Average time between "South-Solstices"

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Average time between "South-Solstices"

Peter Meyer
Michael Ossipoff said (typo corrected):

> At a forum interested in astronomy, science or reform, or if interest is
> expressed, justifying further information, I'd add;
>
> "...or closest to an _approximation_ to the South-Solstice, based on the
> assumption that a South-Solstice occurs exactly every 365.2422
> days...starting from the actual South-Solstice of Gregorian 2017."

The assumption is incorrect.  Solstices *never* occur exactly D days
apart, where D is a number stated to the 4th decimal place as above.

A more serious objection is as follows.  At
https://www.hermetic.ch/cal_stud/dst02.htm Duncan Steel (author of the
book 'Marking Time") writes:

"Doing the detailed calculations the average times in [mean solar] days
between the annual [northern hemisphere] marker points are as follows
(they vary over centuries and millennia):
spring equinox:    365.2424
summer solstice: 365.2416
autumn equinox: 365.2420
winter solstice:   365.2427"

Which of these solstice events is the same as Michael's
"Southern-Solstice"?  The average period between solstice events is
either 365.2416 days (summer) or 365.2427 days (winter), neither of
which is the same as Michael's 365.2422 days.

Those who find Michael's calendrical efforts to be worthy of attention
might care to compare them with Irv Bromberg's contributions on the
same subject, for which see his
http://individual.utoronto.ca/kalendis/leap/index.htm#CS

Regards,
Peter
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Re: Average time between "South-Solstices"

Peter Meyer
I said: "Solstices *never* occur exactly D days apart, where D is a
number stated to the 4th decimal place as [in 365.2422]."

Before someone corrects me, I'll add:

Of course, if many thousands of periods between successive solstice
events (of the same kind) are recorded, and expressed to the nearest
4th decimal place, we shall, of course, find a few which are D (days),
since there are only 10,000 possible 4-digit numerals which can be
decimal values expressed to the 4th decimal place.

And if all such periods are in the range 365.23 days to 365.25 days
then we might find that every 200th or so was a D.

Regards,
Peter
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Re: Average time between "South-Solstices"

Michael Ossipoff
In reply to this post by Peter Meyer

[quote]

Michael Ossipoff said (typo corrected):
.
> At a forum interested in astronomy, science or reform, or if interest is
> expressed, justifying further information, I'd add;
>
> "...or closest to an _approximation_ to the South-Solstice, based on the
> assumption that a South-Solstice occurs exactly every 365.2422
> days...starting from the actual South-Solstice of Gregorian 2017."
.
The assumption is incorrect.  Solstices *never* occur exactly D days
apart, where D is a number stated to the 4th decimal place as above.

[/quote]

.

That’s why I spoke of an _approximation_ based on that assumption.

.

Approximations are often based on false assumptions.   …simplifying-assumptions.

.

[quote]
A more serious objection is as follows.  At
https://www.hermetic.ch/cal_stud/dst02.htm Duncan Steel (author of the
book 'Marking Time") writes:
.
"Doing the detailed calculations the average times in [mean solar] days
between the annual [northern hemisphere] marker points are as follows
(they vary over centuries and millennia):
spring equinox:    365.2424
summer solstice: 365.2416
autumn equinox: 365.2420
winter solstice:   365.2427"
.
Which of these solstice events is the same as Michael's
"Southern-Solstice"?  The average period between solstice events is
either 365.2416 days (summer) or 365.2427 days (winter), neither of
which is the same as Michael's 365.2422 days.

[/quote]

.

Starting the calendar year near the South-Solstice doesn’t require using the South-Solstice tropical-year as the reference-tropical-year for the arithmetical year-start rule.

.

I chose the _mean_ tropical year as the reference tropical-year, because it’s most practical, or at least impartial, to reduce drift all around the year, rather than at some particular favored solar ecliptic-longitude.

.

Additionally, the mean tropical year is the one most often heard of and the one whose length is most often given  by various sources, including those on the Internet. Familiarity helps acceptance.
.

6 Th

.

Michael Ossipoff

 

 

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Re: Average time between "South-Solstices"

k.palmen@btinternet.com
In reply to this post by Peter Meyer
Dear Peter and Calendar People

Here Michael is defining a rule-based calendar with a mean year near the mean tropical year and is merely using the South solstice as a starting point for the year.

The definition of the calendar should explicitly state the exact south solstice time of 2017 used, because various calculations of it may differ slightly and this could affect the year start when the approximate solstice occurs very near noon on a Thursday.

