By 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:

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:

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″.

If 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.

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Another good read Maven. Happy 2016-10-10.

BTW you can use [Alt] 230 on windows computers to get a µ for your micro prefixed measures, if you like that kind of thing.

One (very) cheaply made vernier does not prove “We have not even bothered to decimalize the inch.” My dual vernier is the counter-example as it uses decimalized inches (to 0.001″) and millimeters to (0.02 mm). But you can buy verniers with nearly any scale. By Googling, I even found one that had fractional inches on one edge (to 1/16 on main body, to 1/128 with the fractional inch vernier scale) and decimalized inches on the other edge. Not quite sure who would use that but whatever floats their boats.

We have not even bothered to decimalize the inch

on our common everyday rulers.If an “everyday ruler” is what you buy at a big box stationery store, you’re right. It is probably even true that the majority of simple rulers and tape measures are fractional inches.

However, there are plenty of decimal inch rulers and tapes available for disciplines that use them, and even decimal foot tapes, leveling sticks, etc. You may have to buy online or at a specialty store. Similarly, you can buy metric only rulers, tapes, etc.

My favorite ruler is metric only, but my favorite inch ruler has tenths and fiftieths on the two edges of one side, 32nds and 64ths on the other side.

I am learning the metric system in math class, I like it.