U. S. DEPARTMENT OF COMMERCE

R. P. LAMONT, Secretary BUREAU OF STANDARDS

GEORGE K. BURGESS, Director MISCELLANEOUS PUBLICATION No. 135

Supersedes Miscellaneous Publication No. 2

(2d ed., Sept. 21, 1922) THE INTERNATIONAL

METRIC SYSTEM

OF WEIGHTS AND

MEASURES

[Issued May 26, 1932]

UNITED STATES

GOVERNMENT PRINTING OFFICE

WASHINGTON: 1932

For sale by the Superintendent of Documents, Washington, D. C.

M 135 THE INTERNATIONAL METRIC SYSTEM OF WEIGHTS

AND MEASURES 1

ABSTRACT

This publication presents a brief account of the international metric system

of weights and measures. Its purpose is to give such information as will ade- quately answer some of the more simple questions addressed to the bureau on

this subject and to set forth a working knowledge of the system. The publication gives a brief account of the origin of the metric system, information concerning the International Bureau of Weights and Measures, the international standards, and the national prototype standards of the United States. A

synopsis of the system is given which shows the derivation of the primary units, their interrelation one with another, the method of forming the multiples and

submultiples, the abbreviations used, comparisons of the units with those of our customary system of weights and measures, and tables of equivalents. The

status of the metric system in the United States is shown by congressional enactments and departmental orders. CONTENTS

Page

I. Introduction 2

II. Standards of length and mass 3

III. Maintenance of the International Bureau of Weights and Measures. 3 IV. Synopsis of the system 3

1. Formation of multiples and submultiples 4

2. Units of length 4

3. Units of area 5

4. Units of volume 5

5. Units of capacity 6

6. Units of weight (or mass) 6

V. Status of the International Metric System in the United States 7

1. Constitutional authority to fix standards 7

2. The metric system legalized 7

3. The metric standards adopted as fundamental 7

4. Metric balances furnished certain post offices 7

5. Metric weights used for certain coins 7

6. Congress provides metric standards for the States of the Union, land-grant agricultural colleges, and the Smithsonian Institution 8

7. United States joins in estabhshing international bureau 8

8. Congress adopts the metric units for electrical measures 8

9. Metric system required in the medical work of the War

Department, the Navy Department, and the Bureau of the Public Health Service of the Treasury Department- _ 8

10. Metric carat adopted as unit for diamonds and other precious

stones 9

11. Metric system optional in Porto Rico 9

12. Metric system made the legal system in the Philippine Is- lands 9

VI. Equivalents of certain units 10

VII. Comparison of the metric and customary units from lto9 11

1. Length 11

2. Area 11

3. Volume 11

4. Capacity—liquid measure 12

5. Capacity—dry measure 12

6. Mass 12

VIII. Official abbreviations of international metric units 13

1 Revised by William Parry. 107212°—32 1
2 BUREAU OF STANDARDS

I. INTRODUCTION

The following was prepared to answer some of the more simple

questions addressed to the Bureau of Standards in regard to the

metric system of weights and measures and its use. The essential features of the system were embodied in a report

made to the French National Assembly by the Academy of Sciences

in 1791. A number of other nations were invited to cooperate with

France in establishing the new system, and Denmark, Holland,

Spain, Switzerland, and several other countries were represented on

an international commission which met in Paris in 1799 to accept

the metric standards constructed under the direction of the French

Institute. These standards were known as the standards "of the

archives."

Although the metric system very soon attracted the favorable

attention of other nations, it was not until 40 years later that its use became general in France. Since 1840 its use has rapidly spread

until now it is either obligatory or permissive in practically every

civilized country in the world. Its use was made ' ' lawful throughout

the United States" by act of Congress in 1866,2 and at the same time

provision was made to supply every State in the Union with a set of

metric weights and measures. No organized effort had been made up to this time to supply the

different countries with authentic copies of the metric prototypes

which were preserved in the archives of France. In order to meet

the demand for accurate standards whose relation to one another

would be known with the highest precision, metric conventions were held in Paris in 1870 and 1872, which were attended by official delegates from about 30 countries. At these conferences committees were appointed to investigate the best form and material for the

proposed new standards. In 1875 a treaty was signed at Paris by

17 of the principal nations of the world, the United States being

among the number, which provided for the permanent organization

of an International Bureau of Weights and Measures under the

direction of an International Committee. The most important work

of the International Committee was to provide for the construction

of a sufficient number of platinum-iridium meters and kilograms to meet the demand of the interested nations. The comparison of all these standards with one another and with the original meter and

kilogram was made at the International Bureau which had been

established near Paris on neutral territory ceded to the International

Committee by the French Government. Following the completion

of this work in 1889, a certain meter and a certain kilogram were

selected and adopted as the international prototype standards, dis- placing the meter and the kilogram "of the archives" which had

heretofore been regarded as the standards. Prototype meters and

kilograms were distributed by lot to the countries signatory to the

Convention of 1875. The international prototype meter and kilo- gram are preserved in a special underground vault at the International

Bureau and are accessible only to the International Committee.

