MORE WORK NEEDED ON THIS PAGE
CAVEAT
Tables which provide the Equation of Time (e.g. on the Web) and pertain to be 'accurate', should always quote to which time zone they apply. Such tables usually give the EoT values for noon. But noon in Seattle is hours different from noon in Bombay. When the Equation of Time is changing rapidly - some 30 secs/day around Christmas - tables created for one time zone will be incorrect by 15 seconds on the other side of the world.
THE LEAP YEAR CYCLE
The tropical year is about 365¼ days and our calendrical cycle usually runs on a 1461 day cycle (3 x 365 + 366). Thus the 12:00 noon EoT one year will be the 18:00 pm EoT the next.
LONG TERM TRENDS
There are many reasons why the Equation of Time varies between one year and the next. The value of the Equation of Time is dominated by two variables - the Eccentricity & Obliquity of the Earth's orbit - (see section 'The Components of the Equation of Time'). Since we count our days from Jan 1st. we need to see ...
(a) how our calendrical system interferes with the time from Jan 1st → Vernal equinox & Jan 1st → Perihelion.
(b) the actual values of Eccentricity & Obliquity over time
Thus, as shown below, although the time between Jan 1st and the Mean Value of the 
Two views of the variation of the Equation over Time. Graph by the Author, Analemmas by Pete Swanstrom
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