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First and foremost we must point out the following: we did not construct theTopocentric System of Houses – we discovered it. In our search for the true Houses, we did not set out from anypreconceived idea or preliminary postulate, but sought to locate them purely andexclusively by means of the actual events of life. There are many systems of Houses that are built around a given theory or exigency, suchas the trisection of a given arc, a certain kind of pole, etc., which approximate realitywith greater or less accuracy, but a system such as the one we are about to describe,determined exclusively on the basis of actual facts, without any 'a priori' condition– not even the classical trisection - was never achieved in the past. Origins 'We started out from the following reasoning: if it is possible to establish with totalexactitude the precise moment of a birth by means of the important events in the life of agiven person (rectifications we have often achieved), then why not determine the circle ofa House by means of the events of the same nature as that House? To do this, we had onlyto invert the procedure employed in PD's: start off from the directional ecliptic pointthat produced the event, add to it the arc of age (Naibod), and measure the arc upon therespective parallel from the ecliptic point and thus obtain a real point belonging tothe circle of the House which we sought! If we repeated this procedure with other events, characteristic of that House, we wouldobtain various points upon the respective parallels, which, all together, would perforcehave to coincide with a segment of the real circle of the House. Uniting these points in acurve, we would obtain the circle built up out of the actual events in a given life. The idea was put to the test. We collected series of events, related to a givenIntermediate House, of people whose time of birth was known very precisely. Thefirst effective House circle we obtained was of the 9th, by means of the dates of a seriesof long voyages (see Fig. 1).
FIG. 1 DETERMINATION OF HOUSE-CIRCLE WITH AID OF EVENTS. We submitted the curve we thus established to mathematical analysis to see to what poleit belonged, so as to be able to reproduce it mathematically. And here we had our firstsurprise: we found that the curve did not belong to any great circle! Thisdiscovery pointed to the fact that none of the known systems of Houses could be right,since all of them were based on great circles, thus destroying our expectations that oneof the known systems would triumphantly pass our test as being the only one. Originally we had no topocentric solution in mind, but now we were forced to examineanalytically the curve obtained from the point of view of the place of birth as the centreof a topocentric sphere. And here we had our second surprise: this curve seen from theplace of birth proved to be a straight line! This straight line was, for us, for along time, an incomprehensible Chinese puzzle. A circle determines a plane, but not astraight line! And what could a straight line mean in spherical trigonometry? The problembecame more complex because now we needed a pole that determined a curve, which seen fromthe place of birth was a straight line, but, from the centre of the earth, a curve. But itmust not constitute the segment of a great circle. We checked and rechecked all our data;we repeated the experiment for the other intermediate Houses and invariably the samemysterious curve turned up. In vain we sought for the solution upon the sphere, or uponthe cylinder elevated perpendicularly from the Equator. All was useless. Only when we observed the apparent rotation of the firmament in its ascensionand descension around the place of birth and around the 'local axis' (which passesthrough the geographic spot, parallel to the axis of the world), from the point of view ofthe geographical spot as a fixed point, were we able to see light and understand thereason for the straight line, since this, in conjunction with the local axis firstmentioned, determines the plane-of-an-hour angle! And now with this plane we were at lastable to continue our mathematical analysis, only to be confronted with a third surprise– this time most marvellous – for behold: every single point of that line wasisochronous, each trisecting with absolute precision the semi-arc cut, and all seentopocentrically! Is the reader aware of the importance of this finding which is in reality a greatdiscovery?! Observe that this trisection was not a preliminary condition to be fulfilled;it was an 'a posteriori' and effective result obtained by a scientific process thatproved beyond doubt the truth of the astrological principles underlying Houses, aprocedure which can be repeated by anyone who can handle