Zutphen Quadrant

Image from: Davis, John (2014) "THE ZUTPHEN QUADRANT, A Very Early Equal-Hour Instrument Excavated in The Netherlands", 26(i), 36-42.

A Very Early Equal-Hour Quadrant*

The Zutphen quadant is the only equal hour quadrant discovered so far from the early 14th century. It has been dated archeologically to 1300–1320, nearly a century before the next earliest known equal hour quadrants, a set of four made for King Richard II and datable to 1396–1400. The quadrant is of similar size to the Chetwode unequal hour instrument, and is based on the same design, with the same limb graduated arc and noon semicircular arc. However, on the equal hour instrument the other hour lines don't pass through the origin of the quadrant, and it is now designed for a single latitude. Two other differences will be obvious: the maker didn't bother graduating the limb past the highest solar altitude for Zutphen (63°) or labeling the limb arc, and added seven declination arcs for adjusting the bead position by season. These arcs are labeled by month (I=J for the medieval period) and indicate where the sun will enter each of the zodiac signs during the year. 

Image of recreation of Zutphen quadrant with riveted on sites, swivel for plumb-line, plumb line with seed-pearl bead and custom turned brass plumb bob.

Recreated Zutphen Equal Hour Quadrant

Construction

I first laid out and then cut a two and a half inch radius quarter circle from 16G (measured: 1.30mm = 0.053") recycled yellow brass. After filing the edgres smooth I scribed a line parallel to and about 0.1" in from the meridian edge (where the sites will be installed) and a scond ine perpendicular to it and about 0.1" in from the other edge. I then punched a pric at the intersection of these lines to give the vertex of the arcs on the limb of the quadrant. I then used a machinist dividers to lay out the arc bounding the quadrant and additional arcs to box in the graduations of the protractor edge.  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, bounding,  arc at 10° 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. Following the Zutphen example I stopped the graduations at 75°, however I decided to mark the graduations on mine with 1.5mm Italic figure punches at 15° intervals. The next step is to bisect the median and the drw the noon arc between the vertex and the bounding arc. 

Construction of the remaining arcs is more complex. Peter Drinkwater provides a Medieval method for laying out the quadrant based on Oronce Fines early 16th century work**. However, I 'cheated'. When I told a friend of mine, Vsevolod Buravchenko in Kyiv City, Ukraine (aka Master Terebrus, a maker of fine high quality Historical navigational and astronomical devices) that I wanted to replicate the Zutphen quadrant, he kindly offered to provide me with a detailed CAD diagram*** calculated for my latitude, 38.5°.  I transferred the various points for punching to make the appropriate arcs from this diagram. The punched and scribed body of the quadrant is seen below:

I next labeled the various arcs using 1 mm standard font number and figure stamps, as shown in the following images.

black and white image showing monthes scale and partial arcs  intersecting noon arc: D*I, N*F, O*M, S*A, A*M, I*I

Month (Season) Labels

Note I=J (no J in Medieval Latin), so D.I = Dec/Jan, N/F = Nov/Feb, etc.

B&W image of hour scale and hour arcs intersecting limb scale: 5*7, 6*6, 7*5,  8*4, 9*3, 10*2, 11*1.

Hour Line Labels

Note the hour arcs begin on the left with 5am and 7pm and go to 12 noon (unlabeled): 5*7, 6*6, 7*5, 8*4, 9*3, 10*2, 11*1.

I next filed two notches and drilled two holes (1/16" dia) to hold and align the sites on the meridian side of the quadrant, and cut and filed two site blanks with pins to act as rivets as seen in the following images:

Quadrant with notches and holes for Sites

The notches were filed to precise depths to properly align the sites, with rivet holes carefully positioned to give perpendicular site alignment. Note the chamfered edges to allow the rivets to swell and stably hold the sites.

Site blanks (back edges unshaped)

The site blanks were co-filed to give them the identical size. they were then laid out to leave the rivet pins attached when the body of metal was removed by careful filing. the rivet pins were then rounded to 1/16" dia. using a die sinkers riffler (curved) file. (I ground the edge smooth so the body was not removed during rounding.)

