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.

The Metric Mess is Hard Wired in The US

Skeez

By The Metric Maven

Bulldog Edition

Skeez was a person who seemed to be born interesting. He obtained his nickname from a character called Skeezix in the comic strip Gasoline Alley. The comic strip itself is unusual in that Skeezix arrives as a baby on a doorstep and ages as time goes on. Skeez spent much time at his cottage on the shore of a nearby lake. One day I noticed a new bust among his eclectic collection of objects; it was Charles Dickens. Skeez then told me that Dickens had a story about an innkeeper who was so cheap he counted the number of beans he put into his soup, and that’s where the term “bean counter” arose. He was as close to a polymath as I have ever known. When he passed away I ended up with small gargoyles that he had brought back from France during World War II. I have an African shield with a weapon which was used to kill tigers, as well as other books and notes he left behind.

Recently I ran across a an RCA Radiotron Reference Book from 1940 which Skeez had owned. Inside, it contains a small snapshot of how the metric system was viewed by electrical engineers in 1940. It appears that US engineers saw the metric system as a simple drop-in substitute for Olde English measures. For instance, under pressure they equate pounds per square inch to Kilograms per square centimeter. No pascals. The equivalence of kilograms (mass) with pounds (force) is a strange misunderstanding in a reference like this—unless they meant Kilogram-force. It is clear that again Americans see the centimeter as a pseudo-inch and just substitute away without any measurement introspection. I’ve not found a millimeter mentioned in this reference.

It also has a list of miscellaneous conversions that have a couple of interesting aspects. First I had no idea there was a unit of metric horsepower. Apparently notion of horsepower was still considered so important in 1940 that a metric version needed to be defined. Apparently metric horses have less strength than Olde English horses. The definition does not seem to even involve a horse:

DIN 66036 defines one metric horsepower as the power to raise a mass of 75 kilograms against the earth’s gravitational force over a distance of one metre in one second;[13]

The other odd aspect is that meters show up with an er ending, but litre is spelled with re. I’ve often wondered when it was decided, and by whom that in the US we would use er rather than re. Here the situation is mixed.

What really caught my attention, and is the actual subject of this essay, are the tables on wire.  American copper wire is designated in American Wire Gauge (AWG). I have made my view known concerning the vacuous non-term gauge in a previous essay. We note that along the left column is the AWG number. AWG was first used as a designation in 1857. The diameter of the wire is then given using the informal feral unit known as the mil. A mil is a slang term for one-thousandth of an inch—at least in the US. In metric countries it’s a slang term for a millimeter as I understand it. As the gauge number increases, the diameter decreases.

There is also a column to the right of the diameter of the wire in mils, which is the area in circular mils. Let’s take an easy example, say AWG 10, which is a solid wire with  a diameter of 101.9 mils. Now we know the area of a circle is π multiplied by the radius squared.  The answer to the computation is 8155 square mils. But wait–the value in the area column is actually 10 380 circular mils. Well, that’s because apparently our engineering founding fathers, in their infinite wisdom, decided that dividing the area up into the number of circular areas of one mil was the best way to do it. To get circular mils you just square the wire diameter in mils. This produces a value that is not directly usable for any common engineering calculations. The resistance of a solid wire is proportional to the cross-sectional area, and circular mils are essentially a gauge number for area and not a defined area. We have inherited this strange way of determining the area of solid copper wire without questioning its sanity. It also illustrates once again that our Olde English set of measurements has nothing in common with a system. To make matters worse, Wikipedia decided to use the term kcmil for kilo-circular-mil in their wire table. I wish metric prefixes would only be used with metric units, and not feral ones, or medieval ones.

Another page in the RCA Radiotron Reference Book has the number of winding turns which make up a linear inch. For example, the Brown and Sharpe (i.e. AWG) Gauge Number is given on the left. We then see that for enamel coated wire one needs 7.6 turns of AWG 8 wire to have a coil which is one inch in length. This data is useful for computing how long an inductor might be for an electrical engineer.

If one were rationally using the metric system, one could easily compute any of these values from a table which gives the wire diameter in millimeters and the area in millimeters squared. If the wire manufactures were to use preferred numbers with metric diameters, then it would simplify matters further. Their would be no more indirect designation of sizes with meaningless gauge numbers. The values would be directly understandable in millimeters. Let’s suppose we have a wire of 1.25 mm diameter, we would know immediately that ten turns is 12.5 mm. We could use AWG 16 which after we consult the table is seen to have a diameter of 50.8 mils. We then know that ten turns is 500.8 mils, divide by 1000 to get the value in inches or 0.5008 inches. Alternatively, we could have started with a direct metric designation of 1.291 mm and ten turns is immediately seen to be 12.91 mm. Starting with the metric diameter, one knows this is the width of a single turn. Using this, one can quickly evaluate 1/1.291 mm on a calculator which is 0.775 turns per millimeter. To get 10 millimeters it would take 7.75 turns. start with a metric wire diameter and one can quickly compute anything one needs–using common mathematics.

Incidentally the gauge designations for copper wire are not standard across types of wire, so one can’t be certain what diameter other wires might be when  given a gauge number. Clearly,  if the diameter of a wire in milimeters is given, or another appropriate metric length (e.g. micrometers), this allows one to immediately compute any appropriate parameter. Here is an illustration from a vendor who sells wire in Australia:

The wire industry in the US has been using this kludged up system since 1857 and has done nothing to introduce reform. This clearly shows to me that one needs to have a government mandate, like that implemented by Australia, which mandates metric. The voluntary part for industry is how they will introduce metric. If they have any sense they would take the opportunity to reform their industry with preferred numbers, or in some other rational manner. Standard DIN Sizes using ISO6722 in terms of mm² look like a good idea to me. But how they would implement the change would would be up to them—and in ‘merica they just might use “soft” metric and preserve familiarity over simplicity along with 19th century measurement practice. Until then, this mess is hard wired in the US.