Given that the southern solstice of 2017 is reckoned in UT/GMT. I can list the first few approximate solstices along with the actual solstice in ().
2017 Thu 16:27:50  (Thu 16:27:50)
2018 Fri 22:16:36.08 (Fri 22:21:51)
2019 Sun 04:05:22.16 (Sun 04:18:56)
2020 Mon 09:54:08.24  (Mon 10:02:26)
etc

Karl

Friday Alpha February 2019

----Original message----
From : [hidden email]
Date : 31/01/2019 - 11:30 (GMT)
To : [hidden email]
Subject : Average time between "South-Solstices"

Michael Ossipoff said (typo corrected):

> At a forum interested in astronomy, science or reform, or if interest is
> expressed, justifying further information, I'd add;
>
> "...or closest to an _approximation_ to the South-Solstice, based on the
> assumption that a South-Solstice occurs exactly every 365.2422
> days...starting from the actual South-Solstice of Gregorian 2017."

The assumption is incorrect.  Solstices *never* occur exactly D days
apart, where D is a number stated to the 4th decimal place as above.

A more serious objection is as follows.  At
https://www.hermetic.ch/cal_stud/dst02.htm Duncan Steel (author of the
book 'Marking Time") writes:

"Doing the detailed calculations the average times in [mean solar] days
between the annual [northern hemisphere] marker points are as follows
(they vary over centuries and millennia):
spring equinox:    365.2424
summer solstice: 365.2416
autumn equinox: 365.2420
winter solstice:   365.2427"

Which of these solstice events is the same as Michael's
"Southern-Solstice"?  The average period between solstice events is
either 365.2416 days (summer) or 365.2427 days (winter), neither of
which is the same as Michael's 365.2422 days.

Those who find Michael's calendrical efforts to be worthy of attention
might care to compare them with Irv Bromberg's contributions on the
same subject, for which see his
http://individual.utoronto.ca/kalendis/leap/index.htm#CS

Regards,
Peter
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Re: Average time between "South-Solstices"

Michael Ossipoff
Karl--

That's true, it's important for the calendar's definition to state an assumed exact time for the 2017 South-Solstice.  Your 2017 Thu 16:27:50  UTC will do fine. Let's say it's  2017 Thu 16:27:50 UTC.

I was surprised by the amount of the differences, in your table, between the actual and approximate solstices for the next few years. I'd assumed that 365.2422 wouldn't be off by more than .0001 day.  ...which is only 8.64 seconds.

One thing that I should add to what I said earlier:

In case it sounds to anyone as if an approximation based on a false-assumption is too questionable a thing:

It should be emphasized that, for solar calendars, all arithmetical year-start rules (including leapyear-rules) involve an approximation of a tropical-year length, based on a simplifying assumption, a false assumption.  For example, as we all know, the Gregorian leapyear-rule uses an approximation based on a false (assumption about the length of the Northward-Equinox tropical-year.

6 F

Michael Ossipoff


On Fri, Feb 1, 2019 at 6:25 AM K PALMEN <[hidden email]> wrote:
Dear Peter and Calendar People

Here Michael is defining a rule-based calendar with a mean year near the mean tropical year and is merely using the South solstice as a starting point for the year.

The definition of the calendar should explicitly state the exact south solstice time of 2017 used, because various calculations of it may differ slightly and this could affect the year start when the approximate solstice occurs very near noon on a Thursday.

Given that the southern solstice of 2017 is reckoned in UT/GMT. I can list the first few approximate solstices along with the actual solstice in ().
2017 Thu 16:27:50  (Thu 16:27:50)
2018 Fri 22:16:36.08 (Fri 22:21:51)
2019 Sun 04:05:22.16 (Sun 04:18:56)
2020 Mon 09:54:08.24  (Mon 10:02:26)
etc

Karl

Friday Alpha February 2019

----Original message----
From : [hidden email]
Date : 31/01/2019 - 11:30 (GMT)
To : [hidden email]
Subject : Average time between &quot;South-Solstices&quot;

Michael Ossipoff said (typo corrected):

> At a forum interested in astronomy, science or reform, or if interest is
> expressed, justifying further information, I'd add;
>
> "...or closest to an _approximation_ to the South-Solstice, based on the
> assumption that a South-Solstice occurs exactly every 365.2422
> days...starting from the actual South-Solstice of Gregorian 2017."

The assumption is incorrect.  Solstices *never* occur exactly D days
apart, where D is a number stated to the 4th decimal place as above.

