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In the novel Dust of Judea, the land surveyor Quintilius is commissioned to carry out the topographic survey of two fortresses located near the Dead Sea, in Judea.

It has been historically demonstrated that several surveys of this kind used to be made; still surviving are topographic maps of cities, of centuriations of conquered lands and of areas distributed to veterans – all purposes for which it was very important to have a faithful map.

The Forma Urbis Severiana, a large plan of the city engraved on marble plates, was famous in Rome. It occupied a wall of the Temple of Peace, a wall still fortunately preserved although without the marble plates (but you can still see the holes that used to support the plates). The dimensions of the plan, 18 X 13 meters, and the complexity of the topographical survey indicate that it was built and updated with the best tools available at the time. Surely, such a result was possible with the use of the dioptra, which was capable of making angular measurements. Occasionally, fragments of the original plan of the Forma Urbis are found, and at Stanford University, they are putting the pieces back together by integrating a few fragments. But how did the dioptra work?

This was the question I asked myself when writing the novel Dust of Judea, but to find out the answer, I had to build one.

Reconstruction of the appearance that the Forma Urbis, and the room that contained it, must have had.

What remains of the wall on which the marble tables were fixed with the planimetry engraved on them.

Reconstruction of the dioptra

I started by making a drawing of the construction parts. Since none of these tools have ever been found, I was forced to make a 3D drawing to better understand the purpose of the several parts. Basically, the tool consisted of a sighting tube connected to a horizontal and a vertical protractor.

The final drawing of the instrument is this, and in the right part of the image is the head with the protractors.

The stand was made with wooden strips joined together to form solid legs. A three-point ‘star’ was positioned in the middle of the stand to give solidity to the structure. On this star, there is also the reference of the plumb line. The head that unites the whole structure also includes the two protractors.

If you observe the components, you can better understand the function of the parts: the horizontal plate (free to rotate but with the possibility of being blocked by the lower wing nut) contains the 360° protractor. At its center, the support of the sighting tube passes through (to whose rod the pointer is fixed to detect azimuth angles), again locked with a wing nut. In blue is the vertical protractor, integral with the sighting tube.
The head of the stand, on which the protractors and the sighting tube are inserted, allows them to rotate through a vertical through-hole.

Finally, here are the protractors, with relative support and pointers. These are the photos:

  • 1) Finished parts.
  • 2) Support and pointers (obtained from brass plates).
  • 3) Base of the horizontal protractor plate with locking wing nut.
  • 4) Vertical protractor and sighting tube.

The sight, or sighting tube, is one of the more complex parts. Although modern tools were used to build the parts, it should be noted that these could be made with other techniques (e.g., bronze casting), even in Roman times. By examining the sight of a current topography compass (Photo 1), we can see how it is possible to have fairly precise sights without the use of optical lenses. A thin slit acts as an ocular diaphragm and narrows the view, and the collimator is made up of a thin horsehair. To facilitate the processing of the pieces, I first made the drawing in cad, then printed it on an adhesive plastic support (Photo 3) to have a precise guide in subsequent processing. Photo 4 shows the processing of the collimator, in whose flange one of the metal lamellae of the crosshairs is already inserted. The slit diaphragm, designed and cut out of an aluminum sheet, was painted in matte black (Photo 6).

Why do the diaphragm and the collimator, unlike the compass in Photo 1, have 2 slots and 2 wires crossed at 90°? Because the type of dioptra built can also measure angles on the vertical plane as well as on the horizontal one.

The finished tool:

Dietro le Quinte

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