365DaysDate:  January 25, 2009


Title:  The Equation of Time

Podcaster:  John Dalziel

Organization:  The Computus Engine

Description: Why does the time on a sundial rarely match the time on your watch? This podcast investigates the different forms of solar timekeeping and the enigmatic Equation of Time.

Bio:   John Dalziel explores the history and mechanics of measuring time. He studied astronomy at the Royal Greenwich Observatory and is a charter member of the Long Now Foundation. John is a professional Flash Developer. He experiments with digital horology at The Computus Engine.

Today’s Sponsor:  This episode of “365 Days of Astronomy” is sponsored by Greg Thorwald on behalf of his favorite museum, the Denver Museum of Nature and Science.


Hello, and welcome to 365 Days of Astronomy. The official podcast of the International Year of Astronomy. Hi, my name’s John Dalziel and today we’re going to explore sundials, clocks and the enigmatic “Equation of Time”.

The history of timekeeping is a long and fascinating one. All of our present day systems of measuring and marking time have their roots in astronomy. Years, months and days are all celestial approximations. Each one honed and improved by a succession of shamans and astronomers, popes and politicians.

The biggest irony in the history of timekeeping is that we now have a quantum measurement of time that is so precise; it is more accurate than the Earth itself. This presents us with somewhat of a dilemma. How do we measure time?

There’s an old joke in computing that goes, “The nice thing about standards is that there’s plenty to choose from.” (attr: Andrew S. Tanenbaum). I think the same could be said of time standards. You can track solar time, lunar time, atomic time, sidereal time (time by the stars), and any number of legacy calendar systems that attempt to combine them. It’s a bit of a minefield.

Time standards fall into two broad camps. The ones that track and measure some sort of astronomical cycle, and the ones that don’t. The ones that don’t follow a strict mathematical formulae. And that formula very often tries to emulate an astronomical cycle. You can see how this can get confusing.

I think the most familiar example of measuring an astronomical cycle would be a sundial. This tracks the daily rotation of the earth about its axis, and the annual rotation of the earth around the sun.

Of course there have been plenty of other astronomical cycles used for timekeeping over the years. Phases of the moon are common in many calendar systems. The rotation of the galaxy, sunspot activity and probably most recently the duration of pulsars have been found to be extremely accurate timekeepers.

The simplest example of not measuring an astronomical cycle would be a clock or a wristwatch. It’s a lot cheaper and easier to make a mechanical device that works with fixed length intervals.

If you’ve ever compared the time on a sundial to the time on your watch it very probably didn’t match up. Both show their own version of solar time, but unless you’re living on the equator, you’ll find the length of an hour changes throughout the year.

Actually, let me say that again: “The length of an hour changes throughout the year.” Pretty good eh? Now before you think I’ve lost the plot let me explain…

Firstly, I’m not suggesting that anything is happening to your watch. As I said earlier it uses fixed length intervals and the length of a clock hour is always 60 minutes. What’s changing is the length of an apparent solar hour.

When you think about it, this makes sense. The proportion of daytime to nighttime varies throughout the year. In summer the days are longer, and in winter the nights are longer. The thing is, when the Egyptians built their sundials they gave day and night 12 hours each. So an Egyptian hour was said to be temporary (or temporal) because it’s duration changed throughout the year.

Now I’m going to assume that your sundial has been setup correctly. The thing is, a sundial is location specific. They are configured to tell time at a specific longitude and latitude on earth. If you bought yours off eBay, you’re going to be in trouble.

So, getting back to the original problem. If you want to read the time on a sundial (as clock time) you’re going to need to make a few adjustments. Now pay attention as there going to be a test at the end!

Have a look around the base of your sundial. Chances are you’ll find a little plaque with a chart on it. Sometimes you’ll find it on the dial itself. It probably looks like a couple of Sine waves. What your looking at is the difference between apparent solar time (the time on your sundial) and average (or mean) solar time. This conversion is known as the Equation of Time. So find today’s date on the chart and add or remove the corresponding minutes from your reading.

If your sundial has been built correctly then the equation of time marked on the plaque, will also take into account the longitudinal position of the sundial. The time can be a few minutes either way depending on how many degrees east or west you are from the meridian running through the middle of your timezone. Time Zones and standard time are a fairly modern adjustment, brought in initially to make railroad timetables easier to understand. So that’s working well.

Lastly, if you’re taking your reading in summer it’s possible that Daylight Saving Time could be in effect. This is by no means a standard of any kind. If you’re lucky it’s goverened at a national level but in many cases it’s down to local authorities to decide. If it is in effect then then add an hour to your reading.

So there you go. You’ve successfully converted sundial time into local clock time with nothing more than a GPS receiver, a railroad timetable and the equation of time. Nothing to it.

Well, I promised you a test so here it is… If you are standing on the Greenwich meridian and the sun is directly overhead – is it lunch time? Well I’m peckish and in the words of the late Douglas Adams, time is an illusion; lunch time doubly so.

I hope you enjoyed today’s podcast. My name is John Dalziel, and If you’re interested in digital horology then you might like The Computus Engine. You’ll find it www.computus.org. Thanks for your time.

365 Days of Astronomy
The 365 Days of Astronomy Podcast is produced by the New Media Working Group of the International Year of Astronomy 2009. Audio post-production by Preston Gibson. Bandwidth donated by libsyn.com and wizzard media. Web design by Clockwork Active Media Systems. You may reproduce and distribute this audio for non-commercial purposes. Please consider supporting the podcast with a few dollars (or Euros!). Visit us on the web at 365DaysOfAstronomy.org or email us at info@365DaysOfAstronomy.org. Until tomorrow…goodbye.