A more serious objection is as follows.  At
https://www.hermetic.ch/cal_stud/dst02.htm Duncan Steel (author of the
book 'Marking Time") writes:

"Doing the detailed calculations the average times in [mean solar] days
between the annual [northern hemisphere] marker points are as follows
(they vary over centuries and millennia):
spring equinox:    365.2424
summer solstice: 365.2416
autumn equinox: 365.2420
winter solstice:   365.2427"

Which of these solstice events is the same as Michael's
"Southern-Solstice"?  The average period between solstice events is
either 365.2416 days (summer) or 365.2427 days (winter), neither of
which is the same as Michael's 365.2422 days.

Those who find Michael's calendrical efforts to be worthy of attention
might care to compare them with Irv Bromberg's contributions on the
same subject, for which see his
http://individual.utoronto.ca/kalendis/leap/index.htm#CS

Regards,
Peter
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Re: Average time between "South-Solstices"

Michael Ossipoff
...but of course, because the South-Solstice year isn't the MTY, then it the calendar's yearly drift at year-start would depend on the difference between MTY and South-Solstice tropical year, which is more than .0001 days.

So I shouldn't have been surprised by that drift being greater than .0001 days.

6 F

Michael Ossipoff
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Re: Average time between "South-Solstices"

Michael Ossipoff
But it would still take roughly 3000 years for a day's drift at the South-Solstice. 

...which isn't so bad for a leapweek calendar, for which the (actually-achieved) best-possible jitter-amplitude is 3.5 days.

6 F

Michael Ossipoff

On Fri, Feb 1, 2019 at 2:15 PM Michael Ossipoff <[hidden email]> wrote:
...but of course, because the South-Solstice year isn't the MTY, then it the calendar's yearly drift at year-start would depend on the difference between MTY and South-Solstice tropical year, which is more than .0001 days.

So I shouldn't have been surprised by that drift being greater than .0001 days.

6 F

Michael Ossipoff
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Re: Average time between "South-Solstices"

Peter Meyer
In reply to this post by Peter Meyer
I quote from https://www.hermetic.ch/cal_stud/cal_art.html

---  start quote ---

The Gregorian reform consisted of the following:

1.  Ten days were omitted from the calendar, and it was decreed that
the day following (Thursday) October 4, 1582 (which is October 5, 1582,
in the old calendar) would thenceforth be known as (Friday) October 15,
1582.
2.  The rule for leap years was changed. In the Julian Calendar a year
is a leap year if it is divisible by 4. In the Gregorian Calendar a
year is a leap year if either (i) it is divisible by 4 but not by 100
or (ii) it is divisible by 400. In other words, a year which is
divisible by 4 is a leap year unless it is divisible by 100 but not by
400 (in which case it is not a leap year). Thus the years 1600 and 2000
are leap years, but 1700, 1800, 1900 and 2100 are not.
3.  New rules for the determination of the date of Easter were adopted.
4.  The position of the extra day in a leap year was moved from the day
before February 25th to the day following February 28th.

---  end quote ---

Michael Ossipoff said:

"... as we all know [!], the Gregorian leapyear-rule uses an
approximation based on a false (assumption about the length of the
Northward-Equinox tropical-year."

Can Michael specify exactly where (2) uses, or any of (1)-(4) uses, "an
approximation based on a false assumption about the length of the
Northward-Equinox tropical-year"?

And for the benefit of those of us who don't care to wade through
Michael's many prolix and unclear messages, would Michael kindly state
(in one sentence) exactly what he means by "the Northward-Equinox
tropical-year", since this is not standard terminology.  If he cannot
do this, would he kindly enlighten us as to why not?

Regards,
Peter
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Re: Average time between "South-Solstices"

k.palmen@btinternet.com
In reply to this post by Michael Ossipoff
Dear Michael and Calendar People

The difference between the approximate and actual solstices will accumulate to about 3 days then go down and oscillate over a precession period, assuming the calendar is kept accurate to the mean tropical year.

I thought that if one is using the interval of 365.2422 days, one could round the Thu 16:27:50 to the nearest 0.0001 day to aid calculations. This makes it 0.6860 day on Thursday. The actual value for 16:27:50 happens to be very close to this at 0.68599537... day .


The Northward Equinox is another name for the March Equinox that has been used on the list before by people other than Michael.


Karl

Saturday Alpha February 2019
----Original message----
From : [hidden email]
Date : 01/02/2019 - 19:37 (GMT)
To : [hidden email]
Subject : Re: Average time between "South-Solstices"

But it would still take roughly 3000 years for a day's drift at the South-Solstice. 

