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-   -   The Equation of Time(keeping) (http://www.spacebanter.com/showthread.php?t=221820)

Gerald Kelleher November 19th 17 09:33 AM

The Equation of Time(keeping)
 
The basic experiment involves either a sand or water clock. The period of one noon to the next full cycle would generate different volumes of water and sand reflecting the variation in the total length of each individual cycle . If the volumes were combined and divided equally by the number of cycles, an average would be created . This is how the average 24 hour day is created regardless of method or complications.

The Equation of time is the bridge between the unequal quantities (natural noon) and equal quantities (24 hour noon). The bridge which correlates the 24 hour weekday to the natural day is anchored to noon and is a global observation along any line of longitude so it doesn't involve any seasonal components, for example, when it is noon at Conception in Chile, it is also noon in New York as they share roughly the same longitude line but different seasons however both locations will register the same length of the noon cycle as per water/sand clock.









Mikko November 19th 17 10:34 AM

The Equation of Time(keeping)
 
In article ,
Gerald Kelleher wrote:

The basic experiment involves either a sand or water clock. The period of one
noon to the next full cycle would generate different volumes of water and
sand reflecting the variation in the total length of each individual cycle .


Sand and water clocks are too inaccurate to detect the variation in
duration from one noon to the next.

Mikko

Gerald Kelleher November 19th 17 11:38 AM

The Equation of Time(keeping)
 
On Sunday, November 19, 2017 at 10:34:04 AM UTC, Mikko wrote:
In article ,
Gerald Kelleher wrote:

The basic experiment involves either a sand or water clock. The period of one
noon to the next full cycle would generate different volumes of water and
sand reflecting the variation in the total length of each individual cycle .


Sand and water clocks are too inaccurate to detect the variation in
duration from one noon to the next.

Mikko


That is incorrect. The purpose is determine the variations in quantities in sand or water for each full cycle and there is a procedure for that which makes it exceptionally accurate. It means taking a short step back and modifying the procedure -

"Draw a Meridian line upon a floor and then hang two plummets, each
by a small thread or wire, directly over the said Meridian, at the
distance of some two feet or more one from the other, as the smallness
of the thread will admit. When the middle of the Sun (the Eye being
placed so, as to bring both the threds into one line) appears to be in
the same line exactly you are then immediately to set the Watch, not
precisely to the hour of 12. but by so much less, as is the Aequation
of the day by the Table." Huygens

The modification is that there is a beginning and end to the natural noon cycle using a shadow alignment if a quantity like sand or water is used to determine the length of each cycle.




Quadibloc November 19th 17 06:08 PM

The Equation of Time(keeping)
 
On Sunday, November 19, 2017 at 2:33:36 AM UTC-7, Gerald Kelleher wrote:

The Equation of time is the bridge between the unequal quantities (natural noon)
and equal quantities (24 hour noon).


Yes, that is correct.

What you seem to fail to recognize, though, is that the "equal quantities" are
very important in physics, chemistry, electronics, even cooking. One wants to
bake a cake by leaving it in the oven for 30 equal minutes, not half an hour as
the sundial would indicate.

Explaining how things work over time, therefore, requires using equal time, not
natural sundial time.

This includes explaining how the Earth rotates.

So the Earth rotates at an equal pace - if we measure its rotation against the
stars. The unequal pace of natural noon results from combining that rotation
with the Earth's orbit around the Sun, which, because the Earth's orbit is
elliptical, has a slow part and a fast part. (Plus, there are two other slow and
fast parts due to the inclination between the equator and the ecliptic, but that
gets complicated.)

Just as the Earth's orbit has to be taken into account to explain planetary
retrogrades, the Earth's orbit explains the Equation of Time. The Earth rotates
at an equal pace, but natural noon is when the Earth's rotation brings a place
to the meridian on which the Sun is found, which changes over the course of a
year due to the Earth's orbit.

