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KRONOS Vol. I, Issue 3

Michelson And Meton

This paper is a review of a column by Professor Irving Michelson ("Scientifically Speaking . . .", subtitled "19-Year Lunar Calendar Cycle: Accurate Adjustment to 365 1/4-Day Civil Calendar", Pensee, Winter, 19741975, pages 50-52); it will also serve as an introduction to the paper by Professor Alfred de Grazia and to the paper by Professor Livio Stecchini that immediately follow in this issue of KRONOS.

In his column, Professor Michelson discusses the considerable precision with which such quantities as the mean synodic month of 29.530589 days can be measured. He says that this eight-digit precision "stands as an elegant tribute to the 'hard sciences' at their best" (page 50). He repeatedly offers the suggestion but never presents any evidence or arguments that such precision is incompatible with any radical changes of planetary or lunar orbits within historical times.

Whyhe offers this suggestion is never explained, and many readers may find the suggestion inherently implausible. For when an orbiting body has been drastically perturbed, and when the perturbing force is no longer operative or no longer in range, we would then expect the body in question to be on a new orbit, and to remain on that new orbit (except for minor, long-distance perturbations of the sort that are occurring even today) until such time as it is drastically perturbed again. It is puzzling that Michelson believes that even "a thousand years" (page 52) would not be long enough for a perturbed body to emerge on a new orbit. (It might be noted that after a space vehicle has fired its engines for a short time, it is immediately on a new orbit.)

Most of Michelson's column is focused on calendar cycles that give procedures for adding extra or intercalary months to certain years in such a way that at the completion of the cycle the lunar month (29.530589 days) and the seasonal or tropical year (365.2421988 days) will come out fairly even. He is particularly interested in a 19-year cycle that is attributed to Meton, who lived in fifth-century Athens. Michelson notes, however, that many sorts of cycles are found in calendars. In the Gregorian calendar, for example, any two occurrences of the same calendar date that are separated by 28 years will occur on the same day of the week, "provided only that the exceptional end-of-century non-leap-years are avoided"; thus "a 1947 pretty-girl calendar can be dusted off and used again in 1975" (page 51).

For purposes of simplification, Michelson assumes (see page 51) that the ancient calendar-makers would be using a lunar calendar of twelve lunar months of about 29 1/2 days, and that they would also recognize "a civil year of 365 1/4 days". As we shall see, these simplifications do not provide an adequate basis for Michelson's inferences about how long it would take for various lunar calendars to fall out of step with the seasons. Thus he suggests that a lunar year based on "12 New Moons" would last about 354 days, and would fall short of the civil year by up to 11 1/4 days, with the result that "New Year day would slide around the entire cycle of seasons in roughly 32 years". This would be true if the mean lunar month were exactly 29 1/2 days, but it should be noted that if our calendar makers based their months on the observed phases of the Moon (which cycle is in fact slightly greater than 29 1/2 days), then new year's day would actually move through the seasons in well over 33 years, not "32 years".

The same point should be stressed when Michelson considers intercalating one extra lunar month every three years: he claims that 37 lunar months of 29.53 days ("37 x 29.53 = 1,091.61 days") would fall short of three civil years ("3 x 365.25 = 1,095.75 days") by 4.14 days, and he then says that "each new year would regress in season and travel around the whole four seasons in about 266 years". Notice, first, that Michelson's arithmetic is wrong: the product of 37 and 29.53 is actually 1092.61, not 1091.61; and thus the shortfall would be 3.14, not 4.14. Notice also that 29.53 is still not the actual length of the lunar month. If actual new moons determine the months, then the shortfall with respect to the civil year would be only 3.1182 days. And the shortfall with respect to the tropicaL year would be only 3.0948 days, so that the passage of new year's day through the seasons would require just over 354 years, not "266 years". Even if the months did average exactly 29.53 days, a shortfall of 4.14 days would imply a passage through the seasons in less than 265 years, rather than in 266 years. (A shortfall of 3.14 days would imply nearly 349 years.) But I suggest that Michelson did not even use his own figure of 4.14 days in arriving at his answer of 266 years. Instead he probably miscalculated that 37 "months" (37 x 29.53 = 1,091.61 [sic] days") falls short of three tropical years (3 x 365.2421988 = 1095.7265964 days) by 4.1165964 days, and then divided the 1095.7265964 by 4.1165964 to get just over 266 years. He may have used fewer decimal places than this, but the 4.14 was not used at all. If Michelson's arithmetic had not been wrong, his answer would have been well over 351 years, rather than "about 266 years". And with real lunar months of 29.530589 days, instead of the simplified "months" of only 29.53 days, the answer would have been just over 354 years.

The main calendar cycle that Michelson treats is the Metonic cycle of 19 years, which contained seven intercalary months placed in years 3, 6, 8, 11, 14, 17, and 19. He says that these results were "announced at the Olympic Games in Athens" (page 52), and engraved in gold (hence the expression "golden numbers"). Michelson stresses the fact that 235 lunar months comes very close to 19 civil years of 365 1/4 days. (More importantly, it is also a fact that 235 lunar months comes almost as close to 19 tropical years, but Michelson does not point this out.) Michelson does correctly note that the difference between 235 lunar months and 19 years of 365 1/4 days is 0.0616 day; but his remark that this "accumulates to one day only in 303 years" (page 51) is either an error or a misprint, since 19 divided by 0.0616 is actually over 308.

Michelson claims that Meton's "discovery of the 19-year cycle presupposes precise knowledge of the length of the lunar month as well as of the solar (tropical) year of 365.2421988 days, to second-decimal accuracy at least" (page 51). But this is by no means correct. The 19-year cycle could have been discovered simply by counting both the months and the years until they once again came out even. One could count the 235 months and the 19 years, without having precise values for either quantity. This would not even need to take the discoverer 19 years: if records were available going back a number of years, the necessary data could have been found in those empirical records. And no "second decimal accuracy" need have been involved. Meton may very well have had "such second-decimal accuracy", but the point is that Michelson has not shown that the discovery of the 19-year cycle presupposed such accuracy. The question of what Meton was really doing will be explored by de Grazia and by Stecchini in the papers that follow.

Two closing points: (1) I am unaware that Velikovsky or his supporters have ever said (as Michelson implies on page 50 and again on page 52) that Earth's orbital period was ever 354 days long. (2) It is false that the "year 2000 will thus be the first turn-of-the-century leap year of the Gregorian calendar" (page 50): the Gregorian calendar was instituted by Pope Gregory XIII in 1582, and its first turn-of-the-century leap year was in the year 1600.

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