Pushing The Envelope

Guest Post

By James W. Way

Besides our slow adoption of the metric system, the United States differs from the rest of the industrialized world in another way.  We use US Letter (8½ × 11 inch paper), while the vast majority of other nations use A4, a paper size created in Germany in the 1920’s.  Converting to inches, the dimensions for A4 are approximately 8¼ × 1111/16 (US Letter is slightly wider, but not as tall).  A4 is officially defined as 210 mm × 297 mm; after converting to millimeters, US Letter is 216 mm × 279 mm.

The U. S. has a national standard for metric paper, ANSI/ASME Y14.1M, which gives identical dimensions for the A sizes, but does not go smaller than A4.  There exists an A5 size, common for notepads, with A6 used for postcards (as the numbers get larger the sizes become smaller).  A4 is part of a whole series of A and B paper sizes defined by ISO 216 (the International Organization for Standardization).  I will summarize the advantages of these metric sizes, even though the Metric Maven has written on this topic before (see The Metric Paper Tiger from 2014-02-10).

Two sheets of 8½ × 11 inch paper equal one 11 × 17.  Enlarging an image from the former onto the latter, however, results in different margins.

Combining two sheets of A4 side by side equals one A3.  Also, the margins will be correct when enlarging an image from A4 onto A3.  Why is this so?  Because metric sizes use the only height to width ratio where this will work:  H = W × √2 (height = width × the square root of two, or 1.4142).

After the French Revolution, some sizes with this aspect ratio were created, but never became widely known.  In 1911, an institute called Die Brücke (The Bridge) was founded in Munich, which attempted to standardize paper formats.  Sixteen sizes were created, for everything from postage stamps to books:  size I – 1 cm × 1.41 cm, size II – 1.41 cm × 2 cm, etc.

Die Brücke only lasted a few years before going bankrupt.  After World War I, a former associate named Dr. Walter Porstmann improved on the original concept, numbering the sizes in the opposite direction.  A0 is a sheet with an area of one square meter (but a 1: √2 aspect ratio).  Dividing this in half results in two A1 sheets, and so on.  Thus, A4 is one sixteenth of a square meter; if the listed weight on a ream of paper is 80 g/m2, one A4 sheet is 5 g.

In 1922, these sizes became a DIN standard (Deutsches Institut für Normung, or the German Institute for Standardization) and gradually spread throughout the world.

An unfolded A4 sheet fits in a corresponding C4 envelope.  The B sizes are mostly used for books, and don’t have their own envelopes, as shown below.



Another resource for information on ISO paper and envelopes is Markus Kuhn’s excellent webpage, International Standard Paper Sizes.  He writes:

The ISO paper sizes are based on the metric system.  The square-root-of-two ratio does not permit both the height and width of the pages to be nicely rounded metric lengths.

This can be seen in the figure above.  With A and B paper, at least one side is a nice metric length, but this is not the case with C envelopes.

Envelope Name                Common Use                     Dimensions (mm)

C4 A4 unfolded 229 × 324
C5 A4 folded in half 162 × 229
C6 A5 folded in half 114 × 162

However, in a strange coincidence, the three most common C sizes do convert nicely to inches:

Name      Inches                          Exact Conversion            Rounded to mm

C4 9 × 12 ¾ 228.6 × 323.85 229 × 324
C5 6 ⅜ × 9 161.925 × 228.6 162 × 229
C6 4 ½ × 6 ⅜ 114.3 × 161.925 114 × 162

A manufacturer would be justified in labeling these by their correct metric dimensions even if they used inches in-house.  The US already has 9 × 12 and 6 × 9 envelopes; making C4 and C5 would not pose much of a problem.

Of course, a letter is most commonly folded in thirds and sent in a business envelope.  How big is an A4 sheet when folded in exact thirds?  The height is 297 mm, so 297 ÷ 3 = 99, with a width of 210 mm.

The most common metric commercial envelope is DL (110 mm × 220 mm); there is 11 mm of room above if folded in perfect thirds.  DL originally stood for DIN Lang (DIN length); it is separate from the A, B, and C sizes.

Now, how much extra room is there for US Letter in a #10 envelope?  First, let’s divide 11 inches by 3 and …if you’re a teacher, watch your students fumble around with this one!  Of course, things become much easier when inches are converted to millimeters.

