Doubling Down

Double-MeasureBy The Metric Maven

Bulldog Edition

When I lived in Mexico as a boy, it was pointed out by my peers, that rather than drink the more expensive Coke or Pepsi, one should buy a less expensive Cola they called Doblay Cola. I became used to  the pronunciation as Dob-lay and expected it was a Mexican product. Years later I was in the US and saw a bottle of Dob-lay Cola, but suddenly I realized it was actually called Double Cola, and is from the US. When I was surrounded with Spanish, I saw words as all being pronounced as they would be within that environment. The modern bottle of Double Cola shown on the upper left has the marketing copy: “Double Measure Double Pleasure.” In light of the information that follows, it struck me as rather prescient. Recently Amy Young brought an interesting web page to my attention, and again I was faced with an English-French version of what I had experienced with Double Cola.

The university web page has an English translation of the original 1795 metric decree in France. There are a number of declarations about measures, and they are mostly what I would expect, but it offered extra context. It is interesting that the millimeter does not appear to be mentioned, but not exactly shocking.  What did surprise me was item number eight:

8. In weights and measures of volume, each of the decimal measures of these two types shall have its double and  its half, in order to give every desirable facility to the sale of divers items; therefore,  there shall be double liter and demiliter, double hectogram and demihectogram, and so on with the others.

Suddenly, the origin of the incredible name proliferation found in a chart made by the American Metric Association in the 19th Century revealed itself. In my essay Familiarity Versus Simplicity I diagnosed the inclusion of the double gram, demi dekagram, dekagram, double dekagram, demi hectogram, hectogram, double hectogram, demi kilogram and kilogram as a vestigial inclusion of pre-metric thinking. I suspected it had been ad-hoc and was very suspicious that it was introduced by Americans. It had not occurred to me that double in English and double’ in French would both mean well—double or twice an amount. I then realized that double and demi were introduced as concatenation prefixes of sorts. This is not unlike the Ye Olde English prefixes used with metric, like one billion Kilometers or one million Kilometers. The prefix demi (in the linguistic sense) is from Latin dimidium or “divided in half,” via Old French and Middle English, it became demi.

Why on Earth was it so important to include a prefix that is a factor of two rather than ten at the time? We have 3 barleycorns to an inch, but often the inch is divided into halves, quarters, eighths and sixteenths. When moving upward using linear measure it’s 12 inches to a foot, 3 feet to a yard and so on. The interest in doubling and halving is not presented for linear measure in the early metric system. There is no double meter or demimeter offered in the 19th century chart. The value of masses and volumes are given double and half values in this metric chart. Why? Probably because it is fairly easy to use a beam scale to halve flour or sugar or beer or whatever. This binary approach would match our Ye Olde English measures right? Well—not exactly.

Isaac Asimov in his work Realm of Measure has this to say:


Binary relationships quickly breakdown in Ye Olde English linear measure, volume and weight. The Troy pound has 12 ounces and the Avoirdupois pound has 16 ounces. Those who claim our Ye Olde English measures are consistent and binary are simply wrong. What is interesting is that the first draft of the metric system had provisions for doubling and halving values. I can only speculate at this point that this inclusion was an attempt to encompass a binary set of measures as a kind of reform of earlier measures that might have been more useful if they had strictly stayed with doubling and halving. This reform was developed at a time before modern scales with analog or digital readouts. When continuous reading scales were introduced, the idea of using a balance scale for everyday measures was moot. There was little reason to use the double or demi designations. I discuss the importance of the creation of a measurement continuum in my essay The Count Only Counts—He Does Not Measure. Modern measurement instruments are more than likely the reason that binary measures began to vanish. When one was no longer chained to binary quantities, it opened up a world where any measure for a product could be realized. Just look at any set of supermarket shelves.

Section 6 of the document calls for the prefix cluster around unity and the myriameter:

6. One-tenth of a meter shall be called a decimeter; and one one-hundredth thereof, a centimeter.

A measure equal to ten meters shall be called a decameter, which furnishes a very convenient measure for surveying.

Hectometer shall signify the length of 100 meters.

Finally, kilometer and myriameter shall be the lengths of 1,000 and 10,000 meters, and shall designate principally the distances of roads.

The incredibly useful millimeter is not listed in the document. The liter is defined and is asserted to be for both dry and liquid measure, as it is to this day.

The original formulation of the metric system as presented in this document illustrates how far we have come in simplifying and thereby  increasing the utility of this ubiquitous system of measures—well ubiquitous outside of the United States.


The Metric Maven has published a new book titled The Dimensions of The Cosmos. It examines the basic quantities of the world from yocto to Yotta with a mixture of scientific anecdotes and may be purchased here.


