v^.vcv. bo^\ v\)u UNITED STATES DEPARTMENT OF COMMERCE Elliot L. Richardson, Secretary NATIONAL BUREAU OF STANDARDS ' Ernest Ambler. Acting Director Special Publication 304A Revised Augusi 1976 V Brief History of MEASUREMENT S with a Chart of the Modernized Metric System "Weights and measures may be ranked among the necessaries of life to every individual of human society. They enter into the eco- nomical arrangements and daily concerns of every family. They are necessary to every occupation of human industry; to the distribu- tion and security of every species of property; to every transaction of trade and commerce; to the labors of the husbandman; to the in- genuity of the artificer; to the studies of the philosopher; to the researches of the antiquarian, to the navigation of the mariner, and the marches of the soldier; to all the exchanges of peace, and all the operations of war. The knowledge of them, as in established use, is among the first elements of education, and is often learned by those who learn nothing else, not even to read and write. This knowledge is riveted in the memory by the habitual application of it to the em- ployments of men throughout life." , JOHN QUTNCY ADAMS Report to the Congress, 1821 Weights and measures were among the earliest tools invented by man. Primitive societies needed rudimentary measures for many tasks: constructing dwellings of an appropriate size and shape, fashioning clothing, or bartering food or raw materials. Man understandably turned first to parts of his body and his natural sur- roundings for 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 vol- umes. 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. As societies evolved, weights and measures became more complex. The invention of numbering systems and the science of mathematics made it possible to create whole systems of weights and measures suited to trade and commerce, land division, taxation, or scientific re- search. For these more sophisticated uses it was necessary not only to weigh and measure more complex things — it was also necessary to do it accurately time after time and in different places. However, with limited international ex- change of goods and communication of ideas, it is not surprising that different systems for the same purpose developed and became established in different parts of the world — even in different parts of a single continent. Tbe English System The measurement system commonly used in the United States today is nearly the same as that brought by the colo- nists from England. These measures had their origins in a variety of cultures — Babylonian, Egyptian, Roman. Anglo- Saxon, and Norman French. The an- cient "digit," "palm," "span," and "cubit" units evolved into the "inch," "foot," and "yard" through a compli- cated transformation not yet fully un- derstood. Roman contributions include the use of the number 12 as a base (our foot is divided into 12 inches) and words from which we derive many of our present weights and measures names. For exam- ple, the 12 divisions of the Roman "pes," or foot, were called unciae. Our words "inch" and "ounce" are both de- rived from that Latin word. The "yard" as a measure of length can be traced back to the early Saxon kings. They wore a sash or girdle around the waist — that could be re- moved and used as a convenient measur- ing device. Thus the word "yard" comes from the Saxon word "gird" meaning the circumference of a person's waist. Standardization of the various units and their combinations into a loosely related system of weights and measures sometimes occurred in fascinating ways. Tradition holds that King Henry I de- creed that the yard should be the dis- tance from the tip of his nose to the end of his thumb. The length of a fur- long (or furrow-long) was established by early Tudor rulers as 220 yards. This led Queen Elizabeth I to declare, in the 16th century, that henceforth the tradi- tional Roman mile of 5 000 feet would be replaced by one of 5 280 feet, mak- ing the mile exactly 8 furlongs and pro- viding a convenient relationship between two previously ill-related measures. Thus, through royal edicts, England by the 18th century had achieved a greater degree of standardization than the continental countries. The English units were well suited to commerce and trade because they had been developed and refined to meet commercial needs. Through colonization and dominance of world commerce during the 17th, 18th, THE MODERNIZED metric system The International System of Units-SI is a modernized version of the metric system established by international agreement. It provides a logical and interconnected framework tor all measurements