After checking that the two site fit onto the quadrant and that the pins also fit the hole, I clamped them back together so that I could file the decorative curves using round and flat files on the back edges so they would match (see following image). I then scribed cross-lines on each site measured from the notch-fitting surfaces for punching the site holes. The holes were then drilled with a 1/16" drill and chamfered on both sides to assure clear site lines and a clean round spot when projected from one site onto the other. The sites were then fitted onto the respective locations on the quadrant and the rivet ends flattened and rounded over with a small ball-pein jeweler's hammer to secure the sites. 

At this point the quadrant was finished except for attaching the plumb line. With my previous quadrants I simply drilled a hole at the apex and strung a line with a plumb bob (with or without bead) through it. However in this case I decided to follow  the original design using a swivel mount for the plumb line. I first turned a post on a watchmaker's lathe. Starting with some 1/8" brass round stock I turned a 1/16" diameter post on one end just a bit longer than the thickness of the quadrant body. I then left about a 1/16" length of the rod at its original diameter and turned a length of about 3/8" to 1/16" diameter to serve as the shaft of the swivel and cut it free. Pushing the swivel post from the front through a 1/16" hole drilled at the apex of the quadrant that had been chamfered and taped to allow expansion of the post on the back side, I flattened and rounded over the post on the backside with a small ball peen hammer. 

Back of Quadrant showing shaped rear edges of sites

Partially visible is my personalization of the quadrant: R PASELK FECIT 2022 (this was stamped early, before scribing arcs etc to prevent damaging the front-side markings due to stamping).

Turning plumb-line post on Watch-maker's lathe

Note the small post being cut on the end of the rod for riveting the swivel on the quadrant.

I had previously fabricated a small two-holed, bent brass lozenge from 20G brass. A 5/64" hole was drilled for the swivel (making it a little loose) and a 1/16" hole for the plumb line. The fabrication was all done "by eye" with no measurements. After drilling and chamfering the holes, the original retangular shape was rounded by hand with flat fine and jewelers files. It was then bent in the middle to lift the plumb line off the quadrant body to assure free movement. The brass lozenge was slipped over the shaft of the swivel followed by a custom spacer and the shaft was then cut just long enough to allow it to be swagged over with a ball peen hammer. 

I had previously made the plumb bob from 1/4" brass rod. I first drilled a 1/16" carefully centered hole through the side of the rod about 1/8" from th end of the rod. I then chucked the rod onto an engine lathe with a centering chuck and drilled a 1/16" hole in the center of the rod using a tailstock chuck until it reached through the cross-hole. This assured the plumb line would be held in the center of the bob. At this point I used standard metal cutting tool on the cross slide to shape the bob and cut it off. I then tied a loop at the end of the thread for the plumb line and forced it through the center hole of the bob and pushed it out through the cross hole, pulled the loop out and over the end of the bob to catch it on the groove in the bob before pulling it tight. After stringing the seed pearl bead on the line I tied the line onto the swivel with multiple half hitches to finish the quadrant.

The completed quadrant is shown held in my hand in the picture below. The bead is set for the end of March/beginning of October and reads 9 am/3 pm.

Taking a reading with the 'Zutphen' Equal-hour Quadrant

*My reconstruction is based on the article:  Davis, John (2014) "THE ZUTPHEN QUADRANT, A Very Early Equal-Hour Instrument Excavated in The Netherlands", 26(i), 36-42. 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 on the backs of planispheric astrolabes on pp 114–116. I highly recommend both.** Peter Drinkwater (1993) Orance Fine's SECOND BOOK OF SOLAR HOROLOGY, Interpreted in English. Peter Drinkwater, Warwickshire, England.*** Master Terebrus wrote: The remaining arcs are normally built by 3 points matching the altitudes of the Sun for that time on the days of equinox and 2 solstices calculated by the formula:Als =arcsin(sinѲsinΔ + cos ѲcosΔcos h)Al is for the altitudewhereѲ  = geographical latitude;Δ = seasonal declination of the Sun;h = hour angle (at 12.00 h = 0);He also provided the screen shot of the Excel sheet below:

Master Terebrus Excel sheet calculated from formula: Als =arcsin(sinѲsinΔ + cos ѲcosΔcos h)

© R. Paselk; 12 March 2023, Last modified 20 September 2023