The Pseudo-Inch

By The Metric Maven

Bulldog Edition

I have a friend, Pierre, who has a passion for woodworking, but a passion for metric?—not so much. My knowledge of woodworking is at best minimal, but Pierre does his best to enlighten me. One evening I received an email from him after he had watched a woodworking program by Roy Underhill.  Roy is an American, and a bit of legend in woodworking as I understand it. During the program, Roy explained a Swedish method of teaching called sloyd. My friend Pierre then related:

The original Swedish drawings in the book of exercises he used were measured in metric. Underhill says, “I took up woodworking so I wouldn’t have to learn metric.” Thought you’d want to know that.

Next, Underhill was showing how to measure 2 cm over on a board using a Swedish wooden folding rule. He said he got it from some visiting Swedish woodworking friends, because his American one doesn’t have centimeters on the back. He said, they said, and this is really the part I wanted you to know, that in Sweden, his woodworking friends use only inches.

Then, he flipped the Swedish folding rule over, and it showed inches. Here’s another interesting part, I hope you aren’t asleep yet.

The Swedish “inch” is bigger than our inch. Holding the rules one over the other, you could clearly see the Swedish “inch” is about 1/16 bigger.

WTF, man?

Well, the problem is, there is really no such thing as “an inch.”  Why do we think that an inch exists?—well, therein lies the tale. The Wikipedia entry for “the inch” has an enlightening “inch converter” which was used before the age of the metric system. Here is the illustration:

19th Century Inch Converter

19th Century Inch Converter — Wikipedia Commons

One can see that “the inch” has many different lengths in the 19th century. Many of them are considerably different in length. Note the Moscow and Russian inch are not even close to one another. Here’s what I have surmised from this converter about inches:

  • Hamburgh – Inch divided into 8 parts. 1 inch ≈ 23.2 mm
  • Austrian – Inch divided into 8 parts. 1 inch ≈ 25.8 mm
  • Itallian – Inch divided into 8 parts. 1 inch ≈ 28.3 mm
  • Bremen – Inch divided into 10 parts. 1 inch ≈ 23.7 mm
  • Swedish – Inch divided into 12 parts. 1 inch ≈ 24.3 mm
  • Turkish – Inch divided into 12 parts. 1 inch ≈ 31.3 mm
  • Bavarian – Inch divided into 12 parts. 1 inch ≈ 24.0 mm
  • Spanish – Inch divided into 12 parts. 1 inch ≈ 23.0 mm
  • Portuguese – Inch divided into 12 parts. 1 inch ≈ 27.0 mm
  • Moscow – Inch divided into 12 parts. 1 inch ≈ 27.7 mm
  • Russian – Inch divided into 8 parts. 1 inch ≈ 44.1 mm
  • Amsterdam – Inch divided into 12 parts. 1 inch ≈ 23.5 mm
  • Rhynland – Inch divided into 12 parts. 1 inch ≈ 26.1 mm
  • French – Inch divided into 12 parts. 1 inch ≈ 27.0 mm
  • Fr. Metre – Centimetres divided into millimetres
  • English – Inch divided into 32 parts. 1 inch ≈ 25.3 mm
The “inch” is a perfect example of what I call  a retread unit. This is a unit with a name that is used over and over for different quantities, which renders it meaningless as a standard.
This lack of a clear international definition of the inch, produced a strange misunderstanding in the early part of the Twentieth Century between Americans, British and Australians–who were the contractors:
In 1909 the American firm Pratt and Whitney was contracted to supply all the equipment for the Lithgow plant to specifications that  would ensure interchangeability of components with British rifles. But the parts would not fit because no one told the Americans that the British drawings used two different standards of length: dimensions above 2 inches were expressed in inches aligned with the imperial yard; but dimensions below 2 inches were based on the `Enfield inch’, a standard used by the Royal Small Arms Factory at Enfield. (For Good Measure Jan Todd 2004 pg 58)
Here is the history of the Swedish inch according to Wikipedia:
In Sweden, from 1855 to 1863, the existing Swedish “working inch” of ≈24.74 mm was replaced by a “decimal inch” of ≈29.69 mm which was one-tenth of the Swedish foot. Proponents argued that a decimal system would simplify calculations. However, having two different Swedish inch measures (and the English inch on top of that) proved to be complicated. So in a transition period between 1878 and 1889 the metric units were introduced as the overall standard measures. However, the various inches survived some time in building and construction trades.

         click to enlarge image

Originally the Anglo-Saxons used their smallest standard, the barleycorn, to define the inch. We still use barleycorns to define shoe sizes in the US. The standard was three barleycorns in a row make an inch. I call this “The Barleycorn Inch.” The barleycorn is also called the grain. There are 7000 grains to a pound. In the 20th century, the British and Americans decided to define their inch as exactly 25.4 mm. It is sometimes called the “Industrial Inch.” This is what Americans call “The Inch.” This inch was decimalized in many industrial applications and is found on many, many US technical drawings. The decimalization of the inch is the basis for our machine tools, yet finding a ruler in the US with decimalized inches is almost impossible. Our educational system doesn’t even teach decimalized inch units and how they are used by industry. The fascination with fractions in this country is beyond my understanding.

