- #1

Helios

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Today there are "neo-pagans" who have their models of an eight-part year, but they merely attach their cross-quarter days to the Julian or Gregorian calendar. This is naive because there was no Julian calendar in use there around the very time when this wisdom supposedly originated. The question remains as to how an eight-part year could have been perceived long ago. Unless the reconstruction of an eight-part year method of time reckoning, independent of the counting of days, can be demonstrated, the past existence of an extinct eight-part year remains puzzling.

Let's look at the mathematics of this. Let's suppose an eight-part year is defined by the Sun's ecliptic longitude = 0°, 45°, 90°, 135°, 180°, 225°, 270°, 315°. We'll also find the special latitude L* where the summer Sun rises at north-east and sets at north-west. Here are the relevant equations;

sin ( DECLINATION ) = cos ( LATITIDE ) sin ( AMPLITUDE )

sin ( DECLINATION ) = sin ( ECLIPTIC LONGITUDE ) sin ( OBLIQUITY )

[ SQR 2 ] sin ( OBLIQUITY ) = cos ( L* )

[ SQR 2 ] sin( AMPLITUDE ) = sin( ECLIPTIC LONGITUDE ) at L*

The special latitude L* is approximately 55.7682°. Here, the year can be tracked by the azimuth of sunrise from the east at 0°, 30°, 45°, 30°, 0°, -30°, -45°, -30°, or likewise for sunsets from the west. Because all these angles can be easily drawn by any geometer, unlearned in the ways of trigonometry, I think the peoples long ago, indigenous to this vicinity of this special latitude would have discovered this for themselves and it is here that the eight-part year could have originated and be used as seasonal measure.

I know there are little issues like refraction, the apparent size of the sun's disc, or the slightly unequal duration of the eight parts due to the Earth's eccentric orbit.