The equation of time results from the 23 degree tilt of the Earth's rotational axis and the fact that the Earth moves around the Sun in an elliptical orbit. For these two reasons, a "true" solar day, which is the interval of time between two "true" noons when the sun is at its highest point in the sky, is never the same length over the course of the year. It is exactly twenty-four hours long on just four days: 15 April, 14 June, 1 September and 24 December. In an unchanging cycle, all other days are either longer or shorter. This difference, which ranges from less 16 minutes and 23 seconds on 4 November to plus 14 minutes and 22 seconds on 11 February, is the "equation of time".
The display of the equation of time has always been one of the rarest if not the rarest of all watchmaking complications. Only the most sophisticated watches and clocks were fitted with the equation of time display, used to measure the difference between the length of the solar day, which constantly varies over the course of a year, and the length of the standard 24 hour civil day.
The most common indication is by means of a subsidiary dial or arc, graduated from -16 to +14 minutes, requiring some mental arithmetic by the wearer by adding or subtracting the relevant difference from mean time.
The accomplishment of the "equation running" display required the invention of another mechanical marvel. By means of extremely precise calculations based on the irregular path of the earth around the sun, watchmakers have developed a cam shaped like the figure-8 path made by the sun in the sky called "analemma", thus mechanically mimicking the curve derived by astronomers. Turning once per year, this cam is used to drive a finger producing a plus/minus display of the difference between solar time and civil time.
The first of the two minute hands indicates civil time in a conventional fashion. The second minute hand, decorated with the symbol of a golden sun, shows the solar time. Over the course of a year, the equation of time hand slowly overtakes and then slowly falls behind the minute hand as the sun overhead gradually catches up with and then falls behind civil time. This allows the user of the watch to directly read at a glance both civil time and solar time, as well as visualize the ever-changing relationship between the two. It is interesting to note that the first wristwatch fitted with the "running equation" display was launched only in 2004, further emphasizing the rarity of this system.
The rarest and most exclusive version is the equation of time display showing both solar time and civil time on the same dial by means of two co-axial minute hands. In the entire history of watchmaking, only an infinitesimal number of the world's most important clocks and watches were fitted with this exceedingly rare indication, also known as "équation marchante" or "running equation" display. In fact due to their utter exclusivity, nearly every "équation marchante" watch or clock made during the last two centuries has been recorded as historically significant timepiece.
The present "équation marchante" is a spectacular discovery and must be considered the "holy grail" in the family of these ultra rare species. Unknown to literature, it is in fact believed to be the very first pocketwatch featuring this horological masterpiece, indicating both civil time and solar time. Its outstanding rarity is further enhanced by the indication of sunrise and sunset, the simultaneously changing horizon, the months combined with the relevant number of days and the date, rendering it one of the most intricate astronomical timepieces of the early 19th century.
The combination of astronomy and haute horlogerie is paying tribute to Samuel Roi's master watchmakers and designers who have mastered one of the principal challenges in the history of watchmaking: the "équation marchante".
Samuel Roi & Fils
The celebrated firm was founded in 1770 in La Chaux-de-Fonds by Samuel Roi or Roy (1746-1822). Following his apprenticeship with Josue Robert & Fils at the age of 16, he moved to Fontaines which had become a clockmaking centre. Samuel Roi was associated with one of the Maillardets for a few years before returning to his hometown in order to found his own workshop together with his three sons Henri-Louis, Jacques Louis, and Samuel. The firm specialized in the manufacture of scientific clocks, thus establishing the precision clock industry in La Chaux-de-Fonds. Quickly renowned for their horological masterpieces also outside Switzerland, Samuel Roi was honoured in 1783 for the invention of a perpetual clock by the King of Prussia "for his efforts to carry the art of horology and mechanics to the highest degree of perfection".
During the French Revolution, the celebrated watchmaker Abraham-Louis Breguet was working in Switzerland and cooperated with Samuel Roi & Fils on the development of decimal, chimney and other clocks. Such clocks, marine chronometers and most notably three-wheel weight-driven clocks, including a three-wheel weight-driven skeleton clock with compound pendulum, Republican and Gregorian calendar and thermometer, were made to Breguet's design by the manufacture and delivered to Paris. It appears that Breguet invited Samuel Roi to work for him in Paris but he declined (see Swiss Timepiece Makers 1775-1975 by Kathleen H. Pritchard, p. R-94).
The Musée de l'Horlogerie in La Chaux-de-Fonds owns a regulator clock by Samuel Roy & Fils, made in 1780, which was displayed at the National Exhibition of Horology of La-Chaux-de-Fonds in 1881. This quarter repeating 8-day clock is considered a horological "tour de force", comprising a single wheel without pinion, indicating hours, minutes and seconds, the numerals arranged in a spiral which a single hand follows, automatically elongating up to 12 o'clock.
In 1804, Samuel's oldest son Henri-Louis took over the management of the firm.