What if I told you that the specifics of our American system of land measurement, with its miles and acres and such, was the direct result of a bunch of oxen standing tired in a field during a morning’s  plowing more than a thousand years ago.  Would you believe me?  Read on.

If you peruse historical documents pertaining to the great Adirondack surveys you will encounter a variety of measurement units.  Some, like feet and miles, will be common knowledge to you.  Others, like acres, will be familiar terms though you may not know precisely what they are.  But a few, like the chain, which seems to be the fundamental unit of surveying distance, may well be unknown.   Every major land division in the Adirondacks was originally measured in chains using an actual metal chain called a Gunter’s chain.

I know my mathematics and I understand triangulation but I must confess that I was ignorant of the details of surveying measurements until two years ago when I became interested because of our acquisition of Lost Brook Tract.  The sole surveying map relating to the property fixed the position and dimensions of the lot in terms of chains.  I had heard that terminology before but had no idea what it actually meant.  I had to look it up to learn that a chain was 66 feet.  Like anyone would think I took that as a rather unusual number.  I knew enough about the plethora of anachronistic units of measure that have been used in the past to chalk up the 66 foot distance to an accident of history.

Have you ever wondered why our British or Imperial units of measure are so odd?  We are so used to them that we don’t often step back and think how strange it is that, for example, 5,280 feet make a mile.  Why not 5,000 feet (as it was during Roman times)?  Why not some other round number?  The Imperial system is full of opportunities to ask questions like that.  In the metric system the boiling point of water is 100 degrees centigrade and the freezing point is 0 degrees centigrade.  There you have some nice round numbers that seem sensible.  In the Imperial system those numbers are 212 degrees and 32 degrees Fahrenheit, respectively.  Is that not goofy when you think about it?

Look at the dozens of ways we measure volume in the Imperial system and contrast that to the metric system where everything is decimal-based, in other words based upon multiples of ten.  It’s an eye-opener that shows our system to be dumb in comparison.  I would challenge any reader to successfully convert teaspoons to quarts, let’s say, without a happy and involved session of looking up units of measure and writing multiplication problems all over a piece of paper.  In the metric system the closest analog to a teaspoon is the milliliter and the closest analog to the quart is the liter.  A liter is 1,000 milliliters – three places of ten, baby.  If you want to convert milliliters to liters you simply move your decimal point three places and you are done in one second flat.  Because of that a decimal system such as the metric system is much easier to use.  Of course the metric system has the advantage of having been designed from the ground up to be consistent and sensible, whereas the Imperial system is a collection of measurements cobbled together from every corner of the globe over the entire span of human history.  That’s why it’s such a mess.

The chain is an Imperial unit of measure so I was not exactly shocked to learn it was a quirky number.  I think it was a day or two after I looked it up that my casual interest in gave way to obsessive fascination.  My penchant for messing around with numbers had me staring at 66 one afternoon and all of a sudden it hit me.   I grabbed a piece of paper and wrote the number of feet in a mile, 5,280.  Then I divided it by 66.

5,280 ÷ 66 = 80.

Aha!  A round number!  So the length of a Gunter’s chain was no accident after all!  Now I had to know the whole story.

When it comes to the incredible richness of the history of measurement I am pretty much a dilettante.  Fortunately while nosing around on-line I found an extensive dictionary of units of measurement http://www.unc.edu/~rowlett/units/index.html that is concise yet descriptive enough to weave together a narrative of how we came to adopt certain units.  I contacted its creator, Russ Rowlett, Professor of Mathematics Education at the University of North Carolina at Chapel Hill and he generously granted permission for me to use his work.  A portion of what follows , especially a number of details on the old English measurements, comes from his dictionary.

Gunter’s chain was developed in 1620 by an English mathematician named Edmund Gunter.  Gunter was a clergyman, having graduated from Christ Church in Oxford and entered the divinity.  But his greatest love was mathematics.  Gunter was my kind of guy, a master of the triangle magic I have been writing about.  As a theoretician he made important extensions to the mathematics of trigonometry and logarithms.  But he is more typically characterized as a pragmatic mathematician who applied his knowledge to solve practical problems of the day.  His chain was a very clever solution to contemporary land surveying problems that were caused by the inelegant collision of two great measurement systems used in England at the time.  Like all essential English conflicts across the great arc of human endeavor and identity, this one comes down to the Normans and the Saxons.

The story begins back in history far before that, at the dawn of civilization.  As human beings organized into social groups and communities they needed common understandings of all sorts of measurable things like sizes of fields, numbers of seeds or crops, various distances and so on.  All these ancient measurement systems  were based upon the human body in two important ways.  Let’s look at both.

The first way in which the human body was important was in the development of standard units of measurement.  Units of measurement for length were based upon lengths of forearm (the Egyptian cubit) , the palm, the finger and thumb (inches), the distance around a waist (a version of the yard) and a walking pace (the mile), among others.

By far the most important such measure was based upon the human foot.  Here are portions of the entry from Rowlett’s dictionary for the foot:

a traditional unit of distance. Almost every culture has used the human foot as a unit of measurement. The natural foot (pes naturalis in Latin), an ancient unit based on the length of actual feet, is about 25 centimeters (9.8 inches). This unit was replaced in early civilizations of the Middle East by a longer foot, roughly 30 centimeters or the size of the modern unit, because this longer length was conveniently expressed in terms of other natural units:

1 foot = 3 hands = 4 palms = 12 inches (thumb widths) = 16 digits (finger widths)

This unit was used in both Greece and Rome…  …the modern foot (1/3 yard or about 30.5 centimeters) did not appear until after the Norman conquest of 1066. It may be an innovation of Henry I, who reigned from 1100 to 1135. Later in the 1100s a foot of modern length, the “foot of St. Paul’s,” was inscribed on the base of a column of St. Paul’s Church in London, so that everyone could see the length of this new foot. From 1300, at least, to the present day there appears be little or no change in the length of the foot.

