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The Solar System: What is a Planet in Astrology?
by Patrice Guinard, Ph.D.
-- translation Matyas Becvarov --
This text can be considered unpublished, since the corresponding chapter of my doctoral dissertation (Chapter 25) consists of only two pages. It attempts to answer the following question: why choose one "planetary operator" over another?
1. Presentation of the solar system
2. The discovery of the trans-Saturnian planets
3. What is a planet? (A systematic investigation of astrological operators of the planetary type)
4. Orbital and physical data for the principle bodies of the solar system
5. What is an astrological operator? The status of Pluto
6. Harmonies of the solar system: The Great Year
7. Harmony of sidereal revolution: The unity of the solar system
1. Presentation of the Solar System
"The truth of the heavens is the stars
unyoked from their constellations
and traversing it like escaped horses."
(Jean Giraudoux: Sodome et Gomorre)
The solar system is composed of the Sun (which represents 99.8% of its total mass) and of an ensemble of planets with satellites (except Mercury and Venus), all of which turn round the Sun, which occupies one of the foci of their elliptical orbits, some of which are nearly circular (particularly those of Venus and Neptune). To these are joined the asteroids, which probably number in the hundreds and whose orbits are for the most part situated between Mars and Jupiter; the comets, whose orbits are extremely eccentric; meteorites; planetoids discovered since 1992; and interplanetary matter (gas, particles, microscopic dust). Kepler revealed the three laws that underpin the orbital movement of the planets. From a geocentric point of view, the Sun seems to describe a circle called the ecliptic. The planetary orbits, including that of the Moon, have a relatively small orbital inclination with regard to the plane of the ecliptic, the largest ones being those of Pluto (17°15), Mercury (7°), the Moon (5°15) and Venus (3°39).
In his treatise Some Difficulties Relating to the Soul, Plotinus the Stoic expresses the idea of an animal-universe, "a totality sympathetic to itself."  The "influences" of the heavenly bodies are justified by the harmony and the attunement that exist between the various parts of the universe: "We shall not attribute, therefore, either to corporeal causes nor to a voluntary decision those astral influences that affect us and the other animals, and in general all things on the Earth. What cause then remains that could be admissible? This universe is a unique animal that contains within itself all animals; it has a unique soul that extends into all its parts, to the degree that the beings within it are its parts." 
The unity of the solar system is a necessary postulate for any kind of planetary effectiveness: and indeed, Kepler indicates that the solar system forms this organic whole, marking out a defined field in relation to the other heavenly bodies. The solar system is assumed to be a globally stable ensemble, a sort of ecosystem at the heart of the galaxy, a milieu of integration especially for living beings. The philosopher Henri Bergson noted in 1907 that the solar system is probably the "system most isolated objectively and the most independent of all."  In fact, if there are differentiated astral incidences of which the planets are the physical operators, it follows necessarily that these planets should form a totality, and that the differentiation should be in relation to certain physical criteria. Ptolemy and his predecessors searched for a way to justify these differences through supposedly elemental qualities of the planets (heat, wetness). We are all aware of the failure of that attempt at rationalization.
2. The Discovery of the Trans-Saturnian Planets
The British astronomer William Herschel (1738-1822) discovered Uranus on 13 March 1781 and decided to name it Georgium Sidum in honor of King George III. From 1781 on it was called Herschel. In Systême de Copernic ou Abrégé de l'astronomie [=The System of Copernicus, or, Summary of Astronomy] (Paris, 1783), a picture dedicated and presented to the Dauphin of France by one Papillon de La Ferté, the "planet of Herschel" is symbolized by a dolphin because "this planet was discovered a few months before the birth of the Dauphin." The Prussian astronomer Johann Bode (1747-1826) finally suggested the name Uranus, after the Greek sky god Ouranos. The name Uranus appears in the title of a number of astrological treatises well before the discovery of the planet. 
The Englishman John Couch Adams (1819-1892) and the Frenchman Urbain Le Verrier (1811-1877) predicted the existence of another planet beyond Uranus and calculated its hypothetical position after 1845. This was taken up by the German astronomer Johann Galle (1812-1910) and his assistant Heinrich d'Arrest at the Berlin Observatory on the evening of 23 September 1846, following the calculations of Le Verrier. Galle proposed the name of Neptune. Neptune had already been sighted, however, in August of 1846 through a telescope in the observatory of Northumberland by the English astronomer James Challis.
The existence of a trans-Neptunian planet had been put forward in 1879 by Camille Flammarion (1842-1925) and by other astronomers.  Clyde Tombaugh (1906-1997) of the Lowell Observatory in Flagstaff, Arizona discovered Pluto on 18 February 1930, following calculations done in 1915 by Percival Lowell (1855-1916) and from photographic plates Tombaugh had taken on 23 and 29 January 1930. The name Pluto (which incidentally includes the initials of Percival Lowell) was proposed by an eleven year-old English schoolgirl.
Certain temporal coincidences give us food for thought. The planet Uranus was discovered by an astronomer of great repute. The discovery of Neptune is encircled by a halo of circumstances difficult to explain fully, and the discovery of Pluto came as the accomplishment of an astronomer who was an autodidact. In 1783 the Uranian Kant published his Critique of Pure Reason, in 1848 the Neptunian Marx published his Manifesto of the Communist Party, and in 1929 the Plutonian Heidegger published his treatise What is Metaphysics? Finally, these political, economic and social events that seem to correspond to the nature of the planet in question: the independence of the United States in 1776 and the French Declaration of the Rights of Man in 1789 (Uranus); the revolutionary movements of 1848 in Europe and the revolt of the T'ai-ping "Christian-Taoists" in China beginning in 1850 (Neptune); the economic crisis in the United States and subsequently in Europe (1929-30) and Hitler's rise to power in 1933 (Pluto).
3. What is a Planet? (A systematic investigation of astrological operators of the planetary type)
Among the planetary operators -- i.e. those factors of astrological significance (planets, houses, Zodiacal signs, etc.) -- there exists a category that relates specifically to causality, to energy, that one could call physical or astronomical operators. These are the physical bodies, tangible, extant, which influence the psyche by virtue of the organic integration of their cycles. In the Zodiacal circle they are represented by particular points. Among the four categories of body usually taken into account by the astrologer, imaginary points (hypothetical planets), fictive and arithmetical points (parts, nodes and midpoints), insignificant physical bodies, and physical planets, only the latter category fits the definition we gave earlier. When one asks an astrologer why he uses such and such a factor rather than another, and why he positions this factor by projection upon the ecliptic, most often the response is: "because that works."
