Life After Full-time Work Blog

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#205: When Was The Need For An Extra Leap Year Day First Recognized?

Amazingly, it was almost 5,000 years ago! How could they possibly have measured something so tiny?


First, my stunned reaction to the previous blog post, on the total pleasure of my week-long trip to Sydney, Australia. It’s not at all the sort of thing I publish, which is typically focused on aspects of retirement (or, as I prefer to call it, graduation from full-time work). Personal stuff is not what I do. But my feelings of joy were so unexpectedly strong that I spontaneously dashed off my grateful thoughts as I flew back. Well! On LinkedIn there have been more than 3,500 clicks. This astonishes me. I have about 1,300 connections, so the post must have been spread to many others. If I get 500 clicks and 10 reactions, I’m really pleased. So this one amazed me, not only for its clicks but also for getting more than 50 reactions. (I got personal email responses too, and have established contact with a number of former colleagues whom I had been unable to locate online.) I’m so pleased that the post was so well received and spread so widely. Thank you.


Now, as we’ve just gone past February 29, I’m reminded that I’ve always been intrigued by the need for that extra day every 4 years. Obviously science has established that the earth goes round the sun once every 365 ¼ days, hence precision (in the sense that, on any given date, we should see the sun in the same position as a year ago) requires that extra ¼ day every year, and for convenience we don’t add 6 hours to the clock each year but one whole day every fourth year.

(OK, for the mathematically even more precise folks, in round number years like 1800, 1900, 2000 and so on, we actually only add that extra day February 29 in a year when the round number, excluding the zeroes, is itself divisible by 4. So we had a February 29 in 2000, but not in 1900 – not that any reader will remember 1900. That’s because the actual time for the earth going round the sun isn’t 365 days and 6 hours, it’s 365 days, 6 hours and 9 minutes; and those 9 minutes would over-correct by roughly 3 days every 400 years, so we omit 3 leap years every 400 years. Actually, that’s the siderial year, the time for one exact circumlocution of the sun. But now we tend to focus on the tropical year, which is the time between the annual change of the seasons; and that’s not constant, because of the precession of the equinoxes caused by the earth being less than totally spherical and therefore wobbling in its orbit. And the tropical year actually averages roughly 365 days, 5 hours and 49 minutes. I’ll get back to that later. But, for now, moving right along …)

I’ve always thought this was a marvel of the precision of scientific measurement in modern times, positioning us relative to the stars, and so on. So I was totally surprised to learn, from an article in National Geographic (you may not be able to read it, if you’re not a subscriber), that it was in Egypt’s 4th and 5th Dynasties, almost 5,000 years ago, that the difference between a year and a circuit of the sun was first recorded.

Really? How did they know? How could they possibly measure something so tiny, relative to everyday life? I mean, those were primitive times, right? And they didn’t have measuring sticks other than actual sticks, right? So … how?

Well, the times and the science may have been primitive, but human beings weren’t. Even if they couldn’t measure with precision, they could observe. And they did.

Again, my thoughts: Really? They could observe that the earth’s position relative to the stars was changing by a tiny amount every year? Good heavens (ha ha, pun), did they even know that the sun is a star and the stars … Oh, never mind. That couldn’t possibly be the answer.

It turns out that they noticed something different.

A fundamentally important event each year for the Egyptians was the flooding of the Nile, which brought the rich silt that fertilized its farmlands. And they noticed that one particular star, the brightest star in the sky (we call it Sirius today), disappeared from view for 70 days a year (it was too close to the sun) and then reappeared on the eastern horizon in the dawn sky at roughly the time of the annual flood. In fact, they used this reappearance to signal their new year.

And they observed enough to measure the year at 365 days, which they divided into 12 months of 30 days plus 5 extra days of celebration in honor of their gods at the end of the year to ring in the new year. (That was around 2,600 BC, almost 5,000 years ago.)

Well, over time they also observed that the start of their calendar year very gradually didn’t coincide with the flooding. Sure, from year to year there was no reliability about the exact day on which the flooding occurred; but over many, many years (how many? – I’ll come to that) the flooding seemed to start a little bit earlier each year.

