Averaging and the Equation of Time

Here take notice, that the Sun or the Earth passeth the 12. Signes,
or makes an entire revolution in the Ecliptick in 365 days, 5 hours 49
min. or there about, and that those days, reckon'd from noon to noon,
are of different lenghts; as is known to all that are vers'd in
Astronomy. Now between the longest and the shortest of those days, a
day may be taken of such a length, as 365 such days, 5. hours &c. (the
same numbers as before) make up, or are equall to that revolution: And
this is call'd the Equal or Mean day, according to which the Watches
are to be set; and therefore the Hour or Minute shew'd by the Watches,
though they be perfectly Iust and equal, must needs differ almost
continually from those that are shew'd by the Sun, or are reckon'd
according to its Motion. But this Difference is regular, and is
otherwise call'd the Aequation.." Huygens

That description of the Equation of Time has a large error in it that is immediately apparent, at least for those who value their intelligence. If people give up the pretense that they have the faintest idea what Newton was doing with his absolute/relative time(keeping), space and motions definitions they would understand more in a short while than their predecessors understood in 3 centuries.

The Equation of Time fits inside the calendar system as it relies on the noon event to equalize the variations to a 24 hour average so there can be no fractional element left over as a single orbit. Unlike a rotation which equates to one day/night cycle anchored to noon , the year does not equate to one orbital circuit as March 1st to February 28th as one circuit and one year is also valid for March 1st to February 29th as one year.

It was how Sir Isaac got his idea of the all-encompassing inverse square law in equating the Earth around the Sun is the same time period as the Sun around the Earth (found in Huygen's description) -

"That the fixed stars being at rest, the periodic times of the five primary planets, and (whether of the sun about the earth, or) of the earth about the sun, are in the sesquiplicate proportion of their mean distances from the sun...This proportion, first observed by Kepler, is now received by all astronomers; for the periodic times are the same, and the dimensions of the orbits are the same, whether the sun revolves about the earth, or the earth about the sun." Newton

For the slow of mind - Huygen's description of the Equation of Time is wrong as is Sir Isaac's attempt to mimic it as absolute/relative time -

"Absolute time, in astronomy, is distinguished from relative, by the equation of time. For the natural days are truly unequal, though they are commonly considered as equal and used for a measure of time; astronomers correct this inequality for their more accurate deducing of the celestial motions... The necessity of which equation, for determining the times of a phenomenon, is evinced as well from the experiments of the pendulum clock, as by eclipses of the satellites of Jupiter." Principia

Want to really appreciate something really complicated and genuine outside the realm of the wider public and that is it !.