19 Tooth Lunar-driven Cycle

[Brillig]

Dear Karl and Calendar People,

Here is the basic cycle my device attempts to use:

The basic unit of the system is the lunation, periodically calibrated
by observation of eclipses.
A subunit of a lunation is what I call a tooth, because my device uses
a gear for this purpose. The lunation is divided into 19 teeth.

The shortest useful lunisolar cycle consists of 18 Metonic cycles with
an adjustment. In this period of time there are:

80370 teeth
4230 lunations
342 1/235 years

The number of years is a fraction because the solar device is adjusted
by one tooth in this frequency. The cycle completes an integer number
of years in:
18886950 teeth
994050 lunations
80371 years

Note that due to the observational nature of the device, it is immune
from changes id delta-T and should be quite stable as long as the
moon's orbital period remains stable.

I need to revise my illustration that I posted previously. I will do
so when I have time.

Victor

[Karl Palmen]

Dear Calendar People

Actually, the number of years is not exactly 342 1/235 years, but 342
years + 1/19 lunation, which is slightly different. A more useful cycle
would be obtained by subtracting one tooth to get

80369 teeth
4229 18/19 lunations
342 years

when multiplied by 19 you get

1527011 teeth
80369 lunations
6489 years

If you let the gear mechanism truncate one of the 18 Metonic cycles to
11 years, your get a 334-year cycle thus:

78489 teeth
4131 lunations
334 years

These teeth are lunar teeth, it might also be useful in our discussion
to refer to solar teeth of exactly 1/235 year. Victor needs to
differentiate between the two in his thinking.

Karl

10(09(19

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Victor Engel
Sent: 10 June 2009 23:10
To: CALNDR-L@...
Subject: 19 Tooth Lunar-driven Cycle

Dear Karl and Calendar People,

Here is the basic cycle my device attempts to use:

The basic unit of the system is the lunation, periodically calibrated
by observation of eclipses.
A subunit of a lunation is what I call a tooth, because my device uses
a gear for this purpose. The lunation is divided into 19 teeth.

The shortest useful lunisolar cycle consists of 18 Metonic cycles with
an adjustment. In this period of time there are:

80370 teeth
4230 lunations
342 1/235 years

The number of years is a fraction because the solar device is adjusted
by one tooth in this frequency. The cycle completes an integer number
of years in:
18886950 teeth
994050 lunations
80371 years

Note that due to the observational nature of the device, it is immune
from changes id delta-T and should be quite stable as long as the
moon's orbital period remains stable.

I need to revise my illustration that I posted previously. I will do
so when I have time.

Victor

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