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Old November 20th 17, 04:40 PM posted to sci.astro.amateur
Gerald Kelleher
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Default The Equation of Time(keeping)

The only issue so far is how variable quantities are converted into equable ones, in this case the natural variations in each complete noon cycle to the next is equalized by the timekeeping facility to an average.

"Here take notice, that the Sun or the Earth passes through the 12 Signs, or makes an entire revolution in the Ecliptic in 365 days, 5 hours 49 min. or there about, and that those days, reckoned from noon to noon, are of different lengths; as is known to all that are versed 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 equal to that orbital circuit: 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 just and equal, must needs differ almost continually from those that are showed by the Sun, or are reckoned according to its Motion." Huygens

The Equation of timekeeping works off the determination of natural noon and there are 3 years with 365 corrections and one year with 366 such corrections, the last one in 2016 -

http://www.ppowers.com/info/EoT%202016%20one%20page.pdf

Keeping in mind that this was the first attempt to generate the 24 hour average in a meaningful way, Huygens can be forgiven for the false notion that the Equation of Time fits within the 365 day 5 hour 49 minute framework when it is a calendar based entity. You need the average 24 hour day and therefore equable hours minutes and seconds to time everything else so there is no chicken and egg paradox here, the 24 hour day has to be created first with specific references attached.