2 R. S. 3569.
METRIC SYSTEM OF WEIGHTS AISTD MEASURES 3

II. STANDARDS OF LENGTH AND MASS

The United States secured two meters (Nos. 27 and 21) and two

kilograms (Nos. 20 and 4), which are now preserved at the Bureau

of Standards at Washington, D. C. Meter No. 27 and kilogram

No. 20 serve as the primary standards of length and mass of the United

States. It is the plan of the International Committee to intercompare all the national meters and kilograms with the international

prototypes at regular intervals, or whenever considered necessary.

Meter No. 27 has twice been taken to the International Bureau of

Weights and Measures for verification, the first time in 1903 and again

in 1921. No sensible change has taken place. In each instance the

bar was taken personally by a representative of the Bureau of Standards, and the utmost care was exercised for its protection against

damage. Meter No. 21, used as a secondary standard, was taken to the International Bureau of Weights and Measures in August, 1931, for recomparison. Neither of the kilograms has yet been returned to the

International Bureau of Weights and Measures for recomparison.

III. MAINTENANCE OF THE INTERNATIONAL BUREAU

OF WEIGHTS AND MEASURES

At the present time the International Bureau of Weights and

Measures is maintained jointly by the following named 32 countries,

under the terms of the Metric Convention, a treaty agreed upon

May 20., 1875: Argentina; Austria; Belgium; Brazil; Bulgaria;

Canada; Chile; Czechoslovakia; Denmark; Finland; France and

Algeria; Germany; Great Britain; Hungary; Irish Free State; Italy;

Japan; Mexico; Norway; Peru; Poland; Portugal; Rumania; Serbs,

Croats, and Slovenes; Siam; Spain; Sweden; Switzerland; Union of

Soviet Socialist Republics; United States; and Uruguay.

IV. SYNOPSIS OF THE SYSTEM

The units of the metric system at the outset were all derived from

the unit of length, the meter, which was defined as one ten-millionth

part of the earth 's quadrant. The unit of volume, the cubic decimeter

or the liter, was defined as a cube of one-tenth meter on a side; and

the unit of mass, the kilogram, was defined as the mass of a cubic

decimeter, or liter, of pure water when at the temperature of its maximum density, 4° C.

It was found, however, that masses could be compared with a higher degree of accuracy than that with which volumes could be

determined, and it was, therefore, preferable to have a material standard of mass specifically defined, rather than one derived from the

unit of length, through the unit of volume. A specific mass, the

international prototype kilogram, was, therefore, adopted as the

standard of mass, and the unit of volume, the liter, was then redefined

in terms of the standard of mass ; the liter being defined as the volume of a kilogram of pure water at the temperature of its maximum density.

The present basis of the metric system of weights and measures may, therefore, be summarized as follows: (1) A material standard

of length, the international prototype meter; (2) a material standard

of mass, the international prototype kilogram; (3) a standard of

volume, the cubic decimeter, derived from the unit of length; and (4) a standard of volume, the liter, derived from the unit of mass.
4 BUEEAU OF STANDARDS

Some advantages claimed for the metric system are

:

1. The decimal relation between the units.

2. The simple relation of the units of length, area, volume, and

weight to one another.

3. The uniform and self-defining names of units.

1. FORMATION OF MULTIPLES AND SUBMULTIPLES

The metric tables are formed by combining the words " meter,"

"gram," and " liter" with the six numerical prefixes, as in the

following tables:

PREFIXES MEANING UNITS

milli- centi- deci-Unit

dekahectokiloone thousandth one hundredth

one tenth one

ten one hundred

one thousand

i 1000

1 100

110

10

1 100

1 1000

1

0.001

.01

.1 1 10

[100 1,000

meter" for length,

gram" for weight or mass,

liter" for capacity.

2. UNITS OF LENGTH

millimeter centimeter decimeter

METER

dekameter

hectometer

0.001 meter.

.01 meter.

.1 meter.

1 meter.

