The Cross-Quarter Days
The Quarter Days of the year (the Solstices & Equinoxes) can be defined with extreme accuracy - to the nearest nano-second if necessary. The Cross-Quarter Days are somewhat more movable.
The Druidic Cross to the left indicates the Quarter Days with the four arms of the Cross. The Cross-Quarter Days were symbolized by the four much smaller dots in the crotches of the Cross. This would make it seem that they are evenly spaced around the eight-point year. They are in time - but not in space.
Calculating the Cross-Quarter Days
Go to the point on your Orthographic Projection of 51° and locate the declinations of the Summer and Winter Solstice Sun at noon (shown in gray in the illustration).
In half the number of days between the Spring Equinox and the Summer Solstice, at Beltane, around May 1st, the Sun has moved approximately 71% of the distance between these two points on the horizon. 71% of the 23.5° declination of the Summer Solstice Sun would put the Beltane (and Lughnasad) Sun at a declination of +16.6°, and the Samhain and Imbolc Suns at a declination of -16.6°
With your circular protractor, measure 16.6° above and below the declination of the Equinox Sun. Connect the two points, and mark the intersection with the Equinox Sun's path (E2). Put the point of your compass on E2. Your pencil should hit both the +16.6° and the -16.6°.
The paths of the Sun on the
Cross-Quarter Days
(B/L = Beltane / Lughnasad;
I/s = Imbolc / Samhain).
Extend a line from BL1 through BL2 to the point where it breaks the level horizon N-C-S at B/L3. Extend a line from I/s1 through I/s2 to the point where it breaks the level horizon N-C-S at I/s3.
Connect B/L3 and B/L' with a straight (transfer line). Do the same with I/s3 and I/s3.
Now, just as we did with the Solstice Sun, let's move into the next dimension:- what does this look like from above? Put the point of your pair of compasses on C, and make short arcs through B/L3 and I/s3.
Without moving the arms of your compass, put the point on C', and make arcs that break the lower N-C'-S line at B/L' and at I/s'.
Draw lines B/L-I/s and I/s-B/L. They should intersect at C'.
When viewed from C' this will give you the Cross-quarter day Sunrises and Sunsets at a latitude of 51o.
These are the azimuths of the four Cross-quarter day Sunrises and Sunsets at a latitude of 51°, given a level horizon. You would measure these angles (taken in a clockwise direction from North) using as large a circular protractor as possible.
Up until now, we have been assuming that there is a level horizon. This fixes the Sun in two dimensions. In reallity, the horizon is usually elevated, which adds a third dimension.