What is Normal - Part 6: Weights and Measures

© 2012 Rex Jaeschke. All rights reserved.

I was raised in Australia in the 1950s and '60s, where the Imperial System of units was used. In 1970, I started working in chemistry where everything was metric. Then, in the early 1970's, Australia adopted the Metric System. In 1979, I moved to the US, which has a modified version of the Imperial System. However, I still travel regularly to countries that use the metric system. As a result of these varied experiences, I can easily switch from feet to meters, from miles to kilometers, and from pounds to kilograms.

The Imperial System, or variants thereof, is sometimes referred to as the foot-pounds-second (FPS) system. At times, the metric system was referred to as the centimeter-gram-second (CGS) system. Later, there was the meter-kilogram-second (MKS) system, but that was replaced by the International System of Units (SI). Of course, it is perfectly normal that there are other systems as well, including the tongue-in-check FFF system.

The Imperial System

I well remember being in a group of students marching around the yard in elementary school reciting various weights and measure values, such as the following: 12 inches in a foot, 3 feet in a yard, 1,760 yards in a mile, 5,280 feet in a mile, 63,360 inches in a mile, and so on. [I remember doing likewise with multiplication tables!]

Add to those numbers things like 16 ounces in a pound, 2,240 pounds in a ton, 2 pints in a quart, 4 quarts in a gallon, 640 acres in a square mile, and water freezes at 32 degrees Fahrenheit and boils at 212 degrees F, and you soon see the problem. There is neither rhyme nor reason with respect to the multiplier; you simply have to learn these by rote!

It's right about now that I'm reminded of one of my most often-cited quotes: "Nothing is a complete waste; it can always serve as a bad example!" [Anon]

The Metric System

Compared to the Imperial System the metric system is infinitely simpler to teach, learn, and remember. For a given category of measurement such as length/distance there is a single base name, the meter (for which I'll use the US spelling). The quantity is expressed using one of a small family of optional universal prefixes resulting in things like millimeter, centimeter, and kilometer. Here are the basic prefixes:

Other commonly used prefixes are mega- (megabyte, megahertz, megapixel, megaliter), giga- (gigabyte, gigahertz), tera- (terabyte), micro- (microsecond), and nano- (nanosecond, nanometer). For the complete set click here.

Note that in the world of computer science 1KB (one kilobyte) is often understood to be 2¹⁰ bytes, which is 1,024 bytes, a number slightly more than 1,000.

By the way, a milliliter (ml) is the same thing as a cubic centimeter (cc).

Differences between the US and Imperial Systems

According to Wikipedia, "United States customary units are a system of measurements commonly used in the United States. Many U.S. units are virtually identical to their imperial counterparts, but the U.S. customary system developed from English units used in the British Empire before the system of imperial units was standardized in 1824. Several numerical differences from the imperial system are present."

About 20 years ago, I was visiting friends here in the US when their son and I got talking about what he'd been learning at boy scouts. He told me that a gallon of water weighed 8 pounds, to which I replied that that didn't sound right. As far as I knew, a gallon weighed 10 pounds. It turns out we were both right when you took into account the contexts in which we each had learned our measures, he in the US and me in Australia. At approximately 4.5 liters, an Imperial gallon is about 20% bigger than a US gallon (which is about 3.8 liters). Correspondingly, an Imperial pint is 20 fluid ounces while a US pint is only 16.

Back in the early 1970's, when asked how much I weighed, I replied, "12 stone 8 pounds". However, the US does not use the stone. As a stone is 14 pounds, for Americans, the equivalent weight would be 176 pounds.

The US also has short versions of several weight units. For example, the US uses the (short) ton, which has 2,000 pounds, while the long ton used by Imperial unit folks has 2,240 pounds. The Imperial hundredweight has 112 pounds, whereas a US hundredweight is only 100 pounds. Do not confuse a short or long ton with a metric ton (or tonne).

There have been various attempts to have the US "go metric"; however, none has succeeded on any grand scale. In any event, the fact that the US does not require imports to conform to the US system, combined with the influx of products from countries that do use the metric system means that a mixture of measures exists. For example, one can buy a car with 350 cubic-inch engine or a 5-liter V8.

America's immediate neighbors, Canada and Mexico, use the metric system, and as one gets close to those borders, one sees distance signposts in both miles and kilometers.

Abstract systems

If you cook with recipes, you will be familiar with measures such as cup, teaspoon, and tablespoon. And while these have formal definitions, we tend not to think of them as such. For me, I know that to cook white rice, I simply need put 1 cup of rice in 2 cups of cold water, and boil. (Of course, I could just as easily substitute a drinking glass or a bucket for the cup; the proportions stay the same.)

