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In the modern world, we make seven basic measurements: length, mass, time, temperature, electric current, substance, and luminous intensity. The last four arise from scientific advances made since Galileo’s time. The others are of ancient origins. Measurement of time is probably the oldest and, because it is based on the constant motion of the heavens, it is the only one that is not arbitrary. The easy divisibility of some time units (such as the 60-minute hour and the 24-hour day) by two, three, and four foreshadows the basic measures used today. Mass (or weight) can be readily standardized and multiplied with a simple balance so long as the units are not affected by climatic change (such as a sack of grain that weighs more on a humid day). Standards for measurement of length, however, are the most varied and arbitrary, as are the standards for length’s two-dimensional counterpart, area.
Forgotten English terms for land measurement have roots in the history of England and its language. The measurement of length and area, however, is more than a trove for historians and philologists. The economist learns from the Domesday Book, the scientist learns from the continuing revision of the standards of length even over the last 50 years, the political scientist learns from the adoption of the metric system after the French Revolution and its subsequent history, and the student of human nature learns from the xenophobia and "innumeracy" that have left the United Kingdom and the United States as the only major countries that have adopted the metric system (in 1864 and 1866 respectively) but never fully used it. The increasing role of science, commerce, and government in our lives is reflected in the history of measurement.
Units of length in use today have precursors in the Indo-European language that preceded the written word. Their dispersion to England reflects the principal invasions by the Romans in 43 B.C., the Germanic tribes from Denmark and coastal Germany beginning in 449, the Norsemen from Scandinavia beginning in 787 (confined to an area known as the Danelaw in the northeast third of England), and the Norman French in 1066. As a result, many contemporary units of land measurement were used in England more than a millennium ago.
The earliest measurements referred to parts of the body: the digit (the breadth of the middle finger, approximately 3/4 inch); the nail (variously, the distance from the end of the thumbnail to the base of the thumb, or the last two joints of the middle finger, approximately 2 1/4 inches, used in the measurement of cloth); the finger (the length of the middle finger, approximately 4 1/2 inches, used in the measurement of cloth); the thumb (its breadth, approximately one inch); the palm (the width of four fingers excluding the thumb, approximately 3 inches); the hand (the width of the palm including the thumb, approximately 4 inches, still used for measuring horses at their withers); the span (a spread hand of approximately 9 inches); the foot; the cubit (about 18 inches from the elbow to the extended middle finger); the ell (related to the elbow, 45 inches, used for measuring cloth); and the yard (3 feet, sometimes said to be the distance from the nose to the tip of the middle finger of Henry I (1100–1135)). The fathom, which is referred to in Beowulf (about 750), is now primarily a marine measure of six feet. It was originally the length of outstretched arms. The essential reference for mea-surement terms is Ronald Edward Zupko, A Dictionary of Weights and Measures for the British Isles: The Middle Ages to the Twentieth Century (American Philosophical Society 1985). For modern terminology, see American Congress on Surveying and Mapping/American Society of Civil Engineers, Definitions of Surveying and Associated Terms (1978).
The continuing importance of these natural measures is the frequency with which the multiples of two, three, and four recur. This is a meaningful difference between what became known as the imperial system and the metric system, and it focuses on the social, political, and ultimately human aspects of measurement.
There was no certainty to natural measures because they varied by the time period, by region, by the purpose for which they were employed, and by what was being measured. Quaint as they may seem today, however, these were obvious, convenient, and reliable sources for a person working alone and for a group with a leader who acted as a standard. For instance, although the pyramids were based on cubits (perhaps with the aid of a metal standard), the variation in the bases of some pyramids is 1/4000 from one side to another.
Some lengths not susceptible to mea-surement by a body part were mea-sured by reference to physical activity. The labour (about 1/4 of a section) is the most obvious. Some lengths are human activity. The pace, variously described as one step or two, heel-to-heel, and as a result varying from 2.5 to 5 feet, comes most directly from the Latin word for "foot" ( pes) and more remotely from the Latin word for "stretch out" (as in pendulum). The league is one hour’s walking distance. It is an indefinite and poetic term varying from 2.5 to 4.5 miles, now approximately three miles in English-speaking countries and most commonly used in marine measure. When used as a measure of area, a league is equal to 25 labours, or a little more than 4,400 acres. Stadium, also seen as the plural stadia, comes from the Greek measure for a race course and since the fourteenth century has equaled a furlong. In a literary use of physical effort as a measure of area, Tolstoy based "How Much Land Does a Man Need?" on the circumambulation of a farmer’s desired plot.
