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Units and Systems of Weights and Measures
Their Origin, Development, and Present Status
Lewis V. Judson
This Circular brings together in a convenient form information about weights and measures that experience has shown is of interest to the general public. Much of it has been issued previously by the National Bureau of Standards in temporary and scattered form. The Circular discusses the origin and early history of units and standards, gives general information about the metric system, and states and explains the present status of standards of length, mass, time, and capacity in the United States and in Great Britain. It discusses for the benefit of the general reader such matters as the distinction between units and standards, and that between mass and weight. Two items of everyday life relating to weights and measures are considered in some detail: The weight of coal, and the definitions and usages of the terms "ton" and "tonnage." The Circular concludes with tables of weights and measures, prepared for the benefit of those requiring such tables for occasional ready reference. School teachers will find in this Circular considerable material to supplement their textbooks.
The National Bureau of Standards was established by act of Congress in 1901 to serve as a National scientific laboratory in the physical sciences and to provide fundamental measurement standards for science and industry. In carrying out these related functions the Bureau conducts research and development in many fields of physics, mathematics, chemistry, and engineering. At the time of its founding, the Bureau had custody of two primary standardsthe meter bar for length and the kilogram cylinder for mass (or weight). With the phenomenal growth of science and technology over the past half century, the Bureau has become a major research institution concerned not only with everyday weights and measures but also with hundreds of other scientific and engineering standards that have become necessary to the industrial progress of the Nation. Nevertheless, the country still looks to the Bureau for information on the units of weights and measures, particularly their definitions and equivalents.
The subject of weights and measures can be treated from several different standpoints. Scientists and engineers are interested in the methods by which precision measurements are made; State weights and measures officials are interested in laws and regulations on the subject. and in methods of verifying commercial weighing and measuring devices. But a vastly larger group of people are interested in some general knowledge of the origin and development of weights and measures, of the present status of units and standards, and of miscellaneous facts that will be useful in everyday life. This Circular has been prepared to supply that information on weights and measures that experience has shown to be the common subject of inquiry.
2. Units and Systems of Weights and Measures
The expression "weights and measures" is used in this Circular in its basic sense of referring to measurements such as length, mass, and capacity, thus excluding such topics as electrical measurements and thermometry. This section on units and systems of weights and measures presents some fundamental information to clarify thinking on this subject and to eliminate erroneous and misleading use of terms.
2.1. Origin and Early History of Units and Standards
a. Units and Standards
It is essential that there be established and kept in mind the distinction between the terms "units" and "standards."
A unit is a value, quantity, or magnitude in terms of which other values, quantities, or magnitudes are expressed. In general, a unit is fixed by definition and is independent of such physical conditions as temperature. Examples: The yard, the pound, the gallon, the meter, the liter, the gram.
A standard is a physical embodiment of a unit. In general it is not independent of physical conditions, and it is a true embodiment of the unit only under specified conditions. For example, a yard standard has a length of one yard when at some definite temperature and supported in a certain manner. If supported in a different manner, it might have to be at a different temperature in order to have a length of 1 yard.
b. General Survey of Early History of Weights and Measures
The beginnings of the development of weights and measures go back to primitive man in prehistoric times. Hence, there is a great deal of uncertainty about the origin and early history of weights and measures. Many believe that the units first used by primitive man were those of length and weight and that units of area, volume, and capacity were of much later origin. Units of length may have been the earliest. These were derived from the limbs of the human body, and included the length of the foot, the width of the palm, the length of the forearm, etc. Units of weight included weights of kernels of grain and weights of shells.
At first these units were not very definitely defined. Later they became somewhat more definite when, for example, the foot became the length of the foot of a tribal chief or other ruler. At a much later date physical standards were made and deposited for safekeeping in a temple or other place of security. These early physical standards were usually very crude; it is generally considered, however, that they were as satisfactory for the needs of the people at that time as our most modern standards are for our own needs.
Our present knowledge of early weights and measures comes from many sources. Some rather early standards have been recovered by archeologists 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 decide on 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 in a thousand) to the length of the seconds pendulum at Babylon indicate 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 systems of weights and measures: The Babylonian 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.
c. Origin and Development of Some Common Units
The origin and development of units of weights and measures 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.
One of the earliest units was the foot. This was first the length of the human foot without further specification or modification, then the length of the foot of various rulers of tribes and groups of people. Later, by gradual evolution, it was the foot as used in succession by the
Egyptians, Greeks, and Romans, brought to Britain by the Romans, modified with the passing of time, and finally defined in Great Britain as 1/3 of the British Imperial Yard and in this country as 1/3 of the U. S. yard.