US Letter is 279 mm high, so 279 ÷ 3 = 93.  The height of #10 is 4⅛ inches:  4.125 × 25.4 = 104.775 mm.  After rounding this up:  105 – 93 = 12 mm.

The two sizes leave a similar amount of extra space relative to the size of paper that is being used.

When sending a business letter, however, most people do not fold it in exact thirds.  There will be some space between the top (folded down) edge of the letter and the bottom crease.  If you have difficulty estimating this by sight, the following method is a good option.

Put the bottom of an A4 letter against the inside flap of a DL envelope, as shown in the photo below.

The section not resting on the envelope is 187 mm high (297 – 110 = 187).  Fold the top third of the page (at the bottom in the photo) up to the lower edge of the envelope.  To calculate the size of this fold:  187 ÷ 2 = 93.5 mm.

What is the height of the remaining two thirds of the paper when we rotate it right side up?  297 – 93.5 = 203.5 mm.  Now, fold the bottom of the page up to a few millimeters below the first fold, and the letter will fit nicely.  A similar method will work for US Letter inside #10.

DL leaves only 5 mm of room on either side for an A4 sheet – quite narrow for automatic insertion.  Since US Letter is 216 mm wide, DL (at 220 mm) cannot be used as an envelope for both.

ISO 269 (Correspondence envelopes – Designation and sizes) contains the following note about Universal Postal Union regulations:

When processing size A4 documents in inserting machines, the size of DL envelopes may be insufficient.  To satisfy the needs for automatic insertion, an envelope size larger than DL may be used as long as the size can be considered standardized according to UPU regulations.  (Upper limit is at present 120 mm × 235 mm.)

In Australia, the upper limit above corresponds exactly to the DLX size, allowing DL to fit inside as a reply envelope.  The “X” probably stands for maximum, but also brings to mind “XL” as an abbreviation for extra-large, (even though the two letters are reversed).

Between the two is an intermediate DLE size (114 mm × 225 mm) that also fits inside DLX, though the smaller DL is used with automatic machines.  DLE converts to inches quite easily.

Inches                                 Exact Conversion               Rounded to mm

4 ½ × 8 ⅞ 114.3 × 225.425 114 × 225

The above dimensions, when compared with American envelopes, are equal to the short side of #11 and the long side of #9.  A DLE envelope can be used for both US Letter and A4, being slightly wider than DL.

Yes, these conversion tables conflict with Pat Naughtin’s philosophy of “don’t duel with dual.”  But it helps U.S. manufacturers to know that some international sizes have similar dimensions to what they already produce.

Here are some other sizes worth mentioning.

In Germany, C6/5 is popular, using the short side of C6 (114 mm) and the long side of C5 (229 mm).  The U.K. prefers to name this size DL+.  Italians use an envelope 10 mm wider than DL (110 mm × 230 mm).  These are each fine by themselves, but can’t work together as a reply/outer envelope like the three Australian sizes.

Statistics compiled by the Envelope Manufacturers Association (EMA) show that U. S. sales peaked in 2005.  In our electronic age, this market has declined, with total sales now similar to the mid 1980’s.  Here are some places to buy in the U. S., if you are so inclined.

ISO envelopes are sold by amazon.com, but only the most common sizes:  C4, C5, C6, DL, as well as a variety of metric paper.

Another excellent resource is Empire Imports.  While they do not sell envelopes, they specialize in metric paper and related products, stocking items such as hole punches, folders, binders, etc.

Finally, some fountain pen dealers stock a limited number of metric sizes, since these types of pens work best with high quality European and Japanese stationery.  A good example is The Goulet Pen Company.

These are my personal observations; I have no financial relationship with any of these sellers.

If you would like to support the work of The Metric Maven, please visit his Patreon Page.

The Mass of Money

By The Metric Maven

The metric system has always had an odd relationship with money it appears. I’ve had a confused relationship with trying to understand what money actually is as a noun. I’ve read a lot of books that tried their best to provide a definition. I found them all wanting. Finally after a couple of decades I finally arrived at a definition when I was watching Humphrey Bogart in The Maltese Falcon. Money is “the stuff that dreams are made of.” There seem to be a lot of dreams in that bird. The prop used in the movie sold for over 4 million dollars recently.