10 meters. 100 meters. kilometer «= 1,000 meters. Where the mile is used in England and the United States for

measuring distances, the kilometer (1,000 meters) is used in metric

!l|lli!|(Mljll!l lliljllll llll|llll|ll 6 8 CM 10

jiii mi imlim nil hill llll llll

1

1

1

1

1 1 1 j

1

1

1 4^

1

m ^ 12 3 INCHES. 4

i 1 1 f i f i f 1 1 j f 1 1 1 ililihliliiili!ili!i!ilililili!ili[i!ili!ili]ii

Figure 1.

Comparison scale: 10 centimeters and 4 inches. (Actual size) countries. The kilometer is about five-eighths of a mile. There

are about 1,609 meters in a statute mile, 20 meters in a chain, and 5

meters in a rod.

The meter is used for dry goods, merchandise, engineering construe

tion, building, and other purposes where the yard and foot are used

The meter is about 10 per cent longer than the yard.


METRIC SYSTEM OF WEIGHTS AND MEASURES 5

The centimeter and millimeter are used instead of the inch and its fractions in machine construction and similar work. The centimeter, as its name shows, is the hundredth of a meter. It is used

in cabinet work, in expressing sizes of paper, books, and in many

other cases where the inch is used. The centimeter is about twofifths of an inch and the millimeter about one twenty-fifth of an inch.

The millimeter is divided for finer work into tenths, hundredths, and

thousandths.

3. UNITS OF AREA

The table of areas is formed by squaring the length measures, as

in our common system. For land measure 10 meters square is called

and "are" (meaning "area"). The side of one are is about 33 jeet.

The hectare is 100 meters square, and, as its name indicates, is 100 ares, or about 2){ acres. An acre is about 0.4 hectare. A standard United States quarter section contains approximately 65 hectares.

A square kilometer contains 100 hectares.

For smaller measures of surface the square meter is used. The

square meter is about 20 per cent larger than the square yard. For

still smaller surfaces the square centimeter and square millimeter are

used. A square inch contains about 6K square centimeters. For

exact values, see pp. 10, 11.

4. UNITS OF VOLUME

The units of volume are the liter and the cubic decimeter and

their various multiples and subdivisions. The liter is slightly larger

than the cubic decimeter, the relation, as exactly as it has been determined,3 being

1 liter =1.000027 cubic decimeters.

The liter and its one-thousandth part, the milliliter, are ordinarily

employed as the units of volume in measurements of volume and

density of liquids. The milliliter is often improperly designated as the cubic centimeter or the "cc." The correct designation is "ml."

The cubic decimeter and its multiples and subdivisions are employed

in determinations of volume derived from linear measurements.

The cubic measures are the cubes of the linear units. The cubic meter (sometimes called the stere, meaning "solid") is the unit of

volume. The cubic meter is used in place of the cubic yard and is about 30 per cent larger. This is used for "cuts and fills" in grading

land, measuring timber, expressing contents of tanks and reservoirs,

flow of rivers, dimensions of stone, tonnage of ships, and other places

where the cubic yard and foot are used. The thousandth part of

the cubic meter is called the cubic decimeter. (See table of capacity

units.)

For small volumes of liquids the milliliter (ml) is used. This

volume of water weighs a gram, which is the unit of weight or mass. There are about 16 milliliters in a cubic inch. The milliliter is the

unit of volume used by chemists as well as in pharmacy, medicine,

surgery, and other technical work. One thousand milliliters make

one liter.

8 Trav. et Mem. cm Bureau International des Poicls et Mesures, XIV; 1910.


6 BUREAU OF STANDARDS

5. UNITS OF CAPACITY

milliliter = 0.001 liter centiliter == .01 liter deciliter = .1 liter LITER 1 liter dekaliter = 10 liters hectoliter = 100 liters kiloliter = 1,000 liters The hectoliter (100 liters) serves the same purposes as the United

States bushel (2,150.42 cubic inches), and is equal to nearly 3 bushels.

A peck is about 9 liters. The liter is used for measurements com- monly given in the gallon, or in the liquid or dry quarts, a liter being

5 per cent larger than our liquid quart and 10 per cent smaller than

the dry quart. A liter of water at the temperature of its greatest

density, 4° C, weighs exactly a kilogram, that is, 1,000 grams. A

thousand liters of water weigh 1 metric ton.

6. UNITS OF WEIGHT (OR MASS)

milligram = 0.001 gram

centigram = .01 gram

decigram == .1 gram

GRAM = 1 gram

dekagram - 10 grams

hectogram — 100 grams

kilogram = 1,000 grams Measurements commonly expressed in long tons or short tons are

stated in metric tons (1,000 kilograms). The metric ton falls between

Figure 3.

