History
The word "equation" is here used in a somewhat archaic sense, meaning "correction". Prior to the mid-17th Century, when pendulum-controlled mechanical clocks were invented, sundials were the only reliable timepieces, and were generally considered to tell the right time.
A description of apparent and mean time was given by Nevil Maskelyne in the Nautical Almanac for 1767: "Apparent Time is that deduced immediately from the Sun, whether from the Observation of his passing the Meridian, or from his observed Rising or Setting. This Time is different from that shewn by Clocks and Watches well regulated at Land, which is called equated or mean Time." (He went on to say that, at sea, the apparent time found from observation of the sun must be corrected by the equation of time, if the observer requires the mean time.)
The right time was essentially defined as that which was shown by a sundial. When good mechanical clocks were introduced, they usually did not agree with sundials, so the equation of time was used to "correct" their readings to obtain sundial time. Some clocks, called equation clocks, included an internal mechanism to perform this correction. Later, as clocks became the dominant good timepieces, uncorrected clock time was accepted as being accurate. The readings of sundials, when they were used, were then, and often still are, corrected with the equation of time, used in the reverse direction from previously, to obtain clock time. Many sundials therefore have tables or graphs of the equation of time engraved on them to allow the user to make this correction.
The equation of time was used historically to set clocks. Between the invention of accurate clocks in 1656 and the advent of commercial time distribution services around 1900, one of two common land-based ways to set clocks was by observing the passage of the sun across the local meridian at noon. The moment the sun passed overhead, the clock was set to noon, offset by the number of minutes given by the equation of time for that date. (The second method did not use the equation of time; instead, it used stellar observations to give sidereal time, in combination with the relation between sidereal time and solar time.)
Of course, the equation of time can still be used, when required, to obtain solar time from clock time. Devices such as solar trackers, which move to keep pace with the Sun's movements in the sky, are often driven by clocks, with a mechanism that incorporates the equation of time to make them move accurately.
Read more about this topic: Equation Of Time
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