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Re: Accurate Lunisolar Calendar

by Brillig :: Rate this Message:

Dear Karl, Irv, Sepp, and Calendar People,

On Wed, May 20, 2009 at 10:27 AM, Palmen, KEV (Karl) <karl.palmen@...> wrote:

Dear Victor, Irv and Calendar People

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Victor Engel
Sent: 19 May 2009 23:07
To: CALNDR-L@...
Subject: Accurate Lunisolar Calendar

Dear Calendar People,

The following would be a device useful for an observational lunisolar calendar.

The device consists of two gears that intermesh with each other or with a common gear.
The moon gear has 19 teeth.
The sun gear has 235 teeth.
One tooth on the moon gear is specially marked.
One tooth on the sun gear is specially marked.
Both gears are moved together each time there is a new moon. If this results in the specially marked teeth of both gears lining up, then a new year is started. So far, the Metonic cycle has been duplicated.

I’ve had difficulty understanding this. If moved together means moved together by one tooth, then it’d would take 235*19=4465 new moons, which is about 361 years to the two marked teeth to come together. I am aware that if the moon gear wheel were turned one revolution per lunation, the sun gear would turn about once per year and its marked tooth reaching the moon gear wheel would mark the new year.

I now think what Victor meant by moved together was that the moon gear wheel was turned one complete revolution each new moon.

By together, I simply meant that the 19 cog gear and the 235 cog gear were either interlocked to each other or interlocked to a common gear. My original idea was for them to be interlocked to each other, but if that were the case, one gears yin, would be the other's yang, and vice versa, making the peg holes out of phase with respect to each other. So I left it purposely undefined how they would be lined up. One possibility would be for both bears to be cotangent to a common gear that is twice as wide. Another idea would be for the peg holes to be at the cogs on one gear and between the cogs on the other. Then the two gears would simply need to abut each other. The main point, though, is that both gears move at the same speed as measured in cogs per unit time.

Karl is also right that one revolution of the 19 cog gear would correspond to one lunation. One revolution of the 235 cog gear, similarly, would correspond to one year.

An alternative (to one complete revolution on the new moon) is to move it one tooth every 2^nd, 3^rd, 5^th, 6^th, 8^th, 9^th, 11^th, 12^th, 14^th day after a new moon and likewise for the following 14 days, then one more tooth on the new moon to complete one revolution of the moon gear wheel.

I was trying to stay away from days, which would eliminate this idea.

Another alternative is to move the wheels one tooth according the same 14-day cycle till 26 cycles have passed then for a common year move one tooth the next (and 365^th) day to complete a year and in a leap year move one tooth the next but one (and 366^th) day to complete a year. The moon gear wheel would turn close to once per lunation.

Same comment here.

However the lining up of the marked teeth on both the moon and sun gear wheels would occur just once every 19 years.

The Metonic cycle is a good approximation, but the year length is too long for the month length. So the following amends the above procedures:

It can be corrected by making the sun gear wheel slip one tooth against the moon gear wheel , so the sun wheel turns one tooth, the moon gear wheel does not turn.

Instead of slipping gears, I used pegged cogs. The marks can be moved with respect to the gear without altering the interlocking of the gears. Slipping the gears accomplishes the same thing.

I think a much better idea is the move the pegs annually and after each peg cycle make the sun wheel slip a tooth against the moon wheel.

Why is that better?

Victor

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