The Imaginary Objects
It is astronomers who have assumed since the second half of the 19th century the existence of hypothetical planets and satellites, in order to fill in the gaps left unanswered by the state of astronomical knowledge, especially in the cases of an infra-Mercurial planet called Vulcan and an invisible satellite of the Earth called Lilith, the reality of which has never been proven, to which can be added as well a trans-Neptunian planet.  The wave of hypothetical planets took on greater speed in the 20th century within the astrological community. This phenomenon gave astrologers a chance to touch up some of their mistakes: the affirmation of new planets (some fifty by present-day count), invisible, yet to be discovered, acted as a palliative for the inability of some to interpret a natal chart solely on the basis of the known planets. Moreover, the temptation of a congruent model for Rulership and the Houses (12 signs/12 planets) was a fundamental factor in the practice of using hypothetical planets among astrologers and thinkers in the Hermetic tradition.
In 1881 the priest Vassart predicted the existence of three trans-Neptunian planets (Michael, Gabriel and Raphael), for which he gave the period and position for 1 January 1850.  From the 1870's onward the existence of a trans-Neptunian planet "X" was hotly debated in astronomical circles. Astrologers and Hermeticists did nothing more than adapt themselves to the research already underway. The Hermeticist abbot Paul Lacuria (1806-1890), in an unpublished manuscript,  affirmed the existence of Pluto, which was to be discovered half a century later: "This progression [of the planets] goes from Mercury to Uranus, and then decreases in Neptune and in Pluto which will be discovered later and which is more distant and smaller than Neptune."  In 1897 the astrologer Charles Nicoullaud (1854-1923), a Freemason who used the alias Fomalhaut, confirmed that idea: "The planet beyond Neptune exists, it is called Pluto."  Fomalhaut presented a theory of Rulership based on a division by twelve with Pluto in Aries, Vulcan in Gemini, and Juno, a planet destroyed by an astral catastrophe and whose remains are now the asteroids, in Libra.
In 1917 the astrologer C. Libra popularized on the Continent the mythical planet Vulcan,  and one year later Walter Old (1864-1929), who used the alias Sepharial, established Lilith, the second satellite of Earth, in the British astrological community. 
Beginning in the 1920's astrologers were no longer content to speculate about random astronomical discoveries and began to invent their own planets. The most famous of these hypothetical celestial bodies are the trans-Neptunian ones of the Hamburg School, which continue to be used despite the discomfort of Alfred Witte (1878-1941) who could not bring himself to mention Pluto despite the fact that the planet was discovered two years after the publication of his work.  To the four trans-Neptunian planets of Witte (Cupido, Hades, Zeus and Kronos) may be added those of his pupil Friedrich Sieggrün (1877-1951): Apollo, Admetos, Vulkanus and Poseidon.  We know by means of ephemeris data the position of these eight trans-Neptunian bodies, whose sidereal revolutions vary between 262.5 years for Cupido and 740 years for Poseidon.
In 1930 the Scottish Rosicrucian Maurice Weymiss announced the existence of three trans-Plutonian planets (Dido, Hercules and another "Pluto"), and in 1935 that of the planet Jason, located between Saturn and Uranus.  Ernest Britt confirmed the existence of two trans-Plutonian bodies  before the vogue of Proserpine took hold of French astrology in the late 1930's and into the 1940's (Maurice Privat, Dom Néroman, Léon Lasson ...).  In the 1950's the Dutch astrologer Theodor Ram invented three new planets (Persephone, Hermes and Demeter) and in 1972 Charles Jayne offered to American astrology his seven trans-Plutonian bodies: Pan, Isis, Hermes, Osiris, Midas, Lion and Moraya.  In addition, some Russian astrologers used the four trans-Plutonian planets Isis, Proserpine, Anubis and Osiris ...
By taking these hypothetical planets into the astrological repertoire, the astrologer rid himself of any astronomical safeguards, without, however, enriching the semantic range of the planetary keyboard: in effect, the meanings given to these hypothetical bodies remain very close to those associated with the known planets. These superfluous additions, far from enriching the planetary corpus, lead it instead into confusion. What is more, I do not believe that the astrologer is a seer. And even if he were, he would still only be concerned with doing astrology.
The Fictive and Arithmetic Points
These factors do not exist physically: they are arithmetic points, determined by calculation.
* The "Dark Moon," otherwise called the second point of the lunar orbit (also called Lilith), very much in use among astrologers. Its median and true positions can be calculated.
* The "dark" planets: The "dark" values for Sun, Mercury, Mars, Jupiter, Saturn, Uranus and Pluto. It is difficult to imagine a position of Venus or Neptune very distant from the Sun, given the slight eccentricity of their orbits.
* The planetary nodes (geocentric and heliocentric): each planet has an ascending node and a descending one. 
* The three points studied by Theodor Landscheidt, which move approximately 1°24 per century (due to the precession of the equinoxes): the Galactic Center (GC), the center of equilibrium for the Galaxy (which ostensibly indicates the spiritual aspirations of the native), the Galactic Supercenter (SGC, which supposedly indicates the personality's center of organization and is a sort of "super Sun"), and the Solar Apex (SA), the direction of solar movement within the Galaxy (which supposedly represents the ultimate goal of the personality). In the year 2000 the GC was situated at approximately 26°52 Sagittarius, the SGC at 1°47 Libra and the SA at 2°27 minutes Capricorn.  Given that their movement is very slow, it is difficult to see the usefulness of these points in natal astrology, even in horary astrology.
* The famous Part of Fortune (used by Ptolemy) and the so-called "Arabic Parts" are fictive points calculated according to the longitude of three planets, Zodiacal angles and points, most often according to the formula Part = AS + Planet X - Planet Y.
