Measurements 12/15/20

Science by Richard Bleil

Roman chariots were pulled by two horses, and the best designs had the chariots no wider. In routine paths taken by these chariots, grass was killed by the travel, and the grooves were kept clear because it was smoother going following the grooves than veering off to one side or the other. These grooves became the standards width for wagons (regardless of how many horses were pulling them). Technology improved, but the standard was set as horseless carriages and even train track width conformed to this standard width.

In old Downtown Boston are many one-way roads. These roads are just barely enough for single vehicles driving between the walls of two brick buildings, without even room for pedestrians. Oddly enough, these widths were not conforming to the ancient Roman standards, but to a law that actually created a remarkably close standard. As the city was being built, the town government set a law that said any road must have a minimum width such that two horses traveling in opposite directions could pass which is the standard width of a car. Well, obviously this is not dissimilar to the width of a chariot pulled by two horses.

Tales like this gave rise to the English measurement system, a random collection of units (to which we Americans have become accustomed) that eventually came to be fiddled with to find conversions from dissimilar unit types such as volume, mass and length. An inch was defined originally as the width of a man’s thumb, but different men have different size thumbs. An acre is the amount of land that can be plowed by a horse in one hour, but if you’re the buyer you would want a young fast plow horse, but as a seller you’d bring a slow decrepit horse.

Eventually, the metric unit was developed to provide a more uniform and logical measurement system. It was developed for laboratory use, and everything was defined in multiples of 10 (10 mm in 1 cm, 10 cm in 1 dm, 10 dm in 1 m). But to be of practical use in the day when rapid delivery meant three months, there had to be a basis for this measurement system that every laboratory, anywhere, could easily replicate using a chemical easily accessible to them. But what such chemical could possibly exist?

The answer, of course, is water. Easily manipulated in its liquid form, and readily available anywhere in the world, a lab could easily use water to create their own measuring devices. For example, labs then had scales, so it would be easy to measure out, say, one gram of water. This gram of water was the foundation of these measurements, because immediately it creates a relationship between volume and mass since one gram of water is one milliliter. This allows labs to create volumetric equipment, but there is still the need for length. This comes in the form of a definition, specifically that one milliliter is one cubic centimeter. In other words, if you built a cube that was one centimeter wide, one centimeter long and one centimeter high, that cube is one milliliter. And now we have an internally consistent set of measurements reproducible (more or less depending on temperature, purity of the water and accuracy of the lab) around the world.

Sometimes this set of metric units is referred to as the “cgs” system, short of “centimeter, gram and second”. Notice that I didn’t mention time in the metric system. This is because time is the same in both the English and metric measurement units. You might also notice that “cgs” leaves out volume, but volume is derived from length as discussed above. But we do need to be able to convert from the very commonly used English system to metric. If we can find one conversion factor, then all of the cards would fall into place, and that conversion factor is length.

By definition, one inch is exactly 2.54 cm. This is a definition, so you can add as many “zero’s” after the number as you like (2.54000000000000000000000 ad infinitum). Physicists for years have strived to provide increasingly accurate and laboratory verifiable definitions of units. At one time (and it might still be there today for historical reference) and “inch” was defined by a piece of metal kept in an inert atmosphere under several layers of glass in a government building somewhere. Today, length is measured in terms of wavelength from a cadmium vapor laser where 1 millimeter is 1,553 waves of this light. Chances are nobody reading this (including the author) have the equipment to actually measure this ourselves, but there are labs where it’s possible. But this laser is again reproducible, and verifiable anywhere around the world. But the next time you grab a ruler (which I’m using a lot in my new home), just realize that this is all thanks to the Romans.

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