Sundial of the month June

Homogeneous analemmatic sundial

The ellipse of an alemmatic sundial may be considered as constructed from two circles. See Figure 1.

Figuur 1

The hour points on the circles are evenly spaced. They are moved to the ellipse by a translation over A and parallel to the minor axis of the ellipse (the north-south line).
Here, A = C * cos (t) where t is the hour angle, and C² = A² + B².

It is easy to construct the cosine of an angle mechanically. See Figure 2.

Figuur 2

A rod K rotates around a centre p.
A distance C away is a small plug q that moves through slit S.
Rotating the bar will also cause centre p to move through another slit S.
The result is that the grey disk moves with respect to the circle with the homogeneous hour scale.

The grey disk contains the usual date scale that we know from the analemmatic sundial. See Figure 3.
Note that the distance between centre p and the intersection of the slots S is equal to C * cos (t), and therefore equals A.

Figuur 3

If we place a vertical gnomon in position M on bar K, and if we make its shadow fall over the actual date on the disk, then the gnomon indicates the time on the homogeneous hour scale.

Figures 4 to 7 show an implementation of this sundial in brass.
In this example, the sundial is read at the arrow, which is 180 degrees away from the gnomon, but that leaves the principle unchanged.

Figuur 4: top

Figuur 5: bottom

Figuur 6: side

Figuur 7: The sundial in the sun. It is 3 PM around mid-June.

Because the sundial is homogeneous, its reading may be adjusted for longitude. To this end, the bottom shows all time zones (including some “summer time zones”) and a longitude scale.
When the geographical longitude of the location of the sundial is turned opposite the correct time zone, the sundial indicates legal time.
The sundial does not correct for equation of time.

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