John Savard

Quadibloc November 19th 17 06:11 PM

The Equation of Time(keeping)
 
On Sunday, November 19, 2017 at 3:34:04 AM UTC-7, Mikko wrote:

Sand and water clocks are too inaccurate to detect the variation in
duration from one noon to the next.


That may be, but using an atomic clock instead would involve the exact same
principle, so it doesn't affect his point. He just chose to use a...
traditional... example of a mechanical clock, perhaps in reaction to what he may
feel to be a recent trend towards glorifying technology.

John Savard

Gerald Kelleher November 19th 17 07:34 PM

The Equation of Time(keeping)
 
On Sunday, November 19, 2017 at 10:34:04 AM UTC, Mikko wrote:
In article ,
Gerald Kelleher wrote:

The basic experiment involves either a sand or water clock. The period of one
noon to the next full cycle would generate different volumes of water and
sand reflecting the variation in the total length of each individual cycle .


Sand and water clocks are too inaccurate to detect the variation in
duration from one noon to the next.

Mikko


To be fair to you and if your question was genuine, the answer to the quoted text only refers to the natural variations determined by the unequal amounts of sand and water for each respective noon cycle . By accumulating say 10 cycles of sand noting the variation for each and then dividing equally by 10, you get an idea how the average volume in anchored to the natural noon cycle.

It represents how the average 24 hour day is created and subsequently its divisions into equal hours, minutes and seconds. I can't prevent rude people from interjecting as this is an open forum with all its advantages and disadvantages but at least your objection was intelligent.

Paul Schlyter[_3_] November 20th 17 07:48 AM

The Equation of Time(keeping)
 
On Sun, 19 Nov 2017 10:08:59 -0800 (PST), Quadibloc
wrote:
What you seem to fail to recognize, though, is that the "equal

quantities" are
very important in physics, chemistry, electronics, even cooking.

One wants to
bake a cake by leaving it in the oven for 30 equal minutes, not

half an hour as
the sundial would indicate.


Do you really time to a fraction of a second when you bake a cake in
your oven? Because the largest difference between half an hour
sundial time and half an hour mean solar time is about 0.1 seconds,
and if you think that small difference noticeably affects your
cake...well...

Some people don't time their cakes in the oven at all, instead they
regularly check the condition of the cake and takes it out of the
oven when it looks fine.

Quadibloc November 20th 17 03:42 PM

The Equation of Time(keeping)
 
On Monday, November 20, 2017 at 12:48:10 AM UTC-7, Paul Schlyter wrote:

Do you really time to a fraction of a second when you bake a cake in
your oven?


Obviously I am being as pretentious as those people who came up with "leap
seconds"!

You are quite correct I let the basic principle get in the way of practicality in
my choice of example.

John Savard

Gerald Kelleher November 20th 17 04:40 PM

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.


Martin Brown[_3_] November 21st 17 09:05 AM

The Equation of Time(keeping)
 
On 19/11/2017 10:34, Mikko wrote:
In article ,
Gerald Kelleher wrote:

The basic experiment involves either a sand or water clock. The period of one
noon to the next full cycle would generate different volumes of water and
sand reflecting the variation in the total length of each individual cycle .


Sand and water clocks are too inaccurate to detect the variation in
duration from one noon to the next.


Actually they were just about good enough to do it a long time ago.

https://www.researchgate.net/publica...lack_Sea_Coast

They would need to be good to better than 10 minutes in 24 hours to get
a 3 sigma detection of shortest day vs longest day variation. They are
more accurate than that. I built one for a lecture (an equal interval
one constructed as a parabola of revolution). It was surprisingly
reproducible a larger scaled one probably good to

That is how the ancients knew that the suns motion across the heavens
was at a variable speed. Unclear how many times the water clock in its
various guises was invented. There are obvious systematic errors that
vary with temperature and humidity but it wasn't a bad start.

A Chinese inventor even did one with mercury as the working fluid which
avoided problems of freezing up in continental winters.

--
Regards,
Martin Brown


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