Humboldt State University ® Department of Chemistry

Richard A. Paselk

The Graduation of a Bronze Quadrant by Dividers

Tools: The minimum essential toolkit includes an adjustable locking dividers (wing, as shown, or screw-type, as in the small dividers below), a straightedge, and a scriber.

Additional recommended tools include a felt pen (or machinist's ink), a high quality divided scale, a fine punch & hammer (or automatic punch, both are shown), a calculating device (not shown), a magnifier, a beam compass, and small dividers (a C-clamp is also useful, though not shown).

To make the scribe marks easier to see, the blank quadrant is first covered with machinists marking ink, or, as shown, marked with a felt pen covering the areas which will be scribed. (This step may be skipped, but is certainly helpful, especially for the beginner.) Using a felt pen makes it easy to cover-up trial and error marks made later on.
  First the dividers is used to layout the radius. The dividers should be locked at this radius for use later in scribing off a 60° arc.
  Next a line parallel to the edge of the quadrant is scribed. Its intersection with the radius establishes the zero mark. I use a punch to prick a mark for zero as a more reliable point for scribing off additional marks with the dividers.
  A 60° arc is now laid off using the dividers set at the arc radius. I again make a punch mark at this major division.
  The dividers are now used to bisect the 60° arc to give a 30° arc. The bisected angle is marked and punched to establish the 30° mark. The dividers are then set to the bisected 30° arc, then placed at the 60° mark and used to scribe the 90° arc.

The 90° point is now punched and a 90° line is scibed between the center point of the "circle" and the 90° point. This establishes the other edge of the quadrant.
  The 30° arcs are now bisected to give 15° arcs. This is the last bisection, and the last geometrical division possible to give whole degree graduations.
Next the 15° arcs must be trisected, which is done by trial and error since there is no geometrical procedure. However, the trial and error process can be speeded up by measuring the 15° chord with a graduated scale, dividing by three and then setting the dividers for the new 5° value.

Final adjustment is then by trial and error during the trisection to give 5°.
Graduation to single degrees is next accomplished again by trial and error (a graduated rule and calculator is again handy here, as is a smaller dividers).
Once the dividers are set to a 1° interval the arc can be laid out.
  As an alternate procedure one can create a small section of arc on a thin sheet of metal with marks at 1° intervals. This template can then be aligned with the 5° marks and the 1° marks made with a scribe.
Permanent graduations are now cut using a scribe or knife and straightedge based on the layout marks created above.
Permanent arcs are then cut with a beam compass (or with many light passes of the dividers). The beam compass is preferred due to its greater rigidity.

Instruments Medieval Science & Scientific Instruments


© R. Paselk 2002
Last modified 24 August 2007