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2.4. Subdivision of Units

In general, units are subdivided by one of three systems: (a) decimal, that is into tenths; (b) duodecimal, into twelfths; or (c) binary, into halves. Usually the subdivision is continued by the use of the same system. Each method has its advantages for certain purposes and it cannot properly be said that any one method is "best" unless the use to which the unit and its subdivisions are to be put is known.

For example, if we are concerned only with measurements of length to moderate precision, it is convenient to measure and to express these lengths in feet, inches, and binary fractions of an inch, thus 9 feet 4% inches. If, however, these measured lengths are to be subsequently used in calculations of area or volume, that method of subdivision at once becomes extremely inconvenient. For that reason civil engineers, who are concerned with areas of land, volumes of cuts, fills, excavations, etc., instead of dividing the foot into inches and binary subdivisions of the inch, divide it decimally, that is, into tenths, hundredths, and thousandths of a foot.

The method of subdivision of a unit is thus largely made on the basis of convenience to the user. The fact that units have commonly been subdivided into certain subunits for centuries does not preclude these units also having another mode of subdivision in some frequently used cases where convenience indicates the value of such other method. Thus the gallon is usually subdivided into quarts and pints, but the majority of gasoline-measuring pumps of the price-computing type are graduated to show tenths of a gallon. Although the mile has for centuries been divided into rods, yards, feet, and inches, the odometer part of an automobile speedometer indicates tenths of a mile. Although our dollar is divided into 100 parts, we habitually use and speak of halves and quarters. An illustration of rather complex subdividing is found on the scales used by draftsmen. These scales are of two types: (a) architects, which are commonly graduated with scales in which 2, 16, %, 4, 38, 2, 4, 1, 12, and 3 inches, respectively, represent 1 foot full scale, as well as having a scale graduated in the usual manner to 1⁄2 inch; and (b) engineers, which are commonly subdivided to 10, 20, 30, 40, 50, and 60 parts to the inch.

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Proper fitting and functioning of interchangeable mechanical parts depend upon precisely calibrated gage blocks. The NBS checks master gage blocks of industry. Shown on the table are various gage blocks and ring gages used by industry along with some of the equipment used by NBS for this calibration (see page 8).

The dictum of convenience applies not only to subdivisions of a unit but also to multiples of a unit. Elevations of land above sea level are given in feet even though the height may be several miles; the height of aircraft above sea level as given by an altimeter is likewise given in feet, no matter how high it may be.

On the other hand, machinists, toolmakers, gage makers, scientists, and others who are engaged in precision measurements of relatively small distances, even though concerned with measurements of length only, find it convenient to use the inch, instead of the tenth of a foot, but to divide the inch decimally to tenths, hundredths, thousands, etc., even down to millionths of an inch. Verniers, micrometers, and other precision measuring instruments are usually graduated in this manner. Machinist scales are commonly graduated decimally along one edge and are also graduated along another edge to binary fractions as small as 4 inch. The scales with binary fractions are used only for relatively rough


It is seldom convenient or advisable to use binary subdivisions of the inch that are smaller than 64. In fact, 2-, 6-, or %-inch subdivisions are usually preferable for use on a scale to be read with the unaided eye.

2.5. Arithmetical Systems of Numbers

The subdivision of units of measurement is closely associated with arithmetical systems of numbers. The systems of weights and measures used in this country for commercial and scientific work, having many origins as has already been shown, naturally show traces of the various number systems associated with their origins and developments. Thus (a) the binary subdivision has come down to us from the Hindus, (b) the duodecimal system of fractions from the Romans, (c) the decimal system from the Chinese and Egyptians, some developments having been made by the Hindus, and (d) the sexagesimal system (division by 60), now illustrated in the subdivision of units of angle and of time, from the ancient Babylonians. The suggestion is made from time to time that we should adopt a duodecimal number system and a duodecimal system of weights and measures. Another suggestion is for an octonary number system (a system with 8 as the basis instead of 10 in our present system or 12 in the duodecimal) and an octonary system of weights and measures. Such suggestions have certain theoretical merits, but are very impractical because it is now too late to modify our number system and unwise to have arbitrary enforcement of any single system of weights and measures. It is far better for each branch of science, industry, and commerce to be free to use whatever system has been found by experience best to suit its needs. The prime requisite of any system of weights and measures is that the units be definite. It is also important that the relations of these units to the units of other systems be definite, convenient, and known, in order that conversion from one system to another may be accurately and conveniently made.