...which isn't so bad for a leapweek calendar, for which the (actually-achieved) best-possible jitter-amplitude is 3.5 days.

6 F

Michael Ossipoff

On Fri, Feb 1, 2019 at 2:15 PM Michael Ossipoff <[hidden email]> wrote:
...but of course, because the South-Solstice year isn't the MTY, then it the calendar's yearly drift at year-start would depend on the difference between MTY and South-Solstice tropical year, which is more than .0001 days.

So I shouldn't have been surprised by that drift being greater than .0001 days.

6 F

Michael Ossipoff


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Re: Average time between "South-Solstices"

Michael Ossipoff

Karl--

Yes, given the precision of 365.2422, then .6860 is plenty accurate enough for the day-fraction at which the 2017 South-Solstice occurred.  That's what I'd use when stating a formula for the calculation of approximate South-Solstice times.

6 Sa

Michael Ossipoff

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Re: Average time between "South-Solstices"

Walter J Ziobro
In reply to this post by Peter Meyer

Dear Peter et al

If I am not mistaken, the leap day was not moved from the 25th to the 29th by Pope Gregory's bull That only happened in the British Empire when Parliament reformed the calendar in 1753

Walter Ziobro




On Friday, February 1, 2019 Peter Meyer <[hidden email]> wrote:


---  start quote ---

The Gregorian reform consisted of the following:

1.  Ten days were omitted from the calendar, and it was decreed that
the day following (Thursday) October 4, 1582 (which is October 5, 1582,
in the old calendar) would thenceforth be known as (Friday) October 15,
1582.
2.  The rule for leap years was changed. In the Julian Calendar a year
is a leap year if it is divisible by 4. In the Gregorian Calendar a
year is a leap year if either (i) it is divisible by 4 but not by 100
or (ii) it is divisible by 400. In other words, a year which is
divisible by 4 is a leap year unless it is divisible by 100 but not by
400 (in which case it is not a leap year). Thus the years 1600 and 2000
are leap years, but 1700, 1800, 1900 and 2100 are not.
3.  New rules for the determination of the date of Easter were adopted.
4.  The position of the extra day in a leap year was moved from the day
before February 25th to the day following February 28th.

---  end quote ---

Michael Ossipoff said:

"... as we all know [!], the Gregorian leapyear-rule uses an
approximation based on a false (assumption about the length of the
Northward-Equinox tropical-year."

Can Michael specify exactly where (2) uses, or any of (1)-(4) uses, "an
approximation based on a false assumption about the length of the
Northward-Equinox tropical-year"?

And for the benefit of those of us who don't care to wade through
Michael's many prolix and unclear messages, would Michael kindly state
(in one sentence) exactly what he means by "the Northward-Equinox
tropical-year", since this is not standard terminology.  If he cannot
do this, would he kindly enlighten us as to why not?

Regards,
Peter
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Re: Average time between "South-Solstices"

Peter Meyer
In reply to this post by Peter Meyer
A couple of days ago I wrote:

> And for the benefit of those of us who don't care to wade through
> Michael's many prolix and unclear messages, would Michael kindly
> state (in one sentence) exactly what he means by "the
> Northward-Equinox tropical-year", since this is not standard
> terminology.

"Tropical year" may be in common usage, but as Simon Cassidy pointed
out on this list many years ago (before Michael's arrival) this term,
as commonly used, is an average of an average (namely, an average of
the average years as measured from four points in the Earth's orbit)
and thus has no physical meaning.

Did Michael reply?  Perhaps I missed it.  Or is he unable to explain
what he means by "the Northward-Equinox tropical-year" in less than
several sentences?  Well, I think we can put up with that for the sake
of understanding exactly what Michael means by this term.  And what
value (in mean solar days) he gives to it.

Regards,
Peter
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Leap Rule CENTURIAN TO 128th Re: Average time between "South-Solstices"

