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 SouthSolstice, based on the > assumption that a SouthSolstice occurs exactly every 365.2422 > days...starting from the actual SouthSolstice 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 "SouthernSolstice"? 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 
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 4digit 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 
In reply to this post by Peter Meyer
[quote] Michael Ossipoff said (typo
corrected): [/quote] . That’s why I spoke of an _approximation_ based on that assumption. . Approximations are often based on false assumptions. …simplifyingassumptions. . [quote] [/quote] . Starting the calendar year near the SouthSolstice doesn’t require using the SouthSolstice tropicalyear as the referencetropicalyear for the arithmetical yearstart rule. . I chose the _mean_ tropical year as the reference tropicalyear, because it’s most practical, or at least impartial, to reduce drift all around the year, rather than at some particular favored solar eclipticlongitude. . 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

In reply to this post by Peter Meyer
Dear Peter and Calendar People
Here Michael is defining a rulebased 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 "SouthSolstices" 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 SouthSolstice, based on the > assumption that a SouthSolstice occurs exactly every 365.2422 > days...starting from the actual SouthSolstice 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 "SouthernSolstice"? 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 
Karl That's true, it's important for the calendar's definition to state an assumed exact time for the 2017 SouthSolstice. 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 falseassumption is too questionable a thing: It should be emphasized that, for solar calendars, all arithmetical yearstart rules (including leapyearrules) involve an approximation of a tropicalyear length, based on a simplifying assumption, a false assumption. For example, as we all know, the Gregorian leapyearrule uses an approximation based on a false (assumption about the length of the NorthwardEquinox tropicalyear. 6 F Michael Ossipoff On Fri, Feb 1, 2019 at 6:25 AM K PALMEN <[hidden email]> wrote: Dear Peter and Calendar People 
...but of course, because the SouthSolstice year isn't the MTY, then it the calendar's yearly drift at yearstart would depend on the difference between MTY and SouthSolstice 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 
But it would still take roughly 3000 years for a day's drift at the SouthSolstice. ...which isn't so bad for a leapweek calendar, for which the (actuallyachieved) bestpossible jitteramplitude is 3.5 days. 6 F Michael Ossipoff On Fri, Feb 1, 2019 at 2:15 PM Michael Ossipoff <[hidden email]> wrote:

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 leapyearrule uses an approximation based on a false (assumption about the length of the NorthwardEquinox tropicalyear." 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 NorthwardEquinox tropicalyear"? 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 NorthwardEquinox tropicalyear", since this is not standard terminology. If he cannot do this, would he kindly enlighten us as to why not? Regards, Peter 
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 
Karl Yes,
given the precision of 365.2422, then .6860 is plenty accurate enough
for the dayfraction at which the 2017 SouthSolstice occurred. That's
what I'd use when stating a formula for the calculation of approximate
SouthSolstice times. 6 Sa Michael Ossipoff 
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: 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 leapyearrule uses an approximation based on a false (assumption about the length of the NorthwardEquinox tropicalyear." 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 NorthwardEquinox tropicalyear"? 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 NorthwardEquinox tropicalyear", since this is not standard terminology. If he cannot do this, would he kindly enlighten us as to why not? Regards, Peter

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 > NorthwardEquinox tropicalyear", 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 NorthwardEquinox tropicalyear" 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 
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.
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

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="xappledatadetectors://2" dir="ltr" xappledatadetectors="true" xappledatadetectorstype="calendarevent" xappledatadetectorsresult="2" style="webkittextdecorationcolor: 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
image1.jpeg (178K) Download Attachment 
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 
In reply to this post by Peter Meyer
Dear Peter and Calendar People
The "the NorthwardEquinox tropicalyear" 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 "SouthSolstices" 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 > NorthwardEquinox tropicalyear", 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 NorthwardEquinox tropicalyear" 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 
Karl said:
> The "NorthwardEquinox tropicalyear" 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 "NorthwardEquinox tropicalyear" 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 "SouthSolstice" 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 SouthSolstice occurs exactly every 356.2422 days". Well, I'm glad we cleared that up. Regards, Peter 
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.
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

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

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 400year Rule, my 128year cycle ENDS ‘one cycle of 896years/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

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