The parts described by Paul of Alexandria  are, for diurnal charts, the following (for nocturnal charts the signs + and - must be reversed):
* Part of Fortune = AS + Moon - Sun (i.e., the position of the Moon at sunrise)
* Part of Spirit (Daimon) = AS + Sun - Moon (the inverse of the preceding calculation, i.e. the placement of the Sun when the Moon rises)
* Part of Eros = AS + Venus - Part of Spirit = Venus + Moon - Sun (the position of Venus when the Sun and Moon are conjunct)
* Part of Victory = AS + Jupiter - Part of Spirit = Jupiter + Moon - Sun
* Part of Necessity = AS + Part of Fortune - Mercury
* Part of Courage = AS + Part of Fortune - Mars
* Part of Nemesis (Justice, Equity) = AS + Part of Fortune - Saturn
Still from Paul of Alexandria,  among others:
* Part of the Father = AS + Saturn - Sun (for nocturnal charts, invert)
* Part of the Mother = AS + Moon - Venus (for nocturnal charts, invert)
* Part of Siblings = AS + Jupiter - Saturn (= for nocturnal charts)
* Part of Children = AS - Jupiter + Saturn (= for nocturnal charts)
* Part of Marriage (men) = AS + Venus - Saturn (= for nocturnal charts)
* Part of Marriage (women) = AS - Venus + Saturn (= for nocturnal charts)
According to Vetius Valens and the Liber Hermetis: 
* Part of Debt = AS + Saturn - Mercury (= for nocturnal charts)
* Part of Foundation = AS + Fortune - Spirit (= for nocturnal charts)
* Part of Theft = Saturn + Mars - Mercury (for nocturnal charts, invert)
* Part of Betrayal = AS + Mars - Sun (for nocturnal charts, invert)
* Part of Difficulty = AS + Mars - Saturn (for nocturnal charts, invert)
* Part of Exaltation of the Nativity = AS + 19° Aries - Sun (for nocturnal charts = AS + 3° Taurus - Moon ; these degrees of Aries and Taurus are assumed to be the point of Exaltation for the Sun and Moon, respectively)
The system of parts has occupied a place of considerable importance in Arabic astrology: Al-Biruni mentions more than a hundred parts and informs us that astrologers invented more than 150 to respond to horary questions.  One can imagine even more than that, according to the preoccupations of the moment and the imagination of the astrologer. Many new parts have been invented, taking into account the trans-Saturnian planets, such as the Part of Anxiety (= AS + Pluto - Uranus), the Part of Astrology (= AS + Mercury - Uranus), the Part of Depression (= AS + Neptune - Mars), or even the Part of Perversion (= Venus + Mars - Neptune).  One might also try out the Part of the Cake, which ostensibly serves to determine the dessert that your partner has prepared for your dinner, or even the Part (English: "Lot") of Consolation. I propose further that the reader, in order to evaluate his possible relation to our Center, consider the position of his Part of C.U.R.A., which is calculated as follows: URANUS - SATURN + MARS - SUN. 
* The midpoints, popularized by Alfred Witte, are those points of sensitivity where the planetary energies meet and combine. They are calculated by means of the formula Midpoint = (Planet X + Planet Y)/ 2. Reinhold Ebertin (1901-1988) systematized and simplified the midpoint technique of Witte.  The cosmobiology of Ebertin had a brief success in Germany in the 1940's and 1950's, before becoming somewhat popular generally. The midpoint techniques of the Hamburg School (Witte), like those of cosmobiology, are very strongly oriented toward the prediction and interpretation of events.  By limiting the scope to ten planets, the angles AS and MC and the six aspects with an orb of 10, there appear twice as many midpoints in the chart as there are Zodiacal degrees, which leaves a good deal of elbow room for interpretation! In this scheme, one is never abandoned by the stars: every hour of the day and night brings its load of counsels, consolations, messages ...
Speaking more generally, the multiplication of sensitive points and imaginary energy points spells out the failure of modern interpretation in its attempt to pin down the circumstantial. As Geoffrey Dean points out, this plethora of factors leads astrology into the realm of the absurd and makes the indications of the natal chart implode: "The problem can be illustrated by a chart that includes all the factors proposed and tested by astrologers of some repute, that is to say, three angles [AS, MC and Vertex], 10 planets, 4 asteroids, 30 hypothetical planets, together with their nodes and correspondant parts (which gives a total of 120 factors), in relation to an average of eight aspects with an orb of eight degrees, 40 other aspects and their antisces and counterantisces with an average orb of 2 degrees, 2 parallels of declination with an orb of 1 degree, and eight midpoints with an orb of 1.5 degrees. (...) The "super chart" would then contain on average more than 6000 aspects, more than 50,000 midpoints, and close to 1.5 million aspects between midpoints." 
This diarrhea gives cause for great jubilation to those opposed to astrology, just as it gives consolation to the astrologically inept. No practitioner can deal adequately with this "super chart," but all the same, a majority uses more than a dozen planets and some of the arithmetical points. The irrational mathematization of the chart -- although no consensus exists on what reflection should be brought to the representation of the chart, especially concerning the projection of bodies onto the ecliptic and the compatibility of the Zodiac with the "circle" of the Houses -- leads modern astrology into an impasse, untethered from the astronomical imperatives and from the concern for coherence that would insure mindfulness of the fact that any model must attach itself to some versimilitude of physical order. The astrologer no longer feels the impressional; he renders the astrological mathematical. It is as if the chart, limited to a few factors, were not already of immense complexity.
The inverse tendency, that of the partisans of so-called "traditional astrology," is to limit things to the Septenary, i.e. only to those planets known by the Ancients. In this view, astrology is circumscribed knowledge, and contemporary astrologers should restrict themselves to using only the few supposedly tried and true recipes arrived at by their predecessors. This conception, which holds fast to the Model, without giving any thought to the Matrix and the Structures that underlie it, often remains ignorant of the historical variations that have affected the supposed Model as well as of deformations that have occurred as a result of intercultural transmission and numerous variations that have influenced it in the course of its history.
An adequate process would be to question the origin and reasons that induced astrologers of a particular period to introduce into their conception such and such an element, this or that part of theory. A good example is that of Rulership, accepted by Ptolemy, and to which he gives only a specious justification. If the Greek astrologer succeeded in finding a certain balance among the elements at his disposal, it does not follow inevitably that that balance suffices for us. The discovery and introduction of the trans-Saturnian planets demands a new organization of the Planetaries, Rulership, and interplanetary relations.
A third tendency consists of "testing" planetary operators by means of statistics. These studies, greatly multiplied in number since those done by the Gauquelins, have not managed to establish a consensus among astrologers. There is no physical explication that can justify the efficacy or four or five planets to the detriment of the others, and even the "Mars effect," the least liable to being contested, seems to Geoffrey Dean the result of a cultural habit. Moreover, whatever the result and the "success" of these statistical studies may be, astrologers do not pay attention to them, and I know not one among them who has put in place an exclusively "Martian" astrology under the pretext that astro-statistics has only validated that one planet. And they are right to do so, because statistical inquiry, even if it gives us food for thought, cannot legitimate knowledge that arises from another logic than that of the factual, which is the only level of reality accessible by astro-statistics. What is more, and supposing that it can find the means to investigate astrological practices in a pertinent way, which is to say that it manages to adapt its techniques to the matrix-based dimension of astrological knowledge, the conclusions of astrostatistics still do not yield research of a bio-physical nature concerning the functional possibilities of astrological operators.