Relative size of 2-pound and 1-kilogram (brass) weights our long and short tons and serves the purpose of both. The kilo- gram and "half kilo" serve for everyday trade, the latter being about

10 per cent larger than the pound. The kilogram is approximately
METRIC SYSTEM OP WEIGHTS AND MEASURES 7

2.2 pounds. The gram and its multiples and divisions are used for the same purposes as ounces, pennyweights, drams, scruples, and grains.

Figure

5 5.— Relative

size of gram and

scruple (brass)

weights

V. STATUS OF THE INTERNATIONAL METRIC SYSTEM

IN THE UNITED STATES

1. CONSTITUTIONAL AUTHORITY TO FIX STANDARDS

"The Congress shall have power to * * * fix the standard

of weights and measures." (Constitution of the United States, Art.

1, sec. 8, par. 5.)

2. THE METRIC SYSTEM LEGALIZED

"It shall be lawful throughout the United States of America to employ the weights and measures of the metric system, * * *." (Revised Statutes of the United States, sec. 3569.)

3. THE METRIC STANDARDS ADOPTED AS FUNDAMENTAL

" * * * the office of weights and measures * * * will in

the future regard the international prototype meter and kilogram

as fundamental standards, and the customary units, the yard and

the pound, will be derived therefrom in accordance with the act

of July 28, 1866." (Order approved by the Secretary of the Treasury,

April 5, 1893.)

4. METRIC BALANCES FURNISHED CERTAIN POST OFFICES

"The Postmaster General shall furnish to the post offices exchanging mails with foreign countries, and to such other offices as he may

deem expedient, postal balances denominated in grams of the metric

system., fifteen grams of which shall be the equivalent for postal

puposes, of one-half ounce avoirdupois, and so on in progression."

(Revised Statutes of the United States, sec. 3880.)

5. METRIC WEIGHTS USED FOR CERTAIN COINS

" * * * weight, of the half-dollar shall be twelve grams and

one-half of a gram; the quarter-dollar and the dime shall be, respectively, one-half and one-fifth of the weight of said half-dollar."

(Revised Statutes of the United States, sec. 3513.)

Figtjke 4.

Relative size of avoirdupois ounce, 30-gram, and troy ounce (brass) weights
8 BUREAU OF STANDARDS

6. CONGRESS PROVIDES METRIC STANDARDS FOR THE STATES OF

THE UNION, LAND-GRANT AGRICULTURAL COLLEGES, AND THE

SMITHSONIAN INSTITUTION

"Be it resolved by the Senate and House of Representatives oj the United States of America in Congress assembled. That the Secretary

of the Treasury be, and he is hereby, authorized and directed to furnish to each State, to be delivered to the governor thereof, one

set of the standard weights and measures of the metric system for

the use of the States, respectively." (Joint resolution of Congress

approved July 27, 1866.)

"Resolved by the Senate and House of Representatives of the United

States of America in Congress assembled, That the Secretary of the

Treasury be, and he is hereby, directed to cause a complete set of

all the weights and measures adopted as standards to be delivered

to the governor of each State in the Union, for the use of agricultural

colleges in the States, respectively, which have received a grant of

lands from the United States, and also one set of the same for the

use of the Smithsonian Institution: * * *." (Joint resolution

of Congress, approved March 3, 1881.)

7. UNITED STATES JOINS IN ESTABLISHING INTERNATIONAL BUREAU

"The high contracting parties engage to establish and maintain,

at their common expense, a scientific and permanent international

bureau 4 of weights and measures, the location of which shall be at

Paris." (Extract from convention of 1875, signed for the United

States by the United States ambassador to France.)

8. CONGRESS ADOPTS THE METRIC UNITS FOR ELECTRICAL

MEASURES

It was enacted by the Senate and House of Representatives that

the international electrical units based on the metric system shall be the legal units of electrical measure in the United States. (See

Revised Statutes of the United States, Supplement, vol. 2, chap.

131, 1894.)

9. METRIC SYSTEM REQUIRED IN THE MEDICAL WORK OF THE WAR

DEPARTMENT, THE NAVY DEPARTMENT, AND THE BUREAU OF

THE PUBLIC HEALTH SERVICE OF THE TREASURY DEPARTMENT

(a) "Pharmacy management. * *

* "(b) Records.

"1. In time of peace and, so far as practicable, in time of war all prescriptions will be written in the metric system. * * (Army

Regulations, 1929, Regulation 40-590, par. 18, sub.-par. 18-b (1).)

