# Weights and measures

The definition, agreement and practical use of units of weights and measures have played a crucial role in human endeavor from early ages up to this day. Just to underline the importance of agreed units, the NASA Mars Polar Lander in December 1999 crashed on the planet Mars instead of staying in orbit, due to miscommunications about the value of forces: different people used different assumptions about the unit of measure (newton versus pound force). Enormous amounts of effort, time and money were wasted.

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## History of Weights and Measures

Weights and measures were among the earliest tools invented by humans. Primitive societies needed rudimentary measures for many tasks: constructing dwellings of an appropriate size and shape, fashioning clothing, or bartering food or raw materials.

The earliest known uniform systems of weights and measures seem to have all been created sometime in the 4th and 3rd millennia BC among the ancient peoples of Mesopotamia, Egypt and the Indus Valley, and perhaps also Elam in Persia as well. The most astounding of these ancient systems was perhaps that of the Indus Valley Civilization (ca. 2600 BC). The Indus Valley peoples achieved great accuracy in measuring length, mass, and time. Their measurements were extremely precise. Their smallest division, which is marked on an ivory scale found in Lothal, was approximately 1.704mm, the smallest division ever recorded on a scale of the Bronze Age. The decimal system was used. Harappan engineers followed the decimal division of measurement for all practical purposes, including the measurement of mass as revealed by their hexahedron weights. Weights were based on units of 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200, and 500, with each unit weighing approximately 28 grams, similar to the English ounce or Greek uncia, and smaller objects were weighed in similar ratios with the units of 0.871.

Other systems were based on the use of parts of the body and the natural surroundings as measuring instruments. Early Babylonian and Egyptian records and the Bible indicate that length was first measured with the forearm, hand, or finger and that time was measured by the periods of the sun, moon, and other heavenly bodies. When it was necessary to compare the capacities of containers such as gourds or clay or metal vessels, they were filled with plant seeds which were then counted to measure the volumes. When means for weighing were invented, seeds and stones served as standards. For instance, the carat, still used as a unit for gems, was derived from the carob seed.

Our present knowledge of early weights and measures comes from many sources. Archaeologists have recovered some rather early standards and preserved in museums. The comparison of the dimensions of buildings with the descriptions of contemporary writers is another source of information. An interesting example of this is the comparison of the dimensions of the Greek Parthenon with the description given by Plutarch from which a fairly accurate idea of the size of the Attic foot is obtained. In some cases, we have only plausible theories and we must sometimes select the interpretation to be given to the evidence.

For example, does the fact that the length of the double-cubit of early Babylonia was equal (within two parts per thousand) to the length of the seconds pendulum at Babylon suggest a scientific knowledge of the pendulum at a very early date, or do we merely have a curious coincidence? By studying the evidence given by all available sources, and by correlating the relevant facts, we obtain some idea of the origin and development of the units. We find that they have changed more or less gradually with the passing of time in a complex manner because of a great variety of modifying influences. We find the units modified and grouped into measurement systems: the Babylonian system, the Egyptian system, the Phileterian system of the Ptolemaic age, the Olympic system of Greece, the Roman system, and the British system, to mention only a few.

See Ancient weights and measures for a detailed listing of actual units.

## Origins of common customary units

The origin and development of units of measurement has been investigated in considerable detail and a number of books have been written on the subject. It is only possible to give here, somewhat sketchily, the story about a few units.

### Units of length

The Indus Valley units of length referred to above and the Mesopotamian cubit were both used in the 3rd millennium BC and are the earliest known units used by ancient peoples to measure length.

There were several cubits of different magnitudes that were used. The common cubit was the length of the forearm from the elbow to the tip of the middle finger. It was divided into the span of the hand (one-half cubit), the palm or width of the hand (one sixth), and the digit or width of a finger (one twenty-fourth). The Royal or Sacred Cubit, which was 7 palms or 28 digits long, was used in constructing buildings and monuments and in surveying. The inch, foot (length), and yard evolved from these units through a complicated transformation not yet fully understood. Some believe they evolved from cubic measures; others believe they were simple proportions or multiples of the cubit. In any case, the Greeks and Romans inherited the foot from the Egyptians. The Roman foot was divided into both 12 unciae (inches) and 16 digits. The Romans also introduced the mile of 1000 paces or double steps, the pace being equal to five Roman feet. The Roman mile of 5000 feet was introduced into England during the occupation. Queen Elizabeth I (reigned from 1558 to 1603) changed, by statute, the mile to 5280 feet or 8 furlongs, a furlong being 40 rods of 5.5 yards each.