Some years ago, I stayed with a family in Japan, and I asked if I could cook a Mexican meal for them and their neighbors. They were delighted not only to try Mexican, but also to see a man in the kitchen, something that is apparently quite rare in that country except for chefs in restaurants. (It was a challenge to find all the ingredients to make tacos.) The problem arose when the three women pulled out their notepads and were ready to write copious notes on how to prepare the food. I started cooking the ground beef. "How long do you cook it?" I replied, "Until done!" "At what temperature?", they asked. "Adjust the heat as you like", I replied. Of course, when it came to adding spices, I simply said, "Add sufficient to taste." This so frustrated the onlookers that they put away their notepads; it was clear they needed strict rules to cook, and I almost always "fly by the seat of my pants".

Dealing with Conversions

It is likely that relatively few people will experience a change in their weights and measures systems unless they emigrate or their country adopts the metric system. However, for those of us who travel internationally on a semi-regular basis, we do have to change contexts if we are to understand our local environment. Just how much does gasoline cost in Country X? Seeing a price of 1.73 Euros/liter on a pump gives you no clue as to how many US$/gallon that is, and vice versa. And although the signpost says that its 23 miles to the next exit, just how far is that in kilometers? Another example is tire pressure. In the US/Imperial world, we measure the number of pounds-per-square-inch (psi); however, in the metric world, they use kilopascals. And as for fuel efficiency, the familiar miles-per-gallon (mpg) becomes liters/100 km, which employs a reversed ratio. Fortunately, many cars sold in the US today have speedometers in both US and metric units, so drivers can tell just how much over the speed limit they really are driving when they cross into Canada or Mexico.

From my Aussie experience, I remember my mother having trouble with sugar. Previously, it came in 4-lb (pound) bags, and for a whole host of things she made in bulk—think preserving fruit in jars—she knew how many bags to buy/use. However, when the metric system was adopted, the bags were now 2kg, which at about 4.4lbs is more than just a little bit larger. A major adjustment was needed. Similarly, she needed to convert the degrees C in recipes on printed packaging to her degrees F, as she wasn't about to replace her old oven "just because some fool in government changed the measurement system".

A common thing to buy for lunch was a 1-pint carton of flavored milk; however, the metric equivalent was 600 ml, which is significantly larger. Basically, certain assumptions that had been proven correct for years were no longer true, and some manufacturers took advantage of that by downsizing their product yet keeping the price the same. How would the average consumer tell the difference? [I recall that this kind of thing was widespread when various countries converted to the Euro.]

Length, Distance, and Thickness

Depending on the size of the thing being measured, we use different units, for example: A thou (a US mil) is a thousandth of an inch. Although it's used in various contexts in engineering and manufacturing, I first came across it when checking/setting the gap in an automobile's sparkplug, using a feeler gauge. Metric versions measure in hundredths of a millimeter.

Regarding altitude and ocean depth, we talk in thousands of feet (or meters). Occasionally, we use miles, as in Denver, the mile-high city, and in near-earth space.

When it comes to human hair and cells, we use micron, which is a synonym for micrometer. And as the name implies, nanotechnology is measured in nanometers.

Most of us raised in the British Commonwealth learned that the length of the pitch for the game of cricket is exactly 22 yards long; that is, one chain, and that there are 10 chains in a furlong and 80 chains in a mile. A chain is 100 links or 4 rods (or 4 poles or 4 perches). (The length of horse races is often stated in furlongs.)

The term mile is shorthand for statute mile, and is 5,280 feet (1,609 meters). The latter term is used to distinguish it from the nautical mile, which at 6,076.1 feet (1,852 meters) is longer. A nautical mile is approximately one minute of arc of longitude at the equator. An international treaty defines territorial waters as a 12 nautical-mile strip along a coastal at the average low-tide mark.

The fathom is a non-metric unit equaling 6 feet. It is mostly used in the context of water depth. Initially, it was the distance between an average man's outstretched arms. According to Wikipedia, "It is customary, when burying the dead, to inter the corpse at a fathom's depth, or six feet under. A burial at sea (where the body is weighted to force it to the bottom) requires a minimum of six fathoms of water. This is the origin of the phrase 'to deep six' as meaning to discard, or dispose of."

Another nautical measure is the cable, which is one tenth of a nautical mile.