Below is a page that defines metric quantities, including the US dollar:

We see that money is included in the grouping, and provides a relationship between said dreams. I still recall my grandfather calling a twenty dollar denomination a double eagle. He also called a quarter two bits, which comes from the original Spanish dollar. My grandfather called a ten dollar bill a “ten spot”; it was also known as a “sawbuck.” The mill is the origin of the mill-levy.  One hundred dollars has been called a yard.

I decided that money is a concept that is essentially an attempt to put a number on emotional feelings about objects and services, which makes it susceptible to the vicissitudes of the human experience. I could not see writing an essay about money and the metric system at all. A longtime email interlocutor, with whom I shared some of the information to follow, enthusiastically encouraged me to write something.

Recently, I began to read Adam Smith’s The Wealth of Nations. I was a bit surprised when I read Adam Smith’s view of how money originated:

…we are told by Pliny…that till the times of Servius Tullis [575-537 BC], the Romans had no coined money, but made use of unstamped bars of copper, to purchase whatever they had occasion for. These rude bars, therefore, performed at this time the function of money.

The use of metals in this rude state was attended with two very considerable inconveniences; first, with the trouble of weighing, and secondly, with that of assaying them. In the precious metals, where a small difference in the quantity makes a great difference in the value, even the business of weighing, with proper exactness, requires at least very accurate weights and scales. The weighing of gold, in particular, is an operation of some nicety. In the coarser metals, indeed, where a small error would be of little consequence, less accuracy would, no doubt, be necessary. Yet we should find it excessively troublesome if every time a poor man had occasion either to buy or sell a farthing’s worth of goods, he was obliged to weigh the farthing. The operation of assaying is still more difficult, still more tedious, and unless a part of the metal is fairly melted in the crucible, with proper dissolvents, any conclusion that can be drawn from it is extremely uncertain. Before the institution of coined money, however, unless they went through this tedious and difficult operation, people must always have been liable to the grossest frauds and impositions; and instead of a pound weight of pure silver, or pure copper, might receive in exchange for their goods, an adulterated composition of the coarsest and cheapest materials, which had, however, in their outward appearance, been made to resemble those metals. To prevent such abuses, to facilitate exchanges, and thereby to encourage all sorts of industry and commerce, it has been found necessary, in all countries that have made any considerable advances toward improvement, to affix a public stamp upon certain quantities of such particular metals, as were in those countries commonly made use of to purchase goods. Hence the origin of coined money, and of those public offices called mints; institutions exactly of the same nature with those of aulnagers and stamp-masters of woolen and linen cloth. All of them are equally meant to ascertain, by means of
public stamp, the quantity and uniform goodness of those different commodities when brought to market.

Smith goes on to explain that the early metal pieces were stamped only on one side. This only guarantees the purity, but not the weight of the metal. “They are said to be the current money of the merchant, and are yet received by weight, and not by tale, in the same manner as ingots of gold and bars of silver are at present.” The word tale probably meant the amount of weight stamped on the pieces. This seems clear when he goes on:

The inconveniency and difficulty of weighing those metals with exactness, gave occasion to the institution of coins, of which the stamp, covering both sides of the piece, and sometimes the edges too, was supposed to ascertain not only the fineness, but the weight of the metal. Such coins, therefore were received by tale, as as present, without the trouble of weighing.

The public had confidence that the metal was pure and the weight stamped on the coin was accurate and could exchange it for goods and services without concern.

I found what Adam Smith said next of great interest:

The denominations of those coins seem originally to have expressed the weight or quantity of metal contained in them. In the time of Servius Tullius, who first coined money at Rome, the Roman as or pondo contained a Roman pound of good copper. It was divided, in the same manner as our Troyes pound, into twelve ounces, each of which contained a real ounce of good copper. The English pound sterling, in the time of Edward I. contained a pound, Tower weight, of silver of a known fineness. The Tower pound seems to have been something more than a Roman pound and something less than the Troyes pound. …

Smith points out that the Troy weight was used at the “fair of Troyes” in France and the weights and measures used at that market were well known and “esteemed.” This measuring unit has come down to us in the US to this day for determining the weight of precious metals.