The first indication we have as to the precise measurement of this difference between the calendar year and the solar year comes from the year 238 BC (almost 2,500 years ago, and some 2,000+ years after the 365-day calendar is mentioned). It’s from a limestone slab (discovered in 1866) on which was written a decree (now called the Canopus Decree, from the Egyptian city it was issued in) by the pharaoh Ptolemy III and intended to be erected in every major temple.

Written in Egyptian and ancient Greek (like the more famous Rosetta Stone), it contains the following instructions:

“And so that the seasons should always correspond to the established order of the universe, and that it should not happen that some of the public festivals are celebrated in summer, as the sun changes by one day in the course of four years … (it was resolved) to add from now onwards one festival day in honor of the gods … every four years to the five additional days, before the new year, so that all may now know that the former defect in the arrangement of the seasons …”


Oh my goodness, what a magnificent achievement: to recognize that the solar year was a better measure of elapsed time than the calendar year; to measure (simply from observations over long periods of time of the slow drift of the seasons) the difference between the lengths of the calendar and the solar year; and to make a correction to the calendar year so that it would coincide with the more important solar year. It totally transforms my mental picture of what I used to think of as primitive times. Those people were every bit as smart as we are: they just hadn’t yet gained all the knowledge that has accrued to mankind over the centuries since then.

I love National Geographic. Of all its interesting pieces, this one got to me the most.


So, was that the happy ending? Did the calendar change once and for all, and that was that?


Apparently the change was not adopted, though we don’t know why. All we know is that, when the Romans conquered Greece in 30 BC, the Egyptians were using a 365-day calendar, and it was Augustus in 22 BC who added the leap day. Or so the article said. Perhaps that was when it happened in Egypt, where the concept originated. But the Encyclopedia Britannica says that the leap day was added in 46 BC in the Julian calendar in Rome.

And for you advanced mathematicians who wondered: hey, you mentioned those extra 9 minutes for the earth’s circumnavigation of the sun – when did the change for that take effect? It didn’t.

Correcting for the first 6 hours a year means that you add 24 hours (that is, one day) every four years. OK, that’s done. Correcting for a further 9 minutes a year means that you should add a further day once every 160 years. But we don’t do that: we don’t have a year with 367 days, not even once every 160 years. So, what happened?

Answer: The big change was made in 1582 AD, in the Gregorian calendar. By then scientific instruments enabled measurements with amazing precision. And it was decided to use the tropical year rather than the siderial year. Remember, the tropical year averages 5 hours and 49 minutes longer than 365 days. So, correcting for 6 hours becomes over-correcting. We need to subtract 11 minutes every year, which amounts to a full day roughly every 131 years, or roughly 3 days every 400 years. And that’s the adjustment made. So 1600 was a leap year but 1700, 1800 and 1900 weren’t.

And to get the vernal equinox back to March 21 (its ecclesiastically fixed date – hey, Gregory was the Pope, after all), countries adopting the new calendar (which different countries did in different years, wouldn’t you know it) had to advance their calendars and forsake many days in the year of adoption.

So, for example, in the UK they adopted the Gregorian calendar as late as 1752, and by then their tax year ending March 24 (because March 25 used to be their New Year’s Day, since the 12th century) needed to end on the new April 4. Oops, a further correction of a day was needed when 1800 was not a leap year, and the Treasury made April 5 the end of the tax year – and that’s the date that still holds today. (New Year’s Day itself became January 1, essentially because the Gregorian calendar decided to use that date as the start of the year.)

I’m glad I didn’t live in those times. I’d have been terribly confused!



Those ancient Egyptians were remarkably advanced human beings. That’s my main takeaway.


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I have written about retirement planning before and some of that material also relates to topics or issues that are being discussed here. Where relevant I draw on material from three sources: The Retirement Plan Solution (co-authored with Bob Collie and Matt Smith, published by John Wiley & Sons, Inc., 2009), my foreword to Someday Rich (by Timothy Noonan and Matt Smith, also published by Wiley, 2012), and my occasional column The Art of Investment in the FT Money supplement of The Financial Times, published in the UK. I am grateful to the other authors and to The Financial Times for permission to use the material here.

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