in science, industry, and commerce. Officially abbreviated SI, the system is built upon a foundation of seven base units, plus two supplementary units, which appear on this chart along with their defini- tions. All other SI units are derived from these units. Multiples and sub- multiples are expressed in a decimal system. Use of metric weights and measures was legalized in the United States in 1866, and since 1893 the yard and pound have been defined in terms of the meter and the kilogram. The base units for time, electric current, amount of substance, and lumi- nous intensity are the same in both the customary and metric systems. cubic yards 0.764 555 quarts (iq) 946 353 ounces lavrjpl 28.349 5 pounds (avflpl 0.453 592 degrees 'S/9 taller sub FaHrefihell Iractlng32l millimeters 039 370 1 meters 3.280 84 meters 1.093 61 kilometers 0.621 371 square melers t 195 99 -hectares 2,47t 05 cubic melers 1.307 95 "liters 1.056 69 0.035 274 kilograms 2.204 62 MULTIPLES ANC PREFIXES These Pre1i.es Wtay Br, Ap plied fo All SI UnlL. Muliiplos »"<> Submulllples rrtftt. Sy 1 000 000 000 000 000 000 = 10' e.aleVal 1 000 000 000 000 000 = 10' peta ioSi a) 1 000 000 000 000 - 10 lara (lE.'a) 1 000 000 000 = 10* giga fji m 1 000 000 - 10' mega |m5 e a) 1 000 = 10 kilo Ikfi'o] 100 = 10 tieclo (rieVlo 10 = 10 dekaineVal 0.00' 0000 000 000 oo ■ 0,000 000 000 00' 0.000 000 000 000 000 000 000 000 000 00' = 10' 1 decl |deSl) d = 10 ' cent. (se"n' tT) c = 10 d mill) (mft't) m = 10 J micro (mT'kri] M = 10-" nano(nSn'i) n = 10*"plco ipB'ki] p = lO-'Memto (15m li) I SEVEN BASE UNITS LENGTH The meter Is detin&l as 1 650 763.73 wevelenglhs in vacuum of the ormge-red line ol Ihe spectrum of kryplon-86 A% Jk*Aveij U.S. DEPARTMENT OF COMMERCE NATIONAL BUREAU OF STANDARDS The SI unit of am is the The SI unit ol volume Is the cubic mete* {m"). The liter (0.001 cubic meter), although oot in SI unit. Is e fluid volume. MASS The standard Tor the unit ol mass, the kilogram, is a cylindei ot platinum-lridium alloy kept by the Interna- tional Bureau ot Weights and Measures at Paris. A du- plicate in the custody ol the National Bureau ol Stand- ards serves as the mass standard (or the United States. This is the only base unit still defined by an artifact. • "Welghi" r ■ ■ " The SI unit of force is the newton (N). One newton Is the (orce which, when u.a. phototype applied lo a 1-kilogram mass, will give 1 '"'" tha kilogram mass an acceleration of 1 (meter per second) per second. 1 N = 1 kgiti/s' /TOCO The SI unit tor work and energy ol any ' acceleration kind is the Joule (J) ->0)1m/H 1J = 1N'm The SI unit (or power of any kind Is Ihe watlfW). 1 W = 1 J/8 835110 TIME J~ The second Is defined as the duration of 9 192631 770 cycles ol the radiaiion associated with a specified transition ot Ihe ceslum-133 atom. It is realized by tuning an osclllatoi to the resonance frequency of ceslum-133 atoms es they pass through a system of magnets and a rescnant cavity into a detector. OSCjLLATHQ FIELD The number of periods or cycles per second Is called frequency. The SI unil for frequency Is the hertz (Hz), One hertz equals one cycle per second. The SI unit for speed Is the meter per second (m/s). The SI unit (or acceleration is the (meter per second) per second (m/s 1 ). Standard frequencies and correct time are broadcast from WWV. WWVB, and WWVH, and slatlons of the U.S. Navy. Many short- wave receivers pick up WWV and WWVH, on frequencies of 2,5, 5. 10, 15, and 20 megahertz ELECTRIC CURRENT The ampere is delined as that current which, it maintained in each of two long parallel wires separated by one meter in Iree space, would produce a lorce between Ihe two wires (due lo their magnetic fields) ol 2 x 10- newton lor each meter of length. T, TEMPERATURE The kelvin Is delined as the frac- tion 1/273.16 of the thermody- namic temperature of the triple point ol water. The temperature K is called "absolute zero". On Ihe commonly used Celsius temperature scale, wa- ter freezes at about °C end boils at about 100 °C. The °C is defined as an interval of 1 K, and Ihe Celsius tem- perature °C is delined as 273.15 K. 1.8 Fahrenheit degrees are equal to 1.0 °C or 1.0 K; Ihe Fahrenheit scale uses 32 °F as a temperature cor- responding to °C. AMOUNT OF SUBSTANC E The mole is the amount of substance of a system thai contains as many elemen- tary entities es there are atoms in 0.012 kilogram of carbon 12. When Ihe mole is used, the elementary entitles must be specified and may be atoms, molecules, Ions, eleclrons, other particles, or specified groups of such pa rtlctes. The slandard temperature al the triple point ol water is provided by a special cell, an evacuated glass cylinder contain- ing