# Leap Years and Our Calendar

Why do we need to have leap years; what are the rules that determine which years are leap years; and what is the history of these rules?

Firstly, here is the rule. A year is a leap year (and so contains a February 29) if it is divisible by 4. But if the year is also divisible by 100 then it is not a leap year, unless it is divisible by 400. This means that years such as 1992, 1996 are leap years because they are divisible by 4 and are not affected by the rest of the rule which applies to century years such as 1900 and 2000. Century years are not leap years except where they are a multiple of 400. Hence, the years 1700, 1800 and 1900 were not leap years and did not contain a February 29. But the year 2000 was a leap year, the first such century leap year since 1600.

And why do we need leap years and why this particular rule? The need for leap years arises from the fact that the time taken by the Earth to orbit the Sun (the year) is not an exact number of days - the length of the day being determined by the spin of the Earth. This incompatibility is somewhat inconvenient for calendar making, causing it to be more complex.

The exact length of the year (i.e. the revolution of the Earth around the Sun) is 365.2422 days. If we had a calendar with years having only 365 days then the seasons (which are determined by the rotation of the Earth around the Sun) would drift by a quarter of a day in every year. This might seem small, but after a 100 years the seasons would have drifted by 25 days and very quickly there would arise the situation where summer is occurring when winter used to!

A first improvement is the Julian calendar in which there is a leap year every four years. This means that the average calendar year is 365.25 days which is closer to the real value but still too long. Even in this system, the seasons drift by one day in every 128 years.

The Julian calendar is named after Julius Caesar, and between its introduction in Roman times and the middle ages in Europe there was an appreciable drift in the seasons. This forced a reform of the calendar by Pope Gregory in 1582, with 10 days left out of October of that year (with some anguish) to bring the seasons back in phase. It took some time for this system to be introduced in Britain from Europe and this did not occur until 1752. Imagine the confusion of not only a time change when travelling but also a different date.

We use the Gregorian system at present with its rule for leap years as given earlier. In the Gregorian calendar the length of the calendar year averages 365.2425 days which is very close to the true year of 365.2422 days. The drift in the Gregorian calendar is only one day in around 3300 years. With it, we will not need to worry about calendar reform again for some considerable time.

So, next time we have a leap day in February, think about the reasons for it, and the long and interesting history behind our system. Perhaps, it is indeed a privilege to have a birthday on February 29 - a birthday date that is distinctive making that person one in around 1500 people! For more about this special group of people see the Honor Society of Leap Day Babies.

Material prepared by Richard Thompson