So the Normans brought a version of the Roman foot to Saxon England and the foot as we know it was standardized shortly thereafter.

The other way in which the human body affected measurement was in the development and organization of number systems themselves.  The great majority of early number systems counted by tens: in other words they were base-10 or decimal systems.  Ancient Egyptian, Chinese, Hindu, Greek and Roman number systems were all decimal systems in part or in whole.  If you want to understand why this is and how it relates to the human body you need only look at your hands.  As we are still wont to do from time to time, ancient peoples counted on their fingers (in a delightful side note I learned during my research that the Mayans had a base-20 system because they counted on both their fingers and toes!).

As described before, the advantage of a decimal system organized with place value in columns of tens is the ease with which various calculations can be done, since multiplying or dividing by ten simply requires moving the decimal point.  This is the entire rationale behind the metric system.  But while one version or another of the base-10 system was in common use for centuries, the development of a decimal point and its rapid calculating power was just coming into common use on the European continent in Edmund Gunter’s time.   The Flemish mathematician Simon Stevin wrote a book called The Tenth in 1585 the purpose of which was to show people “how to perform with an ease unheard of, all computations necessary between men by integers without fractions .”  Then the Scottish mathematician John Napier took up championing the decimal point, predicting that its calculating power would revolutionize mathematics.  He brought it into common use in the early 16^th century and the decimal point as we know it became the standard in England in 1619, just one year before Gunter developed his chain.  This timing was no coincidence, as we shall see.

Meanwhile in medieval England the Saxons were doing their own thing with measurement.  Like other ancient systems of measurement Saxon units were derived from the need to measure distances in agriculture.  In fact they came directly from Saxons’ experience plowing their fields with teams of oxen.  The details are fascinating.

Teams of oxen were quite difficult to turn; consequently the Saxons would minimize the turns needed by making their fields long and narrow, plowing lengthy strips of furrows. The length of a furrow depended upon how far a team of oxen  could plow before needing to stop for a rest; at that point they would be turned to plow back the other way. This distance – a furrow, long – became the furlong.

For shorter measurements the Saxons had the length of a pole.  There is evidence that it was based upon the pole that was used to urge the oxen along.  Whatever its origin it became known as a rod and it was the fundamental unit of measurement in their system.   The length that oxen could plow before resting was about 40 pole-lengths, so the furlong was standardized as 40 rods.

Oxen were good to plow for a morning, not a full day.  In a full morning of work they could plow furrows to a width of about 4 rods.  Thus the dimensions of a Saxon plowed field was standardized as four rods by one furlong.   The old English word for “field” was acre, the word and dimension we still use today.  Considering that an acre had a length of 40 rods and a width of 4 rods, thus an area of 160 square rods, you can see that the Saxon system was based upon multiples of 4, not multiples of 10.

The Saxons had a version of a foot, from north Germany.  The rod was about 15 of these feet.  Therefore an acre was 600 feet  by 60 feet.  But when the Normans prevailed at the Battle of Hastings they brought with them decimal measurements and the Roman foot, which was a little bit shorter than the north German one.  This led to some adjustments.  From Rowlett’s dictionary:

…when the modern foot became established in the twelfth century, the royal government did not want to change the length of the rod, since that length was the basis of land measurement, land records, and taxes. Therefore the rod was redefined to equal 16 ½ feet, because with reasonable precision that happened to be its length in terms of the new foot.

It is said that Queen Elizabeth herself decreed that the mile be redefined from from it Roman definition of 5,000 feet to fit into the scheme of rods and furlongs.  Since a furlong was now 660 feet under the modern foot (40 rods X 16 ½ feet per rod = 660 feet), the mile was rounded up to the next whole furlong, which was 8 furlongs:  8 furlongs X 660 feet per furlong = 5,280 feet!  Now you now where that odd duck came from.

Land surveys in England continued to be performed with ropes and stakes using rods, furlongs and acres.  But now an acre was no longer 600 feet by 60 feet under the old measurements.  Under the new furlong it was 660 feet long.  And its width?  4 rods X 16 ½ feet per rod = 66 feet.  Does that number ring a bell?

Now we are finally ready for Edmund Gunter in 1620.  He understood well the awkward calculations that were involved in seventeenth-century English surveying with its multiples of 4 and fractional parts of feet.  Decimal calculations using a decimal point, a far superior method of calculation, had just been standardized.  So he figured  out a solution that married the two.  He had a local blacksmith forge a chain of a hundred links, totaling 66 feet.  A chain would be more durable and consistent than a rope.  Now a furlong was ten chains and the the width of an acre was one chain, giving an area of ten square chains.   Parts of a chain, measured in links, were hundredths.   Voila!  Furlongs, acres and portions thereof were now all measurable in decimals.

So well did Gunter’s chain work that it revolutionized surveying and carried the legacy of rods, furlongs and acres – carried figuratively on the backs of medieval English teams of oxen – right into the American colonies, the Adirondacks, the Totten and Crossfield Purchase and even Lost Brook Tract.

If you own some land in the Adirondacks that is measured in chains and acres, you now know what it means and where it came from.  Next week we will take our new knowledge of how surveying distances are calculated and plunge back into the Adirondack wilderness.

Photo One: A team of Saxon oxen, with rod, from the 11th Century.  Photo courtesy of the The Foxearth and District Local History Society , Great Britain.

Photo Two: A Gunter’s chain, courtesy of Wikipedia