Article of the month December

An old construction
for vertical sundials

In Dairago, near Milan, Italy, a bell tower was restored in 2005.
Remnants of an east declining vertical sundial were found under old plasterwork.
Construction lines were still visible.
Surprisingly, the applied construction was unknown until now.
Father Alberto succeeded in recovering the construction method, and Alessandro Gunella wrote an article¹⁾ about it in Compendium.

The two figures below show the difference between a more commonly known construction and the one now discovered.
The principle is that the auxiliary figure with the equatorial sundial is moved horizontally from the substyle to the noon line, and that the equinox line is rotated.
The rotation angle equals the hour angle of the substyle, that is, the hour angle of the moment when the pole style shadow falls on the substyle.
Gunella’s article proves that this surprising construction actually works correctly.