pure water When the cell Is cooled until a mantle ot ice forms around Ihe re- entrant well, the temperature at the Inter- lace ol solid, liquid, and vapor Is 273 16 K Thermometers to be calibrated are placed in the reentrant well. The SI unit ot concentration {of amount of substance) Is the mote per cubic moler (moi/m'). LUMINOUS INTENSITY The candela is defined as the luminous intensity of 1/600 000 of a square meter of a blackbody at the temperature of freezing platinum (2045 K). TWO SUPPLEMENTARY UNITS PLANE ANGLE The radian Is the plane angle with its vertex al Ihe cenler of a circle that Is subtended by an arc equal In length to the radius. SOLID ANGLE The SI unit ot light flux Is the lumen (Im). A source having an intensity of 1 candela In all directions radiates a light flux of 4 TT lumens. The steradian is the solid angle with its vertex at the center of a sphere lhat is sublended by an area of Ihe spherical surface equal to that ol a square wilh sides equal In length to Ihe radius. I 1 -. 'I 1 - !'. CQmilETErTB YARD 30 3! 32 33 34 35 h^W - iWlw^M^^ ^ W^ l VW- il ^ l V METER THE MODERNIZED metric system The International System of Units-SI is a modernized version of the metric system established by international agreement. It provides a logical and interconnected framework for all measurements in science, industry, and commerce. Officially abbreviated SI, the system is built upon a foundation of seven base units, plus two supplementary units, which appear on this chart along with their defini- tions. All other SI units are derived from these units. Multiples and sub- multiples are expressed in a decimal system. Use of metric weights and measures was legalized in the United States in 1866, and since 1893 the yard and pound have been defined in terms of the meter and the kilogram. The base units for time, electric current, amount of substance, and lumi- nous intensity are the same in both the customary and metric systems. cubic yards 0.764 555 0.946 353 Ss mB 28.349 S pounds (avrjpl 0.453 592 kilogram degrees '5/9 (aller sub- decrees Fafirenhelt l ranting 32l 0.039 370 1 3.280 84 Ceisij meter:. 1.093 61 yards MULTIPLES A JD PREFM ES rhess Preflfus May Be Appllod 1,, nil 51 Units Multiples »nd SuBmulllplOi Prefixes Sym 1 000 000 000 000 000 000 = 10" aia (eY a) 1 000 000 000 000 000 = 10' pelatpeVa) 1 000 000 000 000 = to' tera (ife'ft) 1 000 000 ooo = 10' glga (jt ga) 1 000 000 = 10" mega (meg a] 1 000 = 10' kilo (rill 6| 100 = 10' heclofheVlo) 10 = 10 deka ideVa) Base Unit 1 = 10" 0.1 = 10 fled (des- i) 001 = 10 centi IS*/ lT| 0.001 = 10 mllll (mH 000 001 = 10 micro iml'krol 000 000 001 = 10 nano (nan' 5) 000 000 000 001 = 10 'plco(pe'ko) 0.000 000 000 000 001 = 10 'lemtollEm'lii 0.000 000 000 000 000 001 = 10 'allolal'lo] SEVEN BASE UNITS LENGTH The meter Is delined as 1 650 76173 wavelengths In vacuum of the or inge-red line of Ihe spectrum ol Kryplon-86. U.S. DEPARTMENT OF COMMERCE NATIONAL BUREAU OF STANDARDS The SI unit of area is the aquw* meter (m r ). The SI unit ol volume l» the cubic meter (m'V The liter (0001 cubic meter), although not an SI unit, la commonly used to measure lluld volume- MASS The standard lor the unit ol mass, the kilogram, is a cylinder ol platinum-lridium alloy kept by the Interna- tional Bureau ot Weights end Measures at Paris. A du- plicate in the custody ol the National Bureau ot Stand- ards serves as the mass standard tor the United States This is the only base unit still delined by an artifact. £k The SI unit of force is the newton (N). One newion Is the torce which, when .prototype applied to a 1-kilogram mass, will give °£J Mt ttiB kilogram mass an acceleration ot 1 (meter per second) per second. 1 N = 1 kg-m/a* "OTJW ' ACCELERATION The SI unit tor work and energy of any kind Is the joule (J). 1 J = 1 N-m The SI unit tor power of any kind la Ihe wstt(W). 1 W = U/a SMIL TIME Thesecond is defined as the duration of 9 192 631 770 cycles of the radiation associated with a specified transition of the ceilum-133 atom. It is realized by tuning an oscillatoi to the resonance frequency of ceslum-133 atoms es they pass through a system of magnets and a rescnant cavity into a detector. nEcwNfCAvrmoi The number of periods or cycles per second Is called frequency. The SI unit (or Irequency Is Ihe herb (Hz). One hertz equals one cycle per second. The SI unit for speed Is the meter per second (m/s). The SI unit tor acceleration is the (meier per second) per second (tn/s 1 ). Standard frequencies and correct time are broadcast trom WW. WVWB, and WWVH. and stations ol the U.S. Navy Manv short- wave receivers pick up WWV and WWVH, on frequencies of 2.5. 5. 