Trough three points you can always draw a specific circle.
If you do that trough
- the place where you stand on the date scale
- the two foci of the ellipse
then this circle is intersecting the ellipse in the hours of sunrise and sunset.
This circle was named 'Lambert Circle', named for the German scientist Johann Heinrich Lambert (1724 - 1777) who first described this proposition.
The Lambert Circle, a circle trough the position and the two foci, intersects the ellipse in the hour points of sunrise and sunse.
Translation of the words in dutch language at the picture:
zon op: sunrise
zon onder: sunset
Lambertcirkel: Lambert Circle
1 november: november 1
Drawing the 'Lambert Circle' for a certain date, sunrise and sunset for this date can be determined.
Place the wall - at least a line parallel to the wall - trough the date point on the sundial.
Where this line intersects the sundial ellipse you cen read the starting time and the ending time of the insolation period of the wall.
If the starting time is before sunrise, take as starting time the time of sunrise and if the ending time of the insolation time is after sunset, take the time of sunset as the ending time.
Translation of the words in dutch language at the picture:
The text along the ellipse: insolation period of the wall on august 1
muurlijn: line parallel to the wall
zon op: sunrise
zon onder: sunset
Lambertcirkel: Lambert Circle
1 augustus: august 1
The intersecting points of the 'muurlijn' (line parallel to the wall) with the sundial ellipse indicate the starting time and the ending time of the insolation period of the walll, provided, however, to observe the sunrise and sunset time.
For the situation on the figure on august 1, the sun will shine on the wall from 9.30 a.m. to 7.35 p.m. (and not to 8.00 p.m. where the ellipse is intersected because sunset had already taken place on 7.35 p.m.)
In 2013 the stone was examined at the University of Rostov-on-Don (Russia) by Larisa Vodolazhskaya. She remarked that the pattern of an analemmatic sundial, calculated for the local latitude (48 ° 26 ' N), fits more or less the pattern of the bowl-shaped depressions.
When it appeared that even such plates from the same period, discovered in 1991, in burial mounds from the region of Rostov, showed similar patterns, she formulated the scientific hypothesis that it were analemmatic sundials.
The bowl-shaped depressions on the picture are marked in green and the pattern of a analemmatic sundial in yellow is superimposed on the stone. The stone can be contained in a rectangle of 100 cm x 75 cm.
Read more (download PDF)
here
and
here
From a burial mound in the region of Donetsk (Ukraine) - Bronze Age (XIII - XII century BCE)
Background photo: Larisa Vodolazhskaya - University of Rostov-on-Don (Russia)