I would suggest not only that the astrologer limit himself to a few essential that he should define, but also that he focus his interpretation on the essential kernel of the chart, keeping in mind the necessity of an adequate method of evaluation. This approach means not only that the imaginary bodies and the arithmetic points are to be thrown out the window, but also that a certain number of planets have no "influence" whatever in certain charts. One must also question the adequacy of the entire notion of "symbols." Venus is not the "symbol of love." A Saturnian-Mercurian, for example, perceives the external world through the coloration of Saturn and Mercury and acts according to the stimuli that come to him from that domain. To put it another way, he will live out his social relations and his amorous relations as a Saturnian-Mercurian.
Non-Significant Physical Bodies
These concern first of all the physical bodies outside the ecliptic: fixed stars, extra-Zodiacal constellations, and comets. These bodies, by reason of their distance from the circle of the ecliptic, are little used in modern astrology, with the exception of Chiron, hailed by some astrologers as the eleventh planet at the time of its discovery in 1977, then reclassified among the asteroids before being reslotted yet again by astronomers as a comet.
Comets are bodies composed of ice with very elliptical orbits. Supposedly there exist more than a million of them. Their extreme orbital eccentricity puts them at their aphelion in most cases beyond the orbit of Pluto. Their importance in the beginnings of Mesopotamien astrology has been established. Certain sections of the series ENUMA ANU ENLIL EA, such as the 13th and the last of the Babylonian treatise MUL.APIN  , take their inspiration from them and contain astro-meterological predictions concerning comets and stellar constellations. We also know of the political importance of the predictions arising from them.  The adversaries of astrology can find there inexhaustible material for criticism, as does the astronomer Pierre Petit  and the philosopher Pierre Bayle who takes his cue from Petit. 
A second sub-category includes physical bodies with non-significant cycles; planetary satellites and about a hundred fixed stars of large magnitude.  These bodies, although situated in the zone of the ecliptic, do not exhibit significant individual movement in relation to the Earth: the stars remain secondary to the daily cycle, and the planetary satellites do not distinguish them from their center of revolution, as seen from the Earth. Neither are these bodies sufficiently defined: the fixed stars participate in the precessional cycle, a hundred times longer than the cycle Pluto, and the cycle of the planetary satellites (particularly that of the four principal satellites of Jupiter, discovered by Galileo in 1610) becomes conflated, from a geocentric point of view, with that of their orbital compass. Consequently, there is no compelling reason to consider them, even if the astrologers of the past  used the stars in astro-meteorological prediction, perhaps less as an influencing operator than as an astrometric framework. The astronomer Geminos of Rhodes points out that fact forcefully: "It is generally supposed that this star [Sirius] possesses its own force and causes the intense heat concomitant with its helic rising. That simply is not how things occur. It so happens that this star rises at the hottest time of the year, so its rising has been taken as a sign of an intensification of the heat." 
A third sub-category includes small physical objects: essentially, the asteroids and the planetoids that have recently been discovered. The asteroids are bodies composed of rock -- dense, small in dimension, with orbits situated for the most part between Mars and Jupiter. They may be the remains of a planet that exploded, or inversely, they may be the material of a planet that failed to condense into form. The first four asteroids known, frequently used in astrology, were discovered between 1801 and 1807.  An amateur astronomer, the German K. Hencke, discovered Astree, then forty years later Hebe. It has been estimated that there exist as many asteroids as there are family names in common usage in France, so each family could have one named after it. The question whether or not these bodies, like the miniscule planetoids, should be retained as astrological operators, is addressed below.
The Solar System
The orbital and physical data for the asteroids comes from different sources; the information about the planets and their principal satellites is taken from Calvin J. Hamilton (1997-1999). 
Data for the Planets and Their Satellites
Name Sid. Rev. Inclin. Eccen. Equ. Rot. Magn. Dist. Radius Mass Sun -- -- -- 25-36 -26.8 0 695000 1.989e+30 Mercury 87.97 7.004 0.2056 58.6462 -1.9 57910 2439.7 3.303e+23 Venus 224.701 3.394 0.0068 -243.0187 -4.4 108200 6051.8 4.869e+24 Earth 365.256 0.000 0.0167 0.99727 -- 149600 6378.14 5.976e+24 Moon 27.32166 5.1454 0.05 27.32166 -12.74 384.4 1737.4 7.349e+22 Mars 686.98 1.850 0.0934 1.025957 -2.01 227940 3397.2 6.421e+23 Jupiter 4432.71 1.308 0.0483 0.41354 -2.70 778330 71492 1.9e+27 Io 1.769138 0.040 0.004 1.768138 5.02 421.60 1815 8.94e+22 Europa 3.551181 0.470 0.009 3.551181 5.29 670.90 1569 4.8e+22 Ganymede 7.154553 0.195 0.002 7.154553 4.61 1070 2631 1.48e+23 Callisto 16.68902 0.281 0.007 16.68902 5.65 1883 2403 1.08e+23 Saturn 10759.5 2.488 0.056 0.44401 0.67 1429400 60268 5.688e+26 Dione 2.736915 0.02 0.0022 2.736915 10.4 377.4 560 1.05e+21 Rhea 4.517500 0.35 0.001 4.517500 9.7 527.04 765 2.49e+21 Titan 15.94542 0.33 0.0292 15.94542 8.28 1221.85 2575 1.35e+23 Iapetus 79.33018 14.72 0.0283 79.33018 c.11 3561.3 730 1.88e+21 Uranus 30685 0.774 0.0461 -0.71833 5.52 2870990 25559 8.686e+25 Ariel 2.520379 0.31 0.0034 2.520379 14.16 191.24 578.9 1.27e+21 Umbriel 4.144177 0.36 0.005 4.144177 14.81 265.97 584.7 1.27e+21 Titania 8.705872 0.14 0.0022 8.705872 13.73 435.84 788.9 3.49e+21 Oberon 13.46324 0.10 0.0008 13.46324 13.94 582.60 761.4 3.03e+21 Neptune 60190 1.774 0.0097 0.67125 7.84 4504300 24746 1.024e+26 Triton -5.87685 157.35 0.000 -5.87685 13.47 354.80 1350 2.14e+22 Pluto 90800 17.148 0.2482 -6.3872 15.12 5913520 1137 1.27e+22 Charon 6.38725 98.80 0.000 6.38725 16.8 19.64 586 1.90e+21
Data for the Asteroids
No. Name Year Disc. Sid. Rev. Inclin. Eccen. Dist. Period Radius Mass 1 Ceres 1801 G. Piazzi 1681 10.6 0.079 413900 4.60 466 1.17e21 2 Pallas 1802 H. Olbers 1684 34.8 0.235 414500 4.61 251 2.18e20 3 Juno 1804 K. Harding 1594 13 0.256 399400 4.36 123 ? 4 Vesta 1807 H. Olbers 1325 7.1 0.088 353400 3.63 263 2.38e20 2060 Chiron 1977 C. Kowal 18402 6.93 0.38 2051900 50.38 85 ?
