Re: Why not 13 months? (Was La Systeme Metrique)
Michael L. Siemon (mls@panix.com)
Wed, 12 Jul 1995 18:31:10 -0400
In article <5piggkyjcsB@khms.westfalen.de>, kai@khms.westfalen.de (Kai
Henningsen) wrote:
+> mean synodic month of 29.05309...
+Umm ... 365.24189.../29.05309...=12.57152...12.57153. Obviously, one of
+these numbers must be wrong.
oops; someone else has also noticed my typo. that should be 29.53059
+Assuming your .36826 figure is correct ...
This, however, is the correct excess over 12 months.
+Lower bound:
+ 7/ 19= 0.3684210526 (Fehler= -0.0004373340)
+ 67/ 182= 0.3681318681 (Fehler= 0.0003479386)
+ 74/ 201= 0.3681592040 (Fehler= 0.0002737088)
+ 81/ 220= 0.3681818182 (Fehler= 0.0002123006)
+ 88/ 239= 0.3682008368 (Fehler= 0.0001606560)
+ 95/ 258= 0.3682170543 (Fehler= 0.0001166180)
+ 102/ 277= 0.3682310469 (Fehler= 0.0000786213)
+ 109/ 296= 0.3682432432 (Fehler= 0.0000455025)
+So, to get any better, you need nearly a factor of ten; to get
+significantly better, even more.
Thanks! I had done a bit of playing around, but not systematically --
and some of these are pretty good (if impractical :-)) I cut of your
list arbitrarily for number of years less than 304, as that was the
lenght of Hipparkhos' "great year" cycles formed by using 4 Kalippos'
cycles of 78 years plus one day, (the Kalippos cycle being 4 Metonic
cycles of 19 years, less one day.) These last are of interest, but not
strictly generated by ratios of month to year, but rather by making
"corrections" in the smaller order cycles when they accumulated to
a day off.
--
Michael L. Siemon (mls@panix.com)
"Stand, stand at the window, as the tears scald and start;
you shall love your crooked neighbor, with your crooked heart."
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