I have converted my engineering work to be entirely metric, which can cause heartburn for some American vendors. Recently I finished a PCB design for a broadband microwave device. I sent a PCB fabricator gerber files and metric drawings of the device to be fabricated. They requested I give them drawings with dimensions in inches—I demurred. They asked again—again I told them no. Their third email to me pointed out that inches were what their equipment was calibrated to, and what they are trained to use, are used in the US, and they wanted inches.

Dimensional Standard for Barleycorn Inches

The PCB files I sent actually were in inches as forced by US industry, but the drawings were not–so why was the vendor so insistent that I provide inch drawings? Well, in Engineering, engineering drawings define the controlling dimension. The controlling dimension is the one to which the manufacturer is expected to conform. If I have a 100 mm drawing dimension, that is what the length is supposed to be, with a tolerance in mm, not 3.937 inches and a tolerance in mils. The conversion from inch to mm is exact, the conversion from mm to inches is inexact. The vendor did not want to be held to the accuracy required in mm when they had inches on their fabrication equipment.

The point I made to them is that the controlling dimension on all engineering drawings in the US is actually metric. This is because we use the Industrial inch in the US. The definition of the US inch is 25.4 mm exactly. All the “inches” of the vendor’s equipment are calibrated and controlled by the meter, so the controlling dimension of all US drawings in inches, is actually in terms of mm (i.e. meters), we just don’t acknowledge this.  The situation ended up resolving itself, and the boards were successfully fabricated. As a country we pretend that we use something called “the inch,” but it is derived from a metric standard. We use metric as our base standard, but do not adopt the convenience of the actual metric system, preferring to pretend we have “our own American/Standard” system. This is delusional.

The power the inch has over US citizens and others appears to have caused early users of metric to impose vacuous imperial conventions on the metric system. You will note that on the “inch converter” from Wikipedia the centimeter also appears in the list. As I have explained in detail in other blogs, the centimeter impedes the ease of use and soils the elegance the metric system offers. The use of millimeters only, allows for a simple and accurate implementation of metric—often without decimal points. This is experienced by Australian construction workers every day. The fact that Roy Underhill doesn’t understand the power of using millimeters, and slavishly uses centimeters instead, makes him less than a legend to me. He simply embraces folklore. The centimeter is the perfect example of an unnecessary division which appears to exist only to preserve an unnecessary and ill-defined unit of magnitude called “the inch.”. The centimeter is but a pseudo-inch, demanded by tradition and not by necessity. Its utility has proven to be non-existant in practice. Remember friends don’t let friends use centimeters. And The inch?—the definite article?—well, it’s much like fairies, and other mythical creatures, it only exists in our imagination.

Updated 2013-01-31

Related essays:

Metamorphosis and Millimeters

Building a Metric Shed

Stealth Imperial in The Kitchen

By The Metric Maven

Bulldog Edition

Some years back a technician, with whom I worked, gave me a birthday present which I still have. He is a numismatic enthusiast and the present was a cased set of US coins. It has 1 cent, 5 cent, 10 cent, 25 cent, 50 cent and 100 cent coins. Whenever I look at the set, I always think of Sesame Street’s game where they sing a song and ask which of these things is not like the other, which of these things doesn’t belong? Well do you have any idea which of these coins doesn’t belong? Here is the set I was given some years ago:

Now to help you, here are coins used by the EU:

See the one that doesn’t match? Yes, the Euro has a 20 cent coin and not a 25 cent coin. There is no EU equivalent. Why is this? Well most people think that decimalized US currency was adopted with open arms—not so. There were reactionaries that didn’t like this “metric money” stuff and would only allow decimalized currency if it included a 25 cent coin. This compromise allowed the US to become the first country with a decimalized currency. The quarter was insisted upon so the US dollar could be divided in fourths, which corresponds to divisions of the original Spanish dollar which could be divided by up to eight. Hence the jingle: “two bits, four bits, six bits a dollar all for [insert school name here] stand up and holler!” which is repeated at High School Basketball games all over the US each year. Think about what we call the coin. We call it a quarter (1/4) or a twenty five cent piece.. My Grandfather on my mothers side always called a quarter two-bits.

