The Metric System and Coincidence

By The Metric Maven

On July 4th, many, many years ago in Montana, I went out with a group of people to shoot at prairie  dogs. This was a common activity in rural Montana. It was common enough that the prairie dogs understood what was happening and would not surface above their burrow unless they were certain the hunters were far enough away so a .22 rifle was ineffective. It was very hot, and the prairie dogs seemed to have out-smarted us. We were about to leave, when one of us pulled up their rifle and aimed it at a far-off prairie dog. The target was but a tiny shadow on top of its mound, but stood up high, and defiant in the certainty that it was safe. The entire group began laughing and deriding the fellow with the rifle. “You might as well shoot popcorn at that gopher. You’re just wasting a round” they said with ridicule in their voices.  (Montanans sometimes called prairie dogs gophers) This only strengthened  the resolve of the varmint hunter who said “Oh, yeah, well at least I’ll scare him good.”  It must have been 150 meters to the tiny silhouette. He squeezed the trigger and the Prairie dog flopped over instantly. The entire crowd was stunned. One person said “That’s the most incredible shot I’ve ever seen!”  Three people began running over to inspect the scene. They were about three meters from the mound when they all put on the brakes and started screaming: “rattlesnake!  rattlesnake!” and retreated faster than they had arrived. The prairie dog had not been hit by a bullet, but instead, at exactly the same time the shot was fired, a rattlesnake had struck the unfortunate animal. This incident has always stood out in my mind as one of the strangest coincidences I’ve witnessed.

This coincidence however seems tame in comparison to some metric coincidences I’ve come across. One of the strange arguments that is offered by those against metric has been “metric lengths are unnatural” and the sizes of metric products aren’t a product of “natural” dimensions like those of imperial sizes. In his very first newsletter Pat Naughtin states in his Hidden Metric section:

As vinyl records developed, in the 1920s, they were designed and made 250 millimetres and 300 millimetres in diameter. In English speaking countries, they have been called 10 inch and 12 inch records ever since.

This seemed incredibly implausible. I took my trusty Australian mm ruler and measured a 33 1/3 LP. Wow, it was almost exactly 300 mm!–but not quite. It was actually 301 mm. I kept looking at the discrepancy and wondered if the extra mm was from the pressing process. It was hard to imagine if the specification was 300mm that any company would allow 1 mm of waste on each pressing. I did a web search and to my surprise found RIAA specifications for records. In the tradition of American Medieval Unit standards, it is written in the strange and tangled world of fractions:

The Diameter of a 12″ record is: 11 7/8″ + 1/32″ Now assuming the 1/32″ is a one sided tolerance we have in mm:

12″ => 301.625 mm + 0.79375 mm = 302.42 mm

Average = 302.02 mm

This is very close to 300 mm but LP records almost certainly are not based on metric. In the case of a Big Ten Inch Record, the specification is 9 7/8″ + 1/32″ which in mm is:

10″ => 250.825 mm + 0.79375 mm = 251.6187 mm

Average = 251.42 mm

Once again this is really close to 250 mm, but not quite, again it looks like an Olde English specification, that could be confused for a metric one. The other standard size (45 RPM) is 7″ which is 6 7/8″ + 1/32″ according to the specification.

7″ => 174.625 mm + 0.79375 mm = 175.418 mm

One can easily see that Pat might have mistakenly been told that records were 300 mm, 250 mm and 175 mm in diameter. A quick measurement would seem to verify this fact—except if you are a reasonably exacting Engineer like the Metric Maven, the small discrepancy would begin to bother you. Although it was a German-American inventor, Emile Berliner,  who is credited with developing disc records, there is no mention of metric sizes in Wikipedia.  It is quite interesting that these “metric sizes” appear quite natural and have seemed so to American citizens over the decades. Much to my surprise, vinyl is not dead, and seems to be expanding. Every time I ask for an album at my local independent music store the first question is: “vinyl or CD.”

This metric question of vinyl diameter has been superseded by the introduction in the 1980s of the metric defined CD which is 120 mm in diameter, and is indeed specified as metric, independent of the size of the standard case housings.

While LPs might be interesting, there are much bigger metric coincidences. The first has to do with the fact that John Wilkins, the British man who invented the system part of the Metric System, used the length of a seconds pendulum to define what later has become known as the meter. Early on it was suggested that a seconds pendulum be used to define the meter in order to tie its length to a scientific phenomenon. Unfortunately the length of  a seconds pendulum depends on its latitude, which became a point of contention. One can see in the figure below that a seconds pendulum from a 19th century clock is very, very close to the length of a modern meter. The alternating colored sections are 100 mm in length.

Pendulum from 19th Century Clock with Meter Stick

The next idea was to define a meter as one ten-millionth of the distance from the north pole to the equator. James Clerk Maxwell found the idea of using this distance across the Earth to be frivolous, and made sport of it in his understated way, in his famous Treatise on Electromagnetism. Clearly the distance of a meter, as defined by a seconds pendulum, would be quite different than one ten-millionth of the distance from the north pole to the equator—right? Well, no, amazingly enough the circumference of the Earth through the poles is slightly more than forty million meters (40,007,863 m) and the two suggested values of the meter are remarkably close. I find this a very surprising coincidence.