Many of us know that Jules Verne wrote a popular book called 20,000 Leagues Under the Sea, and that some characters in European fairy tales wore seven-league boots. But just how much is a league? Its three miles. Originally, the term referred to the distance a person or a horse could walk in an hour.

By the way, back in the good old days, the meter was defined as "one-quarter of one ten-millionth of the circumference of the Earth (along the great circle coincident with the meridian of longitude passing through Paris)"; however, nowadays, it's based on the speed of light. [Why can't they just leave things alone?]

Speed

Yes, we all know about vehicle speeds of miles/hour (and kilometers/hour), but what about stuff that goes really fast? How do we measure that? The fastest thing we know of is the speed at which light travels in a vacuum. At 186,282 miles/second (299,792,458 meters/second), that's pretty darned fast. [The second fastest thing I know of was my 8-year-old son when spitting out a slice of dill pickle—which he knew in advance that he didn't like—that I had bet him a dollar he wouldn't eat!]

Now we think of seeing things instantaneously; however, with the earth being approximately 93 million miles from the sun, at the speed of light a sunray takes about 500 seconds (that is, 8 1/3 minutes) to reach us. This distance from the Earth to the sun is one astronomical unit. [By the way, sunlight reflected by the moon takes only about 1.2 seconds to reach Earth.] As such, looking very long distances—such as with a space telescope—we see light that has traveled a very long way and thus gives us a picture of what used to be there. We currently have no way to see what is actually there now! A more earthly example is in communicating voice via a satellite link; there is a short delay. And the time it takes to send a message between Earth and Mars takes about 5–20 minutes depending on those planets' positions.

For those of you who have a lot of time on your hands, there is the light year, which is the distance that light travels in a vacuum in one Julian year (that is, in 365.25 days). That's 6 trillion miles (10 trillion kms). [Of course, if you worked in astrometry, you'd prefer the parsec instead.]

For all of you budding interstellar space travelers, after the sun, our nearest known star is Proxima Centauri, which is about 4.22 light-years away. As that is some 32 trillion miles (42 trillion kms) away, you'll need to get an early start.

Compared to light, sound travels v-e-r-y s-l-o-w-l-y, at a mere 1,126 feet/second (343.2 meters/second). According to Wikipedia, "The speed of an object … divided by the speed of sound … is called the Mach number. Objects moving at speeds greater than Mach 1 are traveling at supersonic speeds." (By my calculation, my subcompact car tops out around 0.08 Mach; don't blink or you'll miss me as I race on by!) One application of this knowledge is in figuring out how far away a storm is. When the lightning flashes, it reaches an observer more or less instantaneously; however, the accompanying thunder takes 5 seconds to travel each mile (3 seconds each km), so each second delay between seeing the lightning and hearing the thunder is 1/5 of a mile (0.32 km).

To all you "Sesame Street" sailors, today is brought to you by the letter arrrr (as pronounced like a pirate), and a knot is one nautical mile (1.85 km) per hour, which is about 15% faster than 1 statute mile/hour. And yes, the name comes from counting the number of knots in a line.

Area

In the metric system, smaller areas—including a house lot—are measured in square meters, while a farm would be measured in hectares, with a hectare being about 2.5 acres. Every so often, I meet a farmer in my area here in rural Northern Virginia. When I ask him how much land he has, he typically replies, "About 75 acres." To which I reply, "That's not a farm! In Australia, my sheep dog had a yard bigger than that!" [The farm on which I was raised had 4,000 acres, and the average size farm in my hometown area these days is 6,000 acres.] Now if you go into the Aussie outback to visit a sheep or cattle station, you're talking property sizes in the hundreds of square miles, and where people commute by light aircraft. There are 640 acres in a square mile.

In Australia during the Imperial days, the floor space of a house was measured in squares where a square was 10x10 feet. An average-size house in my hometown area was 12–13 squares. The 3-storey townhouse I lived in for many years here in the US was 26 squares, and many McMansions in the area I now live are 50+ squares and sit on 5 acres; what a country!

If you are looking to measure teeny, tiny things, check out the unit barn.

Temperature

The two most common temperature scales are Fahrenheit, written as °F, and Celsius (also known as Centigrade), written as °C. Water freezes as 32 °F (0 °C) and boils at 212 °F (100 °C). And just in case you don't know the conversion formulas, here they are:

°F = ((°C × 9) ÷ 5) + 32
°C = ((°F – 32) × 5) ÷ 9

Trivia question: Which temperature is exactly the same number in both °F and °C? Answer: –40. Don't believe me; use the conversion formulas above.

