The Incorporeal Ruler

By The Metric Maven

It has been noted that on Star Trek (TOS) that one never sees a ruler. Measurements are made, but only using a tricorder or some other device it appears. Rulers had somehow been banished to the past. Technological change has apparently rendered rulers obsolete in the 22nd Century.

One evening I was watching an episode of World’s Toughest Fixes. Sean Riley, the host and participator in the fixes was involved in dealing with a problem where the clearance of a roof, inside of a giant building, which was many, many meters high needed to be known to within 125 mm or so. This accuracy and precision over such a large distance was causing great heartburn. Riley reached into his complement of tools and produced one which could be placed on the floor and would measure the distance to the roof with millimeter accuracy. It uses a laser. I was dumbfounded. This was such a cool measuring device I wanted one, but could not really justify it in my line of work. After the measurement was performed, the crew was now confident they had enough clearance, even though none of them could have possibly used a tape measure to directly determine the unknown distance. The customary use of a graduated rule was essentially out of the question. This lead me to think about the origins of the common everyday ruler.

The earliest known graduated measuring rod dates from 2650 BC, and comes from ancient Sumer. It is very crude and has six graduated lines across its length. It’s not much to look at and is reproduced below.

Copper Alloy Sumer Cubit Bar (click to enlarge) — Wikimedia Commons

One can see considerable scale refinement in a surviving cubit rod from Ancient Egypt. The rod has a number of equal divisions along its length. This base division has separate divisions of the base length division, into 1/2, 1/3, 1/4, 1/5 … to 1/16. This device is beginning to look remotely like a modern measurement scale, but still has a long way to evolve.

Cubit Rod from the Turin Museum (click to enlarge) — Wikimedia Commons

Rectangular/square bars with fixed graduations continued in use with more precise markings and of more stable materials into the 19th Century.  A British Parliament fire in 1834 destroyed their length standards and new ones were commissioned to replace those lost. The British fabricated one inch square rods which are 38 inches in length. The rods are constructed using Baily’s metal No. 4 consisting of 16 parts copper, 2 1/2 parts tin, and 1 part zinc. A pair of markings on gold plugs, which are recessed into the bar, defined the length of one yard at 62° F. The plugs are recessed into the bar so they would be co-located with the axis of symmetry. This is known as the “neutral plane” where length error due to the sag of the bar under its own weight is minimum. Two protective plugs were used to preserve the defining lines. Despite the fact that the standard provided by the British was not sanctioned as an official version by parliament, only the first five copies were, the English Bronze Yard No. 11 was the official standard of the US until 1893, when the metric system was adopted.

The Official-Unofficial Yard Bar No. 11

The change to metric standards for length definition in the US occurred because the yard and its copies were shrinking at a rate of one part per million every twenty years. This shrinking was due to the relaxation of internal strain which had been introduced in the fabrication process. It was also noted that the pound provided by Britain was also “unfit for use.” By the time these problems were understood, it appears that the technical community in the UK saw the future was with metric and joined in the international collaboration. The best technical minds available were all focused on the best and most stable measurement artifact possible, which did not use a prohibitively large amount of platinum. The book The Evolution of Weights and Measures and the Metric System (1906) has an illustration of the candidate cross-sections which were studied for a meter length standard. The idea was to produce a very rigid bar which would create a very stable “neutral axis” in the center of the bar.

The use of an X cross-section was finally settled upon. Below is what was finally adopted.

There were two versions, one version with a pair of lines, and another which the length of a meter was defined by the ends of the bar. Below is a meter bar with engraved lines.

Meter Bar

This was the first adoption of a non-rectangular cross section measurement artifact for use as a calibration standard. The original meter bar was rectangular (figure 1). This change to a X design illustrates that the metric system continued to evolve, and the English standards atrophied and became neglected. T.C. Mendenhall (1841-1924), superintendent of the U.S. Coast and Geodetic Survey, realized that if the US wished to maintain accurate metrology when compared with the rest of the world, metric standards would have to be used. There was no alternative. Fortunately, the US had signed the Treaty of the Meter and a set of US metric standards existed and were available. Congressional inaction required Mendenhall to make a decision to use the existing metric standards, instead of the British ones, despite the fact that there was no legislation which sanctioned such a change. Mother nature does not succumb to the will of legislative bodies, and so Mendenhall now defined all lengths in the US in terms of the meter so that American metrology would not be left behind.

The neglected British measurement standards no longer kept up with improvements in metrology; they were now technologically dead. All new metrology improvements were only to be found within the metric system. Technical improvement continued to evolve until finally the meter artifact itself became obsolete and  was replaced with a length based on the counting of a number of wavelengths of light (pioneered by Americans). From this point forward, an artifact ruler was no longer the basis for a length standard, but was instead derived using a standard which was tied to a repeatable scientific phenomenon, which meant it could be reproduced anywhere on the planet–or even off the planet. Length definition had outgrown the primitive measuring stick used by our ancestors.

The laser measurement device used in World’s Toughest Fixes points to a possible future when rulers might become less ubiquitous (it is hard to imagine them actually disappearing from use). Unfortunately, we in the US continue to pretend there has been no improvement in measurement and its usage since the days when barleycorns were used to define length, and fractions were the state of the art for tape measures, rather than the use of decimals. It is an embarrassment for the US that our measurement usage has more in common with an ancient hand-carved cubit rod, than a precision laser.

Related Essays:

The Design of Everyday Rulers

Stickin’ it to Yardsticks

The American “Metric Ruler”

America’s Fractional Mind