Brij Bhushan metric VIJ
In reply to this post by Walter J Ziobro
 Walter, Peter Meyer, listserv sirs:
February has had ‘changing number of days’ during Leap Years - 28,29 or even 30 days. The position of Leap Day/Leap Week, however, fluctuated during February:
>2.  The rule for leap years was changed. In the Julian Calendar a year 
is a leap year if it is divisible by 4. In Jithe Gregorian Calendar a 
year is a leap year if either (i) it is divisible by 4 but not by 100 
or (ii) it is divisible by 400. In other words, a year which is 
divisible by 4 is a leap year unless it is divisible by 100 but not by 
400 (in which case it is not a leap year). Thus the years 1600 and 2000 
are leap years, but 1700, 1800, 1900 and 2100 are not.
image1.jpeg
In the format, I promote, the month of February from current 28 days, shall now have 29 days BUT THIS LEAP DAY shall shift to between June 30 & July 01, when Year is divisible by 4 - but NOT a Leap Day year if divisible by 128 getting Mean Year=(365+ 31/128)=365.2421875 days; as such years divisible by 4 including 1600,1700,1800,1900 ,2000,2100 are all having the Leap Day (or planned Leap Week div.6) during ‘Centurian years too’ placed between June end & July 01. This makes sure personnel born on February 29 ENJOY THEIR “birth year - every year on February 29th”. 
Regards,
Flt Lt Brij Bhushan VIJ (Retd.), IAF
Saturday, 2019 February 02H21:74(Decimal)

Sent from my iPhone

On Feb 2, 2019, at 19:30, Walter J Ziobro <[hidden email]> wrote:

2.  The rule for leap years was changed. In the Julian Calendar a year
is a leap year if it is divisible by 4. In the Gregorian Calendar a
year is a leap year if either (i) it is divisible by 4 but not by 100
or (ii) it is divisible by 400. In other words, a year which is
divisible by 4 is a leap year unless it is divisible by 100 but not by
400 (in which case it is not a leap year). Thus the years 1600 and 2000
are leap years, but 1700, 1800, 1900 and 2100 are not.
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Also 896th year Re: Leap Rule CENTURIAN TO 128th Re: Average time between "South-Solstices"

Brij Bhushan metric VIJ
Listserv, sirs: 
>... - but NOT a Leap Day year if divisible by 128 getting M
ean Year=(365+ 31/128)=365.2421875 days; as such years divisible by 4 including 1600,1700,1800,1900 ,2000,2100 are all having the Leap Day (or planned Leap Week div.6) during ‘Centurian years too’ placed between June end & <a href="x-apple-data-detectors://2" dir="ltr" x-apple-data-detectors="true" x-apple-data-detectors-type="calendar-event" x-apple-data-detectors-result="2" style="-webkit-text-decoration-color: rgba(0, 0, 0, 0.258824);">July 01.
      “My appology, sirs, It should be more specific that years ‘divisible by 896 SKIP ‘the leap day like the 400th - this should read: - but NOT a Leap Day year if divisible by 128th and 896th Years, getting Mean Year=(365+ 31/128)=365.2421875 days;....”
Flt Lt Brij Bhushan VIJ (Retd.),IAF
SATURDAY, 2019 February 02H22:08 (Decimal) 

Sent from my iPhone

On Feb 2, 2019, at 21:45, Brij Bhushan metric VIJ <[hidden email]> wrote:

 Walter, Peter Meyer, listserv sirs:
February has had ‘changing number of days’ during Leap Years - 28,29 or even 30 days. The position of Leap Day/Leap Week, however, fluctuated during February:
>2.  The rule for leap years was changed. In the Julian Calendar a year 
is a leap year if it is divisible by 4. In Jithe Gregorian Calendar a 
year is a leap year if either (i) it is divisible by 4 but not by 100 
or (ii) it is divisible by 400. In other words, a year which is 
divisible by 4 is a leap year unless it is divisible by 100 but not by 
400 (in which case it is not a leap year). Thus the years 1600 and 2000 
are leap years, but 1700, 1800, 1900 and 2100 are not.
<image1.jpeg>
In the format, I promote, the month of February from current 28 days, shall now have 29 days BUT THIS LEAP DAY shall shift to between June 30 & July 01, when Year is divisible by 4 - but NOT a Leap Day year if divisible by 128 getting Mean Year=(365+ 31/128)=365.2421875 days; as such years divisible by 4 including 1600,1700,1800,1900 ,2000,2100 are all having the Leap Day (or planned Leap Week div.6) during ‘Centurian years too’ placed between June end & July 01. This makes sure personnel born on February 29 ENJOY THEIR “birth year - every year on February 29th”. 
Regards,
Flt Lt Brij Bhushan VIJ (Retd.), IAF
Saturday, 2019 February 02H21:74(Decimal)

Sent from my iPhone

On Feb 2, 2019, at 19:30, Walter J Ziobro <[hidden email]> wrote:

2.  The rule for leap years was changed. In the Julian Calendar a year
is a leap year if it is divisible by 4. In the Gregorian Calendar a
year is a leap year if either (i) it is divisible by 4 but not by 100
or (ii) it is divisible by 400. In other words, a year which is
divisible by 4 is a leap year unless it is divisible by 100 but not by
400 (in which case it is not a leap year). Thus the years 1600 and 2000
are leap years, but 1700, 1800, 1900 and 2100 are not.

image1.jpeg (178K) Download Attachment
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Re: Average time between "South-Solstices"

k.palmen@btinternet.com
In reply to this post by Michael Ossipoff
Dear Michael

Great! This needs to go in the definition of the year start rule on the Calendar Wikia.

