For every solution, obtained as a result of the astronomical computations done by the program Horos, we created a special table. In this table we compared the properties of the solution with the features shown on the Egyptian zodiac, which were not examined during the verification process of the admissible solutions in Step 2 (see section 6.7).
In particular, the following properties of the solutions were examined:
• Visibility Attributes for Venus, Mercury and other planets, which were located in the proximity of the Sun on the main horoscope (see section 5.7).
• Agreement with Four Partial Horoscopes of the autumn equinox, winter solstice, spring equinox, and the summer solstice (see sections 5.5, 5.6, and 5.8).
• Agreement with Additional Astronomical Symbols and Supplementary Scenes, which are present on the Egyptian zodiac (see section 5.9).
This verification was conducted with the help of a Checkup List, which was set up in a form of a table for every admissible solution. This table had six, or possible even more columns, with the following contents:
(1) VISIBILITY OF VENUS in the main horoscope.
(2) VISIBILITY OF MERCURY in the main horoscope.
(3) PARTIAL HOROSCOPE OF THE AUTUMN EQUINOX.
(4) PARTIAL HOROSCOPE OF THE WINTER SOLSTICE.
(5) PARTIAL HOROSCOPE OF THE SPRING EQUINOX.
(6) PARTIAL HOROSCOPE OF THE SUMMER SOLSTICE.
(7) SUPPLEMENTARY SCENE AND THE PASCHAL FULL MOON. This column was reserved only for those zodiacs, where there was a disc in Libra, or other symbols that could be interpreted as representations of the Paschal Moon.
For some Egyptian zodiacs, depending on the presence of the additional astronomical symbols or supplementary scenes, the number of the columns in the checkup table was even further extended.
In each column, we included a short description of the corresponding chart of the sky, related to the examined solution. If the picture on the chart fully agreed with the situation presented on the Egyptian zodiac, the column was annotated with the sign +. If the full correspondence between the solution and the zodiac couldn't be confirmed, we annotated the column with the sign —. In questionable cases, where some doubt still existed, we annotated such column with the sign ±.
By a complete or ideal solution we understand such final solution, for which all the columns of its checkup table are annotated with plus signs only. Only such solutions were accepted as final solutions, while all other solutions were rejected.
Let us emphasize, that we did not expect in the beginning of our research that it would be possible to find complete (ideal) solutions for all investigated Egyptian zodiacs. In fact, it could happen that our requirements were overstated for the actual ability of ancient artists and astronomers to achieve expected from the zodiac accuracy. Clearly, in such case, it wouldn't be possible to obtain ideal solutions for all the zodiacs.
On the other hand, if the requirements imposed on an ideal (complete) solutions were too low, then at least for some zodiacs there would be more than one ideal solution.
But neither one of these two eventualities occurred in our case. Contrary to our expectations, the results were surprisingly good. For all investigated by us Egyptian zodiacs, always only one admissible solution turned out to be ideal. Therefore, we can say that this method allows a unique dating of practically all Egyptian zodiacs, except the zodiacs with very poor astronomical content or those that are badly damaged. Moreover, for every investigated zodiac, there were always several solutions satisfying almost all the requirements from the checkup list, with possibly one or two —/± annotations. Nevertheless, there was always only one solution with all the plus signs.
Later, in the subsequent chapters, we will present the checkup tables for all the ideal solutions of the specific Egyptian zodiacs. In these tables we will use the following abbreviations:
1. SUH — the submersion of the Sun under the local horizon measured in degrees. For example
SUH=10o means that the submersion of the Sun was 10o.
• The submersion of the Sun is measured at the moment when a planet is raising or setting down over the local horizon (depending on the morning, or respectively on the evening visibility of this planet that is examined). At that moment, if the submersion of the Sun is sufficient, it is possible for an observer to see the planet on the sky. We will always assume that all the submersions of the Sun are calculated for an observer located in Cairo, except the cases when it will be specified otherwise. Let us recall that a planet with an average brightness is visible if the submersion of the Sun is 10o or more, and a bright planet (with the magnitude M = -3.5) is visible if the submersion of the Sun is about 7o-8o, or more (see section 6.7, Step 3 [B]).
2. M — the magnitude of brightness of the planet measured according to the photometric scale.
For example M = -3.2 means that at that moment the brightness of the planet was -3.2. As we explained before, brightness of the planets changes with time.
• Let us recall that the brightness according to the photometric scale can be possibly expressed by negative numbers — smaller the number, higher the brightness of the planet. The brightest planet is Venus. Its magnitude can reach up to M = -5, but the most frequently it is from M = -3 to M = -3.7. The magnitude from M = 0to M = +1 is characteristic not only for the planets but also for bright stars. The planets with such magnitude of brightness are visible on the sky only when it is sufficiently dark. Such conditions exist if the submersion of the Sun is at least 8o-9o. Less bright planets can be observed with the naked eye only if the submersion of the Sun is 10o or more. With the submersion of the Sun of 18o, there is a complete darkness. At that time it is possible to see faint stars. We discussed this issue in subsection 6.7.3.
3. Decimal Number from 0 to 12 in brackets, indicating a position of the planet according to the constellation-sized scale (see section 6.10). For example, (2.5) denotes the middle of Gemini, or a point with the longitude 70o on the ecliptic J2000, and (0.2) - a point in Aries with longitude 31o on the ecliptic J2000 (see section 6.10).
4. Sometimes, in a column related to the visibility conditions of a certain planet, we indicate its distance (in degrees) from the Sun, which we denote using the capital Greek letter delta: A.
We use the last column in the checkup table for comments. At the bottom of this column we placed a sequence of squared boxes, corresponding to the columns in the table. Each of these boxes contains one of the signs +, — or ±, depending on how the solutions agrees with the zodiac. If the solution is complete, in all boxes there are only plus signs. In addition to these boxes, we also included there the mean discrepancy from the best points for this solution, which we denoted by the symbol Aav (see section 6.11).
The Dates Shown on the Monumental Zodiacs in the Denderah and Esna Temples
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