Humboldt State University ® Department of Chemistry

Richard A. Paselk

The Quadrant


The quadrant is one of the earliest and simplest of measuring instruments for astronomy, navigation, and surveying. In operation one sights an object, such as a star, through the two sighting vanes along the 90° line (right edge in picture above), while holding the quadrant in one hand, and then clamps the string against the scale with the other hand. When sighting the Sun, one lines the quadrant up such that the image of the Sun formed by the upper pinnule falls on the lower pinnule. One then clamps the string as above and reads the angle on the scale.
The instrument shown above is constructed of 1/2" Ash plank with a radius from tip to edge of 9 3/8". The straight edges were cut and squared on a table saw, then the arc was rough-cut with a band saw. The straight edges were then finished with a Jack-plane, and the arc finished by hand with a Compass-plane. (I really enjoy using hand tools, but I don't have the time or patience to use them exclusively, so most of my rough work involves power tools.) To provide a better surface for drawing and writing a sheet of "parchment" paper was glued onto the wood base. The graduations, lettering etc. were then done with India ink with drafting and calligraphy pens.
The bob was hand turned on a wood lathe from 3/8" brass round stock with a file (careful, if it grabs you can be damaged). There is a small hole in the top for the thread, with a cross hole through the grooved part to tie it. The sites are fabricated from 12 gauge brass sheet stock with carefully centered holes. The sites have an inverted "J" profile, with the stem in the wood and the curve overhanging the parchment. This allows the holes to align over the 90° line and the thread of the plumb bob to also line up at 90°.
This quadrant has a shadow square (discussed below) as well a the graduated arc for aid in solving surveying type problems.

Making a six inch simple quadrant


This quadrant was one of the projects for my 1998 workshop, "Medieval Scientific and Philosophical Instruments."

Materials (provided at the workshop - illustration below):


Construction :


Adding a Shadow Square. The shadow square is used to find the opposite side of a triangle when the adjacent side is known, or vice-versa. In other words it solves simple trigonometric problems based on the tangent function. If you want to layout a shadow square using angle measurements you must calculate the angles for given ratios using the arctangent function. I have provided a table of sample values and formulae.
Of course the easiest way to layout a shadow square is to base it on similar triangles. Quite simply, you decide on how many divisions you want, divide the length of the side of your square by the number of divisions, and then set a dividers for that distance. You now use the dividers to lay off the required divisions. Finally, line up a straight-edge between the vertex of the quadrant or shadow square and your divisions and draw line segments.
You can add a shadow square to your six inch quadrant as follows. (Shadow squares with 12 divisions seem to be the most common. I have chosen 9 divisions for this quadrant due to the ease of layout with a mm scale.) Layout a 45° line in pencil from the vertex of the quadrant to the innermost (3") arc. Using a square or ruler draw lines to the intersection of the line with the arc perpendicular to the 0° and 90° lines. Next draw a second pair of lines parallel to and above the first pair between the 0° and 90° lines and the 45° layout line at positions where they are exactly 45 mm long. Now mark off 5 mm intervals along these lines. If you now draw lines between the parallel lines which intersect the vertex and the intervals you will create 9 trapazoidal spaces on each side. Traditionally the spaces are alternately left open and filled in, as seen in the figure.



Instruments Medieval Science & Scientific Instruments


© R. Paselk
Last modified 6 August 1999