3. Standards of Length, Mass, Time, and Capacity

3.1. Standards of Length

The primary standard of length in the United States is the United States Prototype Meter 27, a platinum-iridium (90% platinum, 10% iridium) line standard having an X-shaped cross section. The length of this bar, which is deposited at the National Bureau of Standards in Washington, is known in terms of the International Prototype Meter at the International Bureau of Weights and Measures at Sèvres, near Paris, France.


The U. S. yard is defined, following the policy stated in the Mendenhall Order of April 5, 1893, as follows:

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! This order stated that the Office of Weights and Measures, with the approval of the Secretary of the Treasury, would in the future regard the International Prototype Meter and Kilogram as fundamental standards, and that the customary units would be derived therefrom in accordance with the Act of July 28, 1866.

3 600 The relation 1 U. S. yard= meter, derived from the Law of 1866 that made the use of the 3 937 metric system legal in the United States, was confirmed by later comparisons of copies of the British yard with the U. S. national copies of the meter. Since the Mendenhall Order it has been used as an exact relation. From this it follows that 1 U. S. inch is slightly larger than 0.025 400 05 meter, or 25.400 05 millimeters.

For industrial purposes a relation between the yard and the meter has been adopted by the American Standards Association (ASA B48.1-1933), and by similar organizations in 15 other countries. This relation is

1 inch=25.4 millimeters (exactly), that is, 0.025 4 meter (exactly),

from which 1 yard=0.914 4 meter (exactly), or 914.4 millimeters (exactly).

The adoption of this relation by industry, for use in making conversions between inches and millimeters, did not change the official definition of the yard or of the meter. Its legal adoption in the United States and in Great Britain would be a desirable step in the direction of international uniformity in precision length measurements.

In Great Britain the Imperial Yard is represented by a yard bar made of bronze in 1844. The relation between that yard and the meter according to the most recent published determinations is

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Although opinions about the British yard standard are conflicting, there is substantial evidence that the British yard has shortened by a few parts in a million during the past century. Uncertainties in some of the measurements and in the thermometric scale of the early compari

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William F. Meggers positions the eyepiece of an optical train prior to observation of the circular interference fringes of the green light from a mercury 198 lamp. This electrodeless lamp contains about 1 milligram of mercury of atomic weight 198. The lamp is excited in a radiofrequency field (left foreground). The interference pattern portrayed in the background enables researchers to make accurate length measurements. The NBS-Meggers Mercury 198 lamp is one of the light sources proposed for use in defining length by reference to a specified wavelength of light.

sons, however, make it impossible to state the difference between the U. S. and the British yards a century ago or to be certain of the amount that the British Imperial Yard has changedsince that date.

In 1927 the Seventh General (International) Conference on Weights and Measures approved a resolution stating the wavelength of the red cadmium radiation under standard conditions of temperature, pressure, and humidity to be 0.000 643 846 96 millimeter. From this the length of the meter in terms of the wavelength of light was provisionally expressed as equal to 1 553 164.13 wavelengths of cadmium light under the specified conditions. With the advances made in physics in recent years better sources of monochromatic radiation for use as wavelength standards of length have been developed. The National Bureau of Standards has proposed that the wavelength of the green radiation of the 198 isotope of mercury (fig. 3) be adopted as the fundamental standard of length instead of the International Prototype Meter. The change proposed is in the standard; the unit would not be altered. Other laboratories have proposed other radiations, and investigations are now in progress in a number of national laboratories in various countries to determine what length standard will be the most stable and the most suitable for the purpose. It is believed that a natural phenomenon such as monochromatic radiation will be more unchangeable than a metal standard, even though no change in length of the international platinum-iridium bar seems to be detectable.

