This is one of the two most complicated watches made by Louis Berthoud, who never made any others. Both were ordered by King Louis XVI but were never delivered to him because of the Revolution and the King’s ensuing execution. This watch, like no other, ingeniously combines the principles of true longitude watches with equation of time made practically independent of the going train. The solar train mechanism consists of: 1. Motion work driven from the mean time side through the pignon moteur mentioned above. 2. Mechanism compensating the losses of the going train caused by the above. It consists of a two-wheel train (J-H) driven by a spring-loaded rack "B" exerting momentum on the solar hour wheel. It is achieved by spring-loading the rack by the operation of winding the watch, which via 12-tooth star wheel, advanced by a flirt set on the winding arbor, pushes lever "B", which in turn loads the rack against its spring "E" and consequently exerts momentum on the hour wheel thus releasing the load from the going train. The momentum lasts for more than 24 hours. 3. Mechanism of advancing the equation cam by the wearer’s motions of winding the watch. The flirt set on the winding arbor through the 12-tooth star wheel advances the 20-tooth wheel which pinion meshes with the annual wheel. On top of it, the equation of time is true in the sense that not only the minute hand shows solar time but also the hour hand, which is synchronized with solar time. In most other equation mechanisms the hour hand stays with the mean time. The watch was unique and important for Berthoud. He described it in detail in his notes, which he kept from February 23, 1792 to August 22, 1795. They show the obstacles Berthoud had to overcome to make the watch a true "Montre Marin"e: "This watch, ordered by the King, and begun three years ago (1789), has suffered all the delays imaginable… Beat 18,000 per hour, dial diameter is 22 lignes…There is no point in drawing my caliber for I have kept it. I shall speak of what can be of service for the dimensions of other watches. The spring makes 4 revolutions in its barrel and 3 1/4 on the fusee. The latter is cut with 6 turns for 30-hour going. The spring, compressed by a quarter of a turn draws 8 gros (old weight unit), so 48 gros in 30 hours. It is a little stronger at the bottom... The steel cannon pinion (solar motion work) carrying the hour hand has 48 teeth, its sleeve is of brass. It should be of average size between the two other wheels, for such a spring as I have used. It is the upper hour wheel which makes the whole of the minute work function and presses on the extended pinion of the (mean time) under-dial work. The pinion of the intermediate wheel (8 leaves in this piece but should be 10) is thus turned, the wheel turns the cannon pinion, which should be a little smaller, and the cannon pinion entrains the anti-backlash wheel… With respect to the extended pinion (driving pinion) it is clear that if I did not have this spring that presses in front, it still would turn the hour wheel, but with the spring the pinion is decidedly turned. .. In this watch it is too large, but I shall leave it because I can not see that it can cause any problem. It is not the same for that of the cannon pinion because since this is small, the meshing starts well before the center and at this position, the auxiliary spring having little force, the hand rests suspended by the inconvenience of the gearing… If for another piece I should change the size, I ought to preserve the proportions each time when I have an auxiliary spring as I have here…the concerns with thickening of the oil remains. These are very well seen in this piece, for the balance spring, of which the isochronism hardly gives me an error of 15" per day in the little arcs… Whence I have already several times concluded, that in watches with such weak regulator, a ratchet and a set screw should be added as to adjust them in different weather… …The same fault, as in other motion works, is found here, for it is the cannon pinion that ought to be the smallest of the three wheels, since the effect of the auxiliary spring goes only so far… Fortunately, in these wheels, being of a high number of teeth, the meshing is still gentle despite this defect and the largest error is not more than a half minute" Berthoud states himself that the making of the watch took three years and was not easy. The conceptual problems that Berthoud had to overcome were not easy. One of the problems was how to disengage the equation from the going train. At the time this was thought not to be possible. Even 25 years later, when Breguet had the same problem (see lot 35), the solution was far from obvious. Berthoud solved the problem brilliantly. He discarded the former ways of driving the equation cam (which were numerous, but all utilized either the going or motion train) and invented an ingeniously simple way of advancing the annual wheel by the operation of winding the watch. It advanced the solar hands once per day. The maximum daily difference between mean and solar time is about 30 seconds (December). This small difference was not relevant in daily life. The second problem Berthoud faced was the elimination of the load from the driving pinion of the mean time motion work. This he handled equally brilliantly. Since the solar motion work had to be connected to the mean time motion work (to set both times by the same operation), he knew that somehow he had to compensate for the load exerted on the driving pinion. Again, he solved the problem by none of the traditional methods, but by an innovative way of exerting momentum on the hour wheel and consequently releasing the load from the driving pinion. In his hand-written advertisement for his watches, which he apparently sent to his best clients, he mentioned that only two were made, and the cost was 4000 livres. The second most expensive on the list was listed at 1200 livres. This disparity shows the magnitude of the problems Berthoud had to overcome while making it. This remarkable watch is a triumph of French watchmaking, combining