James Clerk Maxwell proposed that light is an electromagnetic wave and used his theory to predict the expected speed of these waves. His answer was 193,308 miles per second. Later in the 20th century the value would be accepted as 186,282.3959 miles/second. It was Albert Einstein who put the speed of light at the center stage of physics and directly related energy and mass using the speed of light in his famous equation E = mc2.

When the meter was finally defined with a scientific phenomenon, it was in terms of counting a number of wavelengths of light of a given color. The next metric coincidence is that the speed of light, when expressed in meters per second, is 299,792,458 meters/second. Don’t see the coincidence? Well this is only 0.07% from 300,000,000 meters per second. I use this approximate value almost daily in my Engineering work. Myself and my peers all use 3.0 x 108 meters per second for hand calculations. It is a nice round number and easy to remember. For instance, let’s compute the wavelength of an electromagnetic wave of 3 GHz (3.0 x 109 Hz) in free space. It’s 99.93 mm if one  uses the exact value for the speed of light. When the 3.0 x 108 m/s approximation is used it is exactly 100.00 mm. The error is 69.17 μm! Yes, micrometers!

When used for everyday engineering computations, there is no need to remember the exact value of the speed of light, as the approximate one is so close, there is no reason to bother. This is an amazing coincidence.

Another coincidence that I find quite interesting (and will discuss in a future blog) is that in Boulder, Colorado one cubic meter of air has a mass of almost exactly 1 kilogram. On the coasts it is about 1.2 Kg.

Here are some other metric coincidences:

The width of a human male hand is about 100 mm.

The length of a stretched human pace is about one meter (1 m)

The distance from the Earth to the Sun is almost exactly 150 Gigameters (150 Gm)*

The volume of the Earth is very close to one Yottaliter (1 YL).

The distance across the Milky Way Galaxy is about one Zettameter (1 Zm).

The diameter of the local group of galaxies is about one hundred Zettameters (100 Zm)

And one engineered non-concidence is that the circumference of the Earth is almost exactly 40 Megameters (40 Mm)

I find these metric coincidences far more interesting than the Fourth of July rattlesnake coincidence. The meter and its divisions seem to me much more attuned to the natural world than the contrived, inconsistent and almost uncountable units of the old remnants of the non-system of Olde English and Imperial, or the even more laughable American designation of same as: “standard.”

It is time for all of us in the United States to give up this unnatural, non-system of measurement for the one that nature clearly intended—the meter and the metric system.

* In other words the “astronomical unit” has a nice integer value in the metric system

Measure for Measure

By The Metric Maven

I have a rather large collection of books. One day I happened to notice a book that was in a plastic sealed bag among the rest, which had clearly been neglected for a considerable period of time. When I investigated, I found a book from 1795 inside. My best guess is that I inherited it from a brilliant family friend known as Skeez. The year 1795 immediately caught my attention as it was in that year the first draft of the metric system was made legal in France. The book is written in English. Unfortunately the title page is but a fragment. Thankfully the fragment has 1795 for a publication date. The book is entitled Secrets Concerning Arts and Trades. It is a sort of combination chemistry and cook book. It has formulas for coffee substitute along with one on how to gild the page edges of books. There is a PDF version at The Internet Archive.

The contents of the book are at the beginning as one would expect. Not unlike books today, it has the contents page numbers paginated with roman numerals. Below is page 13 (xiii) which has the contents of Chapter 6 (VI) entitled Relative to the Art of Gilding. The left column has article numbers which run from 1-20, but beyond that is 1-9 seemingly with the 20 assumed. However at 30 it reverts to double digits from 31-35. This may be done as the numbers cross over to the next page. The article names follow each article number and on the right are the page numbers. When an article is on the same page which has been previously cited, it has ib. below which I suspect is ibid, but does not use the abbreviation id.

Article 33 is of interest, which is A water to gild iron with. When we turn to page 129 we see that article 33 is designated XXXII. Thirty two? The article numbers in the contents are in Arabic numerals, but when you look up the article on its respective page, it is designated with roman numerals. The subsections go back to Arabic. When I first looked through this book I thought that the letter f is also used for s. It appeared that the word glass is spelled glafs.

My friend Sven set me straight that they are not f’s but are actually a version of an s called a long s which was used in old texts. The long s was removed from use in the US and Britain from about 1795 to 1810 according to Wikipedia. Sven pointed out that the long s and short s are used by Sherlock Holmes in The Hound of the Baskervilles to date a manuscript:

Holmes stretched out his hand for the manuscript and flattened it upon his knee. “You will observe, Watson, the alternative use of the long s and the short. It is one of several indications which enabled me to fix the date.”

The formula given for gilding of iron in the book is reproduced below:

In modern usage with long s replaced with s we read:

XXXII. A water to gild iron with.

1. Put in a glass bottle, with a pint of river-water, one ounce of white copperas, and as much of white-alum; two drachms of verdigrise and the same quantity of common salt. Boil all together to the reduction of one half. Then stop the bottle well for fear the contents should lose their strength.