Close Enough for American Work

Rose-QuartzBy The Metric Maven

Metric Day Edition

Recently my Significant Other (SO) requested that I take her to a rock and mineral shop. She had driven past it many times, but never stopped. There were all manner of minerals and small fossils. The displays were all very interesting and it seemed I would be destined to look, but not to make a purchase. Then, I noticed the tools section. There was a common inch ruler with a centimeter scale on its opposite edge. Yet another sad testament to metric “practice” in the US. Nothing unexpected there. To my surprise there was also a small dual-scale caliper with þe olde English and metric, but it had fractional inches on one side and millimeters on the other. I was quite surprised and for $7.50 I could not resist purchasing it. Here is a photo:


Inexpensive Calipers (click to enlarge)

My SO, who had requested we visit, did not make a purchase, but I did. When I arrived at the cash register, an older man with a beard was waiting. I commented on the millimeter scale on the calipers and that it did not have centimeters. The man did not miss a beat and said “We have to have them, all the precious stones are measured in millimeters.”

I looked at the calipers with more care and noticed a lower scale.

Then I said: “Oh my goodness, look at this, it has a vernier scale on the metric side.”

The cashier had no idea what a vernier scale is. I did my best to explain it from memory. I also told him that in my opinion, the creation of the vernier scale was a very important development in the history of engineering and science. I recalled that I had learned to use a vernier scale when using a micrometer during my time working as an offset pressman. It was in Daniel J. Boorstein’s book The Discoverers (pg 400) that I first ran into a historical discussion of the vernier scale. The scale was created by French Mathematician Pierre Vernier (1580–1637) and bears his name.

A U.S. Quarter Dollar coin has a diameter of 24.26 millimeters. I placed a current 25 cent coin into the calipers to measure it. The scale is shown below:


Vernier measurement of a US quarter Dollar (click to enlarge)

The first line of the vernier scale indicates the measured length is between 24 and 25 millimeters. We next look for the vernier line that matches up best with the upper scale. The three is probably the closest to the best alignment and so we could estimate that the diameter is about 24.3 mm. This deviation is only 0.04 mm (40 um) from the design value. This is a very close estimate for such a roughly fabricated device.

Let’s look at upper inch scale. Oh, my, there is no vernier scale. It would appear that because it is graduated in fractions, a vernier scale was not added. The smallest fractional division appears to be in sixteenths of an inch or 0.0625 inch. When converted to a useful metric unit, 1/16″ is 1.588 mm. It also appears that it would be rather easy to confuse the smallest division with 1/8″ rather than 1/16″ and this would complicate the inch measurement considerably. The mark half-way between zero and 1/2 has about the same downward length as 1/8. This is not the “standard” way that U.S. rulers are marked. Below is an example with the first inch divided down to 1/32″ and the second inch down to 1/16″.

Fractional-DivisionsIf you want to know why the divisions are different for the first inch, I invite you to read my blog The Design of Everyday Rulers. This odd set of graduations caused me to wonder if the calipers had been manufactured in a metric country by a person who is not familiar with our complex þe olde English practices. That the word meter is employed, with an er rather than an re, makes one suspicious that an American was behind this muddled design. Clearly the calipers makes measurements in millimeters and not meters. Why use the word meters rather than millimeters or metric?

Assuming we have figured out the inch fractions on the caliper, we see about 15/16″ and “a little more.” How much more is this? Well, because we do not have a vernier scale, we have to estimate the value by eye.  It looks like it maybe about 1/10th of a 1/16″ space if I have to guess—which I do. So what is 1/10th of 1/16″ to divide fractions we invert and multiply as I was told as a youth. We end up with 10/16 — that can’t be right. Oh wait we need to divide 1/16 into 10 parts or 1/16 divided by 10/1. When we invert and multiply now we get 1/160. Now we need a common denominator to add the fractions and obtain a final value. We multiply the top and bottom of 15/16″ by 10 and have 150/160. We now can add 150/160 + 1/160 to get 151/160 inches. Now we can make this fraction a decimal and get 0.94375 inches or, when converted to millimeters, it becomes 23.97 mm which we can compare with the vernier value of 24.3 mm directly. Even after all of that work and estimating, the vernier scale with millimeters is more accurate, and DEFINITELY simpler to read.

Today we have mechanical dial calipers, and also calipers with electronic readouts; but a vernier scale with millimeters is still an accurate and simple way to measure length. This example also illustrates the inaccurate and complicated way we in the US measure with fractional inches. We have not even bothered to decimalize the inch on our common everyday rulers. I have a proposal, let’s just switch-over to the metric system directly, and skip a kludge like decimal inches for the streamlined system that uses millimeters.


The Metric Maven has published a new book titled The Dimensions of The Cosmos. It examines the basic quantities of the world from yocto to Yotta with a mixture of scientific anecdotes and may be purchased here.