Karl

Sunday Alpha February 2019
----Original message----
From : [hidden email]
Date : 02/02/2019 - 19:11 (GMT)
To : [hidden email]
Subject : Re: Average time between "South-Solstices"


Karl--

Yes, given the precision of 365.2422, then .6860 is plenty accurate enough for the day-fraction at which the 2017 South-Solstice occurred.  That's what I'd use when stating a formula for the calculation of approximate South-Solstice times.

6 Sa

Michael Ossipoff



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Northward-Equinox tropical-year Re: Average time between "South-Solstices"

k.palmen@btinternet.com
In reply to this post by Peter Meyer
Dear Peter and Calendar People

The "the Northward-Equinox tropical-year" is the tropical year starting with the March equinox. "Northward equinox" without hyphen has been used on this list by people other than Michael and is mentioned in wikipedia
https://en.wikipedia.org/wiki/March_equinox in the first sentence.

Karl

Sunday Alpha February 2019

----Original message----
From : [hidden email]
Date : 03/02/2019 - 04:31 (GMT)
To : [hidden email]
Subject : Re: Average time between &quot;South-Solstices&quot;

A couple of days ago I wrote:

> And for the benefit of those of us who don't care to wade through
> Michael's many prolix and unclear messages, would Michael kindly
> state (in one sentence) exactly what he means by "the
> Northward-Equinox tropical-year", since this is not standard
> terminology.

"Tropical year" may be in common usage, but as Simon Cassidy pointed
out on this list many years ago (before Michael's arrival) this term,
as commonly used, is an average of an average (namely, an average of
the average years as measured from four points in the Earth's orbit)
and thus has no physical meaning.

Did Michael reply?  Perhaps I missed it.  Or is he unable to explain
what he means by "the Northward-Equinox tropical-year" in less than
several sentences?  Well, I think we can put up with that for the sake
of understanding exactly what Michael means by this term.  And what
value (in mean solar days) he gives to it.

Regards,
Peter
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Re: Northward-Equinox tropical-year Re: Average time between "South-Solstices"

Peter Meyer
Karl said:

> The "Northward-Equinox tropical-year" is the tropical year starting
> with the March equinox. "Northward equinox" without hyphen has been
> used on this list by people other than Michael and is mentioned in
> wikipedia
> https://en.wikipedia.org/wiki/March_equinox in the first sentence.

Thanks for the link.  So the "Northward-Equinox tropical-year" is what
calendrical scientists such as Duncan Steel refer to (see
https://www.hermetic.ch/cal_stud/dst02.htm ) as "the (northern) spring
(or vernal) equinox" (which occurs around March 21), and the average
northern vernal equinox year is (according to DS and Simon Cassidy)
365.2424 (mean solar) days.

So Michael's "South-Solstice" is the northern winter solstice (which
occurs around December 21), and the average northern winter solstice
year is (according to DS) 365.2427 (mean solar) days.

Thus Michael (in a message of January 31) is in error in his
"assumption that a South-Solstice occurs exactly every 356.2422 days".

Well, I'm glad we cleared that up.

Regards,
Peter
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Re: Leap Rule CENTURIAN TO 128th Re: Average time between "South-Solstices"

Walter J Ziobro
In reply to this post by Brij Bhushan metric VIJ

Dear Brij et al

If as you propose the dropped leap year were every 128 years, that would be a simpler rule, but such a calendar would be shorter than the current Gregorian calendar by one day every 3200 years

Walter Ziobro




On Saturday, February 2, 2019 Brij Bhushan metric VIJ <[hidden email]> wrote:

