A circa 1700 Graphometer - Probably Made in Germany

Based on survival rates, I suspect that there were more Graphometers/Semicircles made before 1750 that Theodolites. Graphometers were the instrument of choice for many Continental European countries, especially in France. While the British preferred Theodolites, the population of France dwarfed that of England, which is the main reason why I believe there were more Graphhometers produced than Theodolites before 1750. Graphometers faded pretty quickly after 1750 to 1800, once the English Altazimuth Theodolite (with the superior achromatic lenses) started to be produced in quantity.

The Graphometer/Semicircle is similar in principle to a simple theodolite, but with a semicircle divided into degrees instead of a full circle. There are four sights: the diameter of the semicircle has fixed sights at either end, while at the centre of this diameter a pivot carries a sighting rule or alidade that moves across the divided semicircle.

In early examples the compass is small, is incorporated into the pivot and is used for orientation; later, larger compasses were set in the central space of the semicircle and had a divided scale beneath the needle so that the instrument could also be used as a circumferentor or surveying compass, by sighting with the fixed sights. In the earlier instruments these fixed sights were used only for aligning the instrument with another station, though with the instrument mounted vertically they could have a levelling function.

The use of different orientations - vertical as well as horizontal - is explained in the treatise, Declaration de l'usage du graphometre (Paris, 1597), by Philippe Danfrie, who designed the instrument.


NOTE: In 1600 to 1800 these instruments were often but not always called Graphometers in France and other Continental European countries. In England (and early America) they were more often called Semicircles. If you are searching the internet for these instruments you will need to use the foreign language equivalents of Graphometer and Semicircle (e.g., Graphometre in France).

(The above borrows heavily from the EPACT Glossary - Epact is an electronic catalogue of medieval and renaissance scientific instruments from four European museums: the Museum of the History of Science, Oxford, the Istituto e Museo di Storia della Scienza, Florence, the British Museum, London, and the Museum Boerhaave, Leiden. Together, these museums house the finest collections of early scientific instruments in the world.)

The standard design of the Graphometer didn't change much from Danfrie's 1597 illustration until Graphometers/Semicircles started to phase out of production after 1800. Basically, Danfrie pretty much mailed the design in the late 16th century. The first two pics below show the very simple design of a standard Graphometer/Semicircle. The Butterfield Graphometer on the left has a ring, which means that the surveyor could hang the Graphometer vertically and measure vertical angles. The Marquart Graphometer on the right doesn't have the ring, so it wasn't designed to measure vertical angles. Both the Butterfield and Marquart Graphometers have two divided 180 degree circles - which were offset by half-degrees. This made it easy to read a degree to 30 minutes, and approximate it to every 15 minutes or so. I believe this is a fairly common feature on early French Graphometers.

The next two pics down show a Langlois and a Bion Graphometer. The Langlois has concentric circles while the Bion has diagonals. These approaches allowed surveyors to read degrees to every 6 minutes. In theory this was a pretty nifty approach to making the instrument more precise. The implementation of the approaches was generally wanting, however. As Norwood pointed out at page 80 et seq. in his 1639 book on Fortifications, the mathematics behind the concentric circles and diagonals approach were fairly complicated, with many makers likely missing the mark. Over time most makers opted to use a vernier system instead of the concentric circle and diagonals system.

The final two pics below show the use of telescopes on Graphometers made by Marquart and Ferat. Makers put telescopes on Graphometers fairly early on, certainly prior to 1700. If a Graphometer has a telescope, most of the time it will have two telescopes. Neither telescope will measure vertical angles, however (unless suspended by a ring). The top telescope simply replaces the sight vanes - there is no vertical arc. The bottom telescope is used to make sure that the instrument didn't move while the surveyor used the Graphometer. (You fix the bottom scope on an object, use the Graphometer to measure angles, and then recheck the bottom scope to make sure it is still fixed on the object).

Surveying instruments are tools, and therefore rarely qualify as art objects. Moreover, there is typically little variation in design for each class of instrument. For the most part, it is hard to distinguish at a glance one theodolite from another, one surveyors compass from another, or one transit from another.

Graphometers are a different animal, however. Maybe it's the French artistic influence. Or maybe the Graphometer offers a form factor that allows a maker to add artistic flourishes. Or maybe it's both. Whatever the reason, a meaningful percentage of Graphometers qualify as works of art to my eye, and are priced accordingly.

France was unquestionably the leader in producing Graphometers. Other Continental European countries produced Graphometers as well, but not nearly in the numbers produced in France. France had a very large population compared to most other countries, so it's not surprising that France produced by far the most Graphometers.

While Theodolites were much more popular in England than Semicircles, English makers still made Semicircles to meet the demand.

It's worth noting that early Americans imported some Graphometers and Semicircles, and some American makers made semicircles, mostly out of work. See my webpage discussing this by clicking here.