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1983 or 1583? The calendar recycles

If you're looking for an unusual calendar, you might hunt up one of the old editions from 1583. It's no longer out of date.

We have entered the second 400-year cycle of our Gregorian calendar, which repeats the day-of-the-week, day-of-the month correspondence of 400 years ago.

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To be exact, the cycle began last Oct. 15 - the 400th anniversary of the Gregorian system. Various countries adopted the ''new style'' calendar at different times, often with heated controversy. But all reckoning with this calendar begins with Oct. 15, 1582.

The Gregorian system still has not provided us with a fully accurate calendar. But it may be the best that can be done from a practical point of view , as several experts have pointed out.

A calendar aims to help us order our lives on a day-to-day, month-to-month basis and to know where we are with respect to the seasons. These two requirements are in conflict. To be easily used, a calendar year must contain an integral number of whole days. But the relative motion of Earth and Sun, which determines the timing of the seasons and the length of the actual year, has a rhythm of its own.

The relevant period is the so-called tropical year - the time between one spring equinox and the next. This year is currently estimated to be 365.24219879 days long.

It's that fractional part of the number that causes trouble. Ancient calendars took account of it rather badly. By the time of Julius Caesar, the Roman system was several weeks out of phase with the seasons. Caesar, on the advice of Sosigenes, an astronomer in Alexandria, introduced substantially the calendar we use today. The awkward fraction is roughly a quarter of a day. So the Julian calendar adds an extra ''leap day'' every four years.

That fraction isn't exactly a quarter day, however. By 1582, the spring equinox had drifted back to March 11, dragging the date of Easter with it. To correct this, Pope Gregory dropped 10 days in 1582 (Oct. 15 followed Oct. 4) and adopted a refinement worked out by Luigi Lilio of Naples. Now no century year is a leap year unless evenly divisible by 400 - 1900 was not a leap year, but 2000 will be. This calendar slips only one day in several thousand years.

Can we do better? Gordon Moyer, an American calendar expert living in West Germany, notes that the tropical year itself is growing shorter due to gravitational effects on Earth from the sun and moon. This complicates efforts to further tame the troublesome fraction.

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Picking up this point in Sky and Telescope magazine, Charles Kluepfel, a calendar expert in New York, shows that the decrease of the tropical year would frustrate further calendar refinement. Among other things, the mechanics of the shortening is not fully known and the way the length of the tropical year is computed may be incorrect.

''In any case,'' Kluepfel says, ''it seems that the Gregorian calendar is already at about the limit of possible accuracy.''

That's good to know. We don't need another calendar controversy.

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