 Walter, Peter Meyer, listserv sirs:
February has had ‘changing number of days’ during Leap Years - 28,29 or even 30 days. The position of Leap Day/Leap Week, however, fluctuated during February:
>2.  The rule for leap years was changed. In the Julian Calendar a year 
is a leap year if it is divisible by 4. In Jithe Gregorian Calendar a 
year is a leap year if either (i) it is divisible by 4 but not by 100 
or (ii) it is divisible by 400. In other words, a year which is 
divisible by 4 is a leap year unless it is divisible by 100 but not by 
400 (in which case it is not a leap year). Thus the years 1600 and 2000 
are leap years, but 1700, 1800, 1900 and 2100 are not.
image1.jpeg
In the format, I promote, the month of February from current 28 days, shall now have 29 days BUT THIS LEAP DAY shall shift to between June 30 & July 01, when Year is divisible by 4 - but NOT a Leap Day year if divisible by 128 getting Mean Year=(365+ 31/128)=365.2421875 days; as such years divisible by 4 including 1600,1700,1800,1900 ,2000,2100 are all having the Leap Day (or planned Leap Week div.6) during ‘Centurian years too’ placed between June end & July 01. This makes sure personnel born on February 29 ENJOY THEIR “birth year - every year on February 29th”. 
Regards,
Flt Lt Brij Bhushan VIJ (Retd.), IAF
Saturday, 2019 February 02H21:74(Decimal)

Sent from my iPhone

On Feb 2, 2019, at 19:30, Walter J Ziobro <[hidden email]> wrote:

2.  The rule for leap years was changed. In the Julian Calendar a year
is a leap year if it is divisible by 4. In the Gregorian Calendar a
year is a leap year if either (i) it is divisible by 4 but not by 100
or (ii) it is divisible by 400. In other words, a year which is
divisible by 4 is a leap year unless it is divisible by 100 but not by
400 (in which case it is not a leap year). Thus the years 1600 and 2000
are leap years, but 1700, 1800, 1900 and 2100 are not.
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Re: Also 896th year Re: Leap Rule CENTURIAN TO 128th Re: Average time between "South-Solstices"

Walter J Ziobro
In reply to this post by Brij Bhushan metric VIJ

Dear Brij et al

I'm not sure what you are trying to do every 896 years The 128 year rule seems sufficient What would happen every 896 years is that the weekdays would repeat as it is 128 x 7 years

Walter Ziobro




On Sunday, February 3, 2019 Brij Bhushan metric VIJ <[hidden email]> wrote:

Listserv, sirs: 
>... - but NOT a Leap Day year if divisible by 128 getting M
ean Year=(365+ 31/128)=365.2421875 days; as such years divisible by 4 including 1600,1700,1800,1900 ,2000,2100 are all having the Leap Day (or planned Leap Week div.6) during ‘Centurian years too’ placed between June end & July 01.
      “My appology, sirs, It should be more specific that years ‘divisible by 896 SKIP ‘the leap day like the 400th - this should read: - but NOT a Leap Day year if divisible by 128th and 896th Years, getting Mean Year=(365+ 31/128)=365.2421875 days;....”
Flt Lt Brij Bhushan VIJ (Retd.),IAF
SATURDAY, 2019 February 02H22:08 (Decimal) 

Sent from my iPhone

On Feb 2, 2019, at 21:45, Brij Bhushan metric VIJ <[hidden email]> wrote:

 Walter, Peter Meyer, listserv sirs:
February has had ‘changing number of days’ during Leap Years - 28,29 or even 30 days. The position of Leap Day/Leap Week, however, fluctuated during February:
>2.  The rule for leap years was changed. In the Julian Calendar a year 
is a leap year if it is divisible by 4. In Jithe Gregorian Calendar a 
year is a leap year if either (i) it is divisible by 4 but not by 100 
or (ii) it is divisible by 400. In other words, a year which is 
divisible by 4 is a leap year unless it is divisible by 100 but not by 
400 (in which case it is not a leap year). Thus the years 1600 and 2000 
are leap years, but 1700, 1800, 1900 and 2100 are not.
<image1.jpeg>

In the format, I promote, the month of February from current 28 days, shall now have 29 days BUT THIS LEAP DAY shall shift to between June 30 & July 01, when Year is divisible by 4 - but NOT a Leap Day year if divisible by 128 getting Mean Year=(365+ 31/128)=365.2421875 days; as such years divisible by 4 including 1600,1700,1800,1900 ,2000,2100 are all having the Leap Day (or planned Leap Week div.6) during ‘Centurian years too’ placed between June end & July 01. This makes sure personnel born on February 29 ENJOY THEIR “birth year - every year on February 29th”. 
Regards,
Flt Lt Brij Bhushan VIJ (Retd.), IAF
Saturday, 2019 February 02H21:74(Decimal)

Sent from my iPhone

On Feb 2, 2019, at 19:30, Walter J Ziobro <[hidden email]> wrote:

