
History Online  Astronomy
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Observations of ancient solar and lunar eclipses
Breaking with traditional chronology of the ancient world
Let X be the set of all available observations of ancient solar and lunar eclipses. Their complete list has been given by F. Ginzel. Let A be the set of all eclipses described in the ancient texts X. We have to bear in mind that the same eclipse may be described in several ancient texts. We denote them by Xed. Let fed. be the date ascribed to a particular eclipse in accordance with the traditional chronology. These traditional dates have been fixed in the papers of F. Ginzel and T. Oppolzer . They all form a basis for the computation of D'(t). In computing D'(teci.) (i.e., at a point fed. on the time axis f), the theoretical, calculated characteristics of an eclipse, obtained for the date fed. on the basis of modern lunar theory, are compared with the description of the eclipse, portrayed by the ancient sources Xeci. o The deviation between these two groups of data is exactly what permits us to find the value of the parameter D' at the moment fed. o This value of D' certainly depends on the choice of the eclipse date, and only those ancient texts are important which contain sufficiently much information about it, e.g., the description of the trajectory, phase, and so on. The analysis of all the ancient texts available (see F. Ginzel ) permitted us to distinguish a list of sufficiently complete descriptions of eclipses. We do not have the space to give it here. All our computations in the following are related just to these eclipses.
Newton's attempts to explain the mysterious square wave of the function D'(t) do not touch upon the problem of the precision and correctness of the dates ascribed to the ancient and medieval eclipses by traditional chronology . In other words, the question as to how well the descriptive parameters of an eclipse, ^ftxed in an ancient text, correspond to the calculated eclipse parameters found Tor the moment fed. on the basis of lunar theory, was addressed, with fed. meaning here the date ascribed by traditional chronology . The dating and the description of a given eclipse can be regarded as correct only in the case where the two groups of characteristics, i.e., calculated and fixed in a historical source, coincide. Note that changing the dates of the eclipses will alter the graph of D'.
The relation between the problem of calculating the parameter D' and the known investigations of N.A. Morozov was indicated for the first time in the author's paper which, in particular, touched upon the problem of correctly dating ancient eclipses and their descriptions. On the basis of the analysis of considerable factual data, Morozov suggested and partly substantiated his fundamental conjecture that the traditional chronology of the ancient world might be artificially extended in comparison with the real situation. An important role in forming this conjecture was played by the method of astronomical dating.
The descriptions of eclipses from certain ancient texts started to be employed for dating these sources and related events as early as the 16th century. However, the method was applied only for the purpose of obtaining the dates in a somewhat more precise and, usually, quite narrow, prescribed time interval where traditional chronology placed them and the simultaneous eclipse under investigation.
A method of formal astronomical dating
In paper a method of formal astronomical dating was suggested, consisting of the extraction of the eclipse's descriptive characteristics from a historical text, and then purely mechanically recording all dates of the eclipses with these characteristics from the modern astronomical tables. The recalculation of the ancient eclipse data was performed just by this method in the indicated work, with the dates traditionally being ascribed to the time interval from 700 B.C. to A.D. 400. For the purpose of computing the parameter D', I carried out a new series of calculations of the ancient and medieval eclipse dates, thus confirming, in particular, the effect of shifting the dates of ancient eclipses forwards from 700 B.C. to A.D. 400 .
We now describe the method of formal astronomical dating in more detail. The papers of Ginzel and Oppolzer supply a list of 89 ancient eclipses and indicate the ancient texts which reported them. The latter are usually (traditionally) dated to have occurred in the interval from 700 B.C. to A.D. 592. A list of the eclipses' descriptive characteristics extracted from an ancient text can be complete to varying degrees. For example, the moment of an eclipse during an entire day can be indicated, but not its phase, and so forth. Besides, the canons of Ginzel and Oppolzer contain the complete and theoretically calculated list of eclipses occurring from 900 B.C. to A.D. 1582, with the basic characteristics including the date and phase of an eclipse, the umbra coordinates, and so on. The problem of dating an eclipse described by an ancient text (and, therefore, that of the accompanying events) is solved as follows. We take the eclipses from the canons all of whose calculated characteristics exactly coincide with those in a historical source. At the same time, it is required that (1) there should be no deviation from the description in the document, and (2) the time interval in which the astronomical solution is sought should not be bounded. This means that we do neglect the a priori outside information of 'nonastronomical origin'.
Analysis shows that requirements (1) and (2) are not fulfilled in the classical works and in the overwhelming majority of cases: The date of an eclipse is usually sought there not in the possible whole historical time interval, but only within narrow prescribed limits (normally, one century) in which, according to earlier chronological tradition, an approximate date of the event studied (and, therefore, of the eclipse) was preestablished.
The application of the method of formal astronomical dating to eclipses traditionally dating from 700 B.C. to A.D. 400 shows that the written evidence concerning them can be separated into two classes.
(1) Short and vague evidence (without any details). Here, it is often unclear whether the text describes an eclipse at all. In this class, the astronomical dating of written evidence is either senseless or allows for so many possible astronomical solutions that they all fall into practically any of the prescribed historical epochs.
(2) Detailed evidence. In this class, an astronomical solution often turns out to be unambiguous (or there are two or three solutions).