A very interesting and important unit of length used by many ancient peoples was the cubit, originally defined as the distance from the point of the elbow to the end of the middle finger. This unit was about 18 inches long, but there were important variations in the length of a cubit.
The inch was originally a thumb's breadth. In the Roman duodecimal system it was defined as 2 foot, and was introduced into Britain during Roman occupation, where it became a part of the English system of weights and measures.
The mile was defined by the Romans as 1 000 paces* or double steps, the pace being equal to 5 Roman feet. This Roman mile of 5 000 Roman feet was introduced into Britain, became 5 000 English feet, and in Tudor times (probably in the reign of Henry VII, 1485 to 1509, but definitely by a statute of Queen Elizabeth, who reigned 1558 to 1603) was changed to 5 280 feet in order to make the furlong of % mile equal to the rood of 660 feet, or 220 yards (40 rods of 161⁄2 feet, or 51⁄2 yards each).
The yard as a unit of length is apparently of much later origin than the units previously discussed. It appears to have had a double origin: (1) as the length of an Anglo-Saxon gird or girdle, and (2) as the length of the double cubit. There is an old tradition, often stated as a fact, that Henry I decreed that the yard should thenceforth be the distance from the tip of his nose to the end of his thumb.
The point is the basic unit for measuring type. This unit originated with Pierre Simon Fournier in 1737. It was modified and developed by the Didot brothers, Francois Ambroise and Pierre Francois, in 1755. It was first put into effect in the United States by a Chicago type foundry (Marder, Luse, and Company) in 1878. As adopted in 1886 by the American Type Founders' Association and now defined in the United States, Canada, and Great Britain, it is 0.013 837 inch, a value only slightly less than 2 inch.
Of units of weight, one of the earliest is the grain, which was originally the weight of a grain of wheat or of some specified seed native to some particular locality.
The Roman pound (libra) was the hundredth part of an older weight, the talent, which is believed to have been originally the weight of an Egyptian royal cubic foot of water. The Roman pound was divided into 12 ounces (unciae, meaning twelfth parts) of 437 grains each. This system was introduced into Britain where the pound was increased so as to have 16 of the original ounces. This pound became known as the avoirdupois pound, the word avoirdupois meaning "goods of weight." The idea of a pound divided into 16 parts was not a new one, as the Greeks had divided their pound into 16 parts, as well as into 12 parts. The pound, which in England had long been used for mint purposes and called the troy pound, consisted of 5 760 grains (12 ounces of 480 grains each). The origin of this troy pound and troy ounce is very uncertain. One theory is that the troy pound came from Troyes, France, but there seems to be a serious question whether even the name had its origin in that place. Sometime prior to 1600 A. D., the avoirdupois pound was increased by 8 grains so that it would consist of 7 000 grains instead of 6 992 grains and thus the number of grains in the avoirdupois pound would have a more simple ratio to the number of grains in the troy pound, which, being used for mint purposes, it was considered advisable to keep unchanged.
That the ton was the weight of a certain volume of some material is highly probable. Among the Anglo-Saxons it may have been the weight of a quantity of wheat in 32 bushels, that is, in 1 chaldron.
The stone was an early unit of weight in the British Isles. At one time it appears to have been 16 pounds in the system: 16 pounds 1 stone, 16 stones=1 wey, 16 weys=1 last, and 1⁄2 last=1 ton (not the present ton). The stone is still used to a considerable extent in Great Britain, being now equal to 14 pounds except in special cases. (8 stones 1 hundredweight= 112 lb; 20 hundredweights=1 ton=2 240 lb. This ton is commonly referred to as the long ton in the United States.)
*It should be noted that a space has been inserted instead of commas in all of the numerical values given in this Circular, following a growing practice originating in tabular work to use the space to separate large numbers into groups of three digits.
A unit of antiquity which has survived without change is the degree of arc. The early Babylonians reckoned the year as 360 days. They therefore divided the circle into 360 parts, or degrees. They knew that a chord equal to the radius subtends an arc of 60°. The number 60 became the basis of their sexagesimal number system and is an explanation of the division of the degree into 60 minutes and of the minute into 60 seconds. This is also the basis of the relation between longitude and time. Since the earth makes one complete rotation (360°) on its axis in 24 hours, a time change of 1 hour is represented by each 15° of longitude (360/24=15).