(6) "The metric system of weights and measures shall hereafter be

employed in the Medical Department of the Navy." (Order approved by the Secretary of the Navy, April 15, 1878.) 6 (c) "Officers shall, for all official, medical, and pharmacal purposes,

make use of the metric system of weights and measures." (Regulations of the U. S. Public Health Service, 1931, sec. 856.)

4 This bureau has the custody of the international standards of the metric system, to which all metric

prototypes of the world are referred for verification . It was established and is maintained jointly by various governments, a list of those now contributing to its support is given on page 3.

6 The metric system is now used exclusively only in the medical prescription work of the Bureau of Medicine and Surgery.
METRIC SYSTEM OF WEIGHTS AND MEASURES 9

10. METRIC CARAT ADOPTED AS UNIT FOR DIAMONDS AND OTHER

PRECIOUS STONES

"Beginning July 1, 1913, the Bureau of Standards will recognize the

international metric carat of 200 milligrams as the unit of weight for

diamonds and other precious stones and will use this unit for the purposes of certification of all carat weights submitted to the bureau for

test." (Circular No. 43, Bureau of Standards, issued November 1, 1913.)

"On and after July 1, 1913, the unit of weight for imported diamonds, pearls, and other precious stones will be the metric carat of

200 milligrams.

"Collectors at ports now equipped with scales for weighing precious

stones will make requisition for a new set of weights based upon such

carat.'

7 (Treasury Department order, June 17, 1913, to collectors and

other officers of the customs.)

11. METRIC SYSTEM OPTIONAL IN PORTO RICO

"Section 1.—That the metric system of weights and measures, and

the imperial system customarily used in the United States in so far

as the same is described by this act, are hereby recognized and established in Porto Rico for use in all industrial and commercial transactions, * * *." (Act No. 135, approved, August 18, 1913.)

12. METRIC SYSTEM MADE THE LEGAL SYSTEM IN THE PHILIPPINE

ISLANDS

"The weights and measures to be used througnout the Philippine

Islands are those of the metrie system, with the foliowing units: * * * "The metric system of weights and measures, with its recognized

scales, shall be used in all contracts, deeds, and other instruments

publicly and officially attested, and in all official documents; and,

except as hereinbelow provided, only weights and measures of the

metric system shall be officially sealed and licensed.

"In the purchase and sale of manufactured lumber the English sys- tem of measures may be employed; and in ordering commodities or

articles from abroad such weights and measures may be employed as

are commonly used in the country to which the order is sent or from

which the goods are shipped." (Administrative Code, 1917, vol. 2, Art. IX, p. 8, sees. 32 and 33.)
10 BUREAU OF STANDARDS

. VI. EQUIVALENTS OF CERTAIN UNITS

These values are given to a larger number of decimal places than

will be found in the tables following.

Centimeter Meter

Square centimeter

Square meter

Hectare Cubic meter

Liter Liter Liter Hectoliter Gram

Kilogram

Inch

Yard

Square inch

Square yard Acre Cubic yard

Gallon

Liquid quart

Dry quart

Bushel

Grain

Pound, avoirdupois

0.3937 inch. 39.37 inches (exactly). .1549997 square inch. 1.195985 square yards. 2.47104 acres. 1.3079428 cubic yards. .264178 gallon. 1.05671 liquid quarts. .908102 dry quart. 2.83782 bushels. 15.432356 grains. . 2.204622341 pounds, avoirdupois. 2.540005 centimeters. .9144018 meter. 6.451626 square centimeters. .8361307 square meter. .404687 hectare. .7645594 cubic meter. 3.785332 liters. .946333 liter. 1.101198 liters. 35.23833 liters. .064798918 gram.

.4535924277 kilogram.
VII. COMPARISON OF METRIC AND CUSTOMARY UNITS

FROM 1 TO 9

1. LENGTH

Inches Millimeters

(in.) (mm)

Feet Meters

(ft.) (m) Yards Meters(yd.) (m) Rods Meters

(rd.) (m) U. S. miles Kilometers(mi.) (km)