mathematics and has anunderstanding of PD's. Observe that it was not the trisection of one semi-arc whichwas obtained, but the exact tri-section of all possible semi-arcs, from the Equator to thePoles. This discovery radically changed all our concepts on Houses, since it was evident thatthey were not to be found upon the sphere as it is generally believed, but upon the plane-of-hourangles in function of ascension, with centre at the place of birth. If the tri-sectionof the semi-arcs mentioned gives the exact division of time. the hour planes ensurethe exact division of space around the local axis. In this way, the TopocentricSystem of Houses contains the joint solution of the two premises held by the two mostimportant astrological schools of thought which exact – as a condition – one,the tri-section of time (Placidus), and the other, the tri-section of space (Campanus). Ascension of Planets If the reader desires to form a clear idea of the physical reality of the TopocentricHouses, it is essential that he follow our explanations step by step since this systemdiffers essentially from all others. Let the reader imagine that he, himself, is situated at the place of birth upon thelocal axis. Let him raise his eyes to any planet in the sky and, in his imagination, tracea straight line from the planet to himself. This straight line we shall call a'temporal line'. This is the straight line which caused as so much trouble. Thisline is of enormous importance to the native. It is in reality the line of ascension ofthe planet. The angle that this line forms with the plane of the Prime Vertical is theangle of ascension which we call the 'topocentric pole'. All that has been said is to be understood in its relation to the place of birth astopocentre. But the positions that are given in the ephemeris are not given for thetopocentric sphere, but for the geocentric as seen from the centre of the earth. To beable to compare the purely topocentric data with the data given in the ephemeris, we havebut two alternatives: either we transform the positions given in the ephemerides, or weexpress the topocentric data in geocentric measures. It is evident that the secondalternative is the more practical. Because of this we must also relate this temporal line and its pole with the centre ofthe earth and this may be obtained if we work with the geocentric horizon (see Fig. 2)which passes through it. The plane of this horizon (perpendicular to the drawing) cuts theplane of the Meridian along a straight line which we call the 'temporal line of thehorizon' (commonly known as 'the horizontal polar axis'). This line cuts the localaxis at an angular point (H1) which is common to both the geocentric and thetopocentric systems; therefore, if from the given planet (B) we draw a straight line tothis angular point, we have its geocentric expression. And the pole (j) will be the angle that thisnew line forms with the plane of the local axis. The formula for the topocentric pole,given further on, already gives the topocentric position of the planet in relation to thecentre of the earth.
Physical View of the Houses Let the reader imagine a star situated exactly on the 'temporal line of thehorizon', in other words, upon the line of intersection of the planes of the horizonand meridian. Observing this star in its apparent rotation around the local axis, which,in reality, is the motion of ascension, the reader will see that the star moves upon itsparallel and so also does the temporal line of the horizon, and as a lineal generatrix itdescribes a cone of rotation with vertex at the angular point (H1), which isfixed. In 2, 4 and 6 hours, that star and the line will describe exactly 30, 60 and 90°around the local axis, and the straight line at those points of tri-section will be –in function of the real rotation – the temporal lines of the 8th, 9th and 10thhouses, and the angle that the temporal line of the house forms at those points oftri-section, with the plane that passes vertically through the local axis, will be itspole. If the reader imagines planes passing through those temporal lines of the houses andthe local axis, he will have a vision of the topocentric houses in function of ascensionand of-the-hour angles. Where the temporal line of a house cuts the ecliptic, there is tobe found the cusp, which automatically trisects its semi-arcs (time), and the quadrantbetween the meridian and horizon (space). This is illustrated in Fig. 3. Since in thecelestial sphere the local axis may be coincident with the axis of the world, they areplaced together in the figure. Starting from the 12h. meridian, the 14-, 16- and 18-hourcircles are seen; also, the temporal lines of ascension of 12, 14, 16 and 18 hs. whichcoincide with the hour planes determining houses 10, 11, 12 and Asc.
