Today, with the atomic clocks that are accurate to a few seconds every billion years, beating records of precision is no longer a challenge. These records are regularly overthrown, and awards for chronometry regularly given by the C.O.S.C. (Contrôle Officiel Suisse des Chronomètres).

Fabien Chicha
Technical Service Assistant

Accurately measuring time has become an everyday matter. It is perhaps for this reason in order to exercize their creativity, or to render homage to tradition and know-how, that the great names in Swiss horology have devoted their attention to an extremely rare and little-known horological complication : equation of time.

We do not live by solar time. When, for example, my watch says it is noon, the sun is not at its zenith. In order to find a solution to this problem, a distinction needs to be made between:

Usual time, called mean solar time. This is the time indicated by our watches, in which time is mathematically divided into days of exactly 24 hours.
Solar time, or true solar time, which was the time shown on the sundials of the past. This time is variable, a day being the amount of time elapsed between two passages of the sun at the meridian ; the length of the days varies throughout the year, according to the season.Since, for practical reasons, the true solar day could not be used as a universal reference, the mean solar day was adopted. It is 24 hours in length, and is based on the imaginary movement of the sun along the earth’s equator. Equation of time is the difference between mean solar time and true solar time.

Breguet, No. 4254/717, sold on Nov. 1, 1828

18k gold extra-flat, pair-cased, astronomical, moon phase, jump-hour, quarter -repeating, triple calendar, equation of time pocked watch, constructed along the principles of the Garde-Temps. Dim 46mm.

Other factors are involved in the difference between true and mean times; among them are eccentricity, which makes the distance between sun and earth vary, or the longitude of the observation point.

Four times a year, mathematical calculations and nature become reconciled : on April 15th, June 14th, September 1st, and December 24th, mean solar time and true solar time are the same. The rest of the year, the variations between the true position of the sun and the mean position can reach up to 16 minutes : from less than 16 minu-
tes and 23 seconds on November 4th to more than 14 minutes 22 seconds on February 11th.
The curve of the equation of time, called the analemma, shows the variations in the sun’s passage at the meridian of a given place. It is in the shape of an asymmetrical eight and its approximate equation is E=9.84*sin(2B)-7.53*cos(B)-1.5*sin(B) with B=360*(N-81)/365 N being the number of the date (on January 1st, N=1).

But the equation of time can be calculated more simply, with the help of a calendar that gives the times of sunrise and sunset. These times are added and the result is divided by two.

The calculation of the equation of time is used to create a kidney-shaped cam. Driven by the main going train, this cam makes one revolution around its axis per year. A finger with a hand at its extremity remains in contact with it like the stylus of a record player, following the cam’s contours as it effects its revolution and thereby indicating the equation of time in minutes by means of the hand.
Equation of time timekeepers can be of several types :

Some have one dial showing the hours and mi-nutes of mean time, and another indicating the number of minutes to be added or subtracted in order to obtain the true solar time. These watches are generally fitted with a sectorial dial and a hand running over it, from one extremity to the other.

Others feature a type of equation of time indication called "marchante" in French. The true solar time minute hand, with a small sun at its extremity, is coupled with the mean time minute hand. Thus, the mean time, the solar time, and the increment of time separating them can be perceived all at once.


Breguet, No. 220, sold to the Count de Montalva on Oct. 28, 1947, for the sum of 4000 francs.

One month-going, weight-driven, astronomical, long case regulator with one-minute passing striking, annual calendar and equation of time. Dim 200 x 50 cm.

This difference exists because the speed of the earth’s trajectory, as it traces its elliptical path around the sun, is not constant. The point of maximum speed is reached at the perihelion (the point in a planet’s orbit at which it is closest to the sun) around the 31st of December. Its minimal speed occurs at the aphelion (the point in a planet’s orbit at which it is furthest away from the sun) around July 1st.

Patek Philippe & Cie, Genene, No. 80772, case No. 215215, made in 1890.
18k pink gold keyless pocket chronometer with equation of time and perpetual calendar

True solar time can also be indicated on a revolving auxiliary disk concentric with the mean time dial. The minute hand thus indicates either mean or solar time, according to the disk which which one chooses to read.

Alternately, the main dial may have two auxiliary dials, one for mean time and the other for solar time.

Very few horological instruments with equation of time were produced during the 18th and early 19th century, and always by the most important of horo-
logists : Ferdinand and Louis Berthoud, Lepaute, Lépine, Leroy and Breguet in France, or Mudge, Ellicott, Dent and Payne in England. The oldest equation of time clock known was constructed by Nicholas Mercator (1640 - 1687), mathematician and member of the "Royal Society".

The most impressive pieces featuring equation of time are : the “Marie-Antoinette” watch made by Abraham-Louis Breguet, the Leroy no. 01, and by Patek Philippe, the “Graves”, more recently the Calibre 89, and the Star Caliber 2000. In “astronomical” watches and clocks, equation of time is often enhanced with sidereal time, the phases and age of the moon, a perpetual ca-lendar, the times of sunrise and sunset and the sun’s declination, the movement of the planets, the map of the skies, or the ephémérides (solstices, equinoxes, seasons).

If these functions excite our admiration today, they were extremely useful in the past, for setting clocks to the correct time, or to set out on a journey at dawn.

Breguet, No 2807, sold to General Yermoloff on August 26, 1817, for the sum of 4000 francs.

18k gold and enamel, astronomical wath with annual calendar, manual perpetual calendar, phases of the moon and mean and true solar time.

In the year 2000, Audemars Piguet presented the "Jules Audemars" wristwatch in a limited edition, with a perpetual calendar, the hours of sunrise and sunset, and the indication by means of a hand of the equation of time, which allowed a very precise reading of its daily variations.
Patek Philippe’s Star Caliber features many proofs of technical prowess. Among them is the fact that the equation of time mechanism is synchronized with the perpetual calendar. Whereas other horological instruments, when stopped for a prolonged period or for a date correction, require the cam to be dismounted and similarly adjusted at the same time, in the Star Caliber this is not necessary.

Today, equation of time reflects the skill of the Master Horologists who seek to reproduce the celestial movements. These masterpieces of technique, these exceptional watches, are intended for a knowledgeable public, one not unfamiliar with astronomy. The greatest horologists have not forgotten that in the past, our lives followed the rhythm of the sun. And indeed, why not succumb to the temptation – and the pleasure - of wearing a portable sundial on one’s wrist?

Bibliography:
G. Daniels " La Montre "
Jean-Claude Sabrier " La Longitude en Mer "
The site www.montrespassion.ch features a 3D animation of an equation of
time mechanism.