Chances are fairly good that you never noticed this imposition of a non-decimal currency value onto our decimalized money. It’s there, but we just work with it each day, without a clue to its origin, or even taking notice.

When I began metric cooking, I immediately adopted the idea that a teaspoon was 5 mL and a tablespoon was 15 mL. I also used a 1/2 teaspoon or 2.5 mL or a 1/4 teaspoon which is 1.25 mL without giving the measurement spoons much thought. When I began putting together a metric cookbook it slowly sank in, that there were no good “metric equivalents” for the Tsp and Tbl written in recipes. That is, there are no modular values or integer values.  I would see 2 1/2 teaspoons and it would become 12.5 mL. This is true, but doesn’t seem to give you an immediate idea of how many of each measuring spoon one should use. It gradually struck me that what had occurred with my metric cooking was an attempt to “metricate” traditional imperial cooking measures, rather than starting from scratch. And we all know cooking from scratch is also the best way. The volumes of measuring spoons were not chosen in a rational manner using “Preferred Numbers,” (I will have a blog on this in the future) but had been chosen by convention and transmitted by tradition. Because of this, their origins are a mystery, and no one can explain why it was done—they just were. Perhaps three teaspoons in a tablespoon like three barleycorn to an inch?—no, probably too logical.

I quickly realized that to my knowledge, there has never been a set of “metric” measuring spoons created. It was clear to me that this would probably consist of a set of 1 mL 2 mL, 5 mL, 10 mL, 20 mL and 50 mL measuring spoons. This would eliminate the need for a decimal point when using metric measurements. In the case of my 12.5 mL value, I could round up to 13 and use a 1, 2 and 10 mL spoon, or down to 12 and only need 2 and 10 mL spoons. These would be very close to the current measurement values of 1/4 tsp (1.25 mL), 1/2 tsp (2.5 mL), 1 tsp (5.0 mL), and 1 tbl (15 mL) that cooks could convert without too much difficulty. One could also have an optional 100 μL, 200 μL, 500μL set of spoons. Using Naughtin’s Laws one can be certain that the mL and μL would not be easily confused in a recipe. Not even the Australians have metricated their spoon cooking measures. When Australia decided to convert to metric, cooking was exempted. As Kevin Wilkes relates in Metrication in Australia:

Domestic cookery scales were exempted from the prohibition of imperially marked measuring instruments, but the decision by the cookery sector committee to recommend the use of cup and spoon measures meant that most writers of recipes adopted this system, Thus obviating much of the need for metric cooking scales.

***

Spoon measures were unchanged, the existing standard having defined a tablespoon as 20 mL [15 mL in the US] and the teaspoon as 5 mL, but a metric cup of 250 mL was adopted to replace the existing eight fluid ounce measure which was equal to 227 mL

In the conversion of existing recipes, 30 g was adopted as the equivalent of one oz and 30 mL as the equivalent of one fl oz.(tip of the hat to Klystron for providing this information)

Metric cups!  Metric spoons!  Metric ounces! I’ve written about the idea of the use of metric as a modifier for imperial measures. They are ridiculous oxymoron units. I have also written about how the Tsp and Tbl are killers. An Australian teaspoon is 20 mL and in the US it’s 15 mL. The introduction of metric measurement spoons of 1, 2, 5, 10, 20 and 50 mL, would eliminate this disparity and directly use only mL, instead of employing an antiquated proxy unit like teaspoons and tablespoons. It would allow for an international cooking standard to be created.

What truly shows the wasted metrication opportunities and material we will tolerate, and which many people apparently also find entertaining, is a set of “measurement spoons” like these:

click on image to enlarge

One set came “free” with a set of measuring spoons I ordered. The other was a Christmas present I received this year. They are obviously a joke novelty, but the effort was made to manufacture them rather than offering a metric-only 1, 2, 5, 10, 20, 50 mL set of cooking spoons as an alternative. The measuring spoons above are functional, but are never meant for any actual use I suspect, as I do not believe most people commonly use a pinch, tad, smidgeon, nip or dash these days. Nor, I suspect, is there common agreement on each value. I’m sure there are “scads” of definitions. These “units” are good example of unit proliferation. It would be far better to offer a “free” metric set of spoons in place of the novelty ones. I have written about the opportunity for the medical mis-dosage of people because of the teaspoon-tablespoon abbreviation confusion before. If most homes had a “metric set” of measuring spoons, which came with the common imperial ones, people would have the option to directly use mL, even if a dosage cup was not provided on a medicine—or was lost.

During a US metric switch-over, the implementation of a logical set of measuring spoons for cooking, would be a good way to break with the past, and make cooking more accurate and consistent. With metric cooking spoons we could lead the world in metrication instead of bringing up the rear.