0.03937=1 .07874=2 .11811=3 .15748=4

1=0. 304801 2= .609601 3= .914402 4=1. 219202

1=0.914402 2=1.828804 3 =2. 743205 4=3. 657607

0. 198838 = 1

.397677 = 2

.596515=3 .795354=4

0. 621370=1

1. 242740=2

1.864110 =3

2. 485480=4

.19685=5

. 23622=6

.27559=7

.31496 =8

.35433 =9

5 = 1. 524003 6=1.828804 7=2. 133604 8 =2. 438405 9=2. 743205

5 =4. 572009 6=5. 486411 7=6. 400813 8=7.315215 9=8. 229616.994192=5

1. 193030=6

1. 391869=7

1. 590707=8

1. 789545=9

3. 106850=5

3. 728220=6

4.349590=7

4.970960=8

5. 592330 =9

1= 25.4001 2= 50.8001 3 = 76.2002 4=101. 60023. 28083 = 1

6. 56167=2

9. 84250=3

13. 12333 = 4

1. 093611 = 1

2. 187222=2

3. 280833 =3

4. 374444 =4

1= 5.02921 2=10. 05842 3 = 15. 08763 4=20. 11684

1= 1.609347 2 = 3.218694 3 = 4.828042 4= 6.437389 5=127.0003

6=152.4003

7=177.8004 8 =203. 2004 9 =228. 6005

16.40417=5

19. 68500 =6

22. 96583=7

26.24667=8

29. 52750=9

5. 468056=5

6. 561667=6

7. 655278=7

8.748889=8

9. 842500=9

5 =25. 14605 6=30. 17526 7 =35.20447 8=40. 23368 9=45. 26289

5= 8.046736 6= 9.656083 7=11.265431 8 = 12. 874778 9=14. 484125

2. AREA

Square Square

inches centimeters

(sq. in.) (cm2 )

Square Square

feet meters

(sq. ft.) (m2 )

Square Square

yards meters

(sq. yd.) (m2 )

Acres Hectares

(A.) (ha)

Square Square

miles kilometers

(sq. mi.) (km2)

0. 15500=1 .31000=2

.46500=3

. 62000=4

1=0. 09290 2= .18581 3= .27871 4= .37161

1=0.8361 2 = 1.6723 3 =2. 5084 4=3. 3445

1=0.4047 2= .8094 3 = 1.2141 4=1. 6187

0. 3861 = 1 .7722=2

1.1583=3

1. 5444 =4

. 77500=5

.93000=6

1.08500=7 1.24000=8

1. 39500=9

5= .46452 6= .55742 7= .65032 8= .74323 9= .83613

5=4. 1807 6=5. 0168 7 =5. 8529 8 =6. 6890 9=7. 5252

5=2.0234 6=2. 4281 7 =2. 8328 8=3. 2375 9=3. 6422

1. 9305=5

2.3166=6

2.7027=7

3. 0888=8

3. 4749 =9

1= 6.452 2 = 12.903 3 = 19. 355 4=25. 80710.764=1

21. 528 =2

32. 292 =3

43. 055=4

1. 1960=1

2. 3920=2

3. 5880=3

4. 7839 =4

2. 471 = 1

4. 942=2

7.413=3

9.884 =4

1= 2.5900 2= 5.1800 3= 7.7700 4=10. 3600 5=32. 258 6=38. 710 7=45. 161 8=51.613

9=58. 065

53. 819=5

64. 583=6

75. 347=7

86.111=8

96. 875=9

5. 9799=5

7. 1759=6

8. 3719=7

9. 5679=8

10. 7639=9

12. 355=5

14. 826=6

17. 297=7

19. 768=8

22. 239=9

5=12.9500 6=15. 5400 7 = 18. 1300 8 =20. 7200 9=23. 3100

3. VOLUME

Cubic Cubic

inches centimeters

(cu. in.) (cm3)

Cubic Cubic

feet meters

(cu. ft.) (m3)

Cubic Cubic

yards meters

(cu. yd.) (m3) Cubic Liters inches(cu. in.) (1)

Cubic Liters

feet

(cu. ft.) (1)

