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Bill Thayer

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The Meridian in the Cathedral of Fossombrone
43°41′17.1″N 12°48′19.9″E

[image ALT: The side aisle of a medium-sized church, cluttered with wooden pews on the right, and a confessional on the left. In the background, a small arched chapel, the vault of which is dark except for a pinpoint of light. The floor of the aisle is of hexagonal ceramic tiles, except for a long straight line heading, at a slight angle, towards the chapel. It is a view of the meridian line in the cathedral of Fossombrone in the Marche (central Italy).]

The eighteenth century was much given to ingenious contrivances, and longitude had been constantly on its mind: what more natural than an efflorescence of meridian lines thruout Europe?

Since churches were a town's most prominent, central, and accessible public buildings, sundials are found on their outer walls, and sometimes, when there was money in the community and a large dark church, we also find the specialized sun indicators known as meridian lines. If you are going to put a pinhole in a southern wall and register the sun's passage on a line on the floor, you need a rather large space to make the meridian accurate, a dark one to make it readable, and money to do the job carefully; the principle is very simple, but the execution has to be quite precise to allow generations of townspeople to come in and set their watches by the device.

In the 18c, Fossombrone was rich from its silk weaving industry, and its cathedral was large and dark; a local mathematician named Sempronio Pace did the job in 1780.

In this photograph, you can just make out the pinhole, in the upper part of the vault of the S apsidal chapel.

[image ALT: A square stone plaque with a long inscription, the text of which is given and commented on this webpage. To the left, a small circular medallion bears the inscription 'Solstizio d'inverno 21. Decemb.' and is surmounted by the intarsio figure of a capricorn. It is an 18c inscription explaining the operation of the meridian line in the cathedral of Fossombrone in the Marche (central Italy).]

Indica mihi ubi pascas ubi cubes in meridie · Cant. I V.6a

Meridian line
from one tropic to the other

When the Sun's ray falls on it,​b it indicates that the Sun is halfway thru its course. Its height and the hour that corresponds to it are shown by the numbers touched by the same ray. The upper numbers in increments of 1 indicate the degrees of the sun's distance from the zenith. The numbers on the metal strip mark hundredths of the perpendicular.​c The Roman numerals incrementing by 5 indicate the time of noon, in hours and minutes of Italian time. Rising signs of the zodiac are white, setting signs are yellow.

[image ALT: A small square stone intarsio plaque with the figure of a sagittarius, and an inscription reading 'Il di Nove.' It is a detail of the meridian line in the cathedral of Fossombrone in the Marche (central Italy).]

Il di nove[mbre]
The one of November: Sagittarius, setting sign.


a Song of Songs 1.6 reads in full:

Indica mihi, tu, quem diligit anima mea, ubi pascas ubi cubes in meridie, ne vagari incipiam post greges sodalium tuorum.

"Tell me, you in whom my soul delights, where you graze your flocks, where you rest them at midday, lest I start to wander behind the herds of your companions." (The New English Bible, going to the Hebrew text and finding it obscure, offers us: ". . . that I may not be left picking lice as I sit among your companions' herds.")

b Since I was in the cathedral of Fossombrone at the wrong time — i.e., it wasn't noon — these photos are not as useful as they could be to a layperson who wants to get an idea of how the meridian works. (For that, you should see this page on the August 11, 1999 solar eclipse as seen on meridian lines in Italian churches: bearing in mind that normally you'd see the entire disc of the Sun.)

c A phrase that must surely be to many readers as obscure as it proved to me. I owe the following explanation (written up though in my own inimitable prose) and diagram to the kindness of sundial expert Mario Gioia:

The numbers engraved on the inner metal rule measure the distance from the foot of a vertical drawn from the pinhole to the floor, in hundredths of the perpendicular height of the pinhole above the floor. That hundredth is called the "modulus" (and the diameter of the hole is usually ⅒ of the modulus).

If then A is the angle the sun makes with the vertical at noon on a given day — identical with the angle A′ formed by the same lines projected inside the church — and we wish to measure the distance L from the vertical of the hole to where the sunbeam strikes the floor, simple trig of the kind we all learned in school gives us the answer:

L = H × tan (A′)


H = 100 moduli.

The distance L is thus equal to 100 tan (A) moduli.

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For many years the reader of this page would have seen here a note I had written — quite reasonably, but altogether wrong — of measuring angles not in degrees (ninetieths of the perpendicular) but in what became a unit of the metric system, one of the rare ones to have failed: the grade (symbol: gon).

The only thing that I can say by way of apology for having misled half a generation of Web-surfers, is that that earlier note of mine is . . . gon.

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Page updated: 29 Nov 21