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SPICA, 1964, vol. 3, nš 3, p. 3-10 THE TOPOCENTRIC SYSTEM OF HOUSES by Wendel Polich & A. P. Nelson Page (Buenos Aires, Argentina) |
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First and foremost we must point out the following: we did not construct the Topocentric System of Houses – we discovered it. In our search for the true Houses, we did not set out from any
preconceived idea or preliminary postulate, but sought to locate them purely and
exclusively by means of the There are many systems of Houses that are built around a given theory or exigency, such
as the trisection of a given arc, a certain kind of pole, etc., which approximate reality
with 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
– Origins 'We started out from the following reasoning: if it is possible to establish with total
exactitude the precise moment of a birth by means of the important events in the life of a
given person (rectifications we have often achieved), then why not determine the circle of
a House by means of the events of the same nature as that House? To do this, we had only
to invert the procedure employed in PD's: start off from the directional ecliptic point
that produced the event, add to it the arc of age (Naibod), and measure the arc upon the
respective parallel from the ecliptic point and thus obtain If we repeated this procedure with other events, characteristic of that House, we would
obtain various points upon the respective parallels, which, all together, would perforce
have to coincide with a segment of the real circle of the House. Uniting these points in a
curve, we would obtain the circle built up out of the The idea was put to the test. We collected series of events, related to a given
Intermediate House, of people whose FIG. 1 DETERMINATION OF HOUSE-CIRCLE WITH AID OF EVENTS. We submitted the curve we thus established to mathematical analysis to see to what pole
it belonged, so as to be able to reproduce it mathematically. And here we had our first
surprise: we found that Originally we had no topocentric solution in mind, but now we were forced to examine
analytically the curve obtained from the point of view of the place of birth as the centre
of a topocentric sphere. And here we had our second surprise: this curve seen from the
place of birth proved to be Only when we observed Is the reader aware of the importance of this finding which is in reality a great
discovery?! Observe that this trisection was not a preliminary condition to be fulfilled;
it was an This discovery radically changed all our concepts on Houses, since it was evident that
they were not to be found upon the sphere as it is generally believed, but upon the Ascension of Planets If the reader desires to form a clear idea of the physical reality of the Topocentric Houses, it is essential that he follow our explanations step by step since this system differs essentially from all others. Let the reader imagine that he, himself, is situated at the place of birth upon the local axis. Let him raise his eyes to any planet in the sky and, in his imagination, trace a 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. This line is of enormous importance to the native. It is in reality the line of ascension of the planet. The angle that this line forms with the plane of the Prime Vertical is the angle 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 as topocentre. But the positions that are given in the ephemeris are not given for the topocentric sphere, but for the geocentric as seen from the centre of the earth. To be able to compare the purely topocentric data with the data given in the ephemeris, we have but two alternatives: either we transform the positions given in the ephemerides, or we express the topocentric data in geocentric measures. It is evident that the second alternative is the more practical. Because of this we must also relate this temporal line and its pole with the centre of
the 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 the
plane of the Meridian along a straight line which we call the "temporal line of the
horizon" (commonly known as 'the horizontal polar axis'). This line cuts the local
axis at an angular point (H
Physical View of the Houses Let the reader imagine a star situated exactly on the "temporal line of the
horizon", in other words, upon the line of intersection of the planes of the horizon
and 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 its
parallel and so also does the temporal line of the horizon, and as a lineal generatrix it
describes a cone of rotation with vertex at the angular point (H 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 10th houses, and the angle that the temporal line of the house forms at those points of tri-section, with the plane that passes vertically through the local axis, will be its pole. If the reader imagines planes passing through those temporal lines of the houses and the local axis, he will have a vision of the topocentric houses in function of ascension and of-the-hour angles. Where the temporal line of a house cuts the ecliptic, there is to be found the cusp, which automatically trisects its semi-arcs (time), and the quadrant between the meridian and horizon (space). This is illustrated in Fig. 3. Since in the celestial sphere the local axis may be coincident with the axis of the world, they are placed together in the figure. Starting from the 12h. meridian, the 14-, 16- and 18-hour circles are seen; also, the temporal lines of ascension of 12, 14, 16 and 18 hs. which coincide 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 a certainty and exactitude hitherto unknown. The reader cannot imagine the formidable power and importance that the topocentric
poles have in The ecliptic aspects, as sources of energy and reflections of the internal potentials
of the native, are the 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,
Practical Procedure
The non-mathematically minded astrologer should not be put off by the seeming complexity of the formulae that follow. He need not understand their essence. They have been 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, by far the most important and personal factors in any chart – all he requires are tables of common (decimal) and trigonometric logarithms and of ascendants or of oblique ascension, 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 soon see if he experiments with our example. To calculate the House Cusps, their poles are needed. The general formula for the topocentric 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 obtains
the real position of the stars and cusps in purely It must be realized that the houses stem from the Equator and that consequently the SA will be 90° and the MD 30° and 60°, according to the intermediate house. Thus: (for houses 11/5 and 3/9) (for houses 12/6 and 2/8) 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 the poles 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 Oblique Ascensions 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 to subtract six hours from the S.T. of birth to obtain the "Table" S.T. of the 10th House. If two hours are added successively to this "T" S.T. for each House, as we have done in the example, the reader will immediately be ready to extract the cusps sought from the Tables, under the respective topocentric poles. It is necessary, of course, to effect 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 more practical, 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 well within 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 Mundane Transits. NOTE Observe that although the Moon in this example is in close 207°30' – 103°27'=104°03' for it to take form or have an outlet in the physical circumstances and events in his life. But .... "As a man thinketh in his heart, so is he." December 1963 |