The Length Of The Year

To make some statement of when an eclipse is anticipated, a framework is needed to which to fit the event of interest. That is, a calendar is required. To us, that seems an obvious concept, but only because we are habituated to a certain dating convention and think little about how it governs our lives. When the ancients studied eclipses this was not the case. There was no universal calendar, and even within a well-governed state such as the Roman Republic the calendar used was by no means regular. That is why Julius Caesar added 80 days to 46 B.C., to bring January 1, 45 B.C. near the time he thought it should be according to the seasons.

The situation was similar elsewhere. Although King Ptolemy III of Egypt had decreed in 238 B.C. that a quadrennial cycle of leap years should be used, to reflect the real duration of a year, his dictate was not put into common use. Different nations used calendars that drifted against the seasons, such drift either being allowed to continue, as with the earlier Egyptian Sothic cycle, or being abruptly corrected from time to time, as with the Roman calendar before Julius Caesar rectified matters.

The design of any perennial calendar obviously would require a detailed knowledge of the year length far beyond the flowers and floods mentioned earlier. The tapestry laid down by the eclipse records made this possible. Imagine that one vertical thread in our wall-hung tapestry represents a year and that you have somehow managed to get the year length correct. Time starts at far left and proceeds to the right until the present, which is where the tapestry turns a convex corner and is not yet visible to us.

Under this circumstance of one thread per year we can begin to pick up some features of the pattern that must result. The 19-year Metonic cycle produces numerous sets of four or five dots arranged horizontally. Each individual dot will be a component part of one of the sequences of 70 or 80 dots produced by the saronic cycle, these being slanted from bottom left towards upper right because their time spacing is 18.03 years. The origins of various other components of the tapestry pattern are detailed in the Appendix. For example, there will be sharply downwards-sloping lines produced by eclipses coming 10.88 days earlier from year to year, because 12 lunar months are that amount short of a full solar year.

It is not necessary to continue with more features of the pattern, such as the 3.8-year gaps (a subdivider of the 19-year Metonic cycle). You can refer to Figures 3-1 and 3-2 to see what I mean. The thing to recognize here is that if an incorrect length for the year were employed, then the complex pattern of the tapestry would be skewed. Getting the tapestry straight and agreeable provides in effect a precise evaluation of the length of the year. This measure is far more accurate than floods or flowers, cuckoo calls or salmon spawning, sunrises at solstices or equinoxes, or waiting for Sirius to emerge again from the glare of the Sun, as we shall see below.

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