I found it very interesting that the value of money was originally in terms of a weight (or because they used scales, the mass) of the known metal in a coin. In other words, the numerical value of worth assigned to a metal was exactly equal to the measurement unit used to define the mass of the volume of metal. If you measure a metal in grams, then it’s financial value is expressed numerically in grams. This implies that mass is identical to  monetary value. This means that a universally accepted standard for mass is of paramount importance to determine the monetary value of a metal. This illustrates why people in the past might have the audacity to include money with defined metric system quantities. The current price of gold is about $41 per gram, but if we used gold directly, we could have US money in terms of grams. We could go with a milligram of gold which would be about 41 cents as our base unit for money, as could the entire world. Rather than use dollars, you could purchase items with 2, 5, and 10 mg coins. The value of the money would now be in milligrams. I think it is probably obvious to my readers, and it was to Adam Smith, that if the use of a value other than an accepted and standardized mass unit was used, nothing would prevent this from occurring:

I believe the avarice and injustice of princes and sovereign states, abusing the confidence of their subjects, have by degrees diminished the real quantity of metal, which had been originally contained in their coins. The Roman as, as in the later ages of the republic, was reduced to the twenty-fourth part of its original value, and, instead of weighing a pound, came to weigh only half an ounce.

…By means of those operations, the princes and sovereign states which performed them were enabled, in appearance, to pay their debts and fulfill their engagements with a smaller quantity of silver than would otherwise have been requisite. It was indeed in appearance only; for their creditors were really defrauded of a part of what was due to them.

When I was a boy, I recall watching a television program for children that explained how money had been invented. It is rational, reasonable, and I suspect apocryphal, and probably wrong. The person explained that when everyone came to the market at a big city from the small surrounding bergs, they would leave the items they wanted to sell, say a pair of oxen, at a place outside of town. The oxen would be kept by the people running this “hat check” for merchandise, and the owner given a slip of paper, a receipt, which listed what they had left for save keeping. When they were at the market they might decide to sell the oxen for a horse and some grain. The person could give his piece of paper to the person, and she would give him a piece of paper for a horse and the grain. The two would not have to go back to the “hat check” area make the transaction in person.

I suspect the truth is probably less local, and more at a governmental level. One of the amazing abstract notions created by humans was the idea that one could survey land, and once this was done, that plot of land would have a paper that allowed for a person to possess it when they had paper with a government certification. The Charter Oak is a tale of how important a certified paper document had become. The problem with physical gold is that it is tied by physics to retain the same mass and atoms, and therefore remain finite in quantity. If you want more gold, then tough luck. Go look in the mountains for ore. But, if you had a piece of paper that represented the gold, you could pass them out rather than issue coins. The new piece of paper can have a denomination that is defined with respect to the physical amount of gold, but not tied to any annoying reality based value like a gram of gold physically in your possession. Of course the values of these different currency denominations could be manipulated, and vary with respect to one another.  One could also control the amount of gold in circulation and manipulate the value of currency that way. This lead to the demand that silver be used as an alternative, which also had its problems. When one has a land deed, one does not expect the legal area defined square meters by the document to change, but that is how quantifying dreams with metal works.

To combat the monetary denomination versus mass of metal problem, some nations would place a quantity of gold or silver on the paper currency, not in terms of grams, but in terms of dollars. When I was a boy, I recall the recall of silver certificates. I still have one in my possession. Everyone was to surrender them to the bank. Most did, but one fellow my father knew went to the bank and demanded physical silver, as it said on the note it was his right to demand. The note states “This certifies that there is on deposit in the treasury of The United States of America Five Dollars in silver payable to the bearer on demand.” See the example below:

Silver Certificate — Wikimedia Commons – click to enlarge

But how much silver in grams is in a dollar? That is not defined on the bill, and so produces an uncertainty for dreams and schemes.

In the 1922 US Metric Hearings, there was a proposal to create a standard-ounce silver dollar divided into dimes, cents, and mills, just like the decimal divisions of the current version. Then they finally decided to get back to using  gold as a universal metallic standard, and try to undo the decoupling of a currency unit, such as dollars, yen, rubles, drachmas and so on, from the mass value of a metal, which is not fungible. A table that does its best to equate currencies was offered at the hearing:

click to enlarge

In the end, it is still a kludge at best, as the closest equivalent mass values in gold are only approximate, and because currency values are political definitions, they cannot be expected to be exactly equivalent. It is suggested that the 23.22 Troy grain dollar be replaced by a 24 grain dollar. I don’t see how this makes sense for international trading, but to someone in 1922 it did. The last line in this documentation is a bit surprising: “Standard gold weights for coins are only second in importance to standard uniform weights and measures.” In the end, did they realize that an accurate measure of the mass of the physical metal was more important than the arbitrarily assigned values put on the coins?—which can be manipulated. I have no idea, but if weights and measures were that important, and the need for accuracy so acute, then why would they not push for the metric system to be adopted?