2.2. The Metric System
a. The Metric System: Definition, Origin, and Development
The metric system is the international decimal system of weights and measures based on the meter and the kilogram. The essential features of the system were embodied in a report made to the French National Assembly by the Paris Academy of Sciences in 1791. The definitive action taken in 1791 was the outgrowth of recommendations along similar lines dating back to 1670. The adoption of the 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 International Metric Convention was signed providing for an International Bureau of Weights and Measures, thus insuring "the international unification and improvement of the metric system." The metric system is now either obligatory or permissive in every civilized country of the world.
Although the metric system is a decimal system, the words "metric" and "decimal” are not synonymous, and care should be taken not to confuse the two terms.
b. Units and Standards of the Metric System
In the metric system the fundamental units are the meter and the kilogram. The other units of length and mass, as well as all units of area, volume, and capacity, also compound units, such as pressure, are derived from these two fundamental units.
The meter was originally intended to be 1 ten-millionth part of a meridional quadrant of the earth. The Meter of the Archives, the platinum end-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. The present international metric standard of length, the International Prototype Meter, a graduated line standard of platinum-iridium, was selected from a group of bars because it was found by precise measurements to have the same length as the Meter of the Archives. The meter is now defined as the distance under specified conditions between the lines on the International Prototype Meter without reference to any measurements of the earth or to the Meter of the Archives, which it superseded. The kilogram was originally intended to be the mass of one cubic decimeter of water at its maximum density, but it is now defined as the mass of the International Prototype Kilogram without reference to the mass of a cubic decimeter of water or to the Kilogram of the Archives. Each of the countries which subscribed to the International Metric Convention was assigned one or more copies of the international standards; these are known as National Prototype Meters and Kilograms. The liter is a unit of capacity based on the mass standard and is defined as the volume occupied, under standard conditions, by a quantity of pure water having a mass of 1 kilogram. This volume is very nearly equal to 1 000 cubic centimeters or 1 cubic decimeter; the actual metric equivalent is, 1 liter = 1 000.028 cubic centimeters. (The change in this equivalent from the previously published value of 1 000.027 is based on a recomputation of earlier data carried out at the International Bureau of Weights and Measures.) Thus the milliliter and the liter are larger than the cubic centimeter and the cubic decimeter, respectively, by 28 parts in 1 000 000; except for determinations of high precision, this difference is so small as to be of no consequence.
The metric system, by itself, is not a complete system covering all physical measurements. A complete system requires certain additional units such, for example, as units of temperature and time.
FIGURE 1. International Bureau of Weights and Measures.
c. The International Bureau of Weights and Measures
The International Bureau of Weights and Measures (fig. 1) was established at Sèvres, a suburb of Paris, France, in accordance with the International Metric Convention of May 20, 1875. At the Bureau there are kept the International Prototype Meter and the International Prototype Kilogram, many secondary standards of all sorts, and equipment for comparing standards and making precision measurements. The Bureau, maintained by assessed contributions of the signatory governments, is truly international.
In recent years the scope of the work at the International Bureau has been considerably broadened. It now carries on researches in the fields of electricity and photometry in addition to its former work in weights and measures with which were included such allied fields as thermometry and the measurement of barometric pressures.
d. Present Status of the Metric System in the United States
The use of the metric system in this country was legalized by Act of Congress in 1866, but was not made obligatory.
The United States Prototype Meter No. 27 and United States Prototype Kilogram No. 20 are recognized as the primary standards of length and mass for both the metric and the customary systems of measurement in this country because these standards are the most precise and reliable standards available. Obviously it is not possible to accept both a meter and a yard, and both a kilogram and a pound as "primary" standards, unless there is willingness to accept the possibility of continually changing the ratio between the corresponding units. In each case one must be accepted as the primary standard and the other derived therefrom by means of an accepted relation. In the United States the yard is defined in terms of the meter, and the pound in terms of the kilogram. There is in the United States no primary standard either of length or mass in the customary system.
The use of metric units in certain athletic events in this country is undoubtedly of considerable interest to many people. Initial action by the Amateur Athletic Union was taken in November 1932, when it adopted metric distances for track events to be run in athletic meets held under the jurisdiction of that organization. Metric units for track and field events were adopted by various athletic organizations but this movement soon began to lose ground. In 1951 the use of metric distances in track and field events on national championship programs held under AAU auspices was restricted to Olympic years.
e. Arguments For and Against the Metric System
That there are arguments for and against the metric system is evidenced by the rather voluminous literature on the subject.