Re: 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.

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:

The moon gear has two pegs that travel around the gear. The pegs at epoch start out together, and one is taller than the other. At epoch, the shorter one sits in the cog with the mark that's used to align with the sun gear. Each time the marks on the moon and sun gears line up, the tall peg is moved one cog. The cogs have only one hole used by both pegs, so when the tall peg catches up to the short peg, they trade places (the short peg is moved to where the tall peg was when the tall peg is moved).

If this last leap-frog operation results in the short peg landing in the marked cog, then the sun gear is advanced one cog.

This operation effectively introduces a leap month every 342 Metonic cycles. This gives a month:year ratio of:

19*342 : 235*342-1

One need not wait several thousand years for this device to be useful. The distance between the small peg and the mark is a measure of how far the year and month are drifting with respect to each other. You can extend that precision by using the long peg. Perhaps short and long hands, clock style, should be used instead, since we're familiar with that.

Victor