The **Leap Day**, February 29, depicts a day that occurs only once every four years, every **Leap Year** or *intercalary year* when an extra day is inserted. But not every forth year, if that year ends in “00” like 1900, then it is not a Leap Year. Except if that year ending in 00 is also divisible by 400 then it *is *a Leap Year. Unless it is a Tuesday and it is dark. OK, I made up that last rule. So, years like 2008 *are *Leap Years, being divisible by 4. 1900 is *not *a Leap Year as it ends in 00. The year 2000, you remember, the famous Y2K, when computers programmers only obeyed the first two rules and assumed that it *wasn’t* a Leap Year so that all the computers failed and the world came to and end? That *was *a Leap Year, as it was divisible by 4, and though it ended in 00, it was divisible by 400 (indeed, it’s divisible five times, if you’re still with me.)

How did we get into this calculatory conundrum? It has to do with a *cumulative rounding error* in trying to reconcile the Julian calendar with the tropical or astronomical calendar. The **Julian calendar**, established by Julius Caesar in 46 B.C. lasted from 45 B.C. until A.D. 1582 and stipulated that the year should be 365 days for 3 years in a row, with every 4th year having 366 days. This meant that an average year was 365.25 days. But according to the tropical calendar, the year has 365.24219 days.

This tropical (or seasonal) calendar recognizes that the year is marked by two successive passages of the Sun through the vernal equinox (*equal nights*). You and I know that the Sun does not pass through the Earth’s sky, but rather the Earth orbits around the Sun — or at least you probably realized it since the Sun came up this morning — but it’s easier to explain this by considering this apparent motion of the Sun in our sky. And of course, this is just the easy explanation. A **Leap Second** is the fraction 1/31,556,925.9747 of the tropical year for 1900 January 0 at 12 hours *ephemeris* time. But that was determined back in 1960. Since then, the **second **has been defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the Cesium 133 atom. Perhaps that’s intuitively obvious to the most casual observer of the Newtonian dynamical theory of motion.

So where does this *cumulative rounding *error come in? Back in A.D. 730, an Anglo-Saxon monk named the **Venerable Bede** recognized that the Julian year was 11 minutes and 14 seconds too long, which would produce an error of about one day every 128 years. But there were a lot of other things going on then, and the Venerable Bede didn’t have a blog, so nothing was done about it for 800 years.

In A.D. 1582 this accumulated error was estimated at 10 days, and **Pope Gregory XIII** decreed that the day following Oct. 4 would be Oct. 15, pretty handy if you had a library book due during that time. This **Gregorian calendar** was adopted throughout much of the Catholic world, but not everywhere. Uncivilized parts of the British Empire, like America, made the change in 1752 when 2 September was followed by 14 September and New Year’s Day was changed from 25 March to 1 January.

Ultimately, to make future adjustments for the error, which amounts to about three days every 400 years, it was decided that years ending in “00” would be normal years rather than Leap Years, with the exception of those divisible by 400. Unless it is a Tuesday and it is dark.

Bill Petro, your friendly neighborhood historian

www.billpetro.com

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A leap second is not that fraction of the tropical year for 1900; it is exactly one second of TAI. The length of the atomic second was initially chosen to match that fraction of the tropical year, but the uncertainty was 2 parts in 10 to the 9, and the rate of TAI was adjusted by 1 part in 10 to the 12 at the beginning of 1977.

Well Steve, apparently I’ve oversimplified to the point of error! Thanks for the comment.

Hey Bill, another quick note. Unfortunately the earth’s rotation is slowing down at a rate of .005 seconds per year. So, if you extrapolate the math out … carry the 2 … divide by 3.14 … In about 2,000,000,000 we will need to add another leap year to keep us in sync.

Thanks Austin. I only update this article every 4 years, but I’ll put this in my To Do list to update the article when the cumulative rotational deterioration reaches a threshold of notice.

Thank you for sharing.