Math Chat: That Shifting First Day of Spring

Old spring challenge (Ilan Vardi)

Why is the first day of spring in London sometimes on March 20 and sometimes on March 21? Spring arrives when the earth is tilted at a right angle to the sun, not toward the sun as in the summer or away from the sun as in the winter. Consequently night has the same length as day; hence the term spring equinox meaning "equal night."

Answer

Mike Bevan, George Dillard, Ron Douglass, Aubrey Dunne, William Hasek, Mary Lou Holmes, Erik Randolph, and Clint Staley explain that the extra day in a leap year, such as 1996, makes the first day of spring come about a day earlier (March 20, 1996) than the year before (March 21, 1995). Since the year is actually about 365-1/4 days long, spring continues to come about 1/4 day or six hours later every year, reaching March 21 in 1999, until the next leap year, 2000, brings it back to March 20.

Actually, the year is a bit less than 365-1/4 days long, by about 11 minutes, and this effect accumulates. In the early years of this century, spring generally arrived on March 21, whereas now it usually comes on March 20. (This is why many sources still incorrectly say that spring generally arrives on March 21.) The accumulated error is about 3/4 day a century.

Fortunately, our current Gregorian calendar takes this error into account, and omits a leap year in three of every four centuries: A century year is a leap year only if it is divisible by 400.

The year 1900, which is not divisible by 400, was not a leap year. In the late 1800s spring had fallen back to March 20 as it has now, but the omission of a leap year in 1900 advanced it to March 21. Since 2000 is divisible by 400, it will be a leap year, and the next adjustment will not come until 2100. By then, spring will often be arriving on March 19.

The old Julian calendar did not omit any century leap years, and spring kept coming earlier and earlier. By the 16th century, the beginning of spring fell in early March. Pope Gregory XIII therefore created our current calendar by excising 10 days from October 1582 and omitting the future century leap years not divisible by 400. Many European nations adopted the papal reform relatively quickly, although England and its colonies, for example, held out until 1752. The current Gregorian calendar repeats every 400 years.

Erik Randolph points out that the spring equinox does not guarantee the arrival of spring weather!

Careful examination of the table of spring equinoxes shows a certain irregularity in the advance from year to year. It averages about five hours and 49 minutes, but from 1997 to 1998 the spring equinox advances by six full hours.

New spring challenge

What causes the irregularities on the order of 10 minutes in the time from one arrival of spring to the next?

* Send answers and new questions to:

Math Chat

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or by e-mail to:

fmorgan@princeton.edu

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