The introduction of the yard as a unit of length came later, but its origin is not definitely known. Some believe the origin was the double cubit, others believe that it originated from cubic measure. Whatever its origin, the early yard was divided by the binary method into 2, 4, 8, and 16 parts called the half-yard, span, finger, and nail. The association of the yard with the "gird" or circumference of a person's waist or with the distance from the tip of the nose to the end of the thumb of King Henry I (reigned 1100 - 1135) are probably standardizing actions, since several yards were in use in Britain.

### Typographical units

The point, which is a unit for measuring print type, is recent. It originated with Pierre Simon Fournier in 1737. It was modified and developed by the Didot brothers, Francois Ambroise and Pierre Francois, in 1755. The point was first used in the United States in 1878 by a Chicago type foundry (Marder, Luse, and Company). Since 1886, a point has been exactly 0.3514598 millimetres, or 1/72.27 inch.

### Units of mass

The grain was the earliest unit of mass and is the smallest unit in the apothecary, avoirdupois, Tower, and troy systems. The early unit was a grain of wheat or barleycorn used to weigh the precious metals silver and gold. Larger units preserved in stone standards were developed that were used as both units of mass and of monetary currency. The pound was derived from the mina used by ancient civilizations. A smaller unit was the shekel, and a larger unit was the talent. The magnitude of these units varied from place to place. The Babylonians and Sumerians had a system in which there were 60 shekels in a mina and 60 minas in a talent. The Roman talent consisted of 100 libra (pound) which were smaller in magnitude than the mina. The troy pound used in England and the United States for monetary purposes, like the Roman pound, was divided into 12 ounces, but the Roman uncia (ounce) was smaller. The carat is a unit for measuring gemstones that had its origin in the carob seed, which later was standardized at 1/144 ounce and then 0.2 gram.

Goods of commerce were originally traded by number or volume. When weighing of goods began, units of mass based on a volume of grain or water were developed. For example, the talent in some places was approximately equal to the mass of one cubic foot of water. Was this a coincidence or by design? The diverse magnitudes of units having the same name, which still appear today in our dry and liquid measures, could have arisen from the various commodities traded. The larger avoirdupois pound for goods of commerce might have been based on volume of water which has a higher bulk density than grain. For example, the Egyptian hon was a volume unit about 11 per cent larger than a cubic palm and corresponded to one mina of water. It was almost identical in volume to the present U.S. pint.

The stone, quarter, hundredweight, and ton were larger units of mass used in Britain. Today only the stone continues in customary use for measuring personal body weight. The present stone is 14 pounds, but an earlier unit appears to have been 16 pounds. The other units were multiples of 2, 8, and 160 times the stone, or 28, 112, and 2240 pounds, respectively. The hundredweight was approximately equal to two talents. In the United States the ton of 2240 pounds is called the "long ton". The "short ton" is equal to 2000 pounds.

### Units of time and angle

We can trace the division of the circle into 360 degrees and the day into hours, minutes, and seconds to the Babylonians who had a sexagesimal system of numbers. The 360 degrees may have been related to a year of 360 days.

## Origin of the metric system

Metric systems of units have evolved since the adoption of the first well-defined system in France in 1791. During this evolution the use of these systems spread throughout the world, first to the non-English-speaking countries, and more recently to the English speaking countries.

The first metric system was based on the centimetre, gram, and second (cgs) and these units were particularly convenient in science and technology. Later metric systems were based on the metre, kilogram, and second (mks) to improve the value of the units for practical applications.

The present metric system is the Système international d'unités (SI, International System of Units). It is also based on the metre, kilogram and second as well as additional base units for temperature, electric current, luminous intensity, and amount of substance.

