The Tourbillon is essentially a gravity compensator. it was designed and patented by Abraham-Louis Breguet in 1801 to correct errors of rate caused by the effect of Earth's gravity on the movements and gears of a watch.
It consists of a revolving cage with a balance (called a regulating organ by experts) at the centre. The cage revolves about once a minute and compensates for the errors of rate caused by the vertical position in which pocket and wrist watches are usually found. The Tourbillonin will even adjust the watch mechanism for the slight difference in gravity between the poles and the equator.
This type of ingenious error correction is absolutely necessary for astronomical calculation of any reasonable precision, yet it is found in only a few astrometric watches. The idea of power storage in a mechanical watch, which is based on physical monitoring of the tension of the mainspring, is fascinating enough, but this device is truly a testimony to the ingenuity of engineers and watchmakers.
Astronomical watches have a lineage that dates back to the great astronomical clocks of the 14th and 15th centuries, and the pocket watches of the Renaissance. The minute hand, a late 17th century innovation, was not used at the time, but these watches displayed the hour, date, day of the week, months with their duration, moon phases and the signs of the zodiac. Their roots were in 13th century Islamic astronomical and chronological computers, which researchers believe were based on the ancient Antikythera mechanism, the subject of a coming feature.
One of the most important factors in making the correct astronomical calculations is the equation of time. It enables us to tell the difference between "true" solar time, as it exists in nature, and "mean" solar time, which is our convenient 24 hour day.
As the Earth makes its elliptical orbit around the Sun, it's axis is tilted away from the plane of the equator. Consequently, the length of a day counted by the interval between two astronomical noons (when the Sun is at it's highest point in the sky) varies throughout the year. This difference is 24 hours long on only four days during the year, April 15th, June 14th, September 1st and December 24th. All other days are either longer or shorter, and the difference, which can be from (approximately) -16 to +14 minutes is the equation of time.
A precisely made cam that completes a single rotation in a year mechanically programs the equation, but the trick is in displaying it. Some watches have a hand that moves from -16 to +14 on a small dial, but that requires a bit of mental juggling in order to know what the true solar time is. The more complex watches have two minute hands, one showing the true solar time and the other showing the common mean solar time. This complication is called the équation marchante, or running equation. The first type can be seen on the reverse face of the $1.4 million Vacheron-Constantin Tour d'Ile at the top left.
Sidereal time is measured by the rotation of the Earth around its axis as measured against the background of the fixed stars. A sidereal day is apporximately 4 minutes less than a mean solar day of 24 hours, and is indespensible for astronomical/astrological calculations. The skeletonized hands on the back of the Patek Philippe Sky-Moon Tourbillon on the right measure Sidereal time. One was auctioned off in June of 2007 a mere $1.2 million, but only two are made per year, so you may not be able to find one at any price.