Other measurements of area and length are often based on the physical effort of oxen. The furlong is an Old English measure meaning a "furrow long." It is the length of a ditch plowed by two oxen before resting to turn around and the width of 32 plowed rows. In the reign of Elizabeth I (1558–1603), the furlong was defined as 1/8 of a statute mile, or one side of 10 square acres. A boustrophedon, a Greek term for the path that the ox makes, is still the most efficient method to cover a flat surface. The modern computer printer travels the same way, printing one line going forward and the next going backward.
Other Natural Objects
The length of natural objects, other than body parts, was used for several important measures. Three round, dry, medium barleycorns from the center of the ear placed end to end were an inch by a royal Assize of Weights and Measures in the thirteenth century. With improved agriculture, there are more barleycorns to the ear, but their size has remained almost unchanged. A rod, 16.5 feet, is a Scottish term derived from the old English rood in use from the end of the fourteenth century as a straight bar of metal or wood. A pole, coming from the Latin and Anglo-Saxon terms for stake, is equal to the rod. A perch is 16.5 feet and means a pole or staff for measuring. A rood is a stick variously described as 5.5 to 8 yards and is cognate with the rod. When referring to a measure of area, as it did before 830, rood refers to a quarter of an acre; its most common use is to refer to the cross on which Christ died.
In the English and the Roman empires, the basic measures were the inch, the foot, and the mile. The inch has always been 1/12 of a foot. No longer measured by barleycorns, the inch is now defined by equivalence (39.37 inches equal one meter) to avoid imprecision and self-referential definitions. The ounce, similar to the inch, was once 1/12 of a pound and, therefore, took its name from the Latin uncia, a twelfth part.
The pound became two measures: a Troy pound and an avoirdupois ("goods of weight") pound. The Troy pound originated in the fairs in Troyes in the Champagne region of France, where it was a carefully controlled method of measuring gold, silver, and precious metals. Because it also mea-sured drugs, it was often called the apothecaries’ weight. One Troy pound equals 12 ounces and a Troy ounce equals 480 grains. The avoirdupois system, which the United States employs, has a pound of 16 ounces of 437.5 grains each. The grain is the same measure but the number of grains in Troy and avoirdupois ounces is different. The riddle about the relative weights of a pound of feathers and a pound of gold plays on these two measures. A pound of feathers is heavier because it is measured in avoirdupois, not Troy, weights.
As the basic natural unit of length, the foot can be found in Sanskrit; its modern expression is from the Latin pes, for foot. Nevertheless, it has varied from 10 to 27 inches and in the beginning of the twentieth century meant three different lengths in Brooklyn alone. Its use in England since before 1000 has made it the basic modern imperial measure.
The mile has been in use since Anglo-Saxon times as a land measure. Also known as the statute or land mile, it was defined during the reign of Elizabeth I to be 5,280 feet, based roughly upon 1,000 paces of the Roman army (Latin mille passum). The number 5,280 is conveniently divisible by 2, 3, 4, 5, 6, 8, 10, 11, 12, and 16, and thus also easily divisible by the foot, yard, fathom, rod, chain, cable, and furlong. A nautical mile is the length on the earth’s surface of one minute of arc.
Finally, there are important artificial lengths. A chain is 66 feet comprised of 100 links of 7.92 inches each. The chain was known as the Gunter’s or surveyor’s chain after the British mathematician and surveyor Edmund Gunter, who in 1610 doubled the size of the chain from 33 feet to work more conveniently with the rod and furlong already in use. A cable length is 120 fathoms and comes from an Anglo-French term for rope or line or bundle, and ultimately from the Latin to capture or seize.
There are many measures of area in addition to those determined by squaring a linear measure (such as a square yard or a square mile). The Sumerian term corresponding to acre meant water and by extension a watered field. The Sanskrit equivalent meant an open field or hunting ground or pasture. In Latin ( ager) and Greek ( agros) it meant a fertile field giving rise to the term "agriculture." In Old English, it meant the amount of unoccupied land that a yoke of oxen (two oxen) could plow from sunrise to sunset. In the Domesday Book, it referred to a pasture, meadow, or woods. Statutes starting with Edward I (1239–1307) standardized the definition as an area 4 rods wide by 40 rods long, and that remains its size today; however, there were substantial regional variations despite the standard.
