Figure 18 shows a group of people in the process of laying the meridiana at San Petronio. The circles imposed on the diagram make up the analemma used for a geometrical location of the zodiacal plaques along the meridiana. The geometry involved is mentioned in Appendix B of Heilbronís book and this section aims to provide an elaboration.
The vertical circles in Figure 18 have been redrawn in Figure 19 below.
indicates the centre of the gnomon, or an instrument that serves to indicate the
time of day by casting its shadow upon a marked surface. In the case of San
Petronio, the marked surface would refer to the meridiana. The larger circle
centred on S cuts the smaller circle centred on T at points A and B such that
the chord AB of the bigger circle is identical to the diameter of the smaller
circle. Let F be any point on the small circle and CTS be the noon ray at an
equinox. In addition,
and r, R are the
radii of the smaller and bigger circles respectively.
If DF is parallel to AB, in triangle EFT,
Since EF = QR and in triangle RSQ,
refer to Figure 20.
above figure gives the earlier-mentioned angles λ and
on the celestial sphere. S* marks the true Sun while S the projection of the
true Sun on the equinoctial. δ
is the Sunís declination and ε the obliquity of the ecliptic. Let the radius of the celestial sphere be K.
triangles OSS*, VE.SS* and O.VE.S* are approximately right-angled triangles, we
Comparing (1) and (2), Taking λ small, we have
Kλ gives the ecliptic longitude and since K is constant, it is sufficient to mark the point where the noon ray falls on the meridiana at an equinox, and then by increasing λ in steps of 30˚, the rest of the zodiacal plaques could be positioned accordingly.