a. Tests and Calibrations of Length Standards

The National Bureau of Standards tests standards of length including meter bars, yard bars, miscellaneous precision line standards, steel, tapes, invar geodetic tapes (see fig. 4), precision gage blocks, micrometers, and limit gages. It also measures the linear dimensions of miscellaneous apparatus such as penetration needles, cement sieves, and haemacytometer chambers. In general the Bureau accepts for test only apparatus of such material, design, and construction as to ensure accuracy and permanence sufficient to justify test by the Bureau. Tests are made in accordance with test-fee schedules, copies of which may be obtained by application to the Bureau.

The Bureau does not test carpenters rules, machinists scales, draftsmans scales, and the like. Such apparatus, if test is required, should be submitted to State or local weights and measures officials. NBS Circular 572, Calibration of Line Standards of Length and Measur

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In this laboratory the Bureau calibrates steel tapes used by surveyors and engineers and the more precise base-line tapes used by the U. S. Coast and Geodetic Survey.

ing Tapes at the National Bureau of Standards, by Lewis V. Judson (in press) contains additional information on this subject.

3.2. Standards of Mass

The primary standard of mass for this country is United States Prototype Kilogram 20, which is a platinum-iridium standard kept at the National Bureau of Standards. The value of this mass standard is known in terms of the International Prototype Kilogram, a platinumiridium standard which is kept at the International Bureau of Weights and Measures.

For many years the British standards were considered to be the primary standards of the United States. Later, for over 50 years, the U. S. avoirdupois pound was defined in terms of the Troy Pound of the Mint, which is a brass standard kept at the United States Mint in Philadelphia. In 1911 the Troy Pound of the Mint was superseded, for coinage purposes, by the Troy Pound of the National Bureau of Standards. Since 1893 the avoirdupois pound has been defined in terms of the United States Prototype Kilogram 20 by the relation:

1 avoirdupois pound=0.453 592 427 7 kilogram.

Insofar as can be determined, these changes in definition have not made any change in the actual value of the pound.

The grain is 1/7 000 of the avoirdupois pound and is identical in the avoirdupois, troy, and apothecaries systems. The troy ounce and the apothecaries ounce differ from the avoirdupois ounce but are equal to each other, and equal to 480 grains. The avoirdupois ounce is equal to 4371⁄2 grains.

In Great Britain the Imperial Pound, an avoirdupois pound, is represented by a physical standard made in 1845. According to the most recent published determination

1 British Imperial Pound=0.453 592 34 kilogram.

There is substantial evidence that the British standard has diminished by about 1 part in 5 million since 1883 in relation to the kilogram, and is therefore smaller than the U. S. pound by that amount.

a. Distinction Between Mass and Weight

The mass of a body is a measure of the quantity of material in the body. The weight of a body is defined as the force with which that body is attracted toward the earth. Confusion sometimes arises from the practice of referring to standards of mass as "weights" and from the fact that such standards are compared by "weighing" one against another by means of a balance. Standard "weights" are, in reality, standards of mass.

Another practice which tends to confusion is that of using the terms kilogram, gram, pound, etc., in two distinct senses; first, to designate units of mass, and second, to designate units of weight or force. For example, a body having a mass of one kilogram is called a kilogram (mass) and the force with which such a body is attracted toward the earth is also called. a kilogram (force).

The International Kilogram and the U. S. Prototype Kilogram are specifically defined by the International Conference on Weights and Measures as standards of mass. The U. S. pound, which is derived from the International Kilogram, is, therefore, a standard of mass.

So long as no material is added to or taken from a body its mass remains constant. Its weight, however, varies with the acceleration of gravity, g. For example, a body would be found to weigh more at the poles of the earth than at the equator, and less at high elevations than at sea level. (Standard acceleration of gravity, adopted by the International Committee on Weights and Measures in 1901 is 980.665 cm/sec2. This value corresponds nearly to the value at latitude 45° and sea level.)



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