Sid. Rev : Sidereal revolution (in days)
Inclin. : Orbital inclination toward the ecliptic (in degrees)
Eccen. : Eccentricity of orbit
Equ. Rot. : Sidereal period of equatorial rotation (in days); a negative number indicates retrograde rotation
Magnit. : Visible magnitude (bodies in opposition to the Earth)
Dist. : Distance from the Sun, or, for satellites, from the planet's center (in thousands of km)
Radius : radius in km
Mass : mass in kg
No. : Order of discovery (for the asteroids)
Year : Year of discovery (for the asteroids)
Disc. : Discoverer (for the asteroids)
Period : Sidereal revolution in years (for the asteroids)
The following remarks on the physical and orbital characteristics of the planets are presented in order to show some similarities to be drawn between them and the astrological meanings of these planets (indicated by italics). It is simply a question here of coincidences, of "analogies," not of proofs.
Mercury is the most rapid planet (mobility) and its period of equatorial rotation is exactly two-thirds of its period of sidereal revolution (properties due to its proximity to the sun).
Venus is slow: the length of its equatorial rotation is very long, and it occurs in inverse proportion to its period of sidereal revolution. This most luminous of planets can appear as the "morning star" or as the "evening star" (dissociation).
Mars has a period of equatorial rotation of 24 hours 37 minutes (comparable to that of the Earth) and its equatorial inclination in relation to the plane of its orbit is 25°27'. This makes Mars the planet most similar to Earth (and Martian seasons are similar to those of Earth). Its orbital motion is apparently very irregular: slow, then fast (dynamism).
Jupiter is the most massive planet: approximately 2.5 times the mass of all the other planets (simplification).
Saturn has the richest and most diversified system of satellites (complexification).
The equatorial rotation of Uranus is almost perpendicular to the plane of its sidereal revolution (verticality).
The orbit of Neptune crosses that of Pluto (association), or vice versa, since Neptune at its perihelion is more distant from the Sun than Pluto.
Pluto is a planet of very particular characteristics (super-differentiation) by reason of its size, its mass and the properties of its orbit.
5. What is an Astrological Operator? : The Status of Pluto
What makes it possible for a celestial body to be an astrological operator? Are there criteria, reasons, or safeguards -- and of what nature, logical, astronomical, or "astrological"? -- that enable one to distinguish effectively active operators? The recent discovery (beginning in 1992) of a multitude of trans-Neptunian planetoids even calls again into question the status of Pluto as a planet, and the debate is currently open among astronomers.  The astrological question may be posed in these terms: what is a "planet" in astrology, or more precisely, what is a planetary operator?
In 1992 David Jewett and Jane Luu discovered a planetoid beyond Pluto, QB1 (or Smiley), with a radius of approximately 100 km. At the beginning of 1999, 82 such objects were known, in addition to Pluto and its satellite Charon, discovered in 1978 by Jim Christy. All the trans-Neptunian objects (TNO), named planetoids or planetesimals, have sidereal periods comparable to that of Pluto. But Pluto remains the only TNO known to possess a satellite; it is nearly 100 times more massive than the other known planetoids (with the exception of Charon), and the global mass of Pluton and Charon represents about 50% of the total mass of the planetoids. Moreover, Pluto has an atmospheric layer (probably composed of nitrogen, carbon monoxide and methane), like Titan and Triton, the principal satellites of Saturn and Neptune respectively.
Certain arguments have been put forward to deprive Pluto of its status as a planet and to redefine it as the first among the planetoids (the counterarguments follow in italics):
* All the outer planets of the solar system are gassy and of large dimension, with the exception of Pluto, which is small and telluric.
* Pluto is more than twice as small as the smallest planet, Mercury.
=> But the radius of Pluto is also two times larger than that of Ceres, the principal asteroid.
* Pluto's mass is approximately one-fifth that of the Moon.
=> But it is also ten times that of Ceres, whose mass is about a quarter of the total mass of the other asteroids.
* Pluto is smaller and lighter than seven of the satellites in the solar system: the Moon, Io, Europe, Ganymede, Callisto, Titan and Triton.
=> But Mercury is itself smaller than Ganymede and Titan, and the Moon is smaller and lighter than Io, Ganymede, Callisto and Titan.
* The orbit of Pluto is much more inclined vis-a-vis the ecliptic than the orbits of the other planets, and it is also more eccentric.
=> The status of Pluto is comparable to that of Mercury in this regard, which is not surprising given that these planets are in a certain sense the two extremes of the solar system.
* The orbit of Pluto is the only one to cross the orbit of another planet.
=> Certain astronomers, and also the young Kant, find in that fact a criterion that justifies classifying it as the last planet of the solar system. 
* The satellite of Pluto, Charon, is the largest in relation to its planet (the diameter of the Moon = 27% of the Earth's; Charon's diameter = 52% of Pluto's) and it is also the heaviest (the Moon's mass = 1.23% of Earth's; Charon's mass = 15% of Pluto's)
=> This leads us to consider Pluto-Charon as a double planet. In fact, Pluto is the only planet to have a satellite the periodic revolution of which is perfectly synchronous with its own: consequently, their positions relative to each other are always the same. Several hypotheses have been proposed concerning the origin of Pluto: some assume it to be a separated residual body of a planet situated between Mars and Jupiter (that supposedly exploded and also formed the asteroids), or a body attracted by the gravitational field of the solar system, or even an ancient satellite of Neptune that deviated from its trajectory.