0. 06102=1

. 12205=2

.18307=3

. 24409 =4

1=0. 028317 2= .056634 3= .084951 4= .113268

1=0. 7646 2 = 1. 5291 3 =2. 2937 4=3. 0582

1=0. 0163867 2= .0327734 3= .0491602 4= .0655469

1= 28.316 2 = 56.633 3= 84.949 4=113. 265 .30512=5 .36614=6

.42716=7

.48819=8 .54921=9

5= .141585 6= .169902 7= .198219 8= .226536 9= .254853

5 =3. 8228 6=4. 5874 7=5. 3519 8=6.1165 9=6. 8810

5= .0819336 6= .0983203 7= .1147070 8= .1310938 9= .1474805

5=141.581 6=169.898

7 = 198. 214 8 =226. 530 9=254. 846 1= 16.3872 2 = 32.7743 3= 49.1615 4= 65.5486

35.314=1

70. 629=2

105. 943=3

141. 258=4

1. 3079=1

2. 6159=2

3. 9238=3

5.2318=4

61.025=1

122. 050=2

183. 075=3

244. 100=4

0. 035315=1

.070631 = 2

. 105946=3

. 141262 =4

5 = 81.9358 6= 98.3230 7=114. 7101 8 = 131.0973 9=147.4845

176. 572=5

211. 887=6

247.201 = 7

282. 516=8

317. 830 =9

6. 5397=5

7.8477=6

9.1556 =7

10.4635=8 11.7715=9

305. 125=5

366. 150=6

427. 175=7

488.200=8

549. 225 =9

. 176577=5

.211892=6

.247208=7

.282523=8

.317839=911
12 BUREAU OF STANDARDS

4. CAPACITY—LIQUID MEASURE

TT Q

fluid K

mi" drams hters

(fl. dr.) (ml)

TT <3 fl,",;H Millifluid i -j. ounces

llters

(fl. oz.) (ml)

TJ g

liquid Liters pints

(Pt.) (1)

TJ g

liquid Liters quarts

(qt.) (1)

U. S. gallons

(gal.)

Liters

(1)

fl 07H£0 "fl U. UoOolO — X 1=0. 47317 x —u. ytooo 9fi41S — U. ZO^lo — x .54104=2 .067629 = 3 3= ! 94633 3 = 1.89267 . 52836= 2 .81155=3 .101444=3 3 = 1.41950 3=2. 83900 .79253 = 3

1. 08207=4 . 135259=4 4=1.89267 4=3. 78533 1. 05671 = 4

1. 35259=5 . 169074=5 5 =2. 36583 5=4.73167 1. 32089= 5

1. 62311=6 .202888=6 6=2. 83900 6=5. 67800 1. 58507= 6

1. 89363=7 .236703 = 7 7=3.31217 7 =6. 62433 1. 84924= 7

2. 16414=8 .270518=8 8=3. 78533 8 =7. 57066 2. 11342= 8

2.43466=9 .304333=9 9=4. 25850 9=8. 51700 2. 37760= 9 1= 3.6966 1= 29.573 2. 1134=1 1. 05671 = 1 i = 3.78533 3 = 7. 3932 3= 59. 146 4. 2268=^5 Z. 11342= 4 3 = 7. 57066 3=11.0898 3= 88.719 6. 3403 = 3 3. 17013 = 3 3 = 11.35600 4=14. 7865 4=118. 292 8. 4537=4 4. 22684=4 4 =15. 14133 5 = 18. 4831 5=147. 865 10. 5671=5 5. 28355=5 5 = 18. 92666 6=22. 1797 • 6=177. 437 12. 6805=6 6. 34026=9 6 =22. 71199 7 =25. 8763 7 =207. 010 14. 7939 = 7 7. 39697=7 7 =26. 49733 8=29. 5729 8 =236. 583 16. 9074 =8 8. 45368 =8 8 =30. 28266 9=33.2695 9=266. 156 19. 0208=9 9. 51039=9 9 =34. 06799

5. CAPACITY—DRY MEASURE

TJ. S. dry Liters quarts

(qt.) (1) U- ,S" Liters pecks

(pk.) (1)

TJ. S. Dekapecks liters (pk.) (dkl)

TJ. S. Hectobushels liters (bu.) (hi)

U. S. Hectobushels liters per per acre hectare

0. 9081 = 1

1. 8162=3

2.7243=3

3. 6324=4

0.11351 = 1

.22703 = 3

.34054=3

. 45405=4

1=0. 8810 3 = 1.7619 3 =2.6429 4=3. 52381=0. 35238 3= .70477 3 = 1. 05715 4=1. 40953

1=0. 8708 3=1.7415 3=2. 6123 4=3. 4830

4. 5405=5

5. 4486=6

6. 3567=7

7. 2648=8

8. 1729=9

.56756=5

. 68108=6

.79459 = 7 .90810=8

1.02161=9

5=4.4048 6=5. 2857 7=6. 1667 8=7. 0477 9=7. 9286

5=1. 76192 6=2. 11430 7 = 2.46668 8 = 2. 81907 9=3. 17145

5 =4. 3538 6=5. 2245 7 =6. 0953 8 =6. 9660 9=7. 8368 1 = 1. 1012 3=2. 2024 3=3. 3036 4=4. 4048

