On the Invariance of the Tropical Zodiac -- Part III

by Robert Hand

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The following table shows the close coinciding of the zodiacs through the period in which horoscopic astrology comes into being and begins truly to flower. The longitudes are the positions of the vernal point given in terms of the sidereal zodiac of Fagan-Allen. It is clear that only the most precise astronomical computations could allow us to clearly distinguish the two zodiacs in the main period of Greek astrology.

301 B.C.E7 Ar 13
201 B.C.E5 Ar 50
101 B.C.E4 Ar 27
1 B.C.E.3 Ar 04
100 C.E.1 Ar 41
200 C.E.0 Ar 18
300 C.E.28 Pi 55
400 C.E.27 Pi 32

So do we see evidence of the astrologers of this period having a clear idea of their zodiac? Of course there is the example of Ptolemy (roughly 175 C.E.) who explicitly states that the zodiac begins with the vernal point. And we also have his witness that Hipparchos supported the same position about 300 years before. But was this issue clearly delineated in the minds of astrologers in general? That is the question.

Let's explore the answer to this question first of all by means of the ascensional times which we have been describing here.

When astrology clearly emerges into the documentable daylight, the early centuries C.E. (A.D.), the Babylonian doctrine of ascensional times comes along with it.

Vettius Valens was a younger contemporary of Ptolemy, about 175 C.E., but his astrological style is clearly derived from a different tradition than Ptolemy's, one at least as old. In the Anthology, Book I, chapter 6, there is the following passage:

"One must know how much addition or subtraction of the ascension each zoidion has, thusly. Since Aries ascends in 20 times, Libra ascends in 40 in order to fill up the 60 times. For, in comparison to the number of times in which each zoidion ascends, the zoidion diametrically opposite takes a number that fills up 60 times. And in comparison to the number of hours for each zoidion, the hours for the zoidion diametrically opposite fill up 4 hours. And in comparison to the number of days and months, the zoidion opposite takes a number that fills up two years. For, the amount by which each zoidion exceeds, the diametrically opposite zoidion is lacking. "Subtract, then, the least from the present greatest, that is, the 20 times from the 40. The remainder is 20. 1/5 of these becomes 4. The addition or subtraction of each zoidion is four. If, then, we add 4 to the 20 ascensions, 24 ascensions result. Taurus will ascend in these times. Gemini in 28, Cancer in 32, Leo in 36, Virgo in 40, Libra in 40. Then similarly, from Scorpio you subtract 4 up to Pisces. Inquiring thus, you will get to know the ascensions for each zone."

These are the standard System A ascensional times. However, as we know from Books VIII and IX, even though Valens used System A ascensional times, he set the vernal point at 8 degrees of Aries, the position used in System B. And in addition he and the others who used this system did not make the distinction that the Babylonians seemed to have made. He did not locate the 30 degree tropical divisions which gave rise to the ascensional times at 8 degrees of the signs but at 0 degrees of the signs thus identifying the signs of the zodiac with the divisions that gave rise to the ascensional times. And there is no evidence that this was an innovation of Valens, but rather a common convention among the astrologers of the period. This clearly indicates that these astrologers did not have a clear idea of the distinction between sidereal and tropical zodiacs, or that they did not consider the distinction to be important, not a remarkable position given the fact the two zodiacs did nearly coincide at the time.

Also characteristic of the texts of the time are references to the signs in terms that we would clearly recognize as based on seasonal criteria along with factors that we clearly recognize as sidereal. Consider the following description from Valens Book I:

"Aries is the house of Ares, a masculine zoidion, tropical, terrestrial, authoritative, fiery, free, ascending, semi-vocal, good, changeable, administrative, public, civic, unprolific, servile, Midheaven of the cosmos and cause of repute, two-colored (since the Sun and the Moon make leprosies), skin-eruptions; it is also unconnected, a place for eclipses. . ."
". . . This zoidion has 19 bright stars. And it has 13 bright stars through the belt, 27 shadowy ones, 28 underbright bright ones, and 48 faint ones. The first part of Perseus from the northern regions co-rises with it, as does the remaining parts and the left part of Auriga, and from the south the back fin and tail of the Sea Monster. From the north, the [feet] of Bootes set. From the south, the remainder of Lupus."

Note the use of the word "tropical" in the first paragraph, followed by the enumerations of the stars in the second. [Several paragraphs have been omitted.] This kind of thing is typical of the Greek astrologers. Only Ptolemy seems to have been aware of the impending difficulty and made an effort to differentiate clearly.

According to Neugebauer there were others who adopted the vernal point at 0 degrees Aries. From page 600 of HAMA:

"We know from Hipparchus that the majority of old mathematicians divided the ecliptic in this form. This statement agrees with sources still available to us; Euctemon (about -430) placed all four cardinal points on the first day of the respective signs. The same holds for Callipus (about -330) and is underlying the era of Dionysius (beginning -284/3). As far as we know this norm is attested nowhere in Babylonian astronomy."

This last statement is somewhat weakened by the facts given earlier, but I think that it can be taken as correct as far as stellar and planetary positional measurement is concerned. It is not so clear as far as astrological purposes are concerned.

When did the issue of precession become clear to the astrologers? Clearly some sources were aware that stars did not stay in the same place. In the second star list of the Liber Hermetis we have the following passages on the degree of Cancer in reference to Praesaepe:

"From the fourth to the seventh degree according to the Sphaera Barbarica is the Little Cloud, . . ."
"From the seventh degree to the eighth there rises Praesaepe and Lyra playing the lyre. But indeed there are those who say that the Little Cloud should be in the eighth and ninth degree."
"In the ninth degree there rises the Little Cloud of Cancer according to Dorotheus."
"From the eleventh to the twelfth degree is the Little Cloud."
"From the twelfth degree and six minutes to the fourteenth degree and 49 minutes there rises the Little Cloud; but according to Ptolemy it is in the thirteenth degree."

Then we have the evidence of the Anonymous of 379 who may seem to some to be an ambiguous source for reasons which we will explain below. First of all let us look at his own statement on precession:

". . . in what remains we will begin to state the effects concerning the active power of each of the non-wandering stars, after indeed inscribing in the table the degree number in longitude which each of them occupies in the consulship of Olybrius and Ausonius, at which time we wrote this book. This is on account of the fact that the non-wandering stars move 1 degree into the following tropical signs in 100 years, just as the divine Ptolemy exemplified."

This is obviously an explicit reference to a tropical system with the vernal point at 0 degrees Aries and explicitly based on Ptolemy. However, there is a problem with the Anonymous' positions as given in the text. For example, Aldebaran is given in the text as the 15th degree of Taurus. This is exactly the position given in Cyril Fagan's reconstruction of the sidereal zodiac. Similarly Antares is given as the 15th degree of Scorpio. These and other such positions have led certain investigators to assume that the Anonymous was a siderealist! However, if one corrects the positions given in Ptolemy's star catalog using Ptolemy's inaccurate precessional constant, as the Anonymous explicitly did, one gets exactly the same position. The following table shows this:

StarPtol. Long.Anon. Long.Sid. Long.
Aldebaran13 Ta15 Ta15 Ta
Pollux27 Ge29 Ge29 Ge
Regulus3 Le20 Le5 Le
Spica27 Vi29 Vi 29 Vi
Antares13 Sc15 Sc15 Sc

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