10, 15. and 20 megahertz ELECTRIC CURRENT Tr-e ampere is delined as that current which, If maintained in each of two long parallel wires separated by one meter in free space, would produce a force between the two wires (due to their magnetic Fields) ol 2 x 10- nnuutnn Inr r»nnh mater ol lenain newton for each meter of length. The SI unit ol eleclric resistance is the ohm (n). TEMPERATURE The kelvin Is delined as the frac- tion 1/273.16 ol the thermody- namic temperature of Ihe triple point ol water. The temperature K is called "absolute zero". . TEMPERATURE . ;„, MEASUREMENT : ■ut SYSTEMS ■ On the commonly used Celsius lemperalure scale, wa- ter Ireezes at about °C and boils at aboul 100 °C. The °C is delined as an interval ol 1 K, and the Celsius lem- peralure °C is defined as 373.15 K. 1.8 Fahrenheit degrees are equal to 1.0 °C or 1.0 K; the Fahrenheit scale uses 32 °F as a temperature cor- responding lo °C. The standard lemperalure al Ihe triple point ol waler is provided by a special cell, an evacuated glass cylinder contain- ing pure waler When ihe cell Is cooled unlil a manile ol ice lorms around Ihe re- enlranl well, Ihe lemperalure at Ihe Inlor- laceol solid, liquid, and vapor Is 273 16 K Thermometers lo be calibrated are placed inlhereenlrantwell. AMOUNT OF SUBSTANC E The mole is the amount of substance ot a system that contains as many elemen- tary entities as there are atoms in 0.012 kilogram of carbon 12. atoms, molecules. Ions, electrons, other substance) Is the mole per cubic mater particles, or specified groups of such (mol/m a ). particles. m' cubic meters 1307 95 cubic yards yd' filers 1.056 69 quarts'lq) ql 0.000 000 000 000 000 001 = 10 -alto i3,' .4, 3 kg °c grams 0.035 274 ounces (audp) oz kilograms 2.20a 62 pounds (avdpl lb degrees *9/5|inen degrees °F tvrtUgrm ■•>•»( inn Celsius add 32) Fahrenheit ssssss a. "lore .ample, 1 in = 25 i mm, so 3 Indies would be NB^Swn^PuM'MlJwi MO. U1K11 Editor,, Inl.mitlonH Sr> |3ln (25.4^) = 76 2 mm are Is a common name lor 10000 square meters sa common name lor lluid volume ol 001 cubic meter. Most symbols are written wllh lower case letters: encepllons are unlls named aller persons lor wnlch Ihe symbols are capi- CI Crtnin Otr™. unto. avtilUli r,, fpJJ^ZilO.l.mll, ■ : talized Periods are not used wllh any symbols OrtaHlSOSUndudlKXI JS INTENSfTY The candela is defined as Ihe luminous intensity of 1/600 000 of a square meter ol a blackbody at the temperature of freezing platinum (2045 K). TWO SUPPLEMENTARY UNITS PLANE ANGLE The radian Is the plane angle with its vertex al Ihe cenler of a circle that is subtended by an arc equal In length to the radius. .Mi* rl.fi. SOLID ANGLE The SI unit of light ilux is Ihe lumen (Im). A source having art Intensity of 1 candela In all directions radiates a light flux ol -'■ ~ lumens. The steradian Is Ihe solid angle with its vertex at the center of a sphere that Is sublended by an area ot Ihe spherical surlace equal to that ol a square with sides equal In lenglh to Ihe radius. YARD „ ■V+tA^' METER 27 20 29 30 31 32 33 34 35 l . ; , | t | lM . ^.rh l - ; .. ^ .i M *.M- ^ J MT . ^ . T .. MT . ..i m.?. i.i.. iT. ■ iJ^v . U 1 >'i-. , i. i.- T^ . T . 4TH . T .i.i 4 . . -.. A . # .. .4 i. ' .'. %l " ""J" A full-scale wall chart. NBS Special Publication 304 is available Irom the Superintendent ol Documents. U S Go* it Printing Office. Washington. DC 20402, lo. 65 cents-Stock No 003-003-01072-3 and 19th centuries, the English system of weights and measures was spread to and established in many parts of the world, including the American colonies. However, standards still differed to an extent undesirable for commerce among the 13 colonies. The need for greater uniformity led to clauses in the Articles of Confederation (ratified by the origi- nal colonies in 1781) and the Constitu- tion of the United States (ratified in 1790) giving power to the Congress to fix uniform standards for weights and measures. Today, standards supplied to all the States by the National Bureau of Standards assure uniformity throughout the country. The Metric System The need for a single worldwide coor- dinated measurement system was recog- nized over 300 years ago. Gabriel Mou- ton. Vicar of St. Paul in Lyons, proposed in 1670 a comprehensive decimal meas- urement system based on the length of one minute of arc of a great circle of the earth. In 1671 Jean Picard, a French astronomer, proposed the length of a pendulum beating seconds as the unit of length. (Such a pendulum would have been fairly easily reproducible, thus facilitating the widespread distribu- tion of uniform standards.) Other pro- posals were made, but over a century elapsed before any action was taken. In 1790, in the midst of the