under normal circumstances, but under abnormal or anomalous ones. This is, however, only one of several circumpolar phenomena that only a natural method of measuring the houses can reflect.

5. Among the other types of circumpolar phenomena are the production of two or more ecliptic cusps for the same house (whilst others ‘disappear’, that is, although they continue to exist, they do not enjoy zodiacal activity, since the sun never through it passed or touched them) and the retrogradation of the ASC/DES (i.e. parallel, not perpendicular, ascension of the ecliptic above the horizon) while the MC/IC continues to reflect a regular or direct course (i.e. a much less parallel displacement of the ecliptic through said portion of the local horizon).