Here we go again! I promised angles and we’ll get angles, but I found some really fun stuff about length I just can’t resist sharing. If you have read any of my other articles you might now realize I like to measure items. Last month we went into some history on units and this month is no different. I promise we will get into some better stuff this time though. I’d like to talk a little about Imperial units and Metric units and where they came from, kind of like the birds and bees of measurement. Don’t blush!
“How far?”: Many Names for the Same Thing
Imperial units, mostly used by Americans and the Brits, are the units you’re likely most familiar with. Miles, yards, feet, and inches make up the majority of our length measurement units. We also have rods, perches, furlongs, links, and a few other ones we don’t really use any more. We do have fathoms, leagues, and knots that have been adopted and are still the standards around the world.
Mile, yard, foot, and inch, much like degrees in a circle, have their origins in a less than impressive foundation. It all started when people started bartering and trading for goods instead of bashing each other in the head with a big stick and running off with their stuff. There had to be a way of quantifying what you were trading.
“How far?”: Names from Necessity
Imagine you’re down at the market. You bring your freshly ripened squash and you’re looking for some silk fabric for a special someone. You say to the man with silk, “Hey, I have a squash as long as my foot I’d like to trade for 20 paces of silk.” The other fella says, “I’d be happy to trade, my mother really likes squash. If you bring me another squash I’d be happy to do this trade again.” So Mr. Squash-man runs back home and finds another ripe squash and brings it to Mr. Silk-Man. He says, “Here’s another squash now gimme some more silk so my wife will, uh … be happy.” Mr. Silk-Man says, “I would love to but this squash is only as long as ½ of my foot. I will trade you 10 paces of silk.” Although disappointed Mr. Squash-Man cannot dispute this fact and says, “Ok.” Standards and measures are born. The next day Mr. Squash-Man brings in a squash that it only ½ a foot long but is twice as fat. He is offered 10 paces of silk. What do you think happens now? Either the old clubs come out or the scale is born!
The foot truly was a person’s foot. Generally not a bare foot but a shoed foot from all accounts. The yard has a quite foggy background though. It was considered a person’s stride (a long stride if you’re buying and shorter stride if you’re selling, of course), a person’s girth or the length of an outstretched arm. King Henry I even attempted to say it was the distance from his nose to the tip of his thumb on an outstretched arm. The reality is that it was probably used for both the arm and the stride depending on the length that was being measured.
“How far?”: Names from the Logic of the Situation
Attempts were made throughout history in trying to standardize weights and measures. The Greeks, Romans, Henry I, and Charlemagne attempted to standardize measurement. It goes on even today.
The Yard / Meter: Today the yard is considered 0.9144 meters. The meter was originally considered 1/10 millionth the distance from the equator to the North Pole as defined in 1795. This is quite a story in itself as they actually physically surveyed this. It took six years and one of the primary surveyors died and in the end they found out it was wrong. Now the standard is the path travelled by light in a vacuum in 1⁄299,792,458 of a second and it was defined in 1983.
The Mile: On to the mile! The mile was considered the distance a Roman army could march in 1,000 strides. One stride was considered the same foot striking the ground twice. As the mile had a stride as its basis, and it’s a much longer distance, it has had many dimensions depending on how tall the people of the area were. Here is just a sample:
- The modern mile defined as 8 furlongs (1609 meters), and a longer mile similar to the French mille (1949 meters), plus the Scottish mile (1814 meters) and the Irish mile (2048 meters).
As far as I can tell, the definitive definition of the mile is as follows:
- The statute mile was so-named because it was defined by an English Act of Parliament in 1593, during the reign of Queen Elizabeth I. The statute states: “A Mile shall contain eight Furlongs, every Furlong forty Poles, and every Pole fifteen Foot and a half.” It was thus 1760 yards (5280 feet, about 1609 meters). For surveying, the statute mile is divided into eight furlongs; each furlong into ten chains; each chain into four rods (also known as poles or perches); and each rod into 25 links. This makes the rod equal to 5½ yards or 16½ feet in both Imperial and US usage.
“How far?”: The Mile’s Linguistic Impact
Another tribute to Wikipedia is how the mile is used in some modern sayings
- A country mile is used colloquially to denote a very long distance.
- “A miss is as good as a mile” (failure by a narrow margin is no better than any other failure)
- “Give him an inch and he’ll take a mile” – (the person in question will become greedy if shown generosity)
- “Missed by a mile” (missed by a wide margin)
- “Talk a mile a minute” (speak at a rapid rate)
- “To go the extra mile” (to put in extra effort)
- “Miles away” (lost in thought, or daydreaming)
- “Milestone” (an event indicating significant progress)
The Inch, Furlongs, and More
Now for the lowly inch. It was defined as the distance between the two middle knuckles on the first finger. Other measurements still used are furlongs, they are still used exclusively in horse racing and equal 220 yards and rods that are occasionally used in land surveying. And how about that meter! Everything now is based on the meter. Even if you measure an inch it’s traceable to the meter. It was introduced in 1795 in France to simplify measurement. It was considered the measurement “for all people for all time” by philosopher Condorcet. It has continued to evolve ever since. Degrees were to be changed by Jean-Charles de Bordato into Grades which would equal 1/100 of a circle which would in turn have 100 minutes/grade and 100 sec /minute. These units can sometimes be found on some scientific calculators today. Decimal time was proposed in 1793 with 10 hours days, 100 minute hours, and 100 second minutes. This equaled 0.84 seconds. A 10 day work week and a 12 month year. France did do this but Napoleon gave it the boot in 1806 because everyone was, well, not pleased with a 10 day week.