French Revolution, the National Assembly of France requested the French Academy of Sciences to "deduce an invariable standard for all the measures and all the weights." The Commission appointed by the Academy created a system that was, at once, simple and scientific. The unit of length was to be a portion of the earth's circumference. Measures for ca- pacity (volume) and mass (weight) were to be derived from the unit of length, thus relating the basic units of the system to each other and to nature. Furthermore, the larger and smaller versions of each unit were to be created by multiplying or dividing the basic units by 10 and its (powers.. This fea- ture provided a great convenience to users of the system, by eliminating the need for such calculations as dividing by 16 (to convert ounces to pounds) or by 12 (to convert inches to feet). Simi- lar calculations in the metric system could be performed simply by shifting the decimal point. Thus the metric sys- tem is a "base-10" or "decimal" system. The Commission assigned the name metre — which we spell meter — to the unit of length. This name was de- rived from the Greek word metron, meaning "a measure." The physical standard representing the meter was to be constructed so that it would equal one ten-millionth of the distance from the north pole to the equator along the meridian of the earth running near Dun- kirk in France and Barcelona in Spain. The metric unit of mass, called the "gram," was defined as the mass of one cubic centimeter (a. cube that is 1/100 of a meter on each side) of water at its temperature of maximum density. The cubic decimeter (a cube 1 / 10 of a meter on each side) was chosen as the unit of fluid capacity. This measure was given the name "liter." Although the metric system was not accepted with enthusiasm at first, adop- tion by other nations occurred steadily after France made its use compulsory in 1840. The standardized character and decimal features of the metric system made it well suited to scientific and en- gineering work. Consequently, it is not surprising that the rapid spread of the iiiiii adoqovi^osbs system coincided with an age of rapid technological development. In the United States, by Act of Congress in 1866, it was made "lawful throughout the United States of America to employ the weights and measures of the metric system in all contracts, dealings or court proceedings." By the late 1860's, even better metric standards were needed to keep pace with scientific advances. In 1875, an in- ternational treaty, the "Treaty of the Meter," set up well-defined metric stand- ards for length and mass, and estab- lished permanent machinery to recom- mend and adopt further refinements in the metric system. This treaty, known as the Metric Convention, was signed by 1 7 countries, including the United States. As a result of the Treaty, metric standards were constructed and distrib- uted to each nation that ratified the Convention. Since 1893, the interna- tionally agreed-to metric standards have served as the fundamental weights and measures standards of the United States. By 1900 a total of 35 nations — in- cluding the major nations of continental Europe and most of South America — had officially accepted the metric sys- tem. Today, with the exception of the United States and a few small countries, the entire world is using predominantly the metric system or is committed to such use. In 1971 the Secretary of Com- merce, in transmitting to Congress the results of a 3-year study authorized by the Metric Study Act of 1968, recom- mended that the U-S. change to pre- dominant use of the metric system through a coordinated national pro- gram. The Congress is now considering this recommendation. The International Bureau of Weights and Measures located at Sevres, France, serves as a permanent secretariat for the Meter Convention, coordinating the ex- change of information about the use and refinement of the metric system. As measurement science develops more pre- cise and easily reproducible ways of de- fining the measurement units, the Gen- eral Conference on Weights and Meas- ures — the diplomatic organization made up of adherents to the Convention — meets periodically to ratify improve- ments in the svstem and the standards. In 1960, the General Conference adopted an extensive revision and sim- plification of the system. The name Le Systeme International d'Unites (Inter- national System of Units), with the in- ternational abbreviation SI, was adopted for this modernized metric system. Fur- ther improvements in and additions to SI were made by the General Confer- ence in 1964, 1968, 1971, and 1975. U U.S. GOVERNMENT PRINTING Of-FICE : 1976 0-225-562