Now it's worth noting that the boiling temperature mentioned above is not universal. This is because it is defined in terms of one standard atmospheric pressure. Specifically, the boiling point of water is lower at lower pressure and higher at higher pressure. For example, go up 1,000 feet (≈300 meters) and the atmospheric pressure decreases by about 4%. So, when cooking in the mile-high city of Denver, Colorado, for example, you'll need to reinterpret some of your recipes.

As you well know, some people have way too much time on their hands, and so the Kelvin scale was born. The starting point for this is absolute zero (0K is −273.15 °C and −459.67 °F), the temperature at which all thermal motion ceases. [For me, I'm certain that 70 °F (21 °C) is already too cold. In any event, in the Australian vernacular, absolute zero is known as Bloody cold or Colder than a witch's tit!] The Kelvin scale simply is the Celsius scale with 273.15 subtracted. Not to be outdone, some scientists not of the metric faith and with idle hands came up with the Rankine scale, which also represents absolute zero, but with a value of 0 °R. This scale simply is the Fahrenheit scale with 459.67 subtracted.

Here are some numbers you might find interesting:

• The normal human body temperature when taken orally is approximately 98 °F (37 °C).
• The hottest temperature ever recorded on earth was 134 °F (56.7 °C) in 1913 in Death Valley, California
• The surface temperature of the sun is about 9,941 °F (5,505 °C), which as Icarus discovered to his own peril, was a little too hot for high flying especially when his feathered wings were held together with wax.
• At an altitude of 34,000 feet (10,460 meters), the temperature outside my plane while flying recently over remote Canada on my way to Japan was –63 °F (–52.8 °C). As a result, I kept my window wound up tight!

Odds and Ends

Here is a pot-pourri of other units:

According to Wikipedia, a span "is the distance measured by a human hand, from the tip of the thumb to the tip of the little finger. In ancient times, a span was considered to be half a cubit." Do you know how long your hand's span is? I find that useful when I'm buying something whose size I'd like to check, yet I don't have a tape measure handy.

If you want to measure the height of your horse, you'd do so in hands, one of which is 4 inches long. When it comes to fractions, this is a rather interesting unit. Specifically, the "decimal" places use a number in base 4 rather than base 10 (decimal). For example, consider a horse 58 inches high, which is 14½ hands. This is written as 14.2 hands, not as 14.5, as you might expect. A horse an inch taller would be 14.3 hands, and one another inch taller would be 15 hands (not 14.4)!

Now that I've moved to a house in the country and I have a potbelly stove, I'm considering buying some firewood. In the US (and Canada), that comes by the cord. A cord of wood occupies a volume of 128 cubic feet (3.62 cubic meters), or a stack about 4x4x8 feet. The metric folks use the stere. In the UK, the term fathom can be used to measure a quantity of wood. Now, I ask you, "Is that normal?"

We've all heard about gemstones having "x-carats", but just what is a carat? It's a unit of weight equal to 0.007055 ounces (200 mg). A carat is subdivided into 100 points.

If you do enough crossword puzzles or play enough Scrabble games, you'll come across the printers' measures em and en. Some of their siblings are pica and point.

If after reading this you still have free time, check out bushel, dram, grain, pennyweight, and scruple, plus avoirdupois weight, troy weight, and apothecaries' weight.

Conclusion

For more information than you probably will ever want to know about units of measure, click here.

In 1972, in the week following Australia's implementation of the metric system, I was at my neighborhood deli. An elderly gentleman ahead of me said that he wanted two kilograms of milk, at which the owner looked over at me and smiled, and served the man two liters. Yes, it was amusing, but at least the customer was trying to get with the program.

During the changeover Down Under, there was a national debate on the pronunciation of the word kilometer, and even the then Prime Minister, Gough Whitlam, got into the debate. Was it ki·lo·me·ter or ki·lom·eter? The best response I can make is that we don't say ki·log·ram or ki·lol·i·ter. [Regarding Gough, the joke goes that he had a sure-fired way of shortening the unemployment lines; simply ask the people to stand closer together!]

In the 1970's, the band 10CC had quite a few hit songs. If you follow the hyperlink and read carefully the section titled "Original line-up, 1972–76" you'll see that the band's name refers to a volume of a certain body fluid emitted from a male's nether regions. After that, the name The Beatles seems almost banal!

By the way, did you hear about the one-armed fisherman? He caught a fish this long! (Holds up one hand.) Now that joke hardly measures up, does it?