2.  The rule for leap years was changed. In the Julian Calendar a year
is a leap year if it is divisible by 4. In the Gregorian Calendar a
year is a leap year if either (i) it is divisible by 4 but not by 100
or (ii) it is divisible by 400. In other words, a year which is
divisible by 4 is a leap year unless it is divisible by 100 but not by
400 (in which case it is not a leap year). Thus the years 1600 and 2000
are leap years, but 1700, 1800, 1900 and 2100 are not.
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Re: Also 896th year Re: Leap Rule CENTURIAN TO 128th Re: Average time between "South-Solstices"

Brij Bhushan metric VIJ
Walter, Cc sirs:
>...what you are trying to do every 896 years   Personally, perhaps the usual WAIT...wait & wait keeping my fingers crossed. Like the 400-year Rule, my 128-year cycle ENDS ‘one cycle of 896-years/327257 days/11082 moons - short of twice the duration (0.49287326 day), I add in getting Mean Moon=29.53058886 Days.
Thanks anyway, sir.
Flt Lt Brij Bhushan VIJ (Retd.), IAF
Sunday, 2019 February 03H09:94 (decical)

Sent from my iPhone

On Feb 3, 2019, at 09:18, Walter J Ziobro <[hidden email]> wrote:

Dear Brij et al

I'm not sure what you are trying to do every 896 years The 128 year rule seems sufficient What would happen every 896 years is that the weekdays would repeat as it is 128 x 7 years

Walter Ziobro




On Sunday, February 3, 2019 Brij Bhushan metric VIJ <[hidden email]> wrote:

Listserv, sirs: 
>... - but NOT a Leap Day year if divisible by 128 getting M
ean Year=(365+ 31/128)=365.2421875 days; as such years divisible by 4 including 1600,1700,1800,1900 ,2000,2100 are all having the Leap Day (or planned Leap Week div.6) during ‘Centurian years too’ placed between June end & July 01.
      “My appology, sirs, It should be more specific that years ‘divisible by 896 SKIP ‘the leap day like the 400th - this should read: - but NOT a Leap Day year if divisible by 128th and 896th Years, getting Mean Year=(365+ 31/128)=365.2421875 days;....”
Flt Lt Brij Bhushan VIJ (Retd.),IAF
SATURDAY, 2019 February 02H22:08 (Decimal) 

Sent from my iPhone

On Feb 2, 2019, at 21:45, Brij Bhushan metric VIJ <[hidden email]> wrote:

 Walter, Peter Meyer, listserv sirs:
February has had ‘changing number of days’ during Leap Years - 28,29 or even 30 days. The position of Leap Day/Leap Week, however, fluctuated during February:
>2.  The rule for leap years was changed. In the Julian Calendar a year 
is a leap year if it is divisible by 4. In Jithe Gregorian Calendar a 
year is a leap year if either (i) it is divisible by 4 but not by 100 
or (ii) it is divisible by 400. In other words, a year which is 
divisible by 4 is a leap year unless it is divisible by 100 but not by 
400 (in which case it is not a leap year). Thus the years 1600 and 2000 
are leap years, but 1700, 1800, 1900 and 2100 are not.
<image1.jpeg>

In the format, I promote, the month of February from current 28 days, shall now have 29 days BUT THIS LEAP DAY shall shift to between June 30 & July 01, when Year is divisible by 4 - but NOT a Leap Day year if divisible by 128 getting Mean Year=(365+ 31/128)=365.2421875 days; as such years divisible by 4 including 1600,1700,1800,1900 ,2000,2100 are all having the Leap Day (or planned Leap Week div.6) during ‘Centurian years too’ placed between June end & July 01. This makes sure personnel born on February 29 ENJOY THEIR “birth year - every year on February 29th”. 
Regards,
Flt Lt Brij Bhushan VIJ (Retd.), IAF
Saturday, 2019 February 02H21:74(Decimal)

Sent from my iPhone

On Feb 2, 2019, at 19:30, Walter J Ziobro <[hidden email]> wrote:

2.  The rule for leap years was changed. In the Julian Calendar a year
is a leap year if it is divisible by 4. In the Gregorian Calendar a
year is a leap year if either (i) it is divisible by 4 but not by 100
or (ii) it is divisible by 400. In other words, a year which is
divisible by 4 is a leap year unless it is divisible by 100 but not by
400 (in which case it is not a leap year). Thus the years 1600 and 2000
are leap years, but 1700, 1800, 1900 and 2100 are not.
12