Equation clock

An equation clock is a clock that includes a mechanism that simulates the equation of time, so that the user can read or calculate solar time, as would be shown by a sundial. The first accurate clocks, which were controlled by pendulums, were patented by Christiaan Huyghens in 1657. For the next few decades, people were still accustomed to using sundials, and wanted to be able to use clocks to find solar time. Equation clocks were invented to fill this need.

Early equation clocks had a pointer that moved to show the equation of time on a dial or scale. The clock itself ran at constant speed, so the user had to calculate solar time by adding the equation of time to the clock reading. Later equation clocks, made in the early 18th Century, performed the compensation automatically, so the clock directly showed solar time. Some of them also showed mean time, which is often called "clock time".

The equation of time. Above the axis, sundial (solar) time is ahead of clock (mean) time, and vice versa.

Simulation mechanisms

All equation clocks include a mechanism that simulates the equation of time, so a lever moves, or a shaft rotates, in a way that represents the variations of the equation of time as the year progresses. There are two frequently-used types of mechanism:

Cam and lever mechanism

In this type of mechanism, a shaft is driven by the clock so it rotates once a year, at constant speed. The shaft carries a cam, which is shaped so its radius is essentially a graph of the equation of time. A lever rests against the cam, so as the cam rotates the lever moves in a way that represents the changing equation of time. This lever drives other components in the clock.

Double shaft mechanism

To a close approximation, the variations of the equation of time can be represented as the sum of two sine waves, one with a period of one year, and the other with a period of six months. (See explanation in Equation of time.) The double shaft mechanism has two shafts rotating at constant speeds. One turns once a year, and the other twice a year. Cranks or pins attached to the two shafts move the two ends of a rod up and down. If the dimensions are chosen correctly, the mid-point of the rod moves in a way that simulates the equation of time.

Clocks with displays of the equation of time

These clocks are essentially normal pendulum clocks, with an extra dial that shows the equation of time. The simulation mechanism drives the pointer on this dial.

Clocks that directly display solar time

There are several types of these. Examples are:

Clocks with movable minute markings

Clocks have been constructed in which the hour and minute hands are on separate dials. The minute markings are on a circular plate that can be turned around the same axis as the minute hand. The axis passes through a hole in the centre of the plate, and the hand is in front of the plate. The time shown by the clock is given by the position of the hand relative to the markings on the plate. The hand is driven clockwise at constant speed by the clock mechanism, and the plate is turned by the mechanism that simulates the equation of time, rotating anticlockwise as the equation of time increases. If the gear ratios are correct, the clock shows solar time. Mean time can also be shown by a separate, stationary set of minute markings on the dial, outside the edge of the plate. The hour dial is not adjusted for the equation of time, so the hour reading is slightly approximate. This has no practical effect, since it is always easy to see which hour is correct.

Clocks with variable pendulums

These clocks include a device at the top of the pendulum that slightly changes the effective length of the pendulum, so the speed of the clock varies. This device is driven by a slightly modified simulation mechanism, which moves to simulate the rate of change of the equation of time, rather than its actual value. Thus, for example, during the months of December and January, when the equation of time is decreasing so a sundial runs slower than usual, the mechanism makes the pendulum effectively longer than usual, so the clock runs slower and keeps pace with sundial time. At other times of the year, the pendulum is shortened, so the clock runs faster, again keeping pace with sundial time. Clocks with this type of mechanism show only solar (sundial) time. They cannot easily be made to show mean time.

Clocks that do mechanical addition

Some later equation clocks have pendulums that swing at constant speed, controlling normal clock mechanisms. Often, this mechanism drives a display showing mean (clock) time. However, there are additional components: a simulation mechanism as described above, and a device that automatically adds the equation of time to clock time, and drives a second display that shows solar time. The addition is done by an analogue method. For example, a notable clock, made by Joseph Williamson in 1720, uses a differential gear to perform the addition. This clock is notable because it is the earliest device definitely known to have used a differential for any purpose, although earlier ones have been postulated.

Similar modern devices

Equation clocks, as such, are no longer widely used. (It is always possible that someone may be using one somewhere.) However, mechanisms essentially the same as those in equation clocks are still used in, for example, solar trackers, which move so as to follow the movements of the sun in the sky.

See also

• Equation of time
• Sundial

External links

• http://www.britishmuseum.org/research/search_the_collection_database/search_object_details.aspx?objectid=3088493&partid=1&output=Terms%2F!!%2FOR%2F!!%2F23419%2F!%2F%2F!%2Fclock%2F!%2F%2F!!%2F%2F!!!%2F&orig=%2Fresearch%2Fsearch_the_collection_database%2Fadvanced_search.aspx&currentPage=1&numpages=10 Variable pendulum clock in British Museum.
• http://www.britishmuseum.org/research/search_the_collection_database/search_object_details.aspx?objectid=55453&partid=1&output=Terms%2F!!%2FOR%2F!!%2F22791%2F!%2F%2F!%2Fequation+clock%2F!%2F%2F!!%2F%2F!!!%2F&orig=%2Fresearch%2Fsearch_the_collection_database%2Fadvanced_search.aspx&currentPage=1&numpages=10 British Museum equation clocks, with description.
• http://www.britishmuseum.org/explore/highlights/highlight_objects/pe_mla/d/double_dial_cylinder_watch_wit.aspx Pocket watch that works as an equation clock.