The Meter (SI)
In regards to the International System of Units measured meter:
- In 1960, the CGPM launched the International System of Units (in French the Système international d’unités or SI) which had six base units, the meter, kilogram, second, ampere, degree kelvin (subsequently renamed the “kelvin”) and candela, and 22 derived units.
Some of the readers in the age of perfection (50’s) will remember the US had a mandate that we would switch to all metric within 10 years, a committee was formed. The year was 1975 and it was considered voluntary but it never caught on unless you got involved in the sciences. By 1982 under President Regan it was disbanded.
Even now there are many independent standards organizations. The US has NIST, England has NPL, and France has SI. In our machine measurement world there are even more organizations such as ASME, VDI, JIS, and ISO. Luckily they are starting to work together to establish coordinated standards. Actually in our world this is HUGE!
I can’t stop, bear with me a little longer, I have to talk about knots! As I mentioned earlier there were some imperial units, like the Sumerians’ degree, that just could not be extinguished. One would be the knot and the other would be the fathom. These are nautical terms and since the rest of the scientific world was on land contemplating terrestrial things, the mariners were bobbing about the oceans talking in another language, as they do today. How many of you know a sheet is a rope used to control a sail?
Our sailors were quite enthusiastic to embrace new technology, as it might keep them off the rocks, but they were not quite so enthusiastic to use new terminology. The knot is a reference to speed. As has become quite clear its roots are contrived from the obviously practical. To check the speed of a vessel at sea they had no instruments. What they would do is take a long piece of rope with knots tied every 47 feet and 3 inches and throw it over board. Why 47-3? I have no idea. When it hit the water another guy (no women sailors in the old days) would turn a sand 30 second hour glass and everyone would count the knots as they passed by. When it was all over a crusty, un-bathed, deck hand would call out, “Aye Captain, we be makin ‘bout 7 knots!” Then he would spit out another tooth from the scurvy he acquired from the lack of vitamin C.
Just another tidbit of info on dead reckoning, as it was called and still is. Sailors of old knew their position very well in latitude (north-south) by the stars and sun with simple charts; but longitude (east-west) was whole different situation. No GPS in the old days. I gotta stop! There is such a good story about how they solved the longitude problems I could write another article on it. It’s amazing. It was the largest monetary prize ever given for an invention: The Longitude Act of 1714:
- £10,000 for a method that could determine longitude within 60 nautical miles (111 km)
- £15,000 for a method that could determine longitude within 40 nautical miles (74 km)
- £20,000 for a method that could determine longitude within 30 nautical miles (56 km).
Back to the knot. A knot is a knot is a knot, and not a knot per hour, and this is not funny. On land we measure in statue miles; at sea we measure nautical miles. A statue mile is 5380 feet; a nautical mile is 6080 feet. Why the difference? As previously discussed a mile or statue mile is 1000 Roman legion paces, a nautical mile is one minute of angle of the earth’s surface at a distance of 40,000 km. Polar circumference and equatorial circumference is not the same. So a knot is NOT a naut per hour, but a knot has been redefined to a naut per hour = a knot! Knots are used in nautical and aeronautical industries as a measure of speed, but it is incorrect to say a knot per hour.
Enough about knots, knots in a rope that is. Well not, or knot quite. Let’s talk about how deep is the water. When we were young and smart we didn’t venture out further then we could touch the bottom or at least see the bottom. Then we got brave, or silly, and went out further. If you were like me you would take a stick to see how deep it was. Pretty soon the stick didn’t touch the bottom. Now we invent the fathom. We find a big rock and tie a long rope to it. Since King Henry says a yard is an arm’s length, we try that but it takes up too much rope so we double it to 2 yards or 6 feet and call it a fathom. Off we go into the world and sail into a bay no one has ever charted so we need to see how deep it is. We have the deckhands throw over the “sounding line” and count the knots. He’d report back, “Aye Captain, The Sea, she’s so deep she’s unfathomable!” Hence our common saying, “unfathomable,” meaning beyond fathoming, or in modern usage, as beyond comprehension. To this day nautical charts are labeled as “soundings” marked in fathoms or in feet.
Coming Next: Angles
Well I’ve done it again. We didn’t get around to angles for another month. Next month I promise to talk about angles! I hope. Till then, “Keep makin’ chips, and accurate chips.”