The Berlin Gold Hat (see: Wikipedia) is an eclipse record
Geoff Stray's "Beyond 2012" mentions the four or more extant gold cylinders, a.k.a. "gold hats" because there is some evidence that they were worn ceremonially, found in modern times in Germany & France, and maybe Switzerland & Ireland, dating from 1000-1300 BC. The best preserved is the "Berlin Gold Hat", whose provenance is uncertain, but probably southern Germany or Switzerland.
The Berlin Gold Hat has 20 rings with numbers, in a simple, rudimentary number system, that have been straightforwardly decoded as:
44,42,75,38,90,57,105,57,95,60,100,60,105,90,38,66,126,138,162,235.
The total is 1783, so, this is a 1783-year record of total solar eclipses at some location or locations. To find the expected frequency of total eclipses at any given midlatitude location, I consulted Stephenson & Houlden, "Atlas of Historical Eclipse Maps: East Asia", 1986. This book shows calculated partial & total solar eclipse tracks in or near China, since 1500BC. From 1500BC to 316AD, the capital Chinese city conveniently marked on the maps, was one of five northern Chinese cities all between about 35 and 40deg N lat. During this time, totality encompassed the then capital nine times, so at 35-40 N lat, whether in China or in Europe, total eclipses occur at a given location roughly once every 200 years.
This is indeed the average time interval near the end (physically, the bottom) of the Berlin Gold Hat. Apparently, near the end of the recordkeeping, the declining civilization, possibly pre-Celtic and Stonehenge-related, which produced the hat, had a poor communication network and knew only of local eclipses. Earlier, the civilization recorded eclipses over a larger region, so the intervals were shorter.
Only 1/18 of the numbers should be divisible by 18, but 4/20 of them are. The most reliable eclipse cycle is the Saros cycle, 223 synodic months = 18.0 years. The Saros cycle is very close to whole numbers of synodic, draconic and anomalistic months, so, the new moon recurs at the node and at perigee. The time of day is acceptable:
223 synodic months in Saros cycle * 5 = whole# + 0.63day
" * 7 = whole# + 0.28day
" * 9 = whole# + 0.93day
(I used the linear extrapolation estimates for ancient month length and day length, given by Wikipedia; this estimated change in day & month length, affects the above results by no more than 0.04 day)
So, it is likely that a collection of eclipses separated by 5, 5, 7 & 9 Saros cycles could be seen from the same point on Earth, especially if the 5-cycle eclipses were in the summertime.
Only 1/19 of the numbers should be divisible by 19, but 5/20 of them are. Nowadays a less reliable eclipse cycle is the Metonic cycle, 235 synodic months = 19.0 years: its numbers of draconic and of anomalistic months are, on the average, less exactly whole. The time of day again is acceptable:
235 synodic months in Metonic cycle * 2 = whole# + 0.39day
" * 3 = whole# + 0.08day
" * 5 = whole# + 0.47day (thus probably summertime eclipses)
Thus eclipses separated by 2, 2, 3, 3 & 5 Metonic cycles likely could be seen from the same point on Earth, if the 2- and, especially, 5-cycle eclipses were in the summertime.
As an extra check, I wrote a BASIC computer program to find whether it is possible to have two eclipses X +/- 1 yr apart. For all 20 values of X on the Berlin Hat, there was at least one time interval T, with X-1 < T < X+1, such that T was a whole number of synodic months, and within 0.02 months (7.2deg; equivalent to 0.7deg from the ecliptic) of a whole number of mean draconic half-months. This was however also true for 98 of the first 100 integers and 190 of the first 200.
For all 20 values of X, at least one of its values of T that was satisfactory vis-a-vis the node, also was good vis-a-vis the perigee (that is, nearly a whole number of anomalistic months, so both eclipses could be near perigee). Even the poorest performer had a value of T only 0.24 anomalistic month different from a whole number. By contrast, only 82 of the first 100 integers, and 161 of the first 200 integers, had any value of T for which the number of anomalistic months was within 0.25 of a whole number. Only 15 of the 20 Berlin Hat numbers are different, but even allowing for the duplicates, the chance that all 15 nonduplicate Berlin Hat numbers would lie among the best 82%, vis-a-vis perigee, is 0.82^15 = p = 5%.
If the Berlin Hat record ended ~1200BC when the hat most likely was (deliberately and carefully) buried, then its record began ~3000BC. My guess is that the Berlin Hat record began shortly after 4328BC, ended shortly after 4328 - 1783 = 2545BC; then the hat was stored aboveground for ~1300yr before burial.
Is there a location (preferably but not necessarily in northwest Europe) where total eclipses (preferably but not necessarily consecutive) occurred 162 +/-1, then 235 +/-1 yrs apart? (These last two intervals on the hat are likeliest to represent the hatmakers' one remaining observatory.) The answer to this question, could both place and date the hat.