2. To gild the iron with it, make it red hot in the fire, and plunge it in this liquor.

We can see how far these measures and methods are from our modern notions, when one is directed to use river water to produce a chemical mixture. The bottle is designated as glass which is what chemists tend to use currently. The pint in 1795 may well have depended on location, but probably the pint as derived from a Winchester gallon. The ounce?–well that’s less sure. Is it volume or weight? White copperas is said to be iron(II) sulfate, and white-alum?—well, that’s less certain. It’s probably potassium alum or hydrated potassium aluminum sulfate.

The word drachm is an alternative British spelling of dram. The dram was originally both a coin and a weight in ancient Greece. The avoirdupois grouping of measures defines it as a mass. It is equal to 1/256 pound = 1/16 ounce or approximately 1.772 grams. Unfortunately there is an alternative dram. It was defined in a grouping of weights and measures known as the apothecaries’ system which uses the troy pound. That dram is equal to approximately 3.888 grams. So which damn dram is it? I have no idea. Nowhere in the book, that I can find, does it indicate what types of pounds, ounces or drams are used. Two drams of of verdigrise? Well this could be about 3.5 grams or 7.8 grams depending on which type of dram is used.

And what is verdigrise? Well, with the help of the internet one can find the book A Complete History of Drugs published which was published in 1748. The title states it is written in French, but what I have is in English. The book distinguishes between natural verdigrise and common verdigrise. One is found in copper mines and the other is created using “Plates of red Copper, and the Skins of Grapes, after pressing, soaked in good wine put together in a large earthen Pot.” A green “rust” will appear which is scraped off. The authors claim that other authorities assert that one should use vinegar, but state this is untrue. “….the greatest Part of the Verdifrise used in France and other Countries is made, and it is a Commodity very difficult to make and hit right.” There follows a considerable discussion of other claims of manufacture and how easy it is to screw-up making a batch. Thankfully chemistry did not continue in this manner, and today it is called copper carbonate (copper (II) carbonate). The green patina on old copper roofs is verdigrise. Today it is spelled without the e as verdigris. We can be rather certain that common salt is sodium chloride, or table salt.

Well, all that was just to figure out what step 1 was. Step two is easier, but still has a bit of uncertainty as one would not measure a temperature, but by proxy use one’s eyes to judge when the iron is red hot. This is about 700 Celsius.

When I paged though this book, It seemed rather clear to me why scientists in 1795 were very much interested in creating a single measurement system for all to use. I often see blog comments which state “metric is only for scientists” and not for “everyday people.” This is a rather rarefied statement and the most blood-red of red herrings. The name of this 1795 book is SECRETS concerning ARTS and TRADES. It has descriptions of how one can create various types of varnish, pigments for painting, transparent colors for painting, dyes for gloves and skins, colors for painting glass, sealing wax, colors for crayons, dyes for woods and bones. In this book there are explanations of how to cast bronze, along with wine recipes, vinegar recipes, and how to make liquors and oils. The final chapter is entitled Of the Art of taking out Spots and Stains which is still a preoccupation of our modern era. This knowledge was essential for ordinary people to make their way in the world as tradesmen. In our current world, it would be an extraordinary person who is not engaged with the use of measurement on a daily basis. Our entire modern world is based on technology and measurement, and the measurement system of choice is the metric system. If the available draft metric system had been used in 1795 to write this book, the formula for gilding might have been written as:

XXXII. A water to gild iron with.

1. Put in a glass bottle, with 500 mL of river-water, 28 grams of white copperas, and 28 grams of white-alum; 3 grams of verdigrise and the same quantity of common salt. Boil all together to the reduction of one half (250 mL). Then stop the bottle well for fear the contents should lose their strength.

2. To gild the iron with it, make it red hot in the fire (700 C), and plunge it in this liquor.

Had I read this version of the formula in this 1795 book, only the names of the chemicals would have been uncertain, but not the quantities. Even if all the existing metric standards were destroyed, and industrial civilization ceased to exist. The possession of a single metric ruler would allow me to mark off 100 mm, construct a cube from it (which is a liter), fill it with water (which is a kilogram), and have very accurate standards with which to work, and recreate the formula.

Alternatively, only given the original 1795  formula, and sans modern standards, I could find 7000 grains of barleycorn and use it to re-create an avoirdupois pound; but it would not be nearly as accurate as my new metric standards. It would also be uncertain if I had chosen the correct pound. Perhaps it should be 5760 grains for a troy pound instead? This choice would determine which ounce I should use in the original formula. Remember 16 ounces in an avoirdupois pound and 12 ounces in a troy. This could be the difference between the formula working or not.

The metric system was created for “the common person” but is also excellent for engineering and science, and is continuously evolving. The US needs to stop embracing weights and measures from our pre-technological past, and use the best measurement system available in the 18th, 19th, 20th and 21st centuries. Hopefully before the 22nd arrives.