Experiences Since the Topocentric System was constructed exclusively upon the real events of life,naturally the directions and transits calculated with it reflect the events of life with acertainty and exactitude hitherto unknown. The reader cannot imagine the formidable power and importance that the topocentricpoles have in the physical realization of the events. We can now anticipate (thiswe have experimentally proven) that all events, major and minor alike, are realizeddirectly through the agency of these poles. The ecliptic aspects, as sources of energy and reflections of the internal potentialsof the native, are the causes of the events, which act upon the inner life of theindividual within an orb, i.e. either before or after the exact aspect. But theirphysical, realization is always produced by an ascension transit (mundane), that hasno orb and which is discharged exactly at the instant the planet in the sky arrives in itsascensional motion (apparent rotation around the local axis), at the same height ofanother radical planet or cusp. that is to say the same radical pole (conjunctions andoppositions in OA). So potent a factor as ascension has been completely ignored in the preceding systems,in which only the horizon and meridian have ascensional value, i.e. power of realization.In the Topocentric System, the circles of all the planets and of all the houses areof astronomical ascension and hence the physical power of realization of all of them! Practical Procedure The non-mathematically minded astrologer should not be put off by the seemingcomplexity of the formulae that follow. He need not understand their essence. They havebeen included only for the benefit of those who will. To arrive at the exact cusps of those charts where the exact time of birth is known– as indeed he must if he is to reckon transits and directions to and from them, byfar the most important and personal factors in any chart – all he requires are tablesof common (decimal) and trigonometric logarithms and of ascendants or of obliqueascension, such as those recommended hereunder. The rest is a simple matter of addition,subtraction, and rule of three, requiring no other specialized knowledge as he will soonsee if he experiments with our example. To calculate the House Cusps, their poles are needed. The general formula for thetopocentric pole is:
where j is the topocentric pole and F the geographical latitude. This formula is as valid for the stars and planets as it is for the cusps. It obtainsthe real position of the stars and cusps in purely temporal measures, sincedeclination, an expression of the curvature of the sphere, has been eliminated andsubstituted by arcs of time. It must be realized that the houses stem from the Equator and that consequently the SAwill be 90° and the MD 30° and 60°, according to the intermediate house. Thus:
These poles can be obtained with the aid of logarithms, as follows: Example 1 We have chosen the latitude corresponding to the heart of London (51°32 N) and thepoles obtained will invariably be the same for that parallel. House Poles
(The pole of the 10th is always 0°00'). The cusps may be calculated directly or extracted from a Table of Ascendants or ObliqueAscensions under the Topocentric Pole of the House. For this purpose, H. J. Gouchon's'TABLE D'ASCENDANCE' is of inestimable value, since it is necessary only tosubtract six hours from the S.T. of birth to obtain the 'Table' S.T. of the 10thHouse. If two hours are added successively to this 'T' S.T. for each House, as wehave done in the example, the reader will immediately be ready to extract the cusps soughtfrom the Tables, under the respective topocentric poles. It is necessary, of course, toeffect the corresponding interpolations between Poles and Sidereal Times, given in Tables,to seconds for precision. If one prefers to work directly with OA, which is often morepractical, nothing better can be recommended than E. K. Kuhr's magnificent 'PDT'and 'AO TABELLEN'. As a check, let him compare results with Placidus' cusps. These will always be wellwithin one degree of the topocentrics. Example 2 Given S.T. of B: 3h 50m 00s = RAMC 57°30' Lat. 51°32 N
Example 3 Pole and OA or OD of a Planet or Star
This is the true Topocentric Pole and OA to be used in Primary Directions and MundaneTransits. NOTE Observe that although the Moon in this example is in close ecliptic square tothe cusps of Houses 3/9 (an ever-present inner potential inherent in the emotional andmental make-up of this native), it is too far from the mundane square 207°30' – 103°27'=104°03' for it to take form or have an outlet in the physical circumstances and events in hislife. But .... 'As a man thinketh in his heart, so is he.' December 1963 |
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(for houses 11/5 and 3/9)
(for houses 12/6 and 2/8)
