An Unequal-Hour Quadrant*

The first horary quadrants in Europe were known as quadrans vetustissimus (oldest quadrant), giving the unequal-hours commonly used before the widespread use of clocks during the 14th century. This design is documented as early as the 9th century by Islamic scientists in Baghdad and was later described by Sacrobosco in 12th century Europe. Most early sun dials, astrolabes etc. are laid out to give unequal hours, where daylight is broken into 12 equal segments from dawn to dark, with longer hours in summer (longest at the summer solstice) than in winter (shortest at winter solstice). The quadrant found at Chetwode, England is a small (approximately two inch radius) example of a quadrans vetustissimus. As seen in the image of the original piece, the quadrant is badly corroded but enough remains for an accurate reconstruction.

Construction

To approximately match the color and thickness of the original quadrant I chose a piece of 1.25mm thick "red" brass (cut from a scrapped door kick-plate) as my source of metal. I then laid out with a dividers a 2 1/4" radius quarter circle (I generally use a blue permanent marker to color the scribe marks then re-scribe them for visual clarity) before cutting it with power jig saw using a standard wood cutting blade as a faster alternate to a Jewelers saw. The edges of the  resulting quarter circle were then cleaned up with a file, to assure a precise 90° angle between the edges and a smooth circular curve on the outside. A straight line was then scribed about 1/16" in from each of the straight edges. and a center was pricked with a punch at their intersection. The outer arc of the limb was then scribed with a machinist's dividers just inside the edge of the metal. A second arc was then scribed about 1/16" inside to box the degree graduations, and  a third arc boxing in the 15 degree intervals and hour arcs was scribed at about 1.7".  I then used my "dividing engine" to scribe 1° intervals between the outer arcs with extended lines for 5° intervals and lines extended to the innermost arc at 15° intervals (see graduation of ... using a "dividing engine" by clicking here. Alternatively you can use classical Geometrical graduation as described here for a quadrant, or transfer graduations using a protractor. I used 3mm "Bridgette" figure punches to mark the 15° intervals. 

The next step was to inscribe the hour lines. To tell time at hour intervals we will need a total of six arcs. The first, noon or 6hr arc, is has a diameter defined by the vertex and the outer arc along the meridian: bisecting the meridian defines this arc and a punch prick is made, the the noon arc scribed. Subsequent hour line all intersect the vertex, and then the outer arc at 15° intervals The radii of these arcs can be determined in different ways, including simple trial and error or geometrically, which is what I will describe below.

I first created an exact scale drawing of the innermost portion of the quadrant and created the various arcs in pencil in my shop notebook, as seen above. I then transferred the points for punch pricks using a dividers. The first step was to draw the edges and innermost arc, I then used the compass to layout the 60° and 30° points by cutting arcs from the opposite intersections of the arc and edges. Bisecting the 90° arc then gives the 45° point, at which time setting the compass between the 30° and 45° intersections gives a 15° interval that can now be used to layout the 15° and 75° intervals. At this point you are ready to find the radii of the various arcs. I have created a stepwise example by adding red pencil lines to show the chord and perpendicular for the 45° hour line on my shop drawing below:

After completing the hour lines on my brass quadrant I added a shadow square sized arbitrarily for convenience and aesthetics. Each side of the shadow square is divided into 12 equal segments. The bottom scale of the shadow square is referred to as the Umbra recta, (Latin referring to the shadow of an upright or erect gnomen) while the vertical scale is the Umbra versa (Latin referring to the shadow of a horizontal gnomen). The Umbra versa gives the tangent of angles up to 45° (you will get decimal tangent values if the scale is graduated 0-1), while the Umbra recta gives the cotangent. Instructions for dividing the shadow square can be found at the bottom of my pages on simple quadrants. 

Next I stamped the hour figures and shadow square figures using 1mm standard font punches. After drilling a 1/16" hole at the vertex for the plumb bob thread, I cut two notches into the upper edge to accommodate the sites. The notches were carefully filed to a fixed depth to assure proper alignment of the sites. I cut the sites to precise rectangular dimensions, drilled 1/16" holes precisely centered on the sites, then filed the back edges to a 'medieval' decorative shape. Finally I used a small countersink to chamfer the holes to provide clearer spots/optical use of the sights.

Final steps were to silver solder the sites to the quadrant body, then add a thread with a seed pearl bead and a turned brass plumb bob.

The plumb bob was trurned on a lathe from recycled 1/4" brass round stock. I first drilled a 1/16" hole through the rod perpendicular to the rod about 1/4" from the end. I then used a Jacob's lathe chuck to mount it on the lathe and drilled a 1/16" centered hole to intersect with the first hole to accommodate the thread. The bob was then shaped on the lathe with hand files. Careful! If a file slips you can get hurt.

The finish on the quadrant has the oxidation patina left after soldering. I decided to leave the patina for now as it gives an aged look, and I can always clean it up and polish later if I want.

Custom Mahogany Quadrant Case

A few months after completing this quadrant I decided to make a custom case for it and for a similar quadrant I had purchased from Master Terebrus (aka Vsevolod Burachenko) of Kyiv City, Ukraine. Because of the differing sizes and details of the two instruments I had to enlarge the holes in the lid to accommodate the sites. The protrusion of the sites from the backs of the quadrants also led to designing the case to hold the quadrants face down. The case was constructed of 100% recycled materials found in my "stash" i my shop: mahogany recovered from a c. 1940 chemical balance case damaged in a fire, hinges from a doll house my daughter and I never quite finished and water damaged in our move to West Sacramento, and a brass hook from an old lab box of uncertain use. Pictures of the approximately three inch square by 3/4" high case are shown below.

*My reconstruction is based on the article:  Davis, John (2015) "THE CHEWODE QUADRANT, A Medieval Unequal-Hour Instrument", 27(ii). Additional information on the use, making and operation of quadrants was based mostly on Jim Morrison's wonderful book: Morrison, James, E. The Astrolabe. Janus, Rehoboth Beach, DE [2007]. He discusses the shadow square and unequal hours diagram on the backs of planispheric astrolabes on pp 114–119, and unequal hours on horary quadrants pp 217–220. I highly recommend both.