A Perfect Watch is always Fast

Let's say that you bought a perfect watch on January 1, 1972. By perfect, we mean that each and every second measured by this hypothetical watch is exactly equal to a SI second - defined in 1967 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 caesium 133 atom". Let's say also that, comforted by this extreme accuracy, you've never adjusted the watch or had to change to battery or wind it up or whatever. After all it is a perfect watch, right?

Sorry to tell you that your watch is now 24 seconds fast. Yep. You see, measuring the passage of time is not quite the same as telling the time. Time itself is but a concept, a human observation of change if you will. On the other hand, "the time" [of day] is our expression of an agreed instant in the passage of time. In fact, the time of day, or the definition thereof, has been messed around with ever since the first non-sundial clock was invented.

You would think that the invention of atomic clocks would clear everything up. After all, atomic clocks are almost as good as the perfect watch that you bought back in 1972. Unfortunately, we still have the same problem in modern times that the ancients had. Days are still varying in length - not just the period of daylight versus night, but also the actual length of each day varies during the year. Not to mention that the wobble of our planet (about once every 26,000 years) causes a change in the length of each year and that the planet itself is slowing down due to tidal friction.

Before the second was re-defined in 1967, it was defined with respect to the mean solar day and thus measured the passage of ephemeris time. However, the first atomics clocks proved that even ephemeris time was not perfectly constant so, up until 1967, they were actually adjusted to keep ephemeris time, known quaintly as "ET".

These days we still match "the time" to our planetary motion but now it is done by adding leap-seconds when required by our slowing planet. It is only by adjusting atomic time with leap-seconds do we arrive at the familiar UTC which is now truly "the time", as far as everyone on the planet is concerned. In 1972, when UTC was invented, it was already slow to the atomic clock by 10 seconds and since then 24 leap-seconds have been added - which is why your perfect watch is now 24 seconds fast!

Best regards, xpatUSA

The Equation of Time

This is really about the different ways of representing "the equation", but first a little preamble. (or you could Google "equation of time" and view all 94,700 results :wink:)

Watches are, of course, mainly instruments to measure the passage of "time". However, "time" in that context is a man-made concept and is dependent on the machinations of atomic clocks and such-like. Furthermore, the division of the planet into time zones, although good for commerce and the punctuality of trains, has also helped to divorce us even further from the reality of the time by which humanity once lived i.e. solar time; for example - when it is noon at Greenwich (by "noon" I mean when the Sun is at it's highest, not 12 o/clock), the Sun over Rockall Island still has yet to climb quite a bit, even though it's in the same time zone. This also explains why using your watch to find North can send you wandering up to 15 degs off, and that's not including the 6 deg penalty for forgetting to correct for Summer Time (who, me?).

Anyway, the "equation of time" represents the imperfect motion of our planet around the Sun. The equation itself is horrendous, don't even bother to look at it. Generally, we tend to use the term to mean it's result for any given day of the year. Lindbergh used such a result on his epic flight to Paris. The equation of time is also of significance to garden gnomes, strangely enough. "What's the time, Grumpy?" - "Bloody 'ell have I got to climb up the sundial again??". You see, if you set a sundial to your watch on Feb 14th to please SWMBO, I guarantee it will be a half-hour fast when you next look at it on Nov 5 between fireworks.

So, without further ado, here are several ways from worst to best to represent this "equation of time" . . . ta daaa . . !!


The most seriously boring way is a table:

Part of a Sun Data table . . .
Col. 1: Date
Col. 2: Equation of Time. Number of minutes and seconds the Sun is off compared with an accurate clock which shows local mean time.
Col. 3: fast or slow (Sun).
Col. 4: Declination of the Sun in degrees and minutes. When negative, the Sun is south of the celestial equator; when positive, north. Values are averaged over the 4 year leap year cycle.

Jan1	3.12	S	-23.04
Jan2	3.40	S	-22.59
Jan3	4.08	S	-22.54
Jan4	4.36	S	-22.48

A little better - a graph

I prefer, at the very least, a visual approach. Here's the equation plotted out on bog-roll. You'll notice that clocks do agree with the Sun four times a year but it's not really obvious why in this graph form.



Better yet

If the graph is plotted against the angle of the Sun instead of against the time of year, the effect of our wobbly orbit, etc becomes immediately apparent.

The figure below is called an "analemma" (no jokes, please).




and there's an even prettier one on our family globe, I didn't even know what it was until yesterday:




However it does look like the folks below knew all about it. It's a Jaeger-LeCoultre Gyrotourbillon (photo by Ron DeCorte, taken from Timezone.com). The cam rotates just once per year, as you should expect by now ;-) - if anyone knows what the months cam does, please leave a comment to this post.




However I like this one the best. Straight from nature - a time-lapsed sequence of the Sun at 8:30 AM for a year, by Dennis di Cicco



Here's quite a good site on the subject analemma.com.