Is Pluto a planet? Is it really surprising that the planet defined as strange, refractory and super-differentiated by astrologers should be precisely the one whose status is now called into question by astronomers? None of this may cause any discomfort to lax practitioners of astrology, although it must do for those who seek a harmonious confluence of the different planetary rhythms in the integration with living matter. I propose three criteria for the differentiation of a planet from another type of body in a stellar system:
* The question should not be whether the size of a body exceeds a certain arbitrary threshold, but rather what is the relationship of size between the given body with what precedes and what follows it. Hence the quotient of the radius R of the last planet divided by that of the first non-planet (asteroid) should be larger or comparable to the quotient of the radius of the penultimate planet divided by that of the last: R Pluto / R Ceres > R Mercury / R Pluto (the relationship Ceres / Vesta does not verify this formula). The same result emerges from the relationship of the masses if one takes the Moon in place of Mercury.
* Data relative to the planetary orbit.
The orbital inclination of the planet on the ecliptic should not exceed a certain angle. One might choose the angle of inclination on the equator of Earth projected onto the ecliptic, which has a value of 23°30. This criterion disqualifies the asteroid Pallas. The eccentricity of the orbit likewise should not exceed a certain level. In this light Pluto and Mercury are comparable, but the "asteroid" Chiron, now reclassified as a comet, shows too great an eccentricity. To these data we can add the argument of Kant, who thought it logical to define the final planet of the solar system as the one that crosses the orbit of the penultimate one. This is the case with Pluto relative to Neptune.
* The (spherical) aspect and above all the environment (presence of an atmosphere and possibly the present of satellites, as well, which is not the case for Mercury or Venus). This factor by itself enables one to classify Pluto as a planet, albeit a planet very different from the others. [40b]
6. Harmonies of the Solar System: the Great Year
I have allowed myself the mathematical amusement of doing research on the period of the "Great Year" by taking for the sidereal revolutions of the planets approximate whole numbers with as many common divisors in common as possible. The unit taken into account is the sidereal day. The sidereal revolution of the Moon being 27.32166 days, the whole number closest is 27 days (= 3 * 3 * 3), or an approximation of 1.18%, taken as a "natural" limit. I do not know if there exists a better solution.
||S. R. 1||S. R. 2||error|
The average approximation is 0.48%. The approximations for Earth and the Moon are comparable. We should recall that in the Chinese wei-chi (the game of Go), an ideal game unfolds on a board with 361 intersections, each one representing a day of the year. 
The planets can be put into two groups according to their common denominators: one the hand, the Moon, Venus, Saturn, Uranus and Pluto, and on the other hand, Mercury, Ceres (asteroids), Mars, Neptune, Earth (Sun) and Jupiter. The smallest common multiple is 171 547 200 (days) which, divided by the duration of the Earth cycle, yields 469,663 years. The duration of this "Great Year" is comparable to that of the Hindu kali yuga (432,000 years). It is almost exactly 189 times the Great Year (2484 years) of Aristarchos of Samos.  Of course, since the durations of planetary revolutions are incommensurate with each other, as Nicholas of Oresme pointed out,  this "Pythagorean" research can have no other object than to make evident certain correspondences between the planetary cycles.
Other analyses are possible, with an even closer approximation, especially for Mars, Saturn and Uranus, but they bring up very high multiples of the numbers 7 and 2. One can also use the following values, be it either for the sake of a closer approximation (in the case of Earth, Ceres and Uranus), or to bring up the number 19 (in the case of Venus and Saturn):
||S. R. 1||S. R. 2||error|
7. Harmony of the Sidereal Revolutions: Unity of the Solar System
The famous "law" of Titius-Bode that illustrates the regular progression of the average distance of the planets from the Sun, discovered in 1766 by the German physician Johann Titius (1729-1796) and reformulated in 1791 by Johann Bode had immediate success because it was "proven" in 1781 at the time Uranus was discovered and on 1 January 1801 when Giuseppe Piazzi discovered Ceres, the largest asteroid. Neptune and Pluto, however, do not conform to it.
Robin Heath (in: "An Astrological Cinderella," Astrological Journal, 40.6, 1998, p. 35) mentions a finding of Alex Geddes, namely that the products of the distances from the Sun for those planets situated in one part or other of the Asteroid Belt show the following relationship (where k = 1.2): Venus * Uranus = k (Mercury * Neptune) = k2 (Earth * Saturn) = k3 (Mars * Jupiter) [average approximation of 0.98%]
Much research has been done on the sidereal revolutions of the planets (abbreviated here as "S.R."); there follow some of the better known relationships, which have, however, an inadequate approximation:
a1: 1 S.R. of Mars = 3 S.R. of Venus (approximation 1.87%)
a2: 1 S.R. of Jupiter = 12 S.R. of Earth (approximation 1.16%)
a3: 1 S.R. of Uranus = 7 S.R. of Jupiter (approximation 1.16%)
a4: 2 S.R. of Saturn = 5 S.R. of Jupiter (approximation 0.67%)
a5: 4 S.R. of Mercury = 13 S.R. of the Moon (approximation 0.94%) but cf. infra
a6: 8 S.R. of Venus = 5 S.R. of Earth (approximation 1.57%) but cf. infra
The values that follow below have a closer approximation, but the numbers that define the planetary relationships are not significant (Ceres is taken as representative of the asteroids)
b1: 1 S.R. of Saturn = 48 S.R. of Venus (approximation 0.24%)
b2: 3 S.R. of Uranus = 55 S.R. of Ceres (approximation 0.04%)
b3: 7 S.R. of Jupiter = 18 S.R. of Ceres (approximation 0.23%)
b4: 17 S.R. of Mars = 32 S.R. of Earth (approximation 0.08%)
The following values are more solid since they harmonize the three trans--Saturnian planets. They show clearly a simple numeric resonance (1, 2, 3) for the three most distant planets:
c1: 1 S.R. of Neptune = 2 S.R. of Uranus (approximation 1.96%)
c2: 1 S.R. of Pluto = 3 S.R. of Uranus (approximation 1.38%)
c3: 2 S.R. of Pluto = 3 S.R. of Neptune (approximation 0.57%)
c4: from which 1 S.R. of Neptune + 1 S.R. of Uranus = 1 S.R. of Pluto (approximation 0.08%)
[Note: On Nostradamus & the trans-Saturnian planets, see "Nostradamus connaissait-il les planètes trans-saturniennes?", http://cura.free.fr/05nostra.html, soon available in English.]
