The Equation of Time

Across the world, for convenience, we have adopted what is referred to as mean time and think of a day as being twenty four hours in length. This is how most mechanical clocks are set up to measure time. However, technically, a day is the duration between one solar noon, the time when the sun is at the highest point in the sky, to the next, this is solar time. The length of a solar day is not exactly twenty four hours long. It changes throughout the year because of the axial tilt of the Earth and, as Johannes Kepler noted when he published his conclusions in 1609, the elliptical shape of the Earth's orbit which means that its distance from the sun varies throughout the year.

When the earth is further from the sun it moves in its orbit more slowly than when it is closer. A solar day is longer than twenty four hours around the Summer and Winter solstices and shorter than twenty four hours around the Spring and Autumnal equinoxes. During the 17th century most of the population operated by solar time. The public clocks and domestic clocks being of short duration and varying in their time keeping ability by up to 10 minutes in twenty four hours, were wound and set to time each day according to a sundial.

The equation of time is the difference between apparent mean time and apparent solar time. This difference varies across the course of the year. In 1665 Huygens published tables quantifying the equation of time and more practicable tables were published in 1672/1673 by Flamsteed. These showed the correction to be applied to a sundial's apparent solar time to obtain mean, or clock time. Apparent solar time runs up to sixteen minutes ahead of mean time, and up to fourteen minutes behind, the two coincide just four times a year when a clock dial will agree with a sundial on 15th April, 13th June, 1st September and 25th December.

Equation of time table, circa 1752 by Robert Sayer, Fleet Street, London, £3,200

In his book, Horological Dialogues, John Smith writes in 1675, "that if the hours given by a Sun dial, increase and decrease in length, according to the slow and swift motion of the sun, then tis impossible for the most exact Clock that was ever made, to keep time with the Sun dial, but there will be difference, according to the time of the year and the course of the sun."

As science advanced, the timekeeping abilities of clocks and watches became more accurate and the duration between winding increased, the difference between solar time and mean time meant that two different kinds of time ran concurrently, and became noticeable. The advantages of not having to constantly adjust your clock to solar time meant that mean time was adopted.

The difficulty during the 17th and 18th centuries was setting a clock to mean time, as the only way to determine the time and set your clock was by observing a sundial, and using an equation of time table to convert to mean time. Clockmakers, including Thomas Tompion, were known to supply sundials to their wealthy clients, sometimes with an engraved equation of time table for setting the mean time.

With the difficulty and inconvenience of having to use an equation of time table to set the time, some clock and watchmakers at the beginning of the 18th century used their ingenuity and mastery in the mechanical arts to devise a way to display both solar time and mean time directly on the dial without the need for calculations. The sophisticated movements in these timepieces incorporate a kidney shaped cam derived from the analemma, the figure of eight traced out by the sun's position in the sky throughout the year. These equation of time watches and regulators are marvellous machines made by only the finest clockmakers.

Movement from Thomas Mudge month going equation of time longcase regulator, made for the King of Spain, circa 1758

The complex month going movement in Mudge's equation of time regulator shown above, has 18 wheels with a total count of 1,581 teeth, the largest wheel being the annual calendar wheel with 365 teeth. To put this into perspective, a month going regulator without the equation of time function would have 8 wheels and a total count of 266 teeth. Subsequently such timepieces were very expensive and very few were ever produced. Those that were made were commissioned by Royalty and the most wealthy and would have served as talking points and impressive status symbols.

Thomas Mudge month going, equation of time, longcase regulator dial with blued steel and gilt sun solar hand