The are, from area, for open space, began in the French Revolution and is 100 square meters. The hectare, from the Greek hekaton for a hundred, is 100 ares or 10,000 square meters and came into use around 1810 in France. The arpent measured 100 square perches and was used in the Domesday Book with regard to vineyards. In certain parts of the southeastern United States, it survives from the French land grants as approximately 0.85 acre, but its size depends upon whether the original land was English or French, and it varies from one state to another (such as Louisiana and Arkansas). The linear measure of an arpent is approximately 191 feet, and it is the length of one side of a square arpent.
The hide is at its root a German word for household. In the Saxon counties of southern England, it referred to the land sufficient to support one family, which equaled what the family plowed in a year. Depending on the fertility of the land, the hide varied from as little as 60 to as many as 240 acres, but it was typically between 80 and 120. The bovate, 1/8 of a carucate, also appears in the Domesday Book. Its origin is Danish and it is found in the northeastern English counties constituting the Danelaw. A carucata or carucate, like a hide, is approximately 120 acres and like the bovate was found in the Danish counties. Plowland or plowgate is equal to a carucate or an area eight oxen can plow sufficient for a free family to support itself; its origins precede 1100. The plowland compares with the knight’s fee , which was a larger area sufficient to support a knight’s family (perhaps to allow pasture for animal husbandry). Sulung is a Kentish term for two hides. A yoke in Kent is 1/4 of a sulung. A virgate is a rod in linear measure and 1/4 of a hide (or 30 acres) as a measure of area in Saxon counties.
Although the standards were often based on the same amount of animal labor (for example, the area plowed by two oxen in a day), the areas differed. The discrepancies are attributable to the varying fertility of the soil and the development of agricultural techniques and tools that enhanced productivity. One must bear in mind that these mea-surements arose in an era when lives were lived in isolation on a roadless countryside, when people had no need for last names and when they were unlikely to be able to find their way home if they left to fight in a war.
Some (such as Marie Antoinette) would say that the fun stopped with the French Revolution. This is certainly true of measurement and the meter. The meter, based upon the Sanskrit, Greek, and Latin words for measure, was decreed by the French to be 1/10,000,000 of a length of a meridian from the North Pole to the equator through Paris. The French believed this precision was necessary because their basic unit—the pied—varied throughout the country. The scientific work to make the measurement took six years. It was adopted by the National Academy of France in 1796 "for all people for all time" at the request of the Academy of Science and was based upon a decimal system originated in 1670 by a French clergyman, Gabriel Mouton; a decimal system uses a base of ten, which recalls finger counting. Because the calculations did not take into account the flattening of the earth at the North Pole, the measurement was two miles off. It was not corrected even when the error was discovered.
A platinum-iridium bar was used as the standard meter beginning in 1889. It was replaced in 1960 by a measurement based on the wavelength of orange light emitted from krypton-86 when stimulated with an electric discharge. That standard was made yet more precise in 1983, when the meter was defined as the distance traveled by light in a vacuum during 1/299,792,458 of a second.
The concept of an imperial measure originated with the Roman Empire and is still preferred by England to the metric system in many instances. But the United Kingdom has adopted the metric system of lengths, except for miles, yards, feet, and inches, for traffic signs and for other measurements of speed and distance. The acre remains the English measure for land registration. The United Kingdom has been unable to adopt the metric system for all measures because of national pride and the popular inability to manage the arithmetic conversion. When voluntary conversion was proposed, the merchants that priced their goods by the square yard complained they were unable to compete with others that priced theirs on an (apparently cheaper) square meter. The United States does not fully employ the metric system, despite George Washington’s plea for its adoption at the first Congress.
Measurement has gone from a flexible (perhaps, to be blunt, unreliable) standard for art, exchange, and craft to a reliable scientific standard, and it has passed from the body parts of rulers to the laboratories of scientists to explain (or describe) the natural world. Nevertheless, the metric system and the imperial system continue to co-exist because neither seems to "fit" humans satisfactorily. People will continue to divide the inch by factors of two and not by factors of 10, as the metric system would have it. Thousands of years after someone’s foot became a standard, it remains so. A barleycorn is still about one-third of an inch, and people still have 10 fingers.
Mark A. Senn is a shareholder of Senn Lewis & Visciano PC, in Denver, Colorado. This article is based on a similar article published in 19 ACREL News No. 3, Aug. 2001, at 5.