Simple Compasses, Exotic Compasses
It is a bit ironic that what is properly called the “Plain Compass” has become something of an exotic oddity. What we now call “Dividers” after their principal modern use are shown above. This would have been synonymous with “Compass” or plain compass for most of the thousands of years of the history of the instrument.
Some original design drawings survive from the medieval or somewhat later Islamic design tradition. There is a great deal of interest in trying to understand how these patterns were constructed based on the surviving drawings. There is an extensive discussion of “Dead Drawing” lines in the surviving Tashkent and Topkapi design scrolls.** Compass arcs and lines are impressed into the paper but not inked. Those un-inked layout lines were drawn with a steel point plain compass.
This is not some arcane medieval lost art. Layout drawing with steel point compasses was a normal procedure into the 1800’s when pencil leads became somewhat more affordable.*** Graphite marking points, even “pencils”, are relatively old but controlled hardness in a lead suitable for a compass is more recent. By the 1870s, it was no longer considered normal practice to use a steel point compass to scribe layout on paper. It was largely forgotten for drawing. Of course steel point compasses are still used in the same way in metal layout today.
A Pattern laid with “Dead Drawn” Lines
Nothing was erased or removed here. Ball pointed steel points in both compass and lead holder were used to construct this pattern. The pattern is then inked as usual.
I do have one or two steel point compasses that reach back into this era. It was easiest for me to use a ball pointed steel point in a standard compass rather than ball point one of my antique compasses. The point needs to be a polished ball so they need touch up even if they are originally set up for steel point layout.
Steel Point Plain Compasses
The similarity to the medieval examples is quite clear in raking light. The method is easy and accurate.
After the pencil as we know it became more common, the simple compass evolved to exclusive use of a lead point or a steel inking pen. It took on the form it maintains today. The plain compass and dividers had separated into two dedicated instruments.
Demands of Ink
Compass design was driven by the demands of the steel inking pen. It must be vertical to draw well, dictating the introduction of joints in the compass leg to adjust the pen.
By the 19th century there were, as a result, two distinct instruments.
What is left to dividers, and why would you want to use them? As mentioned above, in most of our work the compass is not drawing circles. It is marking out defined arcs or distances. The layout below is the four pentagon 20 fold division at five centers for a classic pattern. There are no random pencil arcs or erasures. All of the transfers of the four 5 fold divisions of the circle were marked out with dividers.
With the compass, a radius equal to the side of a pentagon is set from the exact pentagon construction. That side of the pentagon is marked with a pencil tick on the large circle, the compass is moved to the pencil mark, another side is marked, etc. Generally the procedure needs to be checked to verify accuracy by making a complete trip around the circle and it is quite common to need to adjust the side length and redo the entire process. It makes a mess. Every move of the compass is an opportunity for errors to creep in.
With dividers, the distance to the side of the pentagon is set from the construction and the divider “walks” around the circle. It pivots around the steel points without ever lifting from the paper. In checking the setting, no mark is made. When the precision is satisfactory, very slight pressure at each vertex leaves an index mark to use for drawing. It is faster, tidier and more accurate. The marking function of the pencil point is never needed. This will be obvious in the video link mentioned below. What more can we ask?
If you look, all of the marks of the classic pentagon construction are there, as single pin marks.
It is difficult to “show” the utility of the dividers for our purposes since they do exactly what the compass does in geometric construction but it is done more neatly, more accurately, and usually faster without messy marks and arcs.
One of the most elegant uses of dividers is the division in unusual multiples in combination with proportional dividers. This Link leads to a short youtube video showing the process. Click “Show More” on youtube for a text file describing the process by reference to the video.
Proportional Dividers. Direct Division of Circles, 3 to 20 sides.
Wherever you use a compass to mark a distance, particularly repeated marking off, ask yourself if dividers could do it better. You will be surprised how often they are useful.
Notes to the text:
**See; Gülru Necipoglu, The Topkapi Scrolls, page 13 for an example illustration of these layout lines.
*** See; Simms, A Treatise on the mathematical Drawing Instruments, 2nd Ed 1845 page 2. “As some of the numerous uses to which this instrument may be applied, the following may be mentioned. To take any extent, or length between the points of the compasses, and to set it off, or to apply it successively upon any line. To take any proposed line between the points, and by applying it to the proper scale, to find its length. To set off equal distances upon a given line. To describe circles, intersecting arcs,&c.” He is discussing a plain compass with two steel points, not the replaceable inking and pencil points discussed later on page 4. Almost all of these functions up to the italics would be described for “dividers” today. There is some overlap in the terms until about the 1870s.