John Bemelmans Marciano in his book Whatever Happened To The Metric System, seems to assume the reader understands what I just explained, that originally the unit of mass of a metal was equal to its numerical monetary value. He discusses the idea of creating a universal coin on page 137:

Chevalier and those of like mind wanted weight to equal value; ideally, names like “franc” would be redundant, and coins would simply be stamped ONE GRAM GOLD.

Few thought such a coin possible.

Marciano argues that “pragmatists” tried to equate and consolidate currencies of and in different countries. The same attempt to use the value that dreams are made of, to equate grams of gold, like that later proposed in 1922 with Troy grains as detailed above. One problem was that other countries used silver, and the US effectively was “bimetallic” using both gold and silver. So how does one equate the value of a dollar in gold and in silver? Perhaps by using atomic  number? It was no less than an attempt to equate dreams and metals. Blowing right by this question JBM argues that:

The first [gold] was only slightly more logical than the second [silver], but one indisputable fact was that gold was a lot more convenient.

A silver dollar was a fair-sized disc of metal—-four times the size of our quarter—whereas a gold dollar was a good bit smaller than our current dime.
If you bought a horse for $180 from someone insisting on payment in coin, you could either lug a ten-plus-pound sack (avoirdupois) of 180 silver dollars
to the stable, or slip into your vest pocket a ten–ounce purse of nine double eagles.”

Then JBM states:

With the war, the Union had suspended payment in specie and gone on the paper greenback, a major reason why some Americans were so anxious for a universal
coin—at the moment they had no real currency at all.

Think about the reality of that statement, when contrasted with the dream values that have been assigned to gold and silver. What is their everyday utility?  Can one eat gold or silver? What makes them “real” as a currency? He goes on:

To have that universal coin be gold was an extra bonus, considering that the United States held vast deposits of it

The simple choice of what metal was used for currency determined the financial value of a country?—-and not its actual creation of goods and services?

The origin of the nickel is discussed, and the fact it was exactly 20 mm (yes, JBM says 2 cm) in diameter and “weighed five grams,” or for those who use and understand the metric system, had a mass of five grams. How is a copper-nickel alloy related back to gold or silver? JBM goes on:

The new five-cent piece has achieved the holy grail of coinage, where value equals weight—a cent for every gram.

And the question is never addressed, but clearly JBM sees this as the imposition of metric dimension and mass on the American public. JBM spends a lot of ink artificially conflating metric system concerns of the late 1860s with the lack of a universal coin. He then argues that the death blow to a universal coin was Germany issuing its own gold-backed currency, the mark.

He finishes the chapter seemingly arguing that currencies are very unified with a somewhat unstated assumption that gold is the unifying factor. He

There was now, indisputably, one standard of value, which meant that exchange rates could be permanently fixed. Traveler’s checks, a concept
just about to find wide use, could be printed with their value in multiple currencies……

JBM has only a couple of pages that even mention the euro, and only see it in the context the dream of a universal currency. What is strange is that  the US dollar has not been on the “gold standard” since the 1970s, and so what is the basis for his idea that international currencies have become interchangeable and fixed? I’m not even sure why JBM addressed the issue of currency, unless it is to show that it is stable and fixed without the metric system?

Today, currencies are moving much closer to my definition of “the stuff that dreams are made of” with cryptocurrencies like Bitcoin, and after the fork, Bitcoin Cash, Ethereum, Ehereum Classic, and numerous others. They are but a set of bits, represented by voltage values and magnetic fields. They are at best made of imagination, and at worst made of nightmares. It is possible to see them as but an information theory representation of “the stuff that dreams are made of.” In the case of Bitcoin, recent estimates indicate the annual electrical energy consumption to maintain its blockchain is 83 Petajoules. This is about the amount of electrical energy used by Ecuador each year.

There have been other attempts at creating currencies outside of governments. In the 1970s a group attempted to create a currency denominated in “barter points” which as I recall did not end well. Money, even when we define it in terms of the mass of a pure metal, it still is nothing but a number tied only to our imagination.

If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page.

I would like to thank Amy Young for her inquiries, and persistently suggesting I write this essay.