Editing Equation of time (section)

=== Early modern period ===
{{See also|Equation clock}}

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 [[Sunrise|Rising]] or [[Sunset|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.<ref name=Maskelyne67/>

The right time was originally considered to be that which was shown by a sundial. When good mechanical clocks were introduced, they agreed with sundials only near four dates each year, so the equation of time was used to "correct" their readings to obtain sundial time. Some clocks, called [[equation clock]]s, included an internal mechanism to perform this "correction". Later, as clocks became the dominant good timepieces, uncorrected clock time, i.e., "mean time", became the accepted standard. 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.{{r|Waugh|p=123}}

The equation of time was used historically to [[wikt:clocksetter|set clocks]]. Between the invention of accurate clocks in 1656 and the advent of commercial time distribution services around 1900, there were several common land-based ways to set clocks. A sundial was read and corrected with the table or graph of the equation of time.

If a [[transit instrument]] was available or accuracy was important, the sun's transit across the [[meridian (astronomy)|meridian]] (the moment the sun appears to be due south or north of the observer, known as its [[culmination]]) was noted; the clock was then set to noon and offset by the number of minutes given by the equation of time for that date. A third method did not use the equation of time; instead, it used [[wikt:star|stellar]] observations to give [[sidereal time]], exploiting the relationship between sidereal time and [[mean solar time]].{{r|Olmstead|p=57–58}} The more accurate methods were also precursors to finding the observer's [[longitude]] in relation to a [[prime meridian]], such as in [[geodesy]] on land and [[celestial navigation]] on the sea.

The first tables to give the equation of time in an essentially correct way were published in 1665 by [[Christiaan Huygens]].<ref name="Huygens"/> Huygens, following the tradition of Ptolemy and medieval astronomers in general, set his values for the equation of time so as to make all values positive throughout the year.<ref name="Huygens"/> This meant that any clock being set to mean time by Huygens's tables was consistently about 15&nbsp;minutes slow compared to today's mean time.

Another set of tables was published in 1672–73 by [[John Flamsteed]], who later became the first [[Astronomer Royal]] of the new [[Royal Observatory, Greenwich|Royal Greenwich Observatory]]. These appear to have been the first essentially correct tables that gave today's meaning of Mean Time (previously, as noted above, the sign of the equation was always positive and it was set at zero when the apparent time of sunrise was earliest relative to the clock time of sunrise). Flamsteed adopted the convention of tabulating and naming the correction in the sense that it was to be applied to the apparent time to give mean time.<ref name="Flamsteed"/>

The equation of time, correctly based on the two major components of the Sun's irregularity of apparent motion, was not generally adopted until after Flamsteed's tables of 1672–73, published with the posthumous edition of the works of [[Jeremiah Horrocks]].{{r|Vince|p=49}}

[[Robert Hooke]] (1635–1703), who mathematically analyzed the [[universal joint]], was the first to note that the geometry and mathematical description of the (non-secular) equation of time and the universal joint were identical, and proposed the use of a universal joint in the construction of a "mechanical sundial".{{r|Mills|p=219}}