1= 8.810 3 = 17. 619 3 =26. 429 4=35. 238

1. 1351 = 1

2. 2703=3

3. 4054 =3

4. 5405=4

2.8378=1

5.6756 = 3

8. 5135=3

11.3513=4

1. 1484=1

2. 2969=3

3. 4453=3

4. 5937=4 5=5. 5060 6=6. 6072 7=7. 7084 8 =8. 8096 9=9. 9108

5=44. 048 6=52. 857 7=61.667 8 =70. 477 9=79. 286

5. 6756=5

6.8108=6

7. 9459=7

9. 0810=8

10. 2161 = 9

14. 1891=5

17. 0269=6

19. 8647=7

22. 7026=8

25. 5404=9

5.7421=5

6.8906=6

8.0390 =7

9. 1874=8

10. 3359=9

6. MASS

Grains Grams

(gr.) (g)

Apothecaries' Grams

drams

(dr.ap.or3) (g) a Grams

(oz. t.) (g)

Avoirdupois Grams

ounces

(oz. av.) (g)

Avoirdu- T7-jin

(lb. av.) (kg) 1=0. 064799 3= .129598 3= .194397 4= .259196

0. 25721 = 1

.51441 = 3

.77162=3

1. 02882 =4

0.032151 = 1

.064301 = 3

.096452=3

. 128603=4

0.035274=1 .070548=3

. 105822=3

. 141096=4

1=0. 45359 2= .90718 3=1. 36078 4=1. 81437 5= .323995 6= .388794 7= .453592 8= .518391 9= .583190

1.28603=5 1.54324=6

1.80044 =7

2.05765=8

2. 31485=9

. 160754=5

. 192904=6

.225055=7

.257206=8

. 289357=9

. 176370=5 .211644=6

.246918=7

.282192=8 .317466=9

5=2. 26796 6=2. 72155 7=3. 17515 8 =3. 62874 9=4.08233

15. 4324=1

30. 8647=3

46.2971=3

61. 7294=4

1= 3.8879 3 = 7.7759 3 = 11. 6638 4=15. 55171= 31.103 3= 62.207 3= 93.310 4=124. 414

1= 28.350 3= 56.699 3 = 85.049 4=113. 398

2.20462=1

4. 40924=3

6.61387=3

8. 81849 =4

77.1618=5

92. 5941=6

108. 0265 =7

123. 4589=8

138. 8912=9

5=19. 4397 6=23.3276 7=27. 2155 8=31. 1035 9=34.9914

5 = 155. 517 6=186. 621 7=217. 724 8 =248. 828 9=279.931

5=141.748 6 = 170. 097 7 = 198. 447 8 =226. 796 9=255. 146

11.02311=5

13. 22773=6

15. 43236=7

17. 63698=8

19. 84160=9
METRIC SYSTEM OF WEIGHTS AND MEASURES 13

VIII. OFFICIAL ABBREVIATIONS OF INTERNATIONAL

METRIC UNITS

These abbreviations are used by the Bureau of Standards conformably to the principle followed in the abbreviations adopted by the

International Committee on Weights and Measures, October 2, 1879. (Proces -Verbaux des Seances de 1879, Comite International

des Poids et Mesures; vol. IV, p. 41 ; 1880.)

Metric abbreviations are simply the initial letters of the respective

units combined with the initial letters of the prefixes set solid in lower

case, and without period.

PREFIXES UNITS

k kilo- h hecto dk* deka- d deci- c centi- m millim meter

g gram

1 liter a are

LINEAR

(length) ion kilometer hm hectometer dkm dekameter

m meter dm decimeter cm centimeter mm millimeter

SQUARE

(area) CUBIC

(volume)

km2 square hm2 square dkm2 square m2 square dm2 square cm2 square mm2 square

kilometer hectometer dekameter

meter

decimeter

centimeter

millimeter H micron (=0.001 mm) ju2 square micron

MASS**

(weight)

kg kilogram

hg hectogram

dkg dekagram

g gram

dg decigram

eg centigram

mg milligram

SURFACE

(land area)

ha hectar a are ca centare

km3 cubic hm3 cubic dkm3 cubic m3 cubic dm3 cubic cm3 cubic mm3 cubic

kilometer hectometer dekameter

meter

decimeter

centimeter

millimeter

/u3 cubic micron

CAPACITY

(of containers)

kl kiloliter hi hectoliter dkl dekaliter

1 liter dl deciliter

cl centiliter ml milliliter Note.—A similar plan is used for abbreviations of cgs units and others: mf millifarad (rn milli, f farad) ; ni microfarad; m/z a thousandth of a micron, and

one millionth of a micron. (See Guillaume: Unites et Etalons, p. 7, note.) * "dk" suggested and used by bureau to distinguish from u

d." ** «t" = 1,000 kg =metric ton.