I wrote this is little while ago, but didn't post it as I was trying to find some pictures to support it that I could use without 'stealing' from others. I failed miserably so rather than hold back - here it is. A little shorter than some, but this can rapidly get very somplicated and I didn't want to lose my audience
What would you like me to address next?
It’s been a few weeks since I wrote one of these items, so thought it was about time I stepped up to the plate, and this time I’m going to take a look at arguably the most useless complication available – the equation of time!
I apologise in advance, copyright free images of this are a little hard to find and this is not a simple one! Google can help you out, but as admin is looking to make these articles available beyond the forum I’m reluctant to use images that are not open access.
Let’s start with what the equation of time is. It’s not simply a horological term; it’s a recognised concept among astronomers. Put simply the equation of time is the difference between mean solar time (the time on your wrist) and actual solar time (the time based on the sun). Think of it this way – we know that the sun is at its highest point at noon right? Well actually, it isn’t – at least it only is 4 days a year (April 15th, June 13th, September 1st and December 25th) – the rest of the time it is offset – and that difference is the equation of time.
This difference can result in the sun being 14 minutes ‘behind’ (February) or over 16 minutes ‘ahead’ (November), and the gap is pretty predictable throughout the year.
To explain why the difference occurs you’ll need a smarter man than me, but essentially it is caused by a combination of two factors – first the fact that the earth’s orbit around the sun is not round, but elliptical, and second because the earth is tilted on it’s access. Add this ellipse and the tipping together and you get a variable solar zenith from day to day.
This has long been an interesting complication for watchmakers, and while it is hardly simple, it is something that can be built into a mechanical watch simply because it is predictable. There are two ways of showing the equation of time on a watch – a simpler to implement retrograde style display that varies from +16 to -14 and requires the wearer to ‘adjust’ or the harder to implement, but easier for the wearer, use of a second minute hand that shows actual solar time in the same way as a regular minute hand shows mean solar time.
The retrograde approach makes use of a figure 8 shape cam that rotates once per year. This cam has one loop of the 8 smaller than the other and is pivoted in the middle of the 8, but offset to one side. This allows for the accurate display of the variances which do not vary consistently from day to day (i.e. the 4 times a year that mean solar time and actual solar time are equal are not 3 months apart from one another).
The second minute hand (also known as an equation marchante and most famously used in recent years on the JLC Gyrotourbillon ) uses the same cam approach, but takes it one stage further. The cam makes contact with a spring loaded arm carrying a jewel at the point that it engages with the cam. The other end of the arm connects with the running train of the watch via a toothed wheel and makes adjustments to the solar minute hand based on the position of the arm relative to the cam. The solar minute hand itself is driven by the running train save for these tiny adjustments.
It is common for an equation of time watch to include a perpetual calendar, or at the very least a semi perpetual calendar simply because the equation of time requires a mechanism that rotates once per year. It is therefore logical to use that mechanism in as many ways as possible. This is achieved by mounting the month wheel of a perpetual calendar on the same assembly as the equation of time cam.
So what’s the point of all this – absolutely none in modern times, it’s just an opportunity for the high end manufacturers to demonstrate their abilities. The equation marchante has been produced by JLC as I mentioned, but also by Blancpain and AP (and others).
The AP also features the incredibly rare complication of sunrise and sunset times (that’s another article).
Boy, do I need pictures. Off to the library for me! Thanks Roff the Prof!! Always learning here, I am!!! 
, but great info as usual.