On the Invariance of the Tropical Zodiac -- Part II

by Robert Hand

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The reader will note the differences are small. For all practical purposes the rising times of the tropical signs for any particular latitude are virtually constant over time.

By contrast let us look at the rising times of sidereal signs using the Fagan-Allan ayanamsha [the difference between the tropical and sidereal zodiacs] computed for the same two epochs again using modern methods.

Rising Times of the Sidereal Signs at Babylon
ArTaGeCnLeViLiScSgCpAqPi
501 B.C.E.21 0425 3031 4235 4035 5535 1535 3936 0433 2927 3322 1219 56
2000 B.C.E.20 1320 4924 4230 4435 1235 5735 1635 2836 0134 4028 3422 59

Upon examining the table two things become apparent. First of all the rising times of the sidereal signs are far from constant over time. Note particularly the rising time of sidereal Gemini in 501 B.C.E. which equals 31d 42m. But in the year 2000 C.E. Gemini's rising times will be 24d 42m a difference of 7 degrees!

Second the symmetry that we noted between pairs of signs R1-R12 (Ar-Pi), R2-R11 (Ta-Aq), R3-R10 (Ge-Cp), etc. is not present. In 501 B.C.E. Gemini gets 31d 42m while the sign that ought to be symmetrical with it, Capricorn, gets 27d 33m. In the year 2000 C.E. Gemini gets 24d 42m and Capricorn gets 34d 04m. The symmetry of the rising times of the 30 degree segments requires that the measuring of the segments be done from one of the equinoctial points. This may require some explanation.

Coordinate Table for the Beginnings of the Tropical Signs for 40 Degrees North Latitude:
Long.270.000300.000330.0000.00030.00060.000
R.A.270.000302.183332.0910.00027.90957.817
Decl.-23.450-20.159-11.4770.00011.47720.159
A.D.-21.345-17.942-9.8090.0009.80917.942
O.A.291.345320.125341.9000.00018.10039.875
R.T.28.78121.77518.10018.10021.77528.781
Long.90.000120.000150.000180.000210.000240.000
R.A.90.000122.183152.091180.000207.909237.817
Decl.23.45020.15911.4770.000-11.477-20.159
A.D.21.34517.9429.8090.000-9.809-17.942
O.A.68.655104.241142.282180.000217.718255.759
R.T.35.58638.04137.71837.71838.84135.586

In the table given above we have the following: The first row marked "Long." contains the tropical longitudes of the beginning of each sign. The second row marked "R.A." contains the right ascension of the beginning of each sign. The row marked "Decl." is declination of the ecliptic degree at the beginning of each sign. The row marked "A.D." contains the ascensional difference of the beginning of each sign. This will be explained shortly. The row marked "O.A." contains the oblique ascension of the beginning of each sign. This will also be explained shortly. And last the row marked "R.T." contains the rising times of the signs which begin at the designated longitude.

First an explanation of oblique ascension. On the equator all positions on the celestial sphere, regardless of declination, rise along with their right ascensions at 0 degrees declination. This is because at the terrestrial equator the celestial equator rises in the east exactly perpendicular to the horizon, hence the term "right" ascension, "right" meaning perfectly upright. But either north or south of the terrestrial equator positions on the celestial sphere do not rise with their positions measured in right ascension. They rise along some other degree on the celestial equator. This other degree is the oblique (or slantwise) ascension of our hypothetical position on the celestial sphere. It is called oblique ascension because the celestial equator at latitudes other than 0 degrees north or south rises slantwise or obliquely in the east, the further away from 0 latitude, the more obliquely. Therefore the oblique ascension of position A can be defined as whatever degree on the equator may be rising when A exactly touches the horizon assuming that A is not on the celestial equator, i.e., that A has a declination not equal to 0.

Ascensional difference or A.D. is a measure of the difference between the R.A. or right ascension of a point and its O.A. or oblique ascension. The formula is as follows:

O.A. = R.A. - A.D.

Thus the A.D. of a point is required to find the O.A. of that point. The A.D. of a point in turn is derived from the declination of the point and the terrestrial latitude of the place in question by the following formula.

AD = arcsin(tan Decl. x tan Latitude)

These relationships can be seen in the coordinate table shown above. Note from the table that arc from the O.A. of 330 degrees to the O.A. of 360 or 0 degrees is the same as the arc from the O.A. of 0 degrees to the O.A. of 30 degrees. These arcs are the rising times of tropical Pisces and Aries. This is the consequence of the following two facts: First that the arc in R.A. from 0 degrees tropical Pisces to 0 degrees tropical Aries is the same as the arc in R.A. from 0 degrees tropical Aries to 30 degrees tropical Aries (or 0 degrees Taurus). The second fact is that the declination of 0 degrees tropical Pisces is the exact opposite of the declination of 30 degrees tropical Aries, the first being -11.477 degrees, the second being +11.477. This in turn causes the A.D. of 0 degrees tropical Pisces to be the exact opposite of the A.D. of 30 degrees tropical Aries.

Only if two points are symmetrical with respect to the equinoxes can they possess this symmetry of arcs in O.A. which in turn produces the symmetrical rising times of signs with are equidistant from the equinoxes. This symmetry can occur in a sidereal zodiac only when the vernal point is at exactly 0 degrees of a sign. The Babylonians of Systems A and B knew this which is why they measured the rising times of 30 degree arcs from the vernal point rather than from 0 degrees of Aries in a zodiac in which the vernal point was not at 0 Aries (or any other sign).

This tells us something very important which seems to have escaped the notice of nearly everyone. The Babylonians of Systems A and B had at least two twelvefold divisions of the ecliptic into 30 degree divisions: One was made from a point which was 10 or 8 degrees prior to the vernal point. This "zodiac" may or may not have been consciously sidereal. The second was a "zodiac" which was measured from the vernal point and which clearly was consciously tropical. However, was this "tropical zodiac" actually used for any astrological purpose? For that matter was the other, possibly consciously sidereal, zodiac used for astrological purposes? The usual answer to the latter question is yes, but this is a matter which we will need to examine further. Likewise the answer to the first question is usually said to be no. But the fact remains that there was a twelvefold equal division of the ecliptic in Babylonian times along with the probably sidereal one. This paves the way for the next stage of things.

The central difficulty that has not been dealt with in this controversy is the question of what was the practice of astrologers when they came to do astrology more or less as we know it? What zodiac did they use, and were they really conscious of what they were doing? For it is not enough to show that early charts were computed using a sidereal zodiac if the people who cast them were not aware that they were using a sidereal zodiac. The entire controversy becomes moot if it can be shown that for all practical purposes the two zodiacs were not distinguished.

The oldest known birthchart has been dated by Sachs to 410 B.C.E. It is a cuneiform chart with no degrees given, only sign positions, also no Ascending degree. Computations using both tropical and sidereal zodiacs give the same signs for all of the planets so listed. This chart therefore is of no use in determining zodiac in use. The next several charts in cuneiform date from the 3rd century B.C.E. These do contain degrees for individual planets and these positions are reasonably consistent with positions in the Fagan-Allen sidereal zodiac. However, they could also conceivably be computed in the zodiac in which the vernal point is fixed at 8 Aries, the System B zodiac. None of these charts have Ascendants which means that if these charts are accurate exemplars of the chart technology of the age, we are dealing with a very primitive form of horoscopy, not the sophisticated one that appears in later Greek astrology. Yet we are well within the period that appears to be the date for the Nechepso-Petosiris text which already shows an advanced horoscopic technique. Could Egyptian horoscopy have already outstripped the Babylonian art on which it was undoubtedly based?

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