precision horology with complications, without compromising the former. Equation of Time. We know, from modern astronomical observations and from observations of artificial satellites, that the Earth's rotation rate is not constant but varies both over the short term and over centuries. These small variations are due to real variations in the rotation of the Earth and are compensated for by inserting leap-seconds as appropriate. If a sundial is used to determine the time it rapidly becomes apparent that it does not indicate the same time as clock time. The difference amounts to some 16 minutes at certain times of year. This difference is also seen as an asymmetry in the times of sunrise and sunset. This is called Equation of Time. Equation of Time has two causes. The first is that the plane of the Earth's Equator is inclined to the plane of the Earth's orbit around the Sun. The second is that the orbit of the Earth around the Sun is an ellipse and not a circle. Equation of Time due to Obliquity (the Earth's tilt): The angle between the planes of the Equator and the Earth's orbit around the Sun is called the angle of Obliquity. If the Earth's rotation axis was not tilted with respect to its orbit, the apparent motion of the Sun along the Ecliptic would fall exactly on the Equator, covering equal angles along the Equator in equal time. We measure apparent solar time, however, as a projection of the Sun's motion onto the Equator, and this changes through the year as the Sun moves above and below the Equator. The projection of the Sun's mo-tion onto the Equator will be a maximum when its motion along the Ecliptic is parallel to the Equator (at the summer and winter solstices) and will be a minimum at the equinoxes. The Sun will be on the meridian at noon at both solstices and equinoxes and so Equation of Time due to Obliquity will be zero at these times. Between the solstices and the equinoxes the Sun will be slow relative to clock time with minima near Feb 5 and Aug 5. Between equinoxes and solstices the Sun will be fast relative to clocks with maxima near May 5 and Nov 5. Equation of Time due to unequal Motion (the Earth's elliptical orbit): The orbit of the Earth around the Sun is an ellipse. The distance between the Earth and the Sun is a minimum (perihelion) near Dec 31 and is greatest (aphelion) near July 1. The Sun's apparent longitude changes fastest when the Earth is closest to the Sun. The Sun will appear on the meridian at noon on these two dates and so the Equation of Time due to Unequal Motion will then be zero. Between perihelion and aphelion the Sun will be slow relative to clock time with a minimum around March 31. Between aphelion and perihelion the Sun will be fast relative to clock time with a maximum around Sep 30. The total of these two effects gives the Equation of Time, which is formally defined as the difference between clock time and apparent solar time. Before the first application of the pendulum to clocks by Christian Huygens in 1657, clocks were regulated by a foliot, or balance wheel, and seldom kept time to within a quarter of an hour per day. Therefore, the difference between mean time, the time of the clock, and solar time, the time indicated by a sundial, was of little consequence. After the invention of the pendulum, clocks’ accuracy having improved to roughly two minutes a day, the question of the variation between mean and solar time could be addressed. Books were written on the subject, and both Flamsteed and Huygens produced tables showing the equation of time. The sundial was then consulted using an equation table, a number of which, including one by Tompion, were compiled. An alternative – albeit expensive - to finding the difference between mean and solar time by equation table was a clock which showed the equation of time on its dial. In the late 17th century, the equation clock was regarded as a very ingenious piece of mechanism, a master clock by which all the other clocks in the household were set. The earliest equation clock recorded was one designed by Nicholas Mercator (1640-1687), mathematician and Member of the Royal Society: "Next day, to the Royal Society, where one Mercator, an excellent Mathematician, produced his rare clock and new motions to perform the equation..." wrote Evelyn on the 28th August 1666. Naturally Hooke was interested in equation of time and instructed Tompion on the subject. It has been suggested that the equation kidney was invented by Huygens and that Tompion and other English clockmakers copied it. We do not know when Huygens first designed an equation clock, with or without the kidney mechanism. However, this could not have been before 1669, for at that date he maintained that equation tables should be used rather than "overload the clocks with a great many wheels so that they may show unequal time". It is not known whether the mechanism of Hooke and Tompion’s equation clock followed that of Nicholas Mercator and Fromenteel’s, but it is almost certain that Hooke and Tompion invented the revolving kidney-shaped cam upon which the working of the equation mechanism depends, and thus perfected the equation clock. Tompion in-deed, looked upon himself as the inventor and not just the maker of this equation clock design, for the two earliest extant Tompion clocks with the equation kidney bear on their dials the signature: Tho. Tompion Invenit. Watches with equation of time are extremely rare. Very few were produced in the 18th century and the first part of the 19th century, and always by very eminent makers such as Ferdinand and Louis Berthoud, Lepaute, Lepine, Le Roy and Breguet on the continent, and Mudge and Ellicott in England. Even fewer have been made in modern times, and most of them were produced in Switzerland and carry the most prestigious of signatures, such as Louis Audemars, Audemars Piguet and Patek Philippe. Literature: Described and photographed in detail in J.-C. Sabrier, "La Longitude en mer à l’heure de Louis Berthoud et de Henri Motel," Antiquorum Editions, Geneva, 1993, pp.102, 118-123, 180, 183, 195, 230, 274, 291, 420, 433, 456-475.