The adoption of the metric system in France was slow, but its desirability as an international system was recognized by geodesists and others. On May 20, 1875, an international treaty known as the Convention du Mètre (Metre Convention) was signed by 17 states. This treaty established the following organizations to conduct international activities relating to a uniform system for measurements:

1. Conférence générale des poids et mesures (CGPM), an intergovernmental conference of official delegates of member nations and the supreme authority for all actions;
2. Comité international des poids et mesures (CIPM), consisting of selected scientists and metrologists, which prepares and executes the decisions of the CGPM and is responsible for the supervision of the International Bureau of Weights and Measures;
3. Bureau international des poids et mesures (BIPM), a permanent laboratory and world center of scientific metrology, the activities of which include the establishment of the basic standards and scales of the principal physical quantities and maintenance of the international prototype standards.

Multiples and submultiples of metric units are related by powers of ten; the names for these are formed with SI prefixes. This relationship is compatible with the decimal system of numbers and it contributes greatly to the convenience of metric units.

## International System of Units

At the end of World War II, a number of different systems of measurement still existed throughout the world. Some of these systems were variations of the metric system, and others were based on the customary inch-pound system of the English-speaking countries. It was recognized that additional steps were needed to promote a worldwide measurement system. As a result the 9th GCPM, in 1948, asked the CIPM to conduct an international study of the measurement needs of the scientific, technical, and educational communities. Based on the findings of this study, the 10th CGPM in 1954 decided that an international system should be derived from six base units to provide for the measurement of temperature and optical radiation in addition to mechanical and electromagnetic quantities. The six base units recommended were the metre, kilogram, second, ampere, Kelvin degree (later renamed the kelvin), and the candela.

In 1960, the 11th CGPM named the system based on the six base quantities the International System of Units, abbreviated SI from the French name: Le Système International d'Unités. The SI metric system is now either obligatory or permissible throughout the world. U.S. customary units are now defined as fractions of SI units.

### Units and Standards of the Metric System

In the early metric system there were two fundamental or base units, the metre and the kilogram, for length and mass. The other units of length and mass, and all units of area, volume, and compound units such as density were derived from these two fundamental units.

The metre was originally intended to be one ten-millionth part of a meridional quadrant of the earth. The Metre of the Archives, the platinum length standard which was the standard for most of the 19th century, at first was supposed to be exactly this fractional part of the quadrant. More refined measurements over the earth's surface showed that this supposition was not correct. In 1889, a new international metric standard of length, the International Prototype Metre, a graduated line standard of platinum-iridium, was selected from a group of bars because precise measurements found it to have the same length as the Metre of the Archives. The metre was then defined as the distance, under specified conditions, between the lines on the International Prototype Metre without reference to any measurements of the earth or to the Metre of the Archives, which it superseded. Advances in science and technology have made it possible to improve the definition of the metre and reduce the uncertainties associated with artifacts.

From 1960 to 1983, the metre was defined as the length equal to 1 650 763.73 wavelengths in a vacuum of the radiation corresponding to the transition between the specified energy levels of the krypton-86 atom. Since 1983 the metre has been defined as the length of the path traveled by light in a vacuum during an interval of 1/299,792,458 of a second.

The kilogram, originally defined as the mass of one cubic decimetre of water at the temperature of maximum density, was known as the Kilogram of the Archives. It was replaced after the International Metric Convention in 1875 by the International Prototype Kilogram which became the unit of mass without reference to the mass of a cubic decimetre of water or to the Kilogram of the Archives. Each country that subscribed to the International Metric Convention was assigned one or more copies of the international standards; these are known as National Prototype Metres and Kilograms.

The litre is a unit of capacity or volume. In 1964, the 12th GCPM redefined the litre as being one cubic decimetre. By its previous definition — the volume occupied, under standard conditions, by a quantity of pure water having a mass of one kilogram — the litre was larger than the cubic decimetre by 28 parts per 1 000 000. Except for determinations of high precision, this difference is so small as to be of no consequence.

SI includes two classes of units:

• SI base units for length, mass, time, temperature, electric current, luminous intensity, and amount of substance; and
• SI derived units for all other quantities (e.g., work, force, power) expressed in terms of the seven base units.

The above is based on Appendix B of NIST Handbook 44, 2002 Edition.

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