Compass, divider, and caliper are basically instruments that have two legs pivoted to each other at the top and are concerned with small-distance measurement or transfer. The compass and divider have straight legs; the caliper has curved legs.

The terms compass and divider are often interchanged, for each instrument can be used to draw circles, mark divisions (divide a given distance), or simply mark a distance. Technically, a compass is a drafting instrument that has one pen or pencil point and one sharp point that is positioned at the centre of the circle to be described, while a divider, on the other hand, has two sharp points, one for the centre and the other for scribing or marking. Caliper is a corruption of calibre, the diameter of a hole (as in a firearm) or of a cylindrical or spherical body. The outside caliper has inwardly curved legs that measure the diameters of solids created by rotating tools, such as lathe-turned objects, and the inside caliper has outwardly curved legs for measuring bores.

Dividers and calipers were known to both the Greeks and Romans, though the caliper was uncommon. A divider with a circular sector, or wing, connecting the two legs was sketched in 1245; its modern counterpart is the wing divider with a thumbscrew clamp and screw for fine adjustment. The caliper is mentioned in the Middle Ages, but the divider was the principal tool of the architect working on full-scale layouts of stonework, such as in the construction of a cathedral. Such dividers were large, often half as tall as a man. The divider underwent refinements that made it an important drafting instrument for Albrecht Dürer and Leonardo da Vinci; Leonardo suggested improvements that included the knuckle-joint hinge (to increase rigidity) and the adjustable proportional divider (Roman proportional dividers had a fixed pivot that gave only one ratio). Leonardo’s notes also show the beam compass with a screw adjustment for large radii, as well as a compass that had interchangeable points, in which one leg had a clamp for different drawing media, such as graphite or chalk.

Chalk line

“Snapping a line,” a technique familiar in ancient Egypt, is employed in modern building construction. The procedure uses a taut chalk-covered cord that is stretched between two points: the cord deposits a straight line of chalk when it is plucked and snapped onto the surface. After 5,000 years the only change in this technique is that, whereas the Egyptians used wet red or yellow ochre, the modern craftsperson follows the method of Greek masons who employed white and red chalks in addition to wet ochre.

Rules

The unit of linear measure in the ancient world, the cubit, was simply the length from the elbow to the extremity of the middle finger. Although the cubit gave an order of magnitude, it was hardly a standard, and it varied widely in different times and places.

One of many royal Egyptian cubits had a length of 52.43 cm (20.64 inches). It was divided into seven palms (measured across the fingers, not the knuckles), making a palm almost three inches. Each palm was, in turn, divided into four digits of about three-quarters of an inch apiece. Thus, 1 cubit = 7 palms = 28 digits. On occasion, digits were subdivided into 10ths, 14ths, or 16ths.

The common rule of Egyptian masons and carpenters was made of wood, had a narrow cross section, and had one beveled edge, with the two left-hand palms carrying the smaller divisions of digits. Some Egyptian rods were made of stone and used digits divided into 16ths. These may have been ceremonial rods or, perhaps, master gauges for calibration and comparison; their brittleness would make them unsuitable for the rough handling received by mason’s tools.

The Romans introduced folding rules of bronze in 30- and 15-cm (12- and 6-inch) sizes. These were probably “pocket” instruments for officials—too expensive to be used by ordinary craftspersons, who probably used plain strip rules.

Only scanty evidence exists that graduated rules were used in the Middle Ages and the Renaissance; plain straightedges seem to have predominated. In 1683 an English writer described foot rules as having 1/8-inch (0.32-cm) subdivisions. The folding rule, now made of wood, reappeared at the end of the 17th century.

Measurement was long characterized by great national and regional differences. Because every large city in Europe and most towns had a different but locally standard “foot,” rules with four different graduations (one on each face) were made.