The formula for determining leap years in yesterday's Science Notebook incorrectly reversed a key provision. It should have said that centennial years are not leap years unless evenly divisible by 400. The last such year was 1600. The next is 2000. (Published 3/1/88)

Today is Leap Day -- the extra day inserted into the calendar every fourth February (with a few exceptions) since Julius Caesar authorized it in 46 B.C.

Leap days, or leap years if you wish, are convenient ways of coping with an astronomical mismatch:

The time it takes Earth to spin on its axis, the day, is unrelated to the year, which is the time it takes the Earth to make one orbit around the sun, the so-called solar year.

The year that governs the seasons, the solar year, is 365 days, five hours, 48 minutes and 46 seconds long -- roughly one-fourth of a day beyond 365. Until Caesar's day, the extra time was ignored and the year was counted as exactly 365 days. Each vernal equinox, the official start of the new Roman year, arrived about one-quarter of a day later by the calendar than the previous one. After four years, the calendar was almost one whole day out of step with the seasons.

By 46 B.C. the calendar was so far out of sync that Caesar ordered a correction by adding 67 days to the year, causing considerable confusion. To correct mismatches in the future Caesar also approved his court astronomer's plan to add a leap day every fourth year. The extra day was added to the last month of the Roman year, February.

That took care of most of the mismatch. But now the year was about 11 minutes too long. Some 1,600 years later, when the difference had accumulated so much that the seasons were 10 days off from the calendar, Pope Gregory XIII established a commission to find a better system.

First he dropped 10 days from the calendar. By papal edict, the day after Oct. 4, 1582, became Oct. 15, 1582. Then he ordered fewer leap days according to this rule: Centennial years, which would ordinarily be leap years, will not be leap years if they are evenly divisible by 400. The last such year was 1600. The next is 2000.

The Gregorian calendar, however, still leaves a discrepancy of 26 seconds every year. Today's calendar has accumulated about two hours of mismatch since Gregory's time but the pressure for yet another reform is not yet irresistible.