Professor Gerhard Krüger has shown in his article "Kosmische Signale der technischen Revolution" published in the Kosmobiologisches Jahrbuch of Ebertin (No. 39, Aalen, 1968, p.67-69) that one could represent the periods of the sidereal revolutions of the three slow planets using cubes perfectly arranged in pyramidal form, each cube representing one year. Uranus (84 years) = 1*1 + 3*3 + 5*5 + 7*7 ; Neptune (165 years) = 1*1 + 3*3 + 5*5 + 7*7 + 9*9, and Pluto (249 years) = 1*1 + 3*3 + 5*5 + 7*7 + 9*9 + 7*7 + 5*5 + 3*3 + 1*1. These remarkable relations "would explain" the only approximate harmonization of the three planets (the ideal values of the Uranian and Neptunian sidereal revolutions being 83 years and 166 years), symbolize the closing of the solar system with Pluto, and extend the model of the 5 regular Euclidean solids, worked out by Kepler in his Mysterium cosmographicum (1596).
I have found the following relationships, the second one having a close approximation. They show clearly in a ratio of 1:10 three planetary pairs, the first consisting of the two giant planets, the second of the two "planets" most similar to Earth, the last including Pluto - Earth (or Pluto - Sun), the two planets at the extremes, both by reason of their size but also because they form the boundaries of the solar system.
d1: relationship of S.R. Saturn - Jupiter = 10 times the relationship of S.R. Mars - the Moon (approximation 1.25%)
d2: relationship of S.R. Saturn - Jupiter = 100 times the relationship of S.R. Pluto - Earth (approximation 0.11%)
Other relationships documented by Thomas Schmidt isolate a group of four planets vis-a-vis the number Pi (= 3.1416): Mars, Jupiter, Saturn, and the Moon. 
e1: relationship of S.R. Jupiter - Mars = 2 Pi (approximation 0.38%)
e2: relationship of S.R. Saturn - Mars = 5 Pi (approximation 0.29%)
e3: relationship of S.R. Mars - Moon = 8 Pi (approximation 0.05%)
e4: 1 S.R. Mercury = 28 Pi (approximation 0.005%)
Still other relationships more approximate in nature group the remaining planets, with Mars and the Moon once again, vis-a-vis the golden number Phi, which is equal to 1.618034:
f1: relationship of S.R. Earth - Venus = Phi (approximation 0.46%)
f2: relationship of S.R. Mercury - Moon = 2 Phi (approximation 0.5%)
f3: relationship of S.R. Venus - Moon = 5 Phi (approximation 1.66%)
f4: relationship of S.R. Mars - Mercury = 3 Phi2 (approximation 0.19%)
f5: 1 S.R. of Uranus = 1000 * 19 Phi (approximation 0.19%)
It is useful to observe that in the series c, e and f the equations bring into play the numbers of Fibonacci (2, 3, 5 and 8), linked to Phi. To sum up, then, we can put the planets into three groups: the slow planets (Uranus, Neptune and Pluto), in a simple, arithmetical resonance; the central planets (Saturn, Jupiter, Mars and the Moon) in resonance with the number Pi; and the rapid planets (Mercury, Earth or Sun, and Venus), to which can be added Mars and the Moon, in resonance with the number Phi.
Other work on the planetary harmonies has been undertaken by various authors.  In France, the research of Francis Warrain on the angular velocities of the planets promises to enlarge the harmonic conception of Kepler, still limited in 1619 to the planets of the Septenary: "We have seen that the introduction of the planets unknown to Kepler: Uranus, Neptune, Pluto and the Asteroids, in a certain sense completes a chromatic scale, and in another sense fills out an enharmonic Pythagorean third."  The work of Jean-Pierre Nicola,  in search of of a new helio-planetary order, takes its inspiration from that of Warrain: diverse numerical transformations, at times of a very convoluted nature,  based on astrometric data relative to the planets (linear speed, average distance from the Sun, average surface gravity at the equator ...) enable us to see a harmony in the larger group and give evidence of an axis of symmetry Moon-Mars that legitimizes the grouping of planets into the pairs Sun-Pluto, Venus-Neptune, Mercury-Uranus and Jupiter-Saturn.  Evidence also appears for a division of the planets into the three groups SUN-VENUS-MERCURY, JUPITER-MARS-SATURN, URANUS-NEPTUNE-PLUTO,  which seems to close the system and discourage the introduction of trans-Plutonian planets that may be discovered in future.
 in: Ennéades, IV 4.32, French trans. by Émile Bréhier, Paris, Belles Lettres, 1927; 1964, p. 137. « Text
 Ibid.« Text
 Henri Bergson, L'évolution créatrice, in Oeuvres, Paris, P.U.F., 1959; 1970, p. 503. « Text
 Cf. for example Giovanni Pontano (1475), Antoine Mizauld (1550), Giovanni Paolo Galluci (1593), John Blagrave (1596), Rudolph Göckel (1602 & 1608), Redemptus Baranzanus (1617), Nicolas de Bourdin (1640), Vincent Wing (1649), Eustache Lenoble (1694), John Hill (1754) ... « Text
 Cf. Paul Schlyter, "Hypothetical Planets" (http://www.seds.org/billa/tnp/hypo.html) « Text
 Ibid.« Text
 F. Vassart, Astronomie. Douze planètes, Cambrai, 1881. « Text
 B.M. Lyons, ms 5843-2A. « Text
 Cited by Robert Amadou, "Pour l'astrologie" in L'Autre Monde, 54, 1981, p. 55. « Text
 in: Manuel d'astrologie sphériqueet judiciaire, Paris, Vigot, 1897, p. 316. « Text
 in: Astrology, Its Technics and Ethics, Amersfoort (Netherlands), 1917. « Text
 in: The science of foreknowledge, 1898; London, Foulsham, 1918. « Text
 Cf. Alfred Witte, Regelwerk für Planetenbilder, Hamburg, 1928; 5th rev. ed. Hamburg, 1959. « Text
 Cf. Udo Rudolph, The Hamburg School of Astrology (lecture given in 1973), English translation published in London by the Astrological Association, 1973. « Text
 in: The Wheel of Life, vol. 3, London, Fowler, 1930, and vol. 4, Edinburgh, [1935?] « Text
 in: La lyre d'Apollon, Paris, Véga, 1931 (Ref. Jacques Hallbronn, Bibliotheca Astrologica). « Text
 Cf. Léon Lasson, A la recherche des planètes transplutoniennes, Neuilly-sur-Marne, Claude Depaire, 1955. « Text
 Ref. Geoffrey Dean, Recent Advances in Natal Astrology, Subiaco (Australia), Analogic, 1977, p. 242. « Text
 Rudhyar used them in 1936: cf. for example Dane Rudhyar, The Astrology of Personality, New York, Lucis Press, 1936; French translation Paris, Librairie de Médicis, 1984, p. 237. « Text
 Cf. Theodor Landscheidt, Cosmic Cybernetics (the Foundations of a Modern Astrology), Engl. transl. Linda Kratzsch, Aalen, Ebertin, 1973, p. 21, and Charles Harvey, "The Galactic Center & Beyond: Signposts to Evolution?" in: Astrological Journal 25.2, 1983. « Text
 According to Robert Schmidt and Robert Hand, Companion to the Greek Track, Berkeley Springs, The Golden Hind Press, 1994, p. 38. Cf. also Otto Neugebauer and Henry Van Hoesen, Greek Horoscopes, Philadelphia, American Philosophical Society, 1959, p. 8-9. « Text
 According to Schmidt and Hand, op. cit., p. 38. « Text
 According to Schmidt and Hand, op. cit., p. 39. « Text
 Cf. his Tafhim, 1029; The Book of Instruction in the Elements of the Art of Astrology, edited and translated by R.R. Wright, London, Luzac, 1924, p. 282. « Text
 In the form A + B - C, and with limitation to the Zodiacal position of the ten planets, the AS and the MC, there are more than 1,500. « Text
 My own Part of C.U.R.A. is conjunct my natal Sun with an orb of less than 2 degrees, which bespeaks a good matrix for my project. « Text
 in: Kombination der Gestirneinflüsse (1940; 1973); French translation Combinaison des influences astrales, Monaco, Le Rocher, 1983. « Text
 The midpoint Moon/Saturn at 1350 of the North Node of the Moon is considered by the astrologer Michael Harding as a significant configuration! (in: Hymns to the Ancient Gods, London, Arkana/Penguin, 1992, p. 344). « Text
 Geoffrey Dean, Recent Advances in Natal Astrology, Subiaco (Australia), Analogic, 1977, p. 34. « Text
 Cf. Hermann Hunger and David Pingree, Mul.Apin, an Astronomical Compendium in Cuneiform, Horn (Austria), Archiv für Orientforschung, Beiheft 24, 1989. « Text
 Cf. Lynn Thorndike, Latrin Treatises on Comets (Between 1238 and 1368 AD), University of Chicago Press, 1950, or Jacques Hallbronn, "Les variations d'impact des 'comètes' in France. Étude bibliographique (fin XVè - fin XVIIIè siècles)" in: La comète Halley et l'influence sociale et politique des astres [Actes du Colloque de 1986], Bayeux, 1991. « Text
 In his Dissertation sur la nature des comètes, Paris, Thomas Jolly, 1665. « Text
 In his famous Pensées diverses sur la comète, Rotterdam, 1682; ed. A. Prat, Paris, Nizet, 1984, 2 vols. « Text
 The definitive work on the subject remains that of Vivian Robson: Les étoiles fixes et les constellations en astrologie, 1923, 1984; French translation by Puiseaux (45), Pardès, 1991. « Text
 Ptolemy and the anonymous astrologer of 379, for example. Cf. Ptolemy, The Phases of the Fixed Stars, and The Treatise on the Bright Fixed Stars, Berkeley Springs, The Golden Hind Press, 1993 and 1993. « Text
 in: Introduction aux phenomènes, XVII 26, ed. and trans. by Germaine Aujac, Paris, Belles Lettres, 1975, p. 88. « Text
 It should be noted that there are more than a dozen asteroids larger than Juno. « Text
 Pages data1.htm and data2.htm at the address http://planetscapes.com/solar/eng/ « Text
 The International Astronomical Union is considering the reclassification of Pluto as a trans-Neptunian object. « Text
 "One could, if one wished, name as the last planet or the first comet the body the eccentricity of which is so great that it would intersect at its perihelion the orbit of the nearest planet, perhaps then that of Saturn." (Emmanuel Kant, Histoire générale de la nature et théorie du ciel, 1755; French translation, Paris, Vrin, 1984, p.98. « Text
[40b] Note P.G. (Oct. 8, 2002): A big planetoid has been recently discovered by Michael Brown and Chad Trujillo from the California Institute of Technology in Pasadena. [See CNN News, "Biggest object since Pluto found in solar system", or BBC News, "Large world found beyond Pluto".] The object, named Quaoar, pronounced KWAH-o-ar, after a god of the Tongva American tribe (South California), could have 1,300 kilometers in diameter and a sidereal revolution of 288 years.
The discussion on the nature of Pluto (planet or Kuiper-belt object) is revived. My argumentation for considering Pluto as the "last planet" of the solar system is not changed, even if Pluto-Charon ought to be now best considered as the chief "object" of the Kuiper-belt. « Text
 Cf. the novel of Yasunari Kawabata, Le Maître ou le tournoi de Go, French translation by S. Regnault-Gatier, Paris, Albin Michel, 1975. « Text
 Cf. Censorinus, Le jour natal, 18.11, French translation by Guillaume Rocca-Serra, Paris, Vrin, 1980, p. 29. « Text
 Cf. "Nicole Oresme: Un regard lucide sur l'astrologie" ( http://cura.free.fr/docum/03oresme.html ) « Text
 in: Musik und Kosmos als Schöpfungswunder, Frankfurt, 1974. Cf. Ronald Harvey, "The Harmony of the Spheres" in: Astrological Journal 17.2, 1975. (Thomas Schmidt has also shown the significant relationships that bring into play the golden number Pi and the synodic revolutions of the planets.) « Text
 Cf. Geoffrey Dean, Recent Advances in Natal Astrology, Subiaco (Australia), Analogic, 1977, p. 222-223, and on the Web, the site of John Harris, Spira Solis ( http://www3.bc.sympatico.ca/JNDHA/index.htm ) « Text
 in: Essai sur l'Harmonices Mundi ou Musique du monde de Johannes Kepler, Paris, Hermann, 1942, vol. 2, p. 136. « Text
 Nombres et formes du cosmos, Paris, Ed. Traditionnelles, 1973, and Éléments de cosmogonie astrologique, St-Denis-sur-Huisne, C.O.M.A.C., 1992. « Text
 Cf. Geoffrey Dean, op. cit.,p. 223. « Text
 Éléments de cosmogonie astrologique, fig. 18, p. 140. « Text
 Éléments de cosmogonie astrologique, p. 145. « Text
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