198-part year calendar FW: Calndr-L

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198-part year calendar FW: Calndr-L

Karl Palmen
Dear Calendar People

Here is something Helios attempted to send to the list via Nabble.

Karl

16(06(25

-----Original Message-----
From: rolf wohl [mailto:[hidden email]]
Sent: 16 February 2017 20:44
To: Palmen, Karl (STFC,RAL,ISIS)
Subject: Calndr-L

Dear Karl Palmen,

Here is your formula,

Eclipse Seasons = 200*Years - 16*Months
E = 200*Y - 16*M
or
1/e = 200/y - 16/m

as we use upper case for extensive and lower case for intensive.

Now should we create a 198-part calendar year where the parts are reckoned to equal 16ths of a lunar month, then one of these parts drops off in this many years;

correction ( in years ) = 1/[ 198 - 16*( y/m ) ]

Now we directly equate this to a nodetide
nodetide = 1/[ ( y/e ) - 2 ]

that is, a part drops off every nodetide. The result agrees with the original formula.
The year evaluated is 365.242715 days.

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Re: 198-part year calendar FW: Calndr-L

Karl Palmen
Dear Helios and Calendar People

Helios has suggested a calendar in which each year has 198 parts and each lunar month has 16 parts and once every nodetide the calendar is corrected by removing one part from the year to form a short 197-part year. Such a calendar would give the number E of eclipse seasons in Y years of M months as

E = 200*Y - 16*M.

I show this next.

Noting that the number N of nodetides in Y years of E eclipse seasons is given by

N = E - 2*Y

And so

E = N + 2*Y

Substituting this into my formula (shown 1st) gives

N = 198*Y - 16*M

In a cycle of Y years and M months, we'd have 16*M = 198*Y - K parts, where K is number of the corrections. We then get

K = 198*Y - 16*M = N

Therefore correcting once every nodetide, does implement my formula for eclipse seasons.

I don't know how Helios derived his year of 365.242715 days. Perhaps, it is the mean year for which my formula is most accurate. A year whose mean year is considerably less would require an additional correction once every few thousand years. For example, a mean year of 365.242215 days would require an additional correction about once every 2000 years. The 4160-year cycle would require 448 corrections one of which must be an additional correction to give it 447 nodetides.

K = 198*Y - 16*M = N + A, where A is the number of additional corrections.

These cycles with number of nodetides in () require no additional corrections:
19(2),
372(40), 391(42),
763(82), 782(84),
1135(122), 1154(124), 1173(126),
1526(164), 1545(166), 1564(168),
1917(206).

These cycles each require exactly one additional correction:
2987(321), 3006(323), 3025(325),
3378(363), 3397(365), 3416(367),
3750(403), 3769(405),
4141(445), 4160(447), 4179(449),
4532(487), 4551(489), 4570(491),
4923(529), 4942(531),
5295(569), 5314(571), 5333(573),
5686(611), 5705(613), 5724(615),
6077(653), 6096(655).


Karl

16(06(25



-----Original Message-----
From: Palmen, Karl (STFC,RAL,ISIS)
Sent: 21 February 2017 11:23
To: [hidden email]
Subject: 198-part year calendar FW: Calndr-L

Dear Calendar People

Here is something Helios attempted to send to the list via Nabble.

Karl

16(06(25

-----Original Message-----
From: rolf wohl [mailto:[hidden email]]
Sent: 16 February 2017 20:44
To: Palmen, Karl (STFC,RAL,ISIS)
Subject: Calndr-L

Dear Karl Palmen,

Here is your formula,

Eclipse Seasons = 200*Years - 16*Months
E = 200*Y - 16*M
or
1/e = 200/y - 16/m

as we use upper case for extensive and lower case for intensive.

Now should we create a 198-part calendar year where the parts are reckoned to equal 16ths of a lunar month, then one of these parts drops off in this many years;

correction ( in years ) = 1/[ 198 - 16*( y/m ) ]

Now we directly equate this to a nodetide
nodetide = 1/[ ( y/e ) - 2 ]

that is, a part drops off every nodetide. The result agrees with the original formula.
The year evaluated is 365.242715 days.