Equation Clocks

A sundial and a good clock rarely agree, and the gap can reach about 16 minutes. An equation clock shows both times, using a cam whose outline follows the yearly correction.

What an equation clock is

An equation clock is a clock that shows two kinds of time at once. Its main hands give mean solar time, the steady, even hours that ordinary clocks keep. An extra hand, ring or dial shows apparent solar time, the time a sundial reads from the real Sun. The difference between the two is called the equation of time, which gives the clock its name.

Britannica defines the equation of time as the correction that turns apparent solar time into mean solar time. Depending on the date it has to be added or subtracted, and it never exceeds about 16 minutes.

Why sun time and clock time differ

The Sun does not cross the sky at a perfectly even rate through the year, the U.S. Naval Observatory explains, for two reasons of similar size. The first is the tilt of the Earth's axis, about 23.4 degrees, which changes how fast the Sun appears to move east to west. On its own, that effect is zero at the equinoxes and solstices and reaches about 10 minutes either way in between.

The second is the shape of the Earth's orbit. The Earth moves fastest near perihelion in early January and slowest near aphelion in early July, and that effect alone swings the time by about 7.5 minutes in early April and early October. Put the two together and you get the full equation of time, which the observatory says can reach as much as 16 minutes.

The problem only became obvious once clocks were good enough to notice it. The British Sundial Society credits Christiaan Huygens with making the first accurate mechanical clocks in 1656, after which the seasonal drift between clocks and sundials could no longer be blamed on poor clockwork. Sundials often carry a table or graph of the daily correction for exactly this reason, so the owner can find the date and read off how many minutes to add or subtract.

See also: sunrise and sunset worked out from the real Sun on OnlineClock.app.

How an equation clock works

The heart of the mechanism is a cam: a flat plate with a carefully shaped edge that turns once a year, often on the same arbor as the clock's annual calendar, as on the Fitzwilliam Museum's Tompion timepiece. Its outline encodes the equation of time for every day. A follower rests against the edge, and as the cam turns, the follower moves in and out by an amount that matches the day's correction. In a letter quoted by the British Museum, Joseph Williamson described the part he used as a roller in the form of an ellipsis The Fitzwilliam's record simply calls it the equation cam.

Makers used that movement in different ways. On the Fitzwilliam's Tompion, a bell crank following the cam carries a rack that turns a movable outer minute ring engraved for apparent time, and a gilt-tipped minute hand reads sun time against it. The Royal Collection's Tompion and Banger clock similarly passes the cam's motion through a lever and rack to shift an apparent time dial back and forth with the date. Other makers gave the equation its own separate hand: on a year-going clock in the British Museum, a small hand swings through about half a circle to show the equation, while a long hand takes 365 days to go round and points to the day of the month.

Tompion, Quare and the early equation clocks

Equation clocks appeared in London around 1700. The Fitzwilliam Museum in Cambridge holds a year-going equation timepiece by Thomas Tompion, known as the Drayton House clock, dated about 1695 to 1700. Its dial is signed THO. TOMPION.LONDON.INVENT., its chapter ring is marked EQUAL TIME and its rotating outer ring APPARET TIME. The tall case, of oak veneered with burr walnut, stands about 262 centimeters high.

The Royal Collection's longcase equation clock was made around 1703 by Tompion with Edward Banger; an anonymous description of about 1760 says it was made for Prince George of Denmark, husband of Queen Anne. It runs for 390 days on a single winding and shows the days of the week, the date, the months, the zodiac and the Sun's position as well as apparent time. George III chose it for Buckingham House in 1762, and it was later rescued from a fire at St. James's Palace in 1809.

Who deserves credit for the idea is debated. Tompion's INVENT. signature makes a claim of its own. Against it stands Joseph Williamson, who, the British Museum notes, asserted his right to the invention of clocks that keep time with the Sun's apparent motion, said he had made such clocks for Daniel Quare from about 1700, and said one of them had gone to King Charles II of Spain. The British Museum's own year-going clock has a dial signed Daniel Quare, London, but its curator suggests the movement is probably Williamson's work. Even its date is uncertain: the catalog gives 1690 to 1700, while the curator's note puts it at about 1710.

How to recognize one

Look for a dial that shows more than one kind of time. Tompion's year timepiece at the Fitzwilliam labels its rings equal time and apparent time, and reads sun time with a gilt-tipped minute hand that runs a little ahead of or behind mean time. Other equation clocks have a separate equation hand, or a second set of hands for solar time. Because the cam is driven alongside the annual calendar, equation clocks often show calendar information as well: the Fitzwilliam clock shows the zodiac and the days of the week, and the Royal Collection clock the date, month and zodiac.

See also: how mean time gave way to standard time on OnlineClock.app.

Keep exploring

Sources

1. Equation of time (Britannica)
2. The Equation of Time (U.S. Naval Observatory)
3. Converting sun time to clock time (British Sundial Society)
4. Year Equation Timepiece by Thomas Tompion, M.22-1947 (Fitzwilliam Museum)
5. Longcase equation clock, RCIN 2754 (Royal Collection Trust)
6